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Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile RoboticsasdA
Contents
1 Introduction to Mobile Robotics
2 Intelligent RobotsEthical dilemmas
3 Basic Problems in Mobile RoboticsMappingMotion PlanningLocalizationAdvanced Problems
169
1 Introduction to MobileRobotics
Introduction to Mobile Robotics1 Introduction to Mobile Robotics
Robotics
Robotics is
bull the branch of technology that deals with the design constructionoperation and application of robots (Oxford Dictionaries)
bull the science of perceiving and manipulating the physical worldthrough computer-controlled devices (THRUN 2005)
269
Introduction to Mobile Robotics1 Introduction to Mobile Robotics
Research Topics (Springer Handbook of Robotics 2008)
bull Robot structures legs hands flexible wheeled robots
bull Sensing amp perception tactile odometry ranging visual
bull Manipulation amp interfaces human-robot interaction graspinghaptics exoskeletons
bull Service robotics industrial robots educational robots
bull Mobile robotics navigation mapping localization
bull
369
Introduction to Mobile Robotics1 Introduction to Mobile Robotics
Origin of the term Robotbull The word robot comes from the czech word robota and it means ldquomenial
forced laborerrdquo
bull It was first mentioned in the 1921rsquos science fiction play RUR - RossumoviUniverzaacutelniacute Roboti (Rossumrsquos Universal Robots) from Karel Capek
bull It became popular after movies such as Metropolis (1926) The Day the EarthStood Still (1951) and Forbidden Planet (1956)
RUR play from Capek Popular movies with robots
469
Introduction to Mobile Robotics1 Introduction to Mobile Robotics
A brief history of Roboticsbull In 1942 during the execution of Manhattan Project US scientistsand engineers developed the telemanipulator
bull It was capable to handle radioactive material (eg uranium andplutonium) through teleoperation
A model 8 telemanipulator 0
0R R Murphy An Introduction to AI Robotics (Intelligent Robotics and Autonomous Agents) 2000569
Introduction to Mobile Robotics1 Introduction to Mobile Robotics
A brief history of Robotics (ii)
bull In 1953 the first AGV (Automatic Guided Vehicle) was broughtto market by Barrett Electronics of Northbrook Illinois
bull It was simply a truck that followed a wire in the floor
The first AGV A modern AGV
669
Introduction to Mobile Robotics1 Introduction to Mobile Robotics
A brief history of Robotics (iii)
bull In 1972 Shakey the robot was thefirst general-purpose robot with thecapability of reasoning using ArtificialIntelligence techniques
bull It was developed by the AI group fromthe Stanford Research Institute (SRI)International led by Charles Rosen
Shakey the robot
769
Introduction to Mobile Robotics1 Introduction to Mobile Robotics
Robots nowadays
Pathfinder mission
Unmanned Aerial Vehicle (UAV)
DARPA Autonomous Vehicle
Anthropomorphic
Walking
DaVinci Surgical Robot
Airduct inspection
869
2 Intelligent Robots
Introduction to Mobile Robotics2 Intelligent Robots
Intelligent Robots
bull The definition of robot is connected to the definition of agent inArtificial Inteligence
bull An agent performs actions in an environment based on informationgathered from its sensors
bull There are numerous definitions for agents focusing onbull Survivalbull Perceptionactionbull Learning ability
bull The set of all these concepts compose the autonomy
969
Introduction to Mobile Robotics2 Intelligent Robots
Definition of intelligent robot
bull An intelligent robot is a mechanical device that can operateautonomously
bull The term ldquointelligentrdquo means that the robot does not act withoutthinking repeatedly like common plant-floor robots
bull Autonomous operation implies that the robot is able to operatewithout external supervision The robot is able to adapt tochanges in the environment or even changes in itself and stillmaintain proper functioning
1069
Introduction to Mobile Robotics2 Intelligent Robots
What is an intelligent robot for
bull For tasks that could put human life at riskbull nuclear spatial military
bull For replacing humans in repetitive and boring tasks
bull For humanitarian usebull search and rescue landmines removal
bull For 3D works - Dirty Dull and Dangerous
1169
Introduction to Mobile Robotics2 Intelligent Robots
Ethics
ldquoEthics can be defined as a set of rules principles or ways of thin-king that guide or call to itself the authority to guide the actionsof a particular grouprdquo
Peter Singer 2
2P Singer Ethics 19941269
2 Intelligent Robots
21 Ethical dilemmas
Introduction to Mobile Robotics2 Intelligent Robots
The Trolley Problembull The trolley problem is a thought experiment in ethics first introduced by
Philippa Foot in 1967 (Video3 )
A runaway trolley is headed straight to five people tied up on the tracks and unable tomove You are standing next to a lever If you pull this lever the trolley will switch to adifferent set of tracks However you notice that there is one person tied up on the sidetrack You have two options
bull Do nothing and the trolley kills the five people on the main trackbull Pull the lever diverting the trolley onto the side track where it will kill one person
Which is the most ethical choice
3B R 4 The Trolley Problem httpswwwyoutubecomwatchv=bOpf6KcWYyw Accessed 2018-02-25 20141369
Introduction to Mobile Robotics2 Intelligent Robots
Peoplersquos responses to trolley problems
bull The trolley problem has been the subject of many surveys in whichapproximately 90 of respondents have chosen to kill the one and save the five
bull If the situation is modified where the one sacrificed for the five was a relative orromantic partner respondents are much less likely to be willing to sacrifice theirlife
bull Greene and colleagues (2001) demonstrated using functional magneticresonance imaging that personaldilemmas (like pushing a man off afootbridge) preferentially engage brain regions associated with emotion whereasimpersonaldilemmas (like diverting the trolley by flipping a switch)preferentially engaged regions associated with controlled reasoning
bull Problems analogous to the trolley problem arise in the design of autonomouscars in situations where the carrsquos software is forced during a potential crashscenario to choose between multiple courses of action
1469
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practiceHow Tesla Solves A Self-Driving Crash Dilemma4
bull A class-action lawsuit was filed in December 2016about Teslarsquos decision to not use its AutomaticEmergency Braking (AEB) system when ahuman driver is pressing on the accelerator pedal
bull From the lawsuitldquoWhen a frontal collision is considered unavoidableAutomatic Emergency Braking is designed toautomatically apply the brakes to reduce the severityof the impact But Tesla has programmed the systemto deactivate when it receives instructions from theaccelerator pedal to drive full speed into a fixedobjectrdquo
4P Lin Herersquos How Tesla Solves A Self-Driving Crash Dilemma
httpswwwforbescomsitespatricklin20170405heres-how-tesla-solves-a-self-driving-crash-
dilemma72962be16813 Accessed 2018-02-25 20171569
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
ldquoTesla confirmed that when it stated that Automatic EmergencyBraking will operates only when driving between 5 mph (8 kmh)and 85 mph (140 kmh) but that the vehicle will not automaticallyapply the brakes or will stop applying the brakes ldquoin situationswhere you are taking action to avoid a potential collisionrdquo
bull For examplebull You turn the steering wheel sharplybull You press the accelerator pedalbull You press and release the brake pedalbull A vehicle motorcycle bicycle or pedestrian is no longer detectedaheadrdquo
1669
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
3 Basic Problems in MobileRobotics
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimation in Mobile Robotics
bull An autonomous mobile robot should be able to move in anenvironment to fulfill its tasks which demands that the robotknows its location along with the location of nearby obstacles
bull In realistic scenarios such information is not directly available andthe robot must use its sensors which carry only partial and noisyinformation about the scenario state6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016231969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimationx robotrsquos pose m map zobservations ucontrols
Graphical model
hellip
hellip
1 2 3 hellip
1 2 3 t0
1 2 3 t
t
2069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
3 Basic Problems in Mobile Robotics
31 Mapping
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectory
bull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actions
bull Observationsbull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Mapsbull For environments with locally distinguishable featuresfeature-based (or landmark-based) maps have been extensively used
bull The map is just a set of objects each one with a specific coordinate
(a) Example of a mobile robot mapping a set of stone rocks(b) The image depicts the path and the estimated landmark positions (marked by circles)
Figure extracted from 7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_452369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
2469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Method 8 9 that represents the environment by a discrete grid offixed-size cells
bull Very useful for robots equipped with range-based sensorsbecause the range values of each sensor combined with the absoluteposition of the robot can be used directly to update the cells
bull Each cell has an occupancy value to indicate if it is an obstacle orpart of free space
bull the value 0 indicates that the cell has not been ldquohitrdquo yet thereforeit is likely free space
bull if the cellrsquos value is above a certain threshold (due to several rangingstrikes) the cell is deemed to be an obstacle
8A Elfes ldquoSonar-based real-world mapping and navigationrdquo Em IEEE Journal on Robotics and Automation 33 (1987)
pp 249ndash2659A Elfes ldquoUsing occupancy grids for mobile robot perception and navigationrdquo Em Computer 226 (1989) pp 46ndash57
2669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
2969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
3269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile RoboticsasdA
Contents
1 Introduction to Mobile Robotics
2 Intelligent RobotsEthical dilemmas
3 Basic Problems in Mobile RoboticsMappingMotion PlanningLocalizationAdvanced Problems
169
1 Introduction to MobileRobotics
Introduction to Mobile Robotics1 Introduction to Mobile Robotics
Robotics
Robotics is
bull the branch of technology that deals with the design constructionoperation and application of robots (Oxford Dictionaries)
bull the science of perceiving and manipulating the physical worldthrough computer-controlled devices (THRUN 2005)
269
Introduction to Mobile Robotics1 Introduction to Mobile Robotics
Research Topics (Springer Handbook of Robotics 2008)
bull Robot structures legs hands flexible wheeled robots
bull Sensing amp perception tactile odometry ranging visual
bull Manipulation amp interfaces human-robot interaction graspinghaptics exoskeletons
bull Service robotics industrial robots educational robots
bull Mobile robotics navigation mapping localization
bull
369
Introduction to Mobile Robotics1 Introduction to Mobile Robotics
Origin of the term Robotbull The word robot comes from the czech word robota and it means ldquomenial
forced laborerrdquo
bull It was first mentioned in the 1921rsquos science fiction play RUR - RossumoviUniverzaacutelniacute Roboti (Rossumrsquos Universal Robots) from Karel Capek
bull It became popular after movies such as Metropolis (1926) The Day the EarthStood Still (1951) and Forbidden Planet (1956)
RUR play from Capek Popular movies with robots
469
Introduction to Mobile Robotics1 Introduction to Mobile Robotics
A brief history of Roboticsbull In 1942 during the execution of Manhattan Project US scientistsand engineers developed the telemanipulator
bull It was capable to handle radioactive material (eg uranium andplutonium) through teleoperation
A model 8 telemanipulator 0
0R R Murphy An Introduction to AI Robotics (Intelligent Robotics and Autonomous Agents) 2000569
Introduction to Mobile Robotics1 Introduction to Mobile Robotics
A brief history of Robotics (ii)
bull In 1953 the first AGV (Automatic Guided Vehicle) was broughtto market by Barrett Electronics of Northbrook Illinois
bull It was simply a truck that followed a wire in the floor
The first AGV A modern AGV
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Introduction to Mobile Robotics1 Introduction to Mobile Robotics
A brief history of Robotics (iii)
bull In 1972 Shakey the robot was thefirst general-purpose robot with thecapability of reasoning using ArtificialIntelligence techniques
bull It was developed by the AI group fromthe Stanford Research Institute (SRI)International led by Charles Rosen
Shakey the robot
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Introduction to Mobile Robotics1 Introduction to Mobile Robotics
Robots nowadays
Pathfinder mission
Unmanned Aerial Vehicle (UAV)
DARPA Autonomous Vehicle
Anthropomorphic
Walking
DaVinci Surgical Robot
Airduct inspection
869
2 Intelligent Robots
Introduction to Mobile Robotics2 Intelligent Robots
Intelligent Robots
bull The definition of robot is connected to the definition of agent inArtificial Inteligence
bull An agent performs actions in an environment based on informationgathered from its sensors
bull There are numerous definitions for agents focusing onbull Survivalbull Perceptionactionbull Learning ability
bull The set of all these concepts compose the autonomy
969
Introduction to Mobile Robotics2 Intelligent Robots
Definition of intelligent robot
bull An intelligent robot is a mechanical device that can operateautonomously
bull The term ldquointelligentrdquo means that the robot does not act withoutthinking repeatedly like common plant-floor robots
bull Autonomous operation implies that the robot is able to operatewithout external supervision The robot is able to adapt tochanges in the environment or even changes in itself and stillmaintain proper functioning
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Introduction to Mobile Robotics2 Intelligent Robots
What is an intelligent robot for
bull For tasks that could put human life at riskbull nuclear spatial military
bull For replacing humans in repetitive and boring tasks
bull For humanitarian usebull search and rescue landmines removal
bull For 3D works - Dirty Dull and Dangerous
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Introduction to Mobile Robotics2 Intelligent Robots
Ethics
ldquoEthics can be defined as a set of rules principles or ways of thin-king that guide or call to itself the authority to guide the actionsof a particular grouprdquo
Peter Singer 2
2P Singer Ethics 19941269
2 Intelligent Robots
21 Ethical dilemmas
Introduction to Mobile Robotics2 Intelligent Robots
The Trolley Problembull The trolley problem is a thought experiment in ethics first introduced by
Philippa Foot in 1967 (Video3 )
A runaway trolley is headed straight to five people tied up on the tracks and unable tomove You are standing next to a lever If you pull this lever the trolley will switch to adifferent set of tracks However you notice that there is one person tied up on the sidetrack You have two options
bull Do nothing and the trolley kills the five people on the main trackbull Pull the lever diverting the trolley onto the side track where it will kill one person
Which is the most ethical choice
3B R 4 The Trolley Problem httpswwwyoutubecomwatchv=bOpf6KcWYyw Accessed 2018-02-25 20141369
Introduction to Mobile Robotics2 Intelligent Robots
Peoplersquos responses to trolley problems
bull The trolley problem has been the subject of many surveys in whichapproximately 90 of respondents have chosen to kill the one and save the five
bull If the situation is modified where the one sacrificed for the five was a relative orromantic partner respondents are much less likely to be willing to sacrifice theirlife
bull Greene and colleagues (2001) demonstrated using functional magneticresonance imaging that personaldilemmas (like pushing a man off afootbridge) preferentially engage brain regions associated with emotion whereasimpersonaldilemmas (like diverting the trolley by flipping a switch)preferentially engaged regions associated with controlled reasoning
bull Problems analogous to the trolley problem arise in the design of autonomouscars in situations where the carrsquos software is forced during a potential crashscenario to choose between multiple courses of action
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Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practiceHow Tesla Solves A Self-Driving Crash Dilemma4
bull A class-action lawsuit was filed in December 2016about Teslarsquos decision to not use its AutomaticEmergency Braking (AEB) system when ahuman driver is pressing on the accelerator pedal
bull From the lawsuitldquoWhen a frontal collision is considered unavoidableAutomatic Emergency Braking is designed toautomatically apply the brakes to reduce the severityof the impact But Tesla has programmed the systemto deactivate when it receives instructions from theaccelerator pedal to drive full speed into a fixedobjectrdquo
4P Lin Herersquos How Tesla Solves A Self-Driving Crash Dilemma
httpswwwforbescomsitespatricklin20170405heres-how-tesla-solves-a-self-driving-crash-
dilemma72962be16813 Accessed 2018-02-25 20171569
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
ldquoTesla confirmed that when it stated that Automatic EmergencyBraking will operates only when driving between 5 mph (8 kmh)and 85 mph (140 kmh) but that the vehicle will not automaticallyapply the brakes or will stop applying the brakes ldquoin situationswhere you are taking action to avoid a potential collisionrdquo
bull For examplebull You turn the steering wheel sharplybull You press the accelerator pedalbull You press and release the brake pedalbull A vehicle motorcycle bicycle or pedestrian is no longer detectedaheadrdquo
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Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
3 Basic Problems in MobileRobotics
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimation in Mobile Robotics
bull An autonomous mobile robot should be able to move in anenvironment to fulfill its tasks which demands that the robotknows its location along with the location of nearby obstacles
bull In realistic scenarios such information is not directly available andthe robot must use its sensors which carry only partial and noisyinformation about the scenario state6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016231969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimationx robotrsquos pose m map zobservations ucontrols
Graphical model
hellip
hellip
1 2 3 hellip
1 2 3 t0
1 2 3 t
t
2069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
3 Basic Problems in Mobile Robotics
31 Mapping
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectory
bull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actions
bull Observationsbull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Mapsbull For environments with locally distinguishable featuresfeature-based (or landmark-based) maps have been extensively used
bull The map is just a set of objects each one with a specific coordinate
(a) Example of a mobile robot mapping a set of stone rocks(b) The image depicts the path and the estimated landmark positions (marked by circles)
Figure extracted from 7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_452369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
2469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Method 8 9 that represents the environment by a discrete grid offixed-size cells
bull Very useful for robots equipped with range-based sensorsbecause the range values of each sensor combined with the absoluteposition of the robot can be used directly to update the cells
bull Each cell has an occupancy value to indicate if it is an obstacle orpart of free space
bull the value 0 indicates that the cell has not been ldquohitrdquo yet thereforeit is likely free space
bull if the cellrsquos value is above a certain threshold (due to several rangingstrikes) the cell is deemed to be an obstacle
8A Elfes ldquoSonar-based real-world mapping and navigationrdquo Em IEEE Journal on Robotics and Automation 33 (1987)
pp 249ndash2659A Elfes ldquoUsing occupancy grids for mobile robot perception and navigationrdquo Em Computer 226 (1989) pp 46ndash57
2669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
2969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
3269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
1 Introduction to MobileRobotics
Introduction to Mobile Robotics1 Introduction to Mobile Robotics
Robotics
Robotics is
bull the branch of technology that deals with the design constructionoperation and application of robots (Oxford Dictionaries)
bull the science of perceiving and manipulating the physical worldthrough computer-controlled devices (THRUN 2005)
269
Introduction to Mobile Robotics1 Introduction to Mobile Robotics
Research Topics (Springer Handbook of Robotics 2008)
bull Robot structures legs hands flexible wheeled robots
bull Sensing amp perception tactile odometry ranging visual
bull Manipulation amp interfaces human-robot interaction graspinghaptics exoskeletons
bull Service robotics industrial robots educational robots
bull Mobile robotics navigation mapping localization
bull
369
Introduction to Mobile Robotics1 Introduction to Mobile Robotics
Origin of the term Robotbull The word robot comes from the czech word robota and it means ldquomenial
forced laborerrdquo
bull It was first mentioned in the 1921rsquos science fiction play RUR - RossumoviUniverzaacutelniacute Roboti (Rossumrsquos Universal Robots) from Karel Capek
bull It became popular after movies such as Metropolis (1926) The Day the EarthStood Still (1951) and Forbidden Planet (1956)
RUR play from Capek Popular movies with robots
469
Introduction to Mobile Robotics1 Introduction to Mobile Robotics
A brief history of Roboticsbull In 1942 during the execution of Manhattan Project US scientistsand engineers developed the telemanipulator
bull It was capable to handle radioactive material (eg uranium andplutonium) through teleoperation
A model 8 telemanipulator 0
0R R Murphy An Introduction to AI Robotics (Intelligent Robotics and Autonomous Agents) 2000569
Introduction to Mobile Robotics1 Introduction to Mobile Robotics
A brief history of Robotics (ii)
bull In 1953 the first AGV (Automatic Guided Vehicle) was broughtto market by Barrett Electronics of Northbrook Illinois
bull It was simply a truck that followed a wire in the floor
The first AGV A modern AGV
669
Introduction to Mobile Robotics1 Introduction to Mobile Robotics
A brief history of Robotics (iii)
bull In 1972 Shakey the robot was thefirst general-purpose robot with thecapability of reasoning using ArtificialIntelligence techniques
bull It was developed by the AI group fromthe Stanford Research Institute (SRI)International led by Charles Rosen
Shakey the robot
769
Introduction to Mobile Robotics1 Introduction to Mobile Robotics
Robots nowadays
Pathfinder mission
Unmanned Aerial Vehicle (UAV)
DARPA Autonomous Vehicle
Anthropomorphic
Walking
DaVinci Surgical Robot
Airduct inspection
869
2 Intelligent Robots
Introduction to Mobile Robotics2 Intelligent Robots
Intelligent Robots
bull The definition of robot is connected to the definition of agent inArtificial Inteligence
bull An agent performs actions in an environment based on informationgathered from its sensors
bull There are numerous definitions for agents focusing onbull Survivalbull Perceptionactionbull Learning ability
bull The set of all these concepts compose the autonomy
969
Introduction to Mobile Robotics2 Intelligent Robots
Definition of intelligent robot
bull An intelligent robot is a mechanical device that can operateautonomously
bull The term ldquointelligentrdquo means that the robot does not act withoutthinking repeatedly like common plant-floor robots
bull Autonomous operation implies that the robot is able to operatewithout external supervision The robot is able to adapt tochanges in the environment or even changes in itself and stillmaintain proper functioning
1069
Introduction to Mobile Robotics2 Intelligent Robots
What is an intelligent robot for
bull For tasks that could put human life at riskbull nuclear spatial military
bull For replacing humans in repetitive and boring tasks
bull For humanitarian usebull search and rescue landmines removal
bull For 3D works - Dirty Dull and Dangerous
1169
Introduction to Mobile Robotics2 Intelligent Robots
Ethics
ldquoEthics can be defined as a set of rules principles or ways of thin-king that guide or call to itself the authority to guide the actionsof a particular grouprdquo
Peter Singer 2
2P Singer Ethics 19941269
2 Intelligent Robots
21 Ethical dilemmas
Introduction to Mobile Robotics2 Intelligent Robots
The Trolley Problembull The trolley problem is a thought experiment in ethics first introduced by
Philippa Foot in 1967 (Video3 )
A runaway trolley is headed straight to five people tied up on the tracks and unable tomove You are standing next to a lever If you pull this lever the trolley will switch to adifferent set of tracks However you notice that there is one person tied up on the sidetrack You have two options
bull Do nothing and the trolley kills the five people on the main trackbull Pull the lever diverting the trolley onto the side track where it will kill one person
Which is the most ethical choice
3B R 4 The Trolley Problem httpswwwyoutubecomwatchv=bOpf6KcWYyw Accessed 2018-02-25 20141369
Introduction to Mobile Robotics2 Intelligent Robots
Peoplersquos responses to trolley problems
bull The trolley problem has been the subject of many surveys in whichapproximately 90 of respondents have chosen to kill the one and save the five
bull If the situation is modified where the one sacrificed for the five was a relative orromantic partner respondents are much less likely to be willing to sacrifice theirlife
bull Greene and colleagues (2001) demonstrated using functional magneticresonance imaging that personaldilemmas (like pushing a man off afootbridge) preferentially engage brain regions associated with emotion whereasimpersonaldilemmas (like diverting the trolley by flipping a switch)preferentially engaged regions associated with controlled reasoning
bull Problems analogous to the trolley problem arise in the design of autonomouscars in situations where the carrsquos software is forced during a potential crashscenario to choose between multiple courses of action
1469
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practiceHow Tesla Solves A Self-Driving Crash Dilemma4
bull A class-action lawsuit was filed in December 2016about Teslarsquos decision to not use its AutomaticEmergency Braking (AEB) system when ahuman driver is pressing on the accelerator pedal
bull From the lawsuitldquoWhen a frontal collision is considered unavoidableAutomatic Emergency Braking is designed toautomatically apply the brakes to reduce the severityof the impact But Tesla has programmed the systemto deactivate when it receives instructions from theaccelerator pedal to drive full speed into a fixedobjectrdquo
4P Lin Herersquos How Tesla Solves A Self-Driving Crash Dilemma
httpswwwforbescomsitespatricklin20170405heres-how-tesla-solves-a-self-driving-crash-
dilemma72962be16813 Accessed 2018-02-25 20171569
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
ldquoTesla confirmed that when it stated that Automatic EmergencyBraking will operates only when driving between 5 mph (8 kmh)and 85 mph (140 kmh) but that the vehicle will not automaticallyapply the brakes or will stop applying the brakes ldquoin situationswhere you are taking action to avoid a potential collisionrdquo
bull For examplebull You turn the steering wheel sharplybull You press the accelerator pedalbull You press and release the brake pedalbull A vehicle motorcycle bicycle or pedestrian is no longer detectedaheadrdquo
1669
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
3 Basic Problems in MobileRobotics
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimation in Mobile Robotics
bull An autonomous mobile robot should be able to move in anenvironment to fulfill its tasks which demands that the robotknows its location along with the location of nearby obstacles
bull In realistic scenarios such information is not directly available andthe robot must use its sensors which carry only partial and noisyinformation about the scenario state6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016231969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimationx robotrsquos pose m map zobservations ucontrols
Graphical model
hellip
hellip
1 2 3 hellip
1 2 3 t0
1 2 3 t
t
2069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
3 Basic Problems in Mobile Robotics
31 Mapping
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectory
bull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actions
bull Observationsbull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Mapsbull For environments with locally distinguishable featuresfeature-based (or landmark-based) maps have been extensively used
bull The map is just a set of objects each one with a specific coordinate
(a) Example of a mobile robot mapping a set of stone rocks(b) The image depicts the path and the estimated landmark positions (marked by circles)
Figure extracted from 7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_452369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
2469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Method 8 9 that represents the environment by a discrete grid offixed-size cells
bull Very useful for robots equipped with range-based sensorsbecause the range values of each sensor combined with the absoluteposition of the robot can be used directly to update the cells
bull Each cell has an occupancy value to indicate if it is an obstacle orpart of free space
bull the value 0 indicates that the cell has not been ldquohitrdquo yet thereforeit is likely free space
bull if the cellrsquos value is above a certain threshold (due to several rangingstrikes) the cell is deemed to be an obstacle
8A Elfes ldquoSonar-based real-world mapping and navigationrdquo Em IEEE Journal on Robotics and Automation 33 (1987)
pp 249ndash2659A Elfes ldquoUsing occupancy grids for mobile robot perception and navigationrdquo Em Computer 226 (1989) pp 46ndash57
2669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
2969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
3269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics1 Introduction to Mobile Robotics
Robotics
Robotics is
bull the branch of technology that deals with the design constructionoperation and application of robots (Oxford Dictionaries)
bull the science of perceiving and manipulating the physical worldthrough computer-controlled devices (THRUN 2005)
269
Introduction to Mobile Robotics1 Introduction to Mobile Robotics
Research Topics (Springer Handbook of Robotics 2008)
bull Robot structures legs hands flexible wheeled robots
bull Sensing amp perception tactile odometry ranging visual
bull Manipulation amp interfaces human-robot interaction graspinghaptics exoskeletons
bull Service robotics industrial robots educational robots
bull Mobile robotics navigation mapping localization
bull
369
Introduction to Mobile Robotics1 Introduction to Mobile Robotics
Origin of the term Robotbull The word robot comes from the czech word robota and it means ldquomenial
forced laborerrdquo
bull It was first mentioned in the 1921rsquos science fiction play RUR - RossumoviUniverzaacutelniacute Roboti (Rossumrsquos Universal Robots) from Karel Capek
bull It became popular after movies such as Metropolis (1926) The Day the EarthStood Still (1951) and Forbidden Planet (1956)
RUR play from Capek Popular movies with robots
469
Introduction to Mobile Robotics1 Introduction to Mobile Robotics
A brief history of Roboticsbull In 1942 during the execution of Manhattan Project US scientistsand engineers developed the telemanipulator
bull It was capable to handle radioactive material (eg uranium andplutonium) through teleoperation
A model 8 telemanipulator 0
0R R Murphy An Introduction to AI Robotics (Intelligent Robotics and Autonomous Agents) 2000569
Introduction to Mobile Robotics1 Introduction to Mobile Robotics
A brief history of Robotics (ii)
bull In 1953 the first AGV (Automatic Guided Vehicle) was broughtto market by Barrett Electronics of Northbrook Illinois
bull It was simply a truck that followed a wire in the floor
The first AGV A modern AGV
669
Introduction to Mobile Robotics1 Introduction to Mobile Robotics
A brief history of Robotics (iii)
bull In 1972 Shakey the robot was thefirst general-purpose robot with thecapability of reasoning using ArtificialIntelligence techniques
bull It was developed by the AI group fromthe Stanford Research Institute (SRI)International led by Charles Rosen
Shakey the robot
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Introduction to Mobile Robotics1 Introduction to Mobile Robotics
Robots nowadays
Pathfinder mission
Unmanned Aerial Vehicle (UAV)
DARPA Autonomous Vehicle
Anthropomorphic
Walking
DaVinci Surgical Robot
Airduct inspection
869
2 Intelligent Robots
Introduction to Mobile Robotics2 Intelligent Robots
Intelligent Robots
bull The definition of robot is connected to the definition of agent inArtificial Inteligence
bull An agent performs actions in an environment based on informationgathered from its sensors
bull There are numerous definitions for agents focusing onbull Survivalbull Perceptionactionbull Learning ability
bull The set of all these concepts compose the autonomy
969
Introduction to Mobile Robotics2 Intelligent Robots
Definition of intelligent robot
bull An intelligent robot is a mechanical device that can operateautonomously
bull The term ldquointelligentrdquo means that the robot does not act withoutthinking repeatedly like common plant-floor robots
bull Autonomous operation implies that the robot is able to operatewithout external supervision The robot is able to adapt tochanges in the environment or even changes in itself and stillmaintain proper functioning
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Introduction to Mobile Robotics2 Intelligent Robots
What is an intelligent robot for
bull For tasks that could put human life at riskbull nuclear spatial military
bull For replacing humans in repetitive and boring tasks
bull For humanitarian usebull search and rescue landmines removal
bull For 3D works - Dirty Dull and Dangerous
1169
Introduction to Mobile Robotics2 Intelligent Robots
Ethics
ldquoEthics can be defined as a set of rules principles or ways of thin-king that guide or call to itself the authority to guide the actionsof a particular grouprdquo
Peter Singer 2
2P Singer Ethics 19941269
2 Intelligent Robots
21 Ethical dilemmas
Introduction to Mobile Robotics2 Intelligent Robots
The Trolley Problembull The trolley problem is a thought experiment in ethics first introduced by
Philippa Foot in 1967 (Video3 )
A runaway trolley is headed straight to five people tied up on the tracks and unable tomove You are standing next to a lever If you pull this lever the trolley will switch to adifferent set of tracks However you notice that there is one person tied up on the sidetrack You have two options
bull Do nothing and the trolley kills the five people on the main trackbull Pull the lever diverting the trolley onto the side track where it will kill one person
Which is the most ethical choice
3B R 4 The Trolley Problem httpswwwyoutubecomwatchv=bOpf6KcWYyw Accessed 2018-02-25 20141369
Introduction to Mobile Robotics2 Intelligent Robots
Peoplersquos responses to trolley problems
bull The trolley problem has been the subject of many surveys in whichapproximately 90 of respondents have chosen to kill the one and save the five
bull If the situation is modified where the one sacrificed for the five was a relative orromantic partner respondents are much less likely to be willing to sacrifice theirlife
bull Greene and colleagues (2001) demonstrated using functional magneticresonance imaging that personaldilemmas (like pushing a man off afootbridge) preferentially engage brain regions associated with emotion whereasimpersonaldilemmas (like diverting the trolley by flipping a switch)preferentially engaged regions associated with controlled reasoning
bull Problems analogous to the trolley problem arise in the design of autonomouscars in situations where the carrsquos software is forced during a potential crashscenario to choose between multiple courses of action
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Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practiceHow Tesla Solves A Self-Driving Crash Dilemma4
bull A class-action lawsuit was filed in December 2016about Teslarsquos decision to not use its AutomaticEmergency Braking (AEB) system when ahuman driver is pressing on the accelerator pedal
bull From the lawsuitldquoWhen a frontal collision is considered unavoidableAutomatic Emergency Braking is designed toautomatically apply the brakes to reduce the severityof the impact But Tesla has programmed the systemto deactivate when it receives instructions from theaccelerator pedal to drive full speed into a fixedobjectrdquo
4P Lin Herersquos How Tesla Solves A Self-Driving Crash Dilemma
httpswwwforbescomsitespatricklin20170405heres-how-tesla-solves-a-self-driving-crash-
dilemma72962be16813 Accessed 2018-02-25 20171569
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
ldquoTesla confirmed that when it stated that Automatic EmergencyBraking will operates only when driving between 5 mph (8 kmh)and 85 mph (140 kmh) but that the vehicle will not automaticallyapply the brakes or will stop applying the brakes ldquoin situationswhere you are taking action to avoid a potential collisionrdquo
bull For examplebull You turn the steering wheel sharplybull You press the accelerator pedalbull You press and release the brake pedalbull A vehicle motorcycle bicycle or pedestrian is no longer detectedaheadrdquo
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Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
3 Basic Problems in MobileRobotics
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimation in Mobile Robotics
bull An autonomous mobile robot should be able to move in anenvironment to fulfill its tasks which demands that the robotknows its location along with the location of nearby obstacles
bull In realistic scenarios such information is not directly available andthe robot must use its sensors which carry only partial and noisyinformation about the scenario state6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016231969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimationx robotrsquos pose m map zobservations ucontrols
Graphical model
hellip
hellip
1 2 3 hellip
1 2 3 t0
1 2 3 t
t
2069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
3 Basic Problems in Mobile Robotics
31 Mapping
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectory
bull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actions
bull Observationsbull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Mapsbull For environments with locally distinguishable featuresfeature-based (or landmark-based) maps have been extensively used
bull The map is just a set of objects each one with a specific coordinate
(a) Example of a mobile robot mapping a set of stone rocks(b) The image depicts the path and the estimated landmark positions (marked by circles)
Figure extracted from 7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_452369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
2469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Method 8 9 that represents the environment by a discrete grid offixed-size cells
bull Very useful for robots equipped with range-based sensorsbecause the range values of each sensor combined with the absoluteposition of the robot can be used directly to update the cells
bull Each cell has an occupancy value to indicate if it is an obstacle orpart of free space
bull the value 0 indicates that the cell has not been ldquohitrdquo yet thereforeit is likely free space
bull if the cellrsquos value is above a certain threshold (due to several rangingstrikes) the cell is deemed to be an obstacle
8A Elfes ldquoSonar-based real-world mapping and navigationrdquo Em IEEE Journal on Robotics and Automation 33 (1987)
pp 249ndash2659A Elfes ldquoUsing occupancy grids for mobile robot perception and navigationrdquo Em Computer 226 (1989) pp 46ndash57
2669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
2969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
3269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics1 Introduction to Mobile Robotics
Research Topics (Springer Handbook of Robotics 2008)
bull Robot structures legs hands flexible wheeled robots
bull Sensing amp perception tactile odometry ranging visual
bull Manipulation amp interfaces human-robot interaction graspinghaptics exoskeletons
bull Service robotics industrial robots educational robots
bull Mobile robotics navigation mapping localization
bull
369
Introduction to Mobile Robotics1 Introduction to Mobile Robotics
Origin of the term Robotbull The word robot comes from the czech word robota and it means ldquomenial
forced laborerrdquo
bull It was first mentioned in the 1921rsquos science fiction play RUR - RossumoviUniverzaacutelniacute Roboti (Rossumrsquos Universal Robots) from Karel Capek
bull It became popular after movies such as Metropolis (1926) The Day the EarthStood Still (1951) and Forbidden Planet (1956)
RUR play from Capek Popular movies with robots
469
Introduction to Mobile Robotics1 Introduction to Mobile Robotics
A brief history of Roboticsbull In 1942 during the execution of Manhattan Project US scientistsand engineers developed the telemanipulator
bull It was capable to handle radioactive material (eg uranium andplutonium) through teleoperation
A model 8 telemanipulator 0
0R R Murphy An Introduction to AI Robotics (Intelligent Robotics and Autonomous Agents) 2000569
Introduction to Mobile Robotics1 Introduction to Mobile Robotics
A brief history of Robotics (ii)
bull In 1953 the first AGV (Automatic Guided Vehicle) was broughtto market by Barrett Electronics of Northbrook Illinois
bull It was simply a truck that followed a wire in the floor
The first AGV A modern AGV
669
Introduction to Mobile Robotics1 Introduction to Mobile Robotics
A brief history of Robotics (iii)
bull In 1972 Shakey the robot was thefirst general-purpose robot with thecapability of reasoning using ArtificialIntelligence techniques
bull It was developed by the AI group fromthe Stanford Research Institute (SRI)International led by Charles Rosen
Shakey the robot
769
Introduction to Mobile Robotics1 Introduction to Mobile Robotics
Robots nowadays
Pathfinder mission
Unmanned Aerial Vehicle (UAV)
DARPA Autonomous Vehicle
Anthropomorphic
Walking
DaVinci Surgical Robot
Airduct inspection
869
2 Intelligent Robots
Introduction to Mobile Robotics2 Intelligent Robots
Intelligent Robots
bull The definition of robot is connected to the definition of agent inArtificial Inteligence
bull An agent performs actions in an environment based on informationgathered from its sensors
bull There are numerous definitions for agents focusing onbull Survivalbull Perceptionactionbull Learning ability
bull The set of all these concepts compose the autonomy
969
Introduction to Mobile Robotics2 Intelligent Robots
Definition of intelligent robot
bull An intelligent robot is a mechanical device that can operateautonomously
bull The term ldquointelligentrdquo means that the robot does not act withoutthinking repeatedly like common plant-floor robots
bull Autonomous operation implies that the robot is able to operatewithout external supervision The robot is able to adapt tochanges in the environment or even changes in itself and stillmaintain proper functioning
1069
Introduction to Mobile Robotics2 Intelligent Robots
What is an intelligent robot for
bull For tasks that could put human life at riskbull nuclear spatial military
bull For replacing humans in repetitive and boring tasks
bull For humanitarian usebull search and rescue landmines removal
bull For 3D works - Dirty Dull and Dangerous
1169
Introduction to Mobile Robotics2 Intelligent Robots
Ethics
ldquoEthics can be defined as a set of rules principles or ways of thin-king that guide or call to itself the authority to guide the actionsof a particular grouprdquo
Peter Singer 2
2P Singer Ethics 19941269
2 Intelligent Robots
21 Ethical dilemmas
Introduction to Mobile Robotics2 Intelligent Robots
The Trolley Problembull The trolley problem is a thought experiment in ethics first introduced by
Philippa Foot in 1967 (Video3 )
A runaway trolley is headed straight to five people tied up on the tracks and unable tomove You are standing next to a lever If you pull this lever the trolley will switch to adifferent set of tracks However you notice that there is one person tied up on the sidetrack You have two options
bull Do nothing and the trolley kills the five people on the main trackbull Pull the lever diverting the trolley onto the side track where it will kill one person
Which is the most ethical choice
3B R 4 The Trolley Problem httpswwwyoutubecomwatchv=bOpf6KcWYyw Accessed 2018-02-25 20141369
Introduction to Mobile Robotics2 Intelligent Robots
Peoplersquos responses to trolley problems
bull The trolley problem has been the subject of many surveys in whichapproximately 90 of respondents have chosen to kill the one and save the five
bull If the situation is modified where the one sacrificed for the five was a relative orromantic partner respondents are much less likely to be willing to sacrifice theirlife
bull Greene and colleagues (2001) demonstrated using functional magneticresonance imaging that personaldilemmas (like pushing a man off afootbridge) preferentially engage brain regions associated with emotion whereasimpersonaldilemmas (like diverting the trolley by flipping a switch)preferentially engaged regions associated with controlled reasoning
bull Problems analogous to the trolley problem arise in the design of autonomouscars in situations where the carrsquos software is forced during a potential crashscenario to choose between multiple courses of action
1469
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practiceHow Tesla Solves A Self-Driving Crash Dilemma4
bull A class-action lawsuit was filed in December 2016about Teslarsquos decision to not use its AutomaticEmergency Braking (AEB) system when ahuman driver is pressing on the accelerator pedal
bull From the lawsuitldquoWhen a frontal collision is considered unavoidableAutomatic Emergency Braking is designed toautomatically apply the brakes to reduce the severityof the impact But Tesla has programmed the systemto deactivate when it receives instructions from theaccelerator pedal to drive full speed into a fixedobjectrdquo
4P Lin Herersquos How Tesla Solves A Self-Driving Crash Dilemma
httpswwwforbescomsitespatricklin20170405heres-how-tesla-solves-a-self-driving-crash-
dilemma72962be16813 Accessed 2018-02-25 20171569
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
ldquoTesla confirmed that when it stated that Automatic EmergencyBraking will operates only when driving between 5 mph (8 kmh)and 85 mph (140 kmh) but that the vehicle will not automaticallyapply the brakes or will stop applying the brakes ldquoin situationswhere you are taking action to avoid a potential collisionrdquo
bull For examplebull You turn the steering wheel sharplybull You press the accelerator pedalbull You press and release the brake pedalbull A vehicle motorcycle bicycle or pedestrian is no longer detectedaheadrdquo
1669
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
3 Basic Problems in MobileRobotics
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimation in Mobile Robotics
bull An autonomous mobile robot should be able to move in anenvironment to fulfill its tasks which demands that the robotknows its location along with the location of nearby obstacles
bull In realistic scenarios such information is not directly available andthe robot must use its sensors which carry only partial and noisyinformation about the scenario state6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016231969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimationx robotrsquos pose m map zobservations ucontrols
Graphical model
hellip
hellip
1 2 3 hellip
1 2 3 t0
1 2 3 t
t
2069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
3 Basic Problems in Mobile Robotics
31 Mapping
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectory
bull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actions
bull Observationsbull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Mapsbull For environments with locally distinguishable featuresfeature-based (or landmark-based) maps have been extensively used
bull The map is just a set of objects each one with a specific coordinate
(a) Example of a mobile robot mapping a set of stone rocks(b) The image depicts the path and the estimated landmark positions (marked by circles)
Figure extracted from 7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_452369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
2469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Method 8 9 that represents the environment by a discrete grid offixed-size cells
bull Very useful for robots equipped with range-based sensorsbecause the range values of each sensor combined with the absoluteposition of the robot can be used directly to update the cells
bull Each cell has an occupancy value to indicate if it is an obstacle orpart of free space
bull the value 0 indicates that the cell has not been ldquohitrdquo yet thereforeit is likely free space
bull if the cellrsquos value is above a certain threshold (due to several rangingstrikes) the cell is deemed to be an obstacle
8A Elfes ldquoSonar-based real-world mapping and navigationrdquo Em IEEE Journal on Robotics and Automation 33 (1987)
pp 249ndash2659A Elfes ldquoUsing occupancy grids for mobile robot perception and navigationrdquo Em Computer 226 (1989) pp 46ndash57
2669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
2969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
3269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics1 Introduction to Mobile Robotics
Origin of the term Robotbull The word robot comes from the czech word robota and it means ldquomenial
forced laborerrdquo
bull It was first mentioned in the 1921rsquos science fiction play RUR - RossumoviUniverzaacutelniacute Roboti (Rossumrsquos Universal Robots) from Karel Capek
bull It became popular after movies such as Metropolis (1926) The Day the EarthStood Still (1951) and Forbidden Planet (1956)
RUR play from Capek Popular movies with robots
469
Introduction to Mobile Robotics1 Introduction to Mobile Robotics
A brief history of Roboticsbull In 1942 during the execution of Manhattan Project US scientistsand engineers developed the telemanipulator
bull It was capable to handle radioactive material (eg uranium andplutonium) through teleoperation
A model 8 telemanipulator 0
0R R Murphy An Introduction to AI Robotics (Intelligent Robotics and Autonomous Agents) 2000569
Introduction to Mobile Robotics1 Introduction to Mobile Robotics
A brief history of Robotics (ii)
bull In 1953 the first AGV (Automatic Guided Vehicle) was broughtto market by Barrett Electronics of Northbrook Illinois
bull It was simply a truck that followed a wire in the floor
The first AGV A modern AGV
669
Introduction to Mobile Robotics1 Introduction to Mobile Robotics
A brief history of Robotics (iii)
bull In 1972 Shakey the robot was thefirst general-purpose robot with thecapability of reasoning using ArtificialIntelligence techniques
bull It was developed by the AI group fromthe Stanford Research Institute (SRI)International led by Charles Rosen
Shakey the robot
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Introduction to Mobile Robotics1 Introduction to Mobile Robotics
Robots nowadays
Pathfinder mission
Unmanned Aerial Vehicle (UAV)
DARPA Autonomous Vehicle
Anthropomorphic
Walking
DaVinci Surgical Robot
Airduct inspection
869
2 Intelligent Robots
Introduction to Mobile Robotics2 Intelligent Robots
Intelligent Robots
bull The definition of robot is connected to the definition of agent inArtificial Inteligence
bull An agent performs actions in an environment based on informationgathered from its sensors
bull There are numerous definitions for agents focusing onbull Survivalbull Perceptionactionbull Learning ability
bull The set of all these concepts compose the autonomy
969
Introduction to Mobile Robotics2 Intelligent Robots
Definition of intelligent robot
bull An intelligent robot is a mechanical device that can operateautonomously
bull The term ldquointelligentrdquo means that the robot does not act withoutthinking repeatedly like common plant-floor robots
bull Autonomous operation implies that the robot is able to operatewithout external supervision The robot is able to adapt tochanges in the environment or even changes in itself and stillmaintain proper functioning
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Introduction to Mobile Robotics2 Intelligent Robots
What is an intelligent robot for
bull For tasks that could put human life at riskbull nuclear spatial military
bull For replacing humans in repetitive and boring tasks
bull For humanitarian usebull search and rescue landmines removal
bull For 3D works - Dirty Dull and Dangerous
1169
Introduction to Mobile Robotics2 Intelligent Robots
Ethics
ldquoEthics can be defined as a set of rules principles or ways of thin-king that guide or call to itself the authority to guide the actionsof a particular grouprdquo
Peter Singer 2
2P Singer Ethics 19941269
2 Intelligent Robots
21 Ethical dilemmas
Introduction to Mobile Robotics2 Intelligent Robots
The Trolley Problembull The trolley problem is a thought experiment in ethics first introduced by
Philippa Foot in 1967 (Video3 )
A runaway trolley is headed straight to five people tied up on the tracks and unable tomove You are standing next to a lever If you pull this lever the trolley will switch to adifferent set of tracks However you notice that there is one person tied up on the sidetrack You have two options
bull Do nothing and the trolley kills the five people on the main trackbull Pull the lever diverting the trolley onto the side track where it will kill one person
Which is the most ethical choice
3B R 4 The Trolley Problem httpswwwyoutubecomwatchv=bOpf6KcWYyw Accessed 2018-02-25 20141369
Introduction to Mobile Robotics2 Intelligent Robots
Peoplersquos responses to trolley problems
bull The trolley problem has been the subject of many surveys in whichapproximately 90 of respondents have chosen to kill the one and save the five
bull If the situation is modified where the one sacrificed for the five was a relative orromantic partner respondents are much less likely to be willing to sacrifice theirlife
bull Greene and colleagues (2001) demonstrated using functional magneticresonance imaging that personaldilemmas (like pushing a man off afootbridge) preferentially engage brain regions associated with emotion whereasimpersonaldilemmas (like diverting the trolley by flipping a switch)preferentially engaged regions associated with controlled reasoning
bull Problems analogous to the trolley problem arise in the design of autonomouscars in situations where the carrsquos software is forced during a potential crashscenario to choose between multiple courses of action
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Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practiceHow Tesla Solves A Self-Driving Crash Dilemma4
bull A class-action lawsuit was filed in December 2016about Teslarsquos decision to not use its AutomaticEmergency Braking (AEB) system when ahuman driver is pressing on the accelerator pedal
bull From the lawsuitldquoWhen a frontal collision is considered unavoidableAutomatic Emergency Braking is designed toautomatically apply the brakes to reduce the severityof the impact But Tesla has programmed the systemto deactivate when it receives instructions from theaccelerator pedal to drive full speed into a fixedobjectrdquo
4P Lin Herersquos How Tesla Solves A Self-Driving Crash Dilemma
httpswwwforbescomsitespatricklin20170405heres-how-tesla-solves-a-self-driving-crash-
dilemma72962be16813 Accessed 2018-02-25 20171569
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
ldquoTesla confirmed that when it stated that Automatic EmergencyBraking will operates only when driving between 5 mph (8 kmh)and 85 mph (140 kmh) but that the vehicle will not automaticallyapply the brakes or will stop applying the brakes ldquoin situationswhere you are taking action to avoid a potential collisionrdquo
bull For examplebull You turn the steering wheel sharplybull You press the accelerator pedalbull You press and release the brake pedalbull A vehicle motorcycle bicycle or pedestrian is no longer detectedaheadrdquo
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Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
3 Basic Problems in MobileRobotics
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimation in Mobile Robotics
bull An autonomous mobile robot should be able to move in anenvironment to fulfill its tasks which demands that the robotknows its location along with the location of nearby obstacles
bull In realistic scenarios such information is not directly available andthe robot must use its sensors which carry only partial and noisyinformation about the scenario state6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016231969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimationx robotrsquos pose m map zobservations ucontrols
Graphical model
hellip
hellip
1 2 3 hellip
1 2 3 t0
1 2 3 t
t
2069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
3 Basic Problems in Mobile Robotics
31 Mapping
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectory
bull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actions
bull Observationsbull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Mapsbull For environments with locally distinguishable featuresfeature-based (or landmark-based) maps have been extensively used
bull The map is just a set of objects each one with a specific coordinate
(a) Example of a mobile robot mapping a set of stone rocks(b) The image depicts the path and the estimated landmark positions (marked by circles)
Figure extracted from 7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_452369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
2469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Method 8 9 that represents the environment by a discrete grid offixed-size cells
bull Very useful for robots equipped with range-based sensorsbecause the range values of each sensor combined with the absoluteposition of the robot can be used directly to update the cells
bull Each cell has an occupancy value to indicate if it is an obstacle orpart of free space
bull the value 0 indicates that the cell has not been ldquohitrdquo yet thereforeit is likely free space
bull if the cellrsquos value is above a certain threshold (due to several rangingstrikes) the cell is deemed to be an obstacle
8A Elfes ldquoSonar-based real-world mapping and navigationrdquo Em IEEE Journal on Robotics and Automation 33 (1987)
pp 249ndash2659A Elfes ldquoUsing occupancy grids for mobile robot perception and navigationrdquo Em Computer 226 (1989) pp 46ndash57
2669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
2969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
3269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics1 Introduction to Mobile Robotics
A brief history of Roboticsbull In 1942 during the execution of Manhattan Project US scientistsand engineers developed the telemanipulator
bull It was capable to handle radioactive material (eg uranium andplutonium) through teleoperation
A model 8 telemanipulator 0
0R R Murphy An Introduction to AI Robotics (Intelligent Robotics and Autonomous Agents) 2000569
Introduction to Mobile Robotics1 Introduction to Mobile Robotics
A brief history of Robotics (ii)
bull In 1953 the first AGV (Automatic Guided Vehicle) was broughtto market by Barrett Electronics of Northbrook Illinois
bull It was simply a truck that followed a wire in the floor
The first AGV A modern AGV
669
Introduction to Mobile Robotics1 Introduction to Mobile Robotics
A brief history of Robotics (iii)
bull In 1972 Shakey the robot was thefirst general-purpose robot with thecapability of reasoning using ArtificialIntelligence techniques
bull It was developed by the AI group fromthe Stanford Research Institute (SRI)International led by Charles Rosen
Shakey the robot
769
Introduction to Mobile Robotics1 Introduction to Mobile Robotics
Robots nowadays
Pathfinder mission
Unmanned Aerial Vehicle (UAV)
DARPA Autonomous Vehicle
Anthropomorphic
Walking
DaVinci Surgical Robot
Airduct inspection
869
2 Intelligent Robots
Introduction to Mobile Robotics2 Intelligent Robots
Intelligent Robots
bull The definition of robot is connected to the definition of agent inArtificial Inteligence
bull An agent performs actions in an environment based on informationgathered from its sensors
bull There are numerous definitions for agents focusing onbull Survivalbull Perceptionactionbull Learning ability
bull The set of all these concepts compose the autonomy
969
Introduction to Mobile Robotics2 Intelligent Robots
Definition of intelligent robot
bull An intelligent robot is a mechanical device that can operateautonomously
bull The term ldquointelligentrdquo means that the robot does not act withoutthinking repeatedly like common plant-floor robots
bull Autonomous operation implies that the robot is able to operatewithout external supervision The robot is able to adapt tochanges in the environment or even changes in itself and stillmaintain proper functioning
1069
Introduction to Mobile Robotics2 Intelligent Robots
What is an intelligent robot for
bull For tasks that could put human life at riskbull nuclear spatial military
bull For replacing humans in repetitive and boring tasks
bull For humanitarian usebull search and rescue landmines removal
bull For 3D works - Dirty Dull and Dangerous
1169
Introduction to Mobile Robotics2 Intelligent Robots
Ethics
ldquoEthics can be defined as a set of rules principles or ways of thin-king that guide or call to itself the authority to guide the actionsof a particular grouprdquo
Peter Singer 2
2P Singer Ethics 19941269
2 Intelligent Robots
21 Ethical dilemmas
Introduction to Mobile Robotics2 Intelligent Robots
The Trolley Problembull The trolley problem is a thought experiment in ethics first introduced by
Philippa Foot in 1967 (Video3 )
A runaway trolley is headed straight to five people tied up on the tracks and unable tomove You are standing next to a lever If you pull this lever the trolley will switch to adifferent set of tracks However you notice that there is one person tied up on the sidetrack You have two options
bull Do nothing and the trolley kills the five people on the main trackbull Pull the lever diverting the trolley onto the side track where it will kill one person
Which is the most ethical choice
3B R 4 The Trolley Problem httpswwwyoutubecomwatchv=bOpf6KcWYyw Accessed 2018-02-25 20141369
Introduction to Mobile Robotics2 Intelligent Robots
Peoplersquos responses to trolley problems
bull The trolley problem has been the subject of many surveys in whichapproximately 90 of respondents have chosen to kill the one and save the five
bull If the situation is modified where the one sacrificed for the five was a relative orromantic partner respondents are much less likely to be willing to sacrifice theirlife
bull Greene and colleagues (2001) demonstrated using functional magneticresonance imaging that personaldilemmas (like pushing a man off afootbridge) preferentially engage brain regions associated with emotion whereasimpersonaldilemmas (like diverting the trolley by flipping a switch)preferentially engaged regions associated with controlled reasoning
bull Problems analogous to the trolley problem arise in the design of autonomouscars in situations where the carrsquos software is forced during a potential crashscenario to choose between multiple courses of action
1469
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practiceHow Tesla Solves A Self-Driving Crash Dilemma4
bull A class-action lawsuit was filed in December 2016about Teslarsquos decision to not use its AutomaticEmergency Braking (AEB) system when ahuman driver is pressing on the accelerator pedal
bull From the lawsuitldquoWhen a frontal collision is considered unavoidableAutomatic Emergency Braking is designed toautomatically apply the brakes to reduce the severityof the impact But Tesla has programmed the systemto deactivate when it receives instructions from theaccelerator pedal to drive full speed into a fixedobjectrdquo
4P Lin Herersquos How Tesla Solves A Self-Driving Crash Dilemma
httpswwwforbescomsitespatricklin20170405heres-how-tesla-solves-a-self-driving-crash-
dilemma72962be16813 Accessed 2018-02-25 20171569
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
ldquoTesla confirmed that when it stated that Automatic EmergencyBraking will operates only when driving between 5 mph (8 kmh)and 85 mph (140 kmh) but that the vehicle will not automaticallyapply the brakes or will stop applying the brakes ldquoin situationswhere you are taking action to avoid a potential collisionrdquo
bull For examplebull You turn the steering wheel sharplybull You press the accelerator pedalbull You press and release the brake pedalbull A vehicle motorcycle bicycle or pedestrian is no longer detectedaheadrdquo
1669
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
3 Basic Problems in MobileRobotics
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimation in Mobile Robotics
bull An autonomous mobile robot should be able to move in anenvironment to fulfill its tasks which demands that the robotknows its location along with the location of nearby obstacles
bull In realistic scenarios such information is not directly available andthe robot must use its sensors which carry only partial and noisyinformation about the scenario state6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016231969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimationx robotrsquos pose m map zobservations ucontrols
Graphical model
hellip
hellip
1 2 3 hellip
1 2 3 t0
1 2 3 t
t
2069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
3 Basic Problems in Mobile Robotics
31 Mapping
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectory
bull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actions
bull Observationsbull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Mapsbull For environments with locally distinguishable featuresfeature-based (or landmark-based) maps have been extensively used
bull The map is just a set of objects each one with a specific coordinate
(a) Example of a mobile robot mapping a set of stone rocks(b) The image depicts the path and the estimated landmark positions (marked by circles)
Figure extracted from 7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_452369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
2469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Method 8 9 that represents the environment by a discrete grid offixed-size cells
bull Very useful for robots equipped with range-based sensorsbecause the range values of each sensor combined with the absoluteposition of the robot can be used directly to update the cells
bull Each cell has an occupancy value to indicate if it is an obstacle orpart of free space
bull the value 0 indicates that the cell has not been ldquohitrdquo yet thereforeit is likely free space
bull if the cellrsquos value is above a certain threshold (due to several rangingstrikes) the cell is deemed to be an obstacle
8A Elfes ldquoSonar-based real-world mapping and navigationrdquo Em IEEE Journal on Robotics and Automation 33 (1987)
pp 249ndash2659A Elfes ldquoUsing occupancy grids for mobile robot perception and navigationrdquo Em Computer 226 (1989) pp 46ndash57
2669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
2969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
3269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics1 Introduction to Mobile Robotics
A brief history of Robotics (ii)
bull In 1953 the first AGV (Automatic Guided Vehicle) was broughtto market by Barrett Electronics of Northbrook Illinois
bull It was simply a truck that followed a wire in the floor
The first AGV A modern AGV
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Introduction to Mobile Robotics1 Introduction to Mobile Robotics
A brief history of Robotics (iii)
bull In 1972 Shakey the robot was thefirst general-purpose robot with thecapability of reasoning using ArtificialIntelligence techniques
bull It was developed by the AI group fromthe Stanford Research Institute (SRI)International led by Charles Rosen
Shakey the robot
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Introduction to Mobile Robotics1 Introduction to Mobile Robotics
Robots nowadays
Pathfinder mission
Unmanned Aerial Vehicle (UAV)
DARPA Autonomous Vehicle
Anthropomorphic
Walking
DaVinci Surgical Robot
Airduct inspection
869
2 Intelligent Robots
Introduction to Mobile Robotics2 Intelligent Robots
Intelligent Robots
bull The definition of robot is connected to the definition of agent inArtificial Inteligence
bull An agent performs actions in an environment based on informationgathered from its sensors
bull There are numerous definitions for agents focusing onbull Survivalbull Perceptionactionbull Learning ability
bull The set of all these concepts compose the autonomy
969
Introduction to Mobile Robotics2 Intelligent Robots
Definition of intelligent robot
bull An intelligent robot is a mechanical device that can operateautonomously
bull The term ldquointelligentrdquo means that the robot does not act withoutthinking repeatedly like common plant-floor robots
bull Autonomous operation implies that the robot is able to operatewithout external supervision The robot is able to adapt tochanges in the environment or even changes in itself and stillmaintain proper functioning
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Introduction to Mobile Robotics2 Intelligent Robots
What is an intelligent robot for
bull For tasks that could put human life at riskbull nuclear spatial military
bull For replacing humans in repetitive and boring tasks
bull For humanitarian usebull search and rescue landmines removal
bull For 3D works - Dirty Dull and Dangerous
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Introduction to Mobile Robotics2 Intelligent Robots
Ethics
ldquoEthics can be defined as a set of rules principles or ways of thin-king that guide or call to itself the authority to guide the actionsof a particular grouprdquo
Peter Singer 2
2P Singer Ethics 19941269
2 Intelligent Robots
21 Ethical dilemmas
Introduction to Mobile Robotics2 Intelligent Robots
The Trolley Problembull The trolley problem is a thought experiment in ethics first introduced by
Philippa Foot in 1967 (Video3 )
A runaway trolley is headed straight to five people tied up on the tracks and unable tomove You are standing next to a lever If you pull this lever the trolley will switch to adifferent set of tracks However you notice that there is one person tied up on the sidetrack You have two options
bull Do nothing and the trolley kills the five people on the main trackbull Pull the lever diverting the trolley onto the side track where it will kill one person
Which is the most ethical choice
3B R 4 The Trolley Problem httpswwwyoutubecomwatchv=bOpf6KcWYyw Accessed 2018-02-25 20141369
Introduction to Mobile Robotics2 Intelligent Robots
Peoplersquos responses to trolley problems
bull The trolley problem has been the subject of many surveys in whichapproximately 90 of respondents have chosen to kill the one and save the five
bull If the situation is modified where the one sacrificed for the five was a relative orromantic partner respondents are much less likely to be willing to sacrifice theirlife
bull Greene and colleagues (2001) demonstrated using functional magneticresonance imaging that personaldilemmas (like pushing a man off afootbridge) preferentially engage brain regions associated with emotion whereasimpersonaldilemmas (like diverting the trolley by flipping a switch)preferentially engaged regions associated with controlled reasoning
bull Problems analogous to the trolley problem arise in the design of autonomouscars in situations where the carrsquos software is forced during a potential crashscenario to choose between multiple courses of action
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Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practiceHow Tesla Solves A Self-Driving Crash Dilemma4
bull A class-action lawsuit was filed in December 2016about Teslarsquos decision to not use its AutomaticEmergency Braking (AEB) system when ahuman driver is pressing on the accelerator pedal
bull From the lawsuitldquoWhen a frontal collision is considered unavoidableAutomatic Emergency Braking is designed toautomatically apply the brakes to reduce the severityof the impact But Tesla has programmed the systemto deactivate when it receives instructions from theaccelerator pedal to drive full speed into a fixedobjectrdquo
4P Lin Herersquos How Tesla Solves A Self-Driving Crash Dilemma
httpswwwforbescomsitespatricklin20170405heres-how-tesla-solves-a-self-driving-crash-
dilemma72962be16813 Accessed 2018-02-25 20171569
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
ldquoTesla confirmed that when it stated that Automatic EmergencyBraking will operates only when driving between 5 mph (8 kmh)and 85 mph (140 kmh) but that the vehicle will not automaticallyapply the brakes or will stop applying the brakes ldquoin situationswhere you are taking action to avoid a potential collisionrdquo
bull For examplebull You turn the steering wheel sharplybull You press the accelerator pedalbull You press and release the brake pedalbull A vehicle motorcycle bicycle or pedestrian is no longer detectedaheadrdquo
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Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
3 Basic Problems in MobileRobotics
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimation in Mobile Robotics
bull An autonomous mobile robot should be able to move in anenvironment to fulfill its tasks which demands that the robotknows its location along with the location of nearby obstacles
bull In realistic scenarios such information is not directly available andthe robot must use its sensors which carry only partial and noisyinformation about the scenario state6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016231969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimationx robotrsquos pose m map zobservations ucontrols
Graphical model
hellip
hellip
1 2 3 hellip
1 2 3 t0
1 2 3 t
t
2069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
3 Basic Problems in Mobile Robotics
31 Mapping
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectory
bull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actions
bull Observationsbull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Mapsbull For environments with locally distinguishable featuresfeature-based (or landmark-based) maps have been extensively used
bull The map is just a set of objects each one with a specific coordinate
(a) Example of a mobile robot mapping a set of stone rocks(b) The image depicts the path and the estimated landmark positions (marked by circles)
Figure extracted from 7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_452369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
2469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Method 8 9 that represents the environment by a discrete grid offixed-size cells
bull Very useful for robots equipped with range-based sensorsbecause the range values of each sensor combined with the absoluteposition of the robot can be used directly to update the cells
bull Each cell has an occupancy value to indicate if it is an obstacle orpart of free space
bull the value 0 indicates that the cell has not been ldquohitrdquo yet thereforeit is likely free space
bull if the cellrsquos value is above a certain threshold (due to several rangingstrikes) the cell is deemed to be an obstacle
8A Elfes ldquoSonar-based real-world mapping and navigationrdquo Em IEEE Journal on Robotics and Automation 33 (1987)
pp 249ndash2659A Elfes ldquoUsing occupancy grids for mobile robot perception and navigationrdquo Em Computer 226 (1989) pp 46ndash57
2669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
2969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
3269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics1 Introduction to Mobile Robotics
A brief history of Robotics (iii)
bull In 1972 Shakey the robot was thefirst general-purpose robot with thecapability of reasoning using ArtificialIntelligence techniques
bull It was developed by the AI group fromthe Stanford Research Institute (SRI)International led by Charles Rosen
Shakey the robot
769
Introduction to Mobile Robotics1 Introduction to Mobile Robotics
Robots nowadays
Pathfinder mission
Unmanned Aerial Vehicle (UAV)
DARPA Autonomous Vehicle
Anthropomorphic
Walking
DaVinci Surgical Robot
Airduct inspection
869
2 Intelligent Robots
Introduction to Mobile Robotics2 Intelligent Robots
Intelligent Robots
bull The definition of robot is connected to the definition of agent inArtificial Inteligence
bull An agent performs actions in an environment based on informationgathered from its sensors
bull There are numerous definitions for agents focusing onbull Survivalbull Perceptionactionbull Learning ability
bull The set of all these concepts compose the autonomy
969
Introduction to Mobile Robotics2 Intelligent Robots
Definition of intelligent robot
bull An intelligent robot is a mechanical device that can operateautonomously
bull The term ldquointelligentrdquo means that the robot does not act withoutthinking repeatedly like common plant-floor robots
bull Autonomous operation implies that the robot is able to operatewithout external supervision The robot is able to adapt tochanges in the environment or even changes in itself and stillmaintain proper functioning
1069
Introduction to Mobile Robotics2 Intelligent Robots
What is an intelligent robot for
bull For tasks that could put human life at riskbull nuclear spatial military
bull For replacing humans in repetitive and boring tasks
bull For humanitarian usebull search and rescue landmines removal
bull For 3D works - Dirty Dull and Dangerous
1169
Introduction to Mobile Robotics2 Intelligent Robots
Ethics
ldquoEthics can be defined as a set of rules principles or ways of thin-king that guide or call to itself the authority to guide the actionsof a particular grouprdquo
Peter Singer 2
2P Singer Ethics 19941269
2 Intelligent Robots
21 Ethical dilemmas
Introduction to Mobile Robotics2 Intelligent Robots
The Trolley Problembull The trolley problem is a thought experiment in ethics first introduced by
Philippa Foot in 1967 (Video3 )
A runaway trolley is headed straight to five people tied up on the tracks and unable tomove You are standing next to a lever If you pull this lever the trolley will switch to adifferent set of tracks However you notice that there is one person tied up on the sidetrack You have two options
bull Do nothing and the trolley kills the five people on the main trackbull Pull the lever diverting the trolley onto the side track where it will kill one person
Which is the most ethical choice
3B R 4 The Trolley Problem httpswwwyoutubecomwatchv=bOpf6KcWYyw Accessed 2018-02-25 20141369
Introduction to Mobile Robotics2 Intelligent Robots
Peoplersquos responses to trolley problems
bull The trolley problem has been the subject of many surveys in whichapproximately 90 of respondents have chosen to kill the one and save the five
bull If the situation is modified where the one sacrificed for the five was a relative orromantic partner respondents are much less likely to be willing to sacrifice theirlife
bull Greene and colleagues (2001) demonstrated using functional magneticresonance imaging that personaldilemmas (like pushing a man off afootbridge) preferentially engage brain regions associated with emotion whereasimpersonaldilemmas (like diverting the trolley by flipping a switch)preferentially engaged regions associated with controlled reasoning
bull Problems analogous to the trolley problem arise in the design of autonomouscars in situations where the carrsquos software is forced during a potential crashscenario to choose between multiple courses of action
1469
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practiceHow Tesla Solves A Self-Driving Crash Dilemma4
bull A class-action lawsuit was filed in December 2016about Teslarsquos decision to not use its AutomaticEmergency Braking (AEB) system when ahuman driver is pressing on the accelerator pedal
bull From the lawsuitldquoWhen a frontal collision is considered unavoidableAutomatic Emergency Braking is designed toautomatically apply the brakes to reduce the severityof the impact But Tesla has programmed the systemto deactivate when it receives instructions from theaccelerator pedal to drive full speed into a fixedobjectrdquo
4P Lin Herersquos How Tesla Solves A Self-Driving Crash Dilemma
httpswwwforbescomsitespatricklin20170405heres-how-tesla-solves-a-self-driving-crash-
dilemma72962be16813 Accessed 2018-02-25 20171569
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
ldquoTesla confirmed that when it stated that Automatic EmergencyBraking will operates only when driving between 5 mph (8 kmh)and 85 mph (140 kmh) but that the vehicle will not automaticallyapply the brakes or will stop applying the brakes ldquoin situationswhere you are taking action to avoid a potential collisionrdquo
bull For examplebull You turn the steering wheel sharplybull You press the accelerator pedalbull You press and release the brake pedalbull A vehicle motorcycle bicycle or pedestrian is no longer detectedaheadrdquo
1669
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
3 Basic Problems in MobileRobotics
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimation in Mobile Robotics
bull An autonomous mobile robot should be able to move in anenvironment to fulfill its tasks which demands that the robotknows its location along with the location of nearby obstacles
bull In realistic scenarios such information is not directly available andthe robot must use its sensors which carry only partial and noisyinformation about the scenario state6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016231969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimationx robotrsquos pose m map zobservations ucontrols
Graphical model
hellip
hellip
1 2 3 hellip
1 2 3 t0
1 2 3 t
t
2069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
3 Basic Problems in Mobile Robotics
31 Mapping
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectory
bull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actions
bull Observationsbull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Mapsbull For environments with locally distinguishable featuresfeature-based (or landmark-based) maps have been extensively used
bull The map is just a set of objects each one with a specific coordinate
(a) Example of a mobile robot mapping a set of stone rocks(b) The image depicts the path and the estimated landmark positions (marked by circles)
Figure extracted from 7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_452369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
2469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Method 8 9 that represents the environment by a discrete grid offixed-size cells
bull Very useful for robots equipped with range-based sensorsbecause the range values of each sensor combined with the absoluteposition of the robot can be used directly to update the cells
bull Each cell has an occupancy value to indicate if it is an obstacle orpart of free space
bull the value 0 indicates that the cell has not been ldquohitrdquo yet thereforeit is likely free space
bull if the cellrsquos value is above a certain threshold (due to several rangingstrikes) the cell is deemed to be an obstacle
8A Elfes ldquoSonar-based real-world mapping and navigationrdquo Em IEEE Journal on Robotics and Automation 33 (1987)
pp 249ndash2659A Elfes ldquoUsing occupancy grids for mobile robot perception and navigationrdquo Em Computer 226 (1989) pp 46ndash57
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
3269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics1 Introduction to Mobile Robotics
Robots nowadays
Pathfinder mission
Unmanned Aerial Vehicle (UAV)
DARPA Autonomous Vehicle
Anthropomorphic
Walking
DaVinci Surgical Robot
Airduct inspection
869
2 Intelligent Robots
Introduction to Mobile Robotics2 Intelligent Robots
Intelligent Robots
bull The definition of robot is connected to the definition of agent inArtificial Inteligence
bull An agent performs actions in an environment based on informationgathered from its sensors
bull There are numerous definitions for agents focusing onbull Survivalbull Perceptionactionbull Learning ability
bull The set of all these concepts compose the autonomy
969
Introduction to Mobile Robotics2 Intelligent Robots
Definition of intelligent robot
bull An intelligent robot is a mechanical device that can operateautonomously
bull The term ldquointelligentrdquo means that the robot does not act withoutthinking repeatedly like common plant-floor robots
bull Autonomous operation implies that the robot is able to operatewithout external supervision The robot is able to adapt tochanges in the environment or even changes in itself and stillmaintain proper functioning
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Introduction to Mobile Robotics2 Intelligent Robots
What is an intelligent robot for
bull For tasks that could put human life at riskbull nuclear spatial military
bull For replacing humans in repetitive and boring tasks
bull For humanitarian usebull search and rescue landmines removal
bull For 3D works - Dirty Dull and Dangerous
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Introduction to Mobile Robotics2 Intelligent Robots
Ethics
ldquoEthics can be defined as a set of rules principles or ways of thin-king that guide or call to itself the authority to guide the actionsof a particular grouprdquo
Peter Singer 2
2P Singer Ethics 19941269
2 Intelligent Robots
21 Ethical dilemmas
Introduction to Mobile Robotics2 Intelligent Robots
The Trolley Problembull The trolley problem is a thought experiment in ethics first introduced by
Philippa Foot in 1967 (Video3 )
A runaway trolley is headed straight to five people tied up on the tracks and unable tomove You are standing next to a lever If you pull this lever the trolley will switch to adifferent set of tracks However you notice that there is one person tied up on the sidetrack You have two options
bull Do nothing and the trolley kills the five people on the main trackbull Pull the lever diverting the trolley onto the side track where it will kill one person
Which is the most ethical choice
3B R 4 The Trolley Problem httpswwwyoutubecomwatchv=bOpf6KcWYyw Accessed 2018-02-25 20141369
Introduction to Mobile Robotics2 Intelligent Robots
Peoplersquos responses to trolley problems
bull The trolley problem has been the subject of many surveys in whichapproximately 90 of respondents have chosen to kill the one and save the five
bull If the situation is modified where the one sacrificed for the five was a relative orromantic partner respondents are much less likely to be willing to sacrifice theirlife
bull Greene and colleagues (2001) demonstrated using functional magneticresonance imaging that personaldilemmas (like pushing a man off afootbridge) preferentially engage brain regions associated with emotion whereasimpersonaldilemmas (like diverting the trolley by flipping a switch)preferentially engaged regions associated with controlled reasoning
bull Problems analogous to the trolley problem arise in the design of autonomouscars in situations where the carrsquos software is forced during a potential crashscenario to choose between multiple courses of action
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Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practiceHow Tesla Solves A Self-Driving Crash Dilemma4
bull A class-action lawsuit was filed in December 2016about Teslarsquos decision to not use its AutomaticEmergency Braking (AEB) system when ahuman driver is pressing on the accelerator pedal
bull From the lawsuitldquoWhen a frontal collision is considered unavoidableAutomatic Emergency Braking is designed toautomatically apply the brakes to reduce the severityof the impact But Tesla has programmed the systemto deactivate when it receives instructions from theaccelerator pedal to drive full speed into a fixedobjectrdquo
4P Lin Herersquos How Tesla Solves A Self-Driving Crash Dilemma
httpswwwforbescomsitespatricklin20170405heres-how-tesla-solves-a-self-driving-crash-
dilemma72962be16813 Accessed 2018-02-25 20171569
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
ldquoTesla confirmed that when it stated that Automatic EmergencyBraking will operates only when driving between 5 mph (8 kmh)and 85 mph (140 kmh) but that the vehicle will not automaticallyapply the brakes or will stop applying the brakes ldquoin situationswhere you are taking action to avoid a potential collisionrdquo
bull For examplebull You turn the steering wheel sharplybull You press the accelerator pedalbull You press and release the brake pedalbull A vehicle motorcycle bicycle or pedestrian is no longer detectedaheadrdquo
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Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
3 Basic Problems in MobileRobotics
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimation in Mobile Robotics
bull An autonomous mobile robot should be able to move in anenvironment to fulfill its tasks which demands that the robotknows its location along with the location of nearby obstacles
bull In realistic scenarios such information is not directly available andthe robot must use its sensors which carry only partial and noisyinformation about the scenario state6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016231969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimationx robotrsquos pose m map zobservations ucontrols
Graphical model
hellip
hellip
1 2 3 hellip
1 2 3 t0
1 2 3 t
t
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
3 Basic Problems in Mobile Robotics
31 Mapping
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectory
bull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actions
bull Observationsbull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Mapsbull For environments with locally distinguishable featuresfeature-based (or landmark-based) maps have been extensively used
bull The map is just a set of objects each one with a specific coordinate
(a) Example of a mobile robot mapping a set of stone rocks(b) The image depicts the path and the estimated landmark positions (marked by circles)
Figure extracted from 7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_452369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
2469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Method 8 9 that represents the environment by a discrete grid offixed-size cells
bull Very useful for robots equipped with range-based sensorsbecause the range values of each sensor combined with the absoluteposition of the robot can be used directly to update the cells
bull Each cell has an occupancy value to indicate if it is an obstacle orpart of free space
bull the value 0 indicates that the cell has not been ldquohitrdquo yet thereforeit is likely free space
bull if the cellrsquos value is above a certain threshold (due to several rangingstrikes) the cell is deemed to be an obstacle
8A Elfes ldquoSonar-based real-world mapping and navigationrdquo Em IEEE Journal on Robotics and Automation 33 (1987)
pp 249ndash2659A Elfes ldquoUsing occupancy grids for mobile robot perception and navigationrdquo Em Computer 226 (1989) pp 46ndash57
2669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
2969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
3269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
2 Intelligent Robots
Introduction to Mobile Robotics2 Intelligent Robots
Intelligent Robots
bull The definition of robot is connected to the definition of agent inArtificial Inteligence
bull An agent performs actions in an environment based on informationgathered from its sensors
bull There are numerous definitions for agents focusing onbull Survivalbull Perceptionactionbull Learning ability
bull The set of all these concepts compose the autonomy
969
Introduction to Mobile Robotics2 Intelligent Robots
Definition of intelligent robot
bull An intelligent robot is a mechanical device that can operateautonomously
bull The term ldquointelligentrdquo means that the robot does not act withoutthinking repeatedly like common plant-floor robots
bull Autonomous operation implies that the robot is able to operatewithout external supervision The robot is able to adapt tochanges in the environment or even changes in itself and stillmaintain proper functioning
1069
Introduction to Mobile Robotics2 Intelligent Robots
What is an intelligent robot for
bull For tasks that could put human life at riskbull nuclear spatial military
bull For replacing humans in repetitive and boring tasks
bull For humanitarian usebull search and rescue landmines removal
bull For 3D works - Dirty Dull and Dangerous
1169
Introduction to Mobile Robotics2 Intelligent Robots
Ethics
ldquoEthics can be defined as a set of rules principles or ways of thin-king that guide or call to itself the authority to guide the actionsof a particular grouprdquo
Peter Singer 2
2P Singer Ethics 19941269
2 Intelligent Robots
21 Ethical dilemmas
Introduction to Mobile Robotics2 Intelligent Robots
The Trolley Problembull The trolley problem is a thought experiment in ethics first introduced by
Philippa Foot in 1967 (Video3 )
A runaway trolley is headed straight to five people tied up on the tracks and unable tomove You are standing next to a lever If you pull this lever the trolley will switch to adifferent set of tracks However you notice that there is one person tied up on the sidetrack You have two options
bull Do nothing and the trolley kills the five people on the main trackbull Pull the lever diverting the trolley onto the side track where it will kill one person
Which is the most ethical choice
3B R 4 The Trolley Problem httpswwwyoutubecomwatchv=bOpf6KcWYyw Accessed 2018-02-25 20141369
Introduction to Mobile Robotics2 Intelligent Robots
Peoplersquos responses to trolley problems
bull The trolley problem has been the subject of many surveys in whichapproximately 90 of respondents have chosen to kill the one and save the five
bull If the situation is modified where the one sacrificed for the five was a relative orromantic partner respondents are much less likely to be willing to sacrifice theirlife
bull Greene and colleagues (2001) demonstrated using functional magneticresonance imaging that personaldilemmas (like pushing a man off afootbridge) preferentially engage brain regions associated with emotion whereasimpersonaldilemmas (like diverting the trolley by flipping a switch)preferentially engaged regions associated with controlled reasoning
bull Problems analogous to the trolley problem arise in the design of autonomouscars in situations where the carrsquos software is forced during a potential crashscenario to choose between multiple courses of action
1469
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practiceHow Tesla Solves A Self-Driving Crash Dilemma4
bull A class-action lawsuit was filed in December 2016about Teslarsquos decision to not use its AutomaticEmergency Braking (AEB) system when ahuman driver is pressing on the accelerator pedal
bull From the lawsuitldquoWhen a frontal collision is considered unavoidableAutomatic Emergency Braking is designed toautomatically apply the brakes to reduce the severityof the impact But Tesla has programmed the systemto deactivate when it receives instructions from theaccelerator pedal to drive full speed into a fixedobjectrdquo
4P Lin Herersquos How Tesla Solves A Self-Driving Crash Dilemma
httpswwwforbescomsitespatricklin20170405heres-how-tesla-solves-a-self-driving-crash-
dilemma72962be16813 Accessed 2018-02-25 20171569
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
ldquoTesla confirmed that when it stated that Automatic EmergencyBraking will operates only when driving between 5 mph (8 kmh)and 85 mph (140 kmh) but that the vehicle will not automaticallyapply the brakes or will stop applying the brakes ldquoin situationswhere you are taking action to avoid a potential collisionrdquo
bull For examplebull You turn the steering wheel sharplybull You press the accelerator pedalbull You press and release the brake pedalbull A vehicle motorcycle bicycle or pedestrian is no longer detectedaheadrdquo
1669
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
3 Basic Problems in MobileRobotics
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimation in Mobile Robotics
bull An autonomous mobile robot should be able to move in anenvironment to fulfill its tasks which demands that the robotknows its location along with the location of nearby obstacles
bull In realistic scenarios such information is not directly available andthe robot must use its sensors which carry only partial and noisyinformation about the scenario state6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016231969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimationx robotrsquos pose m map zobservations ucontrols
Graphical model
hellip
hellip
1 2 3 hellip
1 2 3 t0
1 2 3 t
t
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
3 Basic Problems in Mobile Robotics
31 Mapping
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectory
bull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actions
bull Observationsbull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Mapsbull For environments with locally distinguishable featuresfeature-based (or landmark-based) maps have been extensively used
bull The map is just a set of objects each one with a specific coordinate
(a) Example of a mobile robot mapping a set of stone rocks(b) The image depicts the path and the estimated landmark positions (marked by circles)
Figure extracted from 7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_452369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
2469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Method 8 9 that represents the environment by a discrete grid offixed-size cells
bull Very useful for robots equipped with range-based sensorsbecause the range values of each sensor combined with the absoluteposition of the robot can be used directly to update the cells
bull Each cell has an occupancy value to indicate if it is an obstacle orpart of free space
bull the value 0 indicates that the cell has not been ldquohitrdquo yet thereforeit is likely free space
bull if the cellrsquos value is above a certain threshold (due to several rangingstrikes) the cell is deemed to be an obstacle
8A Elfes ldquoSonar-based real-world mapping and navigationrdquo Em IEEE Journal on Robotics and Automation 33 (1987)
pp 249ndash2659A Elfes ldquoUsing occupancy grids for mobile robot perception and navigationrdquo Em Computer 226 (1989) pp 46ndash57
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics2 Intelligent Robots
Intelligent Robots
bull The definition of robot is connected to the definition of agent inArtificial Inteligence
bull An agent performs actions in an environment based on informationgathered from its sensors
bull There are numerous definitions for agents focusing onbull Survivalbull Perceptionactionbull Learning ability
bull The set of all these concepts compose the autonomy
969
Introduction to Mobile Robotics2 Intelligent Robots
Definition of intelligent robot
bull An intelligent robot is a mechanical device that can operateautonomously
bull The term ldquointelligentrdquo means that the robot does not act withoutthinking repeatedly like common plant-floor robots
bull Autonomous operation implies that the robot is able to operatewithout external supervision The robot is able to adapt tochanges in the environment or even changes in itself and stillmaintain proper functioning
1069
Introduction to Mobile Robotics2 Intelligent Robots
What is an intelligent robot for
bull For tasks that could put human life at riskbull nuclear spatial military
bull For replacing humans in repetitive and boring tasks
bull For humanitarian usebull search and rescue landmines removal
bull For 3D works - Dirty Dull and Dangerous
1169
Introduction to Mobile Robotics2 Intelligent Robots
Ethics
ldquoEthics can be defined as a set of rules principles or ways of thin-king that guide or call to itself the authority to guide the actionsof a particular grouprdquo
Peter Singer 2
2P Singer Ethics 19941269
2 Intelligent Robots
21 Ethical dilemmas
Introduction to Mobile Robotics2 Intelligent Robots
The Trolley Problembull The trolley problem is a thought experiment in ethics first introduced by
Philippa Foot in 1967 (Video3 )
A runaway trolley is headed straight to five people tied up on the tracks and unable tomove You are standing next to a lever If you pull this lever the trolley will switch to adifferent set of tracks However you notice that there is one person tied up on the sidetrack You have two options
bull Do nothing and the trolley kills the five people on the main trackbull Pull the lever diverting the trolley onto the side track where it will kill one person
Which is the most ethical choice
3B R 4 The Trolley Problem httpswwwyoutubecomwatchv=bOpf6KcWYyw Accessed 2018-02-25 20141369
Introduction to Mobile Robotics2 Intelligent Robots
Peoplersquos responses to trolley problems
bull The trolley problem has been the subject of many surveys in whichapproximately 90 of respondents have chosen to kill the one and save the five
bull If the situation is modified where the one sacrificed for the five was a relative orromantic partner respondents are much less likely to be willing to sacrifice theirlife
bull Greene and colleagues (2001) demonstrated using functional magneticresonance imaging that personaldilemmas (like pushing a man off afootbridge) preferentially engage brain regions associated with emotion whereasimpersonaldilemmas (like diverting the trolley by flipping a switch)preferentially engaged regions associated with controlled reasoning
bull Problems analogous to the trolley problem arise in the design of autonomouscars in situations where the carrsquos software is forced during a potential crashscenario to choose between multiple courses of action
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Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practiceHow Tesla Solves A Self-Driving Crash Dilemma4
bull A class-action lawsuit was filed in December 2016about Teslarsquos decision to not use its AutomaticEmergency Braking (AEB) system when ahuman driver is pressing on the accelerator pedal
bull From the lawsuitldquoWhen a frontal collision is considered unavoidableAutomatic Emergency Braking is designed toautomatically apply the brakes to reduce the severityof the impact But Tesla has programmed the systemto deactivate when it receives instructions from theaccelerator pedal to drive full speed into a fixedobjectrdquo
4P Lin Herersquos How Tesla Solves A Self-Driving Crash Dilemma
httpswwwforbescomsitespatricklin20170405heres-how-tesla-solves-a-self-driving-crash-
dilemma72962be16813 Accessed 2018-02-25 20171569
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
ldquoTesla confirmed that when it stated that Automatic EmergencyBraking will operates only when driving between 5 mph (8 kmh)and 85 mph (140 kmh) but that the vehicle will not automaticallyapply the brakes or will stop applying the brakes ldquoin situationswhere you are taking action to avoid a potential collisionrdquo
bull For examplebull You turn the steering wheel sharplybull You press the accelerator pedalbull You press and release the brake pedalbull A vehicle motorcycle bicycle or pedestrian is no longer detectedaheadrdquo
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Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
3 Basic Problems in MobileRobotics
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimation in Mobile Robotics
bull An autonomous mobile robot should be able to move in anenvironment to fulfill its tasks which demands that the robotknows its location along with the location of nearby obstacles
bull In realistic scenarios such information is not directly available andthe robot must use its sensors which carry only partial and noisyinformation about the scenario state6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016231969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimationx robotrsquos pose m map zobservations ucontrols
Graphical model
hellip
hellip
1 2 3 hellip
1 2 3 t0
1 2 3 t
t
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
3 Basic Problems in Mobile Robotics
31 Mapping
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectory
bull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actions
bull Observationsbull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Mapsbull For environments with locally distinguishable featuresfeature-based (or landmark-based) maps have been extensively used
bull The map is just a set of objects each one with a specific coordinate
(a) Example of a mobile robot mapping a set of stone rocks(b) The image depicts the path and the estimated landmark positions (marked by circles)
Figure extracted from 7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_452369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
2469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Method 8 9 that represents the environment by a discrete grid offixed-size cells
bull Very useful for robots equipped with range-based sensorsbecause the range values of each sensor combined with the absoluteposition of the robot can be used directly to update the cells
bull Each cell has an occupancy value to indicate if it is an obstacle orpart of free space
bull the value 0 indicates that the cell has not been ldquohitrdquo yet thereforeit is likely free space
bull if the cellrsquos value is above a certain threshold (due to several rangingstrikes) the cell is deemed to be an obstacle
8A Elfes ldquoSonar-based real-world mapping and navigationrdquo Em IEEE Journal on Robotics and Automation 33 (1987)
pp 249ndash2659A Elfes ldquoUsing occupancy grids for mobile robot perception and navigationrdquo Em Computer 226 (1989) pp 46ndash57
2669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
2969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
3269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics2 Intelligent Robots
Definition of intelligent robot
bull An intelligent robot is a mechanical device that can operateautonomously
bull The term ldquointelligentrdquo means that the robot does not act withoutthinking repeatedly like common plant-floor robots
bull Autonomous operation implies that the robot is able to operatewithout external supervision The robot is able to adapt tochanges in the environment or even changes in itself and stillmaintain proper functioning
1069
Introduction to Mobile Robotics2 Intelligent Robots
What is an intelligent robot for
bull For tasks that could put human life at riskbull nuclear spatial military
bull For replacing humans in repetitive and boring tasks
bull For humanitarian usebull search and rescue landmines removal
bull For 3D works - Dirty Dull and Dangerous
1169
Introduction to Mobile Robotics2 Intelligent Robots
Ethics
ldquoEthics can be defined as a set of rules principles or ways of thin-king that guide or call to itself the authority to guide the actionsof a particular grouprdquo
Peter Singer 2
2P Singer Ethics 19941269
2 Intelligent Robots
21 Ethical dilemmas
Introduction to Mobile Robotics2 Intelligent Robots
The Trolley Problembull The trolley problem is a thought experiment in ethics first introduced by
Philippa Foot in 1967 (Video3 )
A runaway trolley is headed straight to five people tied up on the tracks and unable tomove You are standing next to a lever If you pull this lever the trolley will switch to adifferent set of tracks However you notice that there is one person tied up on the sidetrack You have two options
bull Do nothing and the trolley kills the five people on the main trackbull Pull the lever diverting the trolley onto the side track where it will kill one person
Which is the most ethical choice
3B R 4 The Trolley Problem httpswwwyoutubecomwatchv=bOpf6KcWYyw Accessed 2018-02-25 20141369
Introduction to Mobile Robotics2 Intelligent Robots
Peoplersquos responses to trolley problems
bull The trolley problem has been the subject of many surveys in whichapproximately 90 of respondents have chosen to kill the one and save the five
bull If the situation is modified where the one sacrificed for the five was a relative orromantic partner respondents are much less likely to be willing to sacrifice theirlife
bull Greene and colleagues (2001) demonstrated using functional magneticresonance imaging that personaldilemmas (like pushing a man off afootbridge) preferentially engage brain regions associated with emotion whereasimpersonaldilemmas (like diverting the trolley by flipping a switch)preferentially engaged regions associated with controlled reasoning
bull Problems analogous to the trolley problem arise in the design of autonomouscars in situations where the carrsquos software is forced during a potential crashscenario to choose between multiple courses of action
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Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practiceHow Tesla Solves A Self-Driving Crash Dilemma4
bull A class-action lawsuit was filed in December 2016about Teslarsquos decision to not use its AutomaticEmergency Braking (AEB) system when ahuman driver is pressing on the accelerator pedal
bull From the lawsuitldquoWhen a frontal collision is considered unavoidableAutomatic Emergency Braking is designed toautomatically apply the brakes to reduce the severityof the impact But Tesla has programmed the systemto deactivate when it receives instructions from theaccelerator pedal to drive full speed into a fixedobjectrdquo
4P Lin Herersquos How Tesla Solves A Self-Driving Crash Dilemma
httpswwwforbescomsitespatricklin20170405heres-how-tesla-solves-a-self-driving-crash-
dilemma72962be16813 Accessed 2018-02-25 20171569
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
ldquoTesla confirmed that when it stated that Automatic EmergencyBraking will operates only when driving between 5 mph (8 kmh)and 85 mph (140 kmh) but that the vehicle will not automaticallyapply the brakes or will stop applying the brakes ldquoin situationswhere you are taking action to avoid a potential collisionrdquo
bull For examplebull You turn the steering wheel sharplybull You press the accelerator pedalbull You press and release the brake pedalbull A vehicle motorcycle bicycle or pedestrian is no longer detectedaheadrdquo
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Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
3 Basic Problems in MobileRobotics
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimation in Mobile Robotics
bull An autonomous mobile robot should be able to move in anenvironment to fulfill its tasks which demands that the robotknows its location along with the location of nearby obstacles
bull In realistic scenarios such information is not directly available andthe robot must use its sensors which carry only partial and noisyinformation about the scenario state6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016231969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimationx robotrsquos pose m map zobservations ucontrols
Graphical model
hellip
hellip
1 2 3 hellip
1 2 3 t0
1 2 3 t
t
2069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
3 Basic Problems in Mobile Robotics
31 Mapping
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectory
bull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actions
bull Observationsbull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Mapsbull For environments with locally distinguishable featuresfeature-based (or landmark-based) maps have been extensively used
bull The map is just a set of objects each one with a specific coordinate
(a) Example of a mobile robot mapping a set of stone rocks(b) The image depicts the path and the estimated landmark positions (marked by circles)
Figure extracted from 7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_452369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
2469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Method 8 9 that represents the environment by a discrete grid offixed-size cells
bull Very useful for robots equipped with range-based sensorsbecause the range values of each sensor combined with the absoluteposition of the robot can be used directly to update the cells
bull Each cell has an occupancy value to indicate if it is an obstacle orpart of free space
bull the value 0 indicates that the cell has not been ldquohitrdquo yet thereforeit is likely free space
bull if the cellrsquos value is above a certain threshold (due to several rangingstrikes) the cell is deemed to be an obstacle
8A Elfes ldquoSonar-based real-world mapping and navigationrdquo Em IEEE Journal on Robotics and Automation 33 (1987)
pp 249ndash2659A Elfes ldquoUsing occupancy grids for mobile robot perception and navigationrdquo Em Computer 226 (1989) pp 46ndash57
2669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
2969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
3269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics2 Intelligent Robots
What is an intelligent robot for
bull For tasks that could put human life at riskbull nuclear spatial military
bull For replacing humans in repetitive and boring tasks
bull For humanitarian usebull search and rescue landmines removal
bull For 3D works - Dirty Dull and Dangerous
1169
Introduction to Mobile Robotics2 Intelligent Robots
Ethics
ldquoEthics can be defined as a set of rules principles or ways of thin-king that guide or call to itself the authority to guide the actionsof a particular grouprdquo
Peter Singer 2
2P Singer Ethics 19941269
2 Intelligent Robots
21 Ethical dilemmas
Introduction to Mobile Robotics2 Intelligent Robots
The Trolley Problembull The trolley problem is a thought experiment in ethics first introduced by
Philippa Foot in 1967 (Video3 )
A runaway trolley is headed straight to five people tied up on the tracks and unable tomove You are standing next to a lever If you pull this lever the trolley will switch to adifferent set of tracks However you notice that there is one person tied up on the sidetrack You have two options
bull Do nothing and the trolley kills the five people on the main trackbull Pull the lever diverting the trolley onto the side track where it will kill one person
Which is the most ethical choice
3B R 4 The Trolley Problem httpswwwyoutubecomwatchv=bOpf6KcWYyw Accessed 2018-02-25 20141369
Introduction to Mobile Robotics2 Intelligent Robots
Peoplersquos responses to trolley problems
bull The trolley problem has been the subject of many surveys in whichapproximately 90 of respondents have chosen to kill the one and save the five
bull If the situation is modified where the one sacrificed for the five was a relative orromantic partner respondents are much less likely to be willing to sacrifice theirlife
bull Greene and colleagues (2001) demonstrated using functional magneticresonance imaging that personaldilemmas (like pushing a man off afootbridge) preferentially engage brain regions associated with emotion whereasimpersonaldilemmas (like diverting the trolley by flipping a switch)preferentially engaged regions associated with controlled reasoning
bull Problems analogous to the trolley problem arise in the design of autonomouscars in situations where the carrsquos software is forced during a potential crashscenario to choose between multiple courses of action
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Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practiceHow Tesla Solves A Self-Driving Crash Dilemma4
bull A class-action lawsuit was filed in December 2016about Teslarsquos decision to not use its AutomaticEmergency Braking (AEB) system when ahuman driver is pressing on the accelerator pedal
bull From the lawsuitldquoWhen a frontal collision is considered unavoidableAutomatic Emergency Braking is designed toautomatically apply the brakes to reduce the severityof the impact But Tesla has programmed the systemto deactivate when it receives instructions from theaccelerator pedal to drive full speed into a fixedobjectrdquo
4P Lin Herersquos How Tesla Solves A Self-Driving Crash Dilemma
httpswwwforbescomsitespatricklin20170405heres-how-tesla-solves-a-self-driving-crash-
dilemma72962be16813 Accessed 2018-02-25 20171569
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
ldquoTesla confirmed that when it stated that Automatic EmergencyBraking will operates only when driving between 5 mph (8 kmh)and 85 mph (140 kmh) but that the vehicle will not automaticallyapply the brakes or will stop applying the brakes ldquoin situationswhere you are taking action to avoid a potential collisionrdquo
bull For examplebull You turn the steering wheel sharplybull You press the accelerator pedalbull You press and release the brake pedalbull A vehicle motorcycle bicycle or pedestrian is no longer detectedaheadrdquo
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Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
3 Basic Problems in MobileRobotics
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimation in Mobile Robotics
bull An autonomous mobile robot should be able to move in anenvironment to fulfill its tasks which demands that the robotknows its location along with the location of nearby obstacles
bull In realistic scenarios such information is not directly available andthe robot must use its sensors which carry only partial and noisyinformation about the scenario state6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016231969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimationx robotrsquos pose m map zobservations ucontrols
Graphical model
hellip
hellip
1 2 3 hellip
1 2 3 t0
1 2 3 t
t
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
3 Basic Problems in Mobile Robotics
31 Mapping
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectory
bull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actions
bull Observationsbull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Mapsbull For environments with locally distinguishable featuresfeature-based (or landmark-based) maps have been extensively used
bull The map is just a set of objects each one with a specific coordinate
(a) Example of a mobile robot mapping a set of stone rocks(b) The image depicts the path and the estimated landmark positions (marked by circles)
Figure extracted from 7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_452369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
2469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Method 8 9 that represents the environment by a discrete grid offixed-size cells
bull Very useful for robots equipped with range-based sensorsbecause the range values of each sensor combined with the absoluteposition of the robot can be used directly to update the cells
bull Each cell has an occupancy value to indicate if it is an obstacle orpart of free space
bull the value 0 indicates that the cell has not been ldquohitrdquo yet thereforeit is likely free space
bull if the cellrsquos value is above a certain threshold (due to several rangingstrikes) the cell is deemed to be an obstacle
8A Elfes ldquoSonar-based real-world mapping and navigationrdquo Em IEEE Journal on Robotics and Automation 33 (1987)
pp 249ndash2659A Elfes ldquoUsing occupancy grids for mobile robot perception and navigationrdquo Em Computer 226 (1989) pp 46ndash57
2669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
2969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
3269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics2 Intelligent Robots
Ethics
ldquoEthics can be defined as a set of rules principles or ways of thin-king that guide or call to itself the authority to guide the actionsof a particular grouprdquo
Peter Singer 2
2P Singer Ethics 19941269
2 Intelligent Robots
21 Ethical dilemmas
Introduction to Mobile Robotics2 Intelligent Robots
The Trolley Problembull The trolley problem is a thought experiment in ethics first introduced by
Philippa Foot in 1967 (Video3 )
A runaway trolley is headed straight to five people tied up on the tracks and unable tomove You are standing next to a lever If you pull this lever the trolley will switch to adifferent set of tracks However you notice that there is one person tied up on the sidetrack You have two options
bull Do nothing and the trolley kills the five people on the main trackbull Pull the lever diverting the trolley onto the side track where it will kill one person
Which is the most ethical choice
3B R 4 The Trolley Problem httpswwwyoutubecomwatchv=bOpf6KcWYyw Accessed 2018-02-25 20141369
Introduction to Mobile Robotics2 Intelligent Robots
Peoplersquos responses to trolley problems
bull The trolley problem has been the subject of many surveys in whichapproximately 90 of respondents have chosen to kill the one and save the five
bull If the situation is modified where the one sacrificed for the five was a relative orromantic partner respondents are much less likely to be willing to sacrifice theirlife
bull Greene and colleagues (2001) demonstrated using functional magneticresonance imaging that personaldilemmas (like pushing a man off afootbridge) preferentially engage brain regions associated with emotion whereasimpersonaldilemmas (like diverting the trolley by flipping a switch)preferentially engaged regions associated with controlled reasoning
bull Problems analogous to the trolley problem arise in the design of autonomouscars in situations where the carrsquos software is forced during a potential crashscenario to choose between multiple courses of action
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Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practiceHow Tesla Solves A Self-Driving Crash Dilemma4
bull A class-action lawsuit was filed in December 2016about Teslarsquos decision to not use its AutomaticEmergency Braking (AEB) system when ahuman driver is pressing on the accelerator pedal
bull From the lawsuitldquoWhen a frontal collision is considered unavoidableAutomatic Emergency Braking is designed toautomatically apply the brakes to reduce the severityof the impact But Tesla has programmed the systemto deactivate when it receives instructions from theaccelerator pedal to drive full speed into a fixedobjectrdquo
4P Lin Herersquos How Tesla Solves A Self-Driving Crash Dilemma
httpswwwforbescomsitespatricklin20170405heres-how-tesla-solves-a-self-driving-crash-
dilemma72962be16813 Accessed 2018-02-25 20171569
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
ldquoTesla confirmed that when it stated that Automatic EmergencyBraking will operates only when driving between 5 mph (8 kmh)and 85 mph (140 kmh) but that the vehicle will not automaticallyapply the brakes or will stop applying the brakes ldquoin situationswhere you are taking action to avoid a potential collisionrdquo
bull For examplebull You turn the steering wheel sharplybull You press the accelerator pedalbull You press and release the brake pedalbull A vehicle motorcycle bicycle or pedestrian is no longer detectedaheadrdquo
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Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
3 Basic Problems in MobileRobotics
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimation in Mobile Robotics
bull An autonomous mobile robot should be able to move in anenvironment to fulfill its tasks which demands that the robotknows its location along with the location of nearby obstacles
bull In realistic scenarios such information is not directly available andthe robot must use its sensors which carry only partial and noisyinformation about the scenario state6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016231969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimationx robotrsquos pose m map zobservations ucontrols
Graphical model
hellip
hellip
1 2 3 hellip
1 2 3 t0
1 2 3 t
t
2069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
3 Basic Problems in Mobile Robotics
31 Mapping
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectory
bull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actions
bull Observationsbull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Mapsbull For environments with locally distinguishable featuresfeature-based (or landmark-based) maps have been extensively used
bull The map is just a set of objects each one with a specific coordinate
(a) Example of a mobile robot mapping a set of stone rocks(b) The image depicts the path and the estimated landmark positions (marked by circles)
Figure extracted from 7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_452369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
2469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Method 8 9 that represents the environment by a discrete grid offixed-size cells
bull Very useful for robots equipped with range-based sensorsbecause the range values of each sensor combined with the absoluteposition of the robot can be used directly to update the cells
bull Each cell has an occupancy value to indicate if it is an obstacle orpart of free space
bull the value 0 indicates that the cell has not been ldquohitrdquo yet thereforeit is likely free space
bull if the cellrsquos value is above a certain threshold (due to several rangingstrikes) the cell is deemed to be an obstacle
8A Elfes ldquoSonar-based real-world mapping and navigationrdquo Em IEEE Journal on Robotics and Automation 33 (1987)
pp 249ndash2659A Elfes ldquoUsing occupancy grids for mobile robot perception and navigationrdquo Em Computer 226 (1989) pp 46ndash57
2669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
2969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
3269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
2 Intelligent Robots
21 Ethical dilemmas
Introduction to Mobile Robotics2 Intelligent Robots
The Trolley Problembull The trolley problem is a thought experiment in ethics first introduced by
Philippa Foot in 1967 (Video3 )
A runaway trolley is headed straight to five people tied up on the tracks and unable tomove You are standing next to a lever If you pull this lever the trolley will switch to adifferent set of tracks However you notice that there is one person tied up on the sidetrack You have two options
bull Do nothing and the trolley kills the five people on the main trackbull Pull the lever diverting the trolley onto the side track where it will kill one person
Which is the most ethical choice
3B R 4 The Trolley Problem httpswwwyoutubecomwatchv=bOpf6KcWYyw Accessed 2018-02-25 20141369
Introduction to Mobile Robotics2 Intelligent Robots
Peoplersquos responses to trolley problems
bull The trolley problem has been the subject of many surveys in whichapproximately 90 of respondents have chosen to kill the one and save the five
bull If the situation is modified where the one sacrificed for the five was a relative orromantic partner respondents are much less likely to be willing to sacrifice theirlife
bull Greene and colleagues (2001) demonstrated using functional magneticresonance imaging that personaldilemmas (like pushing a man off afootbridge) preferentially engage brain regions associated with emotion whereasimpersonaldilemmas (like diverting the trolley by flipping a switch)preferentially engaged regions associated with controlled reasoning
bull Problems analogous to the trolley problem arise in the design of autonomouscars in situations where the carrsquos software is forced during a potential crashscenario to choose between multiple courses of action
1469
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practiceHow Tesla Solves A Self-Driving Crash Dilemma4
bull A class-action lawsuit was filed in December 2016about Teslarsquos decision to not use its AutomaticEmergency Braking (AEB) system when ahuman driver is pressing on the accelerator pedal
bull From the lawsuitldquoWhen a frontal collision is considered unavoidableAutomatic Emergency Braking is designed toautomatically apply the brakes to reduce the severityof the impact But Tesla has programmed the systemto deactivate when it receives instructions from theaccelerator pedal to drive full speed into a fixedobjectrdquo
4P Lin Herersquos How Tesla Solves A Self-Driving Crash Dilemma
httpswwwforbescomsitespatricklin20170405heres-how-tesla-solves-a-self-driving-crash-
dilemma72962be16813 Accessed 2018-02-25 20171569
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
ldquoTesla confirmed that when it stated that Automatic EmergencyBraking will operates only when driving between 5 mph (8 kmh)and 85 mph (140 kmh) but that the vehicle will not automaticallyapply the brakes or will stop applying the brakes ldquoin situationswhere you are taking action to avoid a potential collisionrdquo
bull For examplebull You turn the steering wheel sharplybull You press the accelerator pedalbull You press and release the brake pedalbull A vehicle motorcycle bicycle or pedestrian is no longer detectedaheadrdquo
1669
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
3 Basic Problems in MobileRobotics
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimation in Mobile Robotics
bull An autonomous mobile robot should be able to move in anenvironment to fulfill its tasks which demands that the robotknows its location along with the location of nearby obstacles
bull In realistic scenarios such information is not directly available andthe robot must use its sensors which carry only partial and noisyinformation about the scenario state6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016231969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimationx robotrsquos pose m map zobservations ucontrols
Graphical model
hellip
hellip
1 2 3 hellip
1 2 3 t0
1 2 3 t
t
2069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
3 Basic Problems in Mobile Robotics
31 Mapping
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectory
bull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actions
bull Observationsbull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Mapsbull For environments with locally distinguishable featuresfeature-based (or landmark-based) maps have been extensively used
bull The map is just a set of objects each one with a specific coordinate
(a) Example of a mobile robot mapping a set of stone rocks(b) The image depicts the path and the estimated landmark positions (marked by circles)
Figure extracted from 7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_452369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
2469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Method 8 9 that represents the environment by a discrete grid offixed-size cells
bull Very useful for robots equipped with range-based sensorsbecause the range values of each sensor combined with the absoluteposition of the robot can be used directly to update the cells
bull Each cell has an occupancy value to indicate if it is an obstacle orpart of free space
bull the value 0 indicates that the cell has not been ldquohitrdquo yet thereforeit is likely free space
bull if the cellrsquos value is above a certain threshold (due to several rangingstrikes) the cell is deemed to be an obstacle
8A Elfes ldquoSonar-based real-world mapping and navigationrdquo Em IEEE Journal on Robotics and Automation 33 (1987)
pp 249ndash2659A Elfes ldquoUsing occupancy grids for mobile robot perception and navigationrdquo Em Computer 226 (1989) pp 46ndash57
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
2969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
3269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics2 Intelligent Robots
The Trolley Problembull The trolley problem is a thought experiment in ethics first introduced by
Philippa Foot in 1967 (Video3 )
A runaway trolley is headed straight to five people tied up on the tracks and unable tomove You are standing next to a lever If you pull this lever the trolley will switch to adifferent set of tracks However you notice that there is one person tied up on the sidetrack You have two options
bull Do nothing and the trolley kills the five people on the main trackbull Pull the lever diverting the trolley onto the side track where it will kill one person
Which is the most ethical choice
3B R 4 The Trolley Problem httpswwwyoutubecomwatchv=bOpf6KcWYyw Accessed 2018-02-25 20141369
Introduction to Mobile Robotics2 Intelligent Robots
Peoplersquos responses to trolley problems
bull The trolley problem has been the subject of many surveys in whichapproximately 90 of respondents have chosen to kill the one and save the five
bull If the situation is modified where the one sacrificed for the five was a relative orromantic partner respondents are much less likely to be willing to sacrifice theirlife
bull Greene and colleagues (2001) demonstrated using functional magneticresonance imaging that personaldilemmas (like pushing a man off afootbridge) preferentially engage brain regions associated with emotion whereasimpersonaldilemmas (like diverting the trolley by flipping a switch)preferentially engaged regions associated with controlled reasoning
bull Problems analogous to the trolley problem arise in the design of autonomouscars in situations where the carrsquos software is forced during a potential crashscenario to choose between multiple courses of action
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Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practiceHow Tesla Solves A Self-Driving Crash Dilemma4
bull A class-action lawsuit was filed in December 2016about Teslarsquos decision to not use its AutomaticEmergency Braking (AEB) system when ahuman driver is pressing on the accelerator pedal
bull From the lawsuitldquoWhen a frontal collision is considered unavoidableAutomatic Emergency Braking is designed toautomatically apply the brakes to reduce the severityof the impact But Tesla has programmed the systemto deactivate when it receives instructions from theaccelerator pedal to drive full speed into a fixedobjectrdquo
4P Lin Herersquos How Tesla Solves A Self-Driving Crash Dilemma
httpswwwforbescomsitespatricklin20170405heres-how-tesla-solves-a-self-driving-crash-
dilemma72962be16813 Accessed 2018-02-25 20171569
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
ldquoTesla confirmed that when it stated that Automatic EmergencyBraking will operates only when driving between 5 mph (8 kmh)and 85 mph (140 kmh) but that the vehicle will not automaticallyapply the brakes or will stop applying the brakes ldquoin situationswhere you are taking action to avoid a potential collisionrdquo
bull For examplebull You turn the steering wheel sharplybull You press the accelerator pedalbull You press and release the brake pedalbull A vehicle motorcycle bicycle or pedestrian is no longer detectedaheadrdquo
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Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
3 Basic Problems in MobileRobotics
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimation in Mobile Robotics
bull An autonomous mobile robot should be able to move in anenvironment to fulfill its tasks which demands that the robotknows its location along with the location of nearby obstacles
bull In realistic scenarios such information is not directly available andthe robot must use its sensors which carry only partial and noisyinformation about the scenario state6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016231969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimationx robotrsquos pose m map zobservations ucontrols
Graphical model
hellip
hellip
1 2 3 hellip
1 2 3 t0
1 2 3 t
t
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
3 Basic Problems in Mobile Robotics
31 Mapping
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectory
bull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actions
bull Observationsbull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Mapsbull For environments with locally distinguishable featuresfeature-based (or landmark-based) maps have been extensively used
bull The map is just a set of objects each one with a specific coordinate
(a) Example of a mobile robot mapping a set of stone rocks(b) The image depicts the path and the estimated landmark positions (marked by circles)
Figure extracted from 7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_452369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
2469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Method 8 9 that represents the environment by a discrete grid offixed-size cells
bull Very useful for robots equipped with range-based sensorsbecause the range values of each sensor combined with the absoluteposition of the robot can be used directly to update the cells
bull Each cell has an occupancy value to indicate if it is an obstacle orpart of free space
bull the value 0 indicates that the cell has not been ldquohitrdquo yet thereforeit is likely free space
bull if the cellrsquos value is above a certain threshold (due to several rangingstrikes) the cell is deemed to be an obstacle
8A Elfes ldquoSonar-based real-world mapping and navigationrdquo Em IEEE Journal on Robotics and Automation 33 (1987)
pp 249ndash2659A Elfes ldquoUsing occupancy grids for mobile robot perception and navigationrdquo Em Computer 226 (1989) pp 46ndash57
2669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
2969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
3269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics2 Intelligent Robots
Peoplersquos responses to trolley problems
bull The trolley problem has been the subject of many surveys in whichapproximately 90 of respondents have chosen to kill the one and save the five
bull If the situation is modified where the one sacrificed for the five was a relative orromantic partner respondents are much less likely to be willing to sacrifice theirlife
bull Greene and colleagues (2001) demonstrated using functional magneticresonance imaging that personaldilemmas (like pushing a man off afootbridge) preferentially engage brain regions associated with emotion whereasimpersonaldilemmas (like diverting the trolley by flipping a switch)preferentially engaged regions associated with controlled reasoning
bull Problems analogous to the trolley problem arise in the design of autonomouscars in situations where the carrsquos software is forced during a potential crashscenario to choose between multiple courses of action
1469
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practiceHow Tesla Solves A Self-Driving Crash Dilemma4
bull A class-action lawsuit was filed in December 2016about Teslarsquos decision to not use its AutomaticEmergency Braking (AEB) system when ahuman driver is pressing on the accelerator pedal
bull From the lawsuitldquoWhen a frontal collision is considered unavoidableAutomatic Emergency Braking is designed toautomatically apply the brakes to reduce the severityof the impact But Tesla has programmed the systemto deactivate when it receives instructions from theaccelerator pedal to drive full speed into a fixedobjectrdquo
4P Lin Herersquos How Tesla Solves A Self-Driving Crash Dilemma
httpswwwforbescomsitespatricklin20170405heres-how-tesla-solves-a-self-driving-crash-
dilemma72962be16813 Accessed 2018-02-25 20171569
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
ldquoTesla confirmed that when it stated that Automatic EmergencyBraking will operates only when driving between 5 mph (8 kmh)and 85 mph (140 kmh) but that the vehicle will not automaticallyapply the brakes or will stop applying the brakes ldquoin situationswhere you are taking action to avoid a potential collisionrdquo
bull For examplebull You turn the steering wheel sharplybull You press the accelerator pedalbull You press and release the brake pedalbull A vehicle motorcycle bicycle or pedestrian is no longer detectedaheadrdquo
1669
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
3 Basic Problems in MobileRobotics
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimation in Mobile Robotics
bull An autonomous mobile robot should be able to move in anenvironment to fulfill its tasks which demands that the robotknows its location along with the location of nearby obstacles
bull In realistic scenarios such information is not directly available andthe robot must use its sensors which carry only partial and noisyinformation about the scenario state6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016231969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimationx robotrsquos pose m map zobservations ucontrols
Graphical model
hellip
hellip
1 2 3 hellip
1 2 3 t0
1 2 3 t
t
2069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
3 Basic Problems in Mobile Robotics
31 Mapping
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectory
bull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actions
bull Observationsbull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Mapsbull For environments with locally distinguishable featuresfeature-based (or landmark-based) maps have been extensively used
bull The map is just a set of objects each one with a specific coordinate
(a) Example of a mobile robot mapping a set of stone rocks(b) The image depicts the path and the estimated landmark positions (marked by circles)
Figure extracted from 7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_452369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
2469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Method 8 9 that represents the environment by a discrete grid offixed-size cells
bull Very useful for robots equipped with range-based sensorsbecause the range values of each sensor combined with the absoluteposition of the robot can be used directly to update the cells
bull Each cell has an occupancy value to indicate if it is an obstacle orpart of free space
bull the value 0 indicates that the cell has not been ldquohitrdquo yet thereforeit is likely free space
bull if the cellrsquos value is above a certain threshold (due to several rangingstrikes) the cell is deemed to be an obstacle
8A Elfes ldquoSonar-based real-world mapping and navigationrdquo Em IEEE Journal on Robotics and Automation 33 (1987)
pp 249ndash2659A Elfes ldquoUsing occupancy grids for mobile robot perception and navigationrdquo Em Computer 226 (1989) pp 46ndash57
2669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
2969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
3269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practiceHow Tesla Solves A Self-Driving Crash Dilemma4
bull A class-action lawsuit was filed in December 2016about Teslarsquos decision to not use its AutomaticEmergency Braking (AEB) system when ahuman driver is pressing on the accelerator pedal
bull From the lawsuitldquoWhen a frontal collision is considered unavoidableAutomatic Emergency Braking is designed toautomatically apply the brakes to reduce the severityof the impact But Tesla has programmed the systemto deactivate when it receives instructions from theaccelerator pedal to drive full speed into a fixedobjectrdquo
4P Lin Herersquos How Tesla Solves A Self-Driving Crash Dilemma
httpswwwforbescomsitespatricklin20170405heres-how-tesla-solves-a-self-driving-crash-
dilemma72962be16813 Accessed 2018-02-25 20171569
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
ldquoTesla confirmed that when it stated that Automatic EmergencyBraking will operates only when driving between 5 mph (8 kmh)and 85 mph (140 kmh) but that the vehicle will not automaticallyapply the brakes or will stop applying the brakes ldquoin situationswhere you are taking action to avoid a potential collisionrdquo
bull For examplebull You turn the steering wheel sharplybull You press the accelerator pedalbull You press and release the brake pedalbull A vehicle motorcycle bicycle or pedestrian is no longer detectedaheadrdquo
1669
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
3 Basic Problems in MobileRobotics
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimation in Mobile Robotics
bull An autonomous mobile robot should be able to move in anenvironment to fulfill its tasks which demands that the robotknows its location along with the location of nearby obstacles
bull In realistic scenarios such information is not directly available andthe robot must use its sensors which carry only partial and noisyinformation about the scenario state6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016231969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimationx robotrsquos pose m map zobservations ucontrols
Graphical model
hellip
hellip
1 2 3 hellip
1 2 3 t0
1 2 3 t
t
2069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
3 Basic Problems in Mobile Robotics
31 Mapping
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectory
bull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actions
bull Observationsbull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Mapsbull For environments with locally distinguishable featuresfeature-based (or landmark-based) maps have been extensively used
bull The map is just a set of objects each one with a specific coordinate
(a) Example of a mobile robot mapping a set of stone rocks(b) The image depicts the path and the estimated landmark positions (marked by circles)
Figure extracted from 7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_452369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
2469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Method 8 9 that represents the environment by a discrete grid offixed-size cells
bull Very useful for robots equipped with range-based sensorsbecause the range values of each sensor combined with the absoluteposition of the robot can be used directly to update the cells
bull Each cell has an occupancy value to indicate if it is an obstacle orpart of free space
bull the value 0 indicates that the cell has not been ldquohitrdquo yet thereforeit is likely free space
bull if the cellrsquos value is above a certain threshold (due to several rangingstrikes) the cell is deemed to be an obstacle
8A Elfes ldquoSonar-based real-world mapping and navigationrdquo Em IEEE Journal on Robotics and Automation 33 (1987)
pp 249ndash2659A Elfes ldquoUsing occupancy grids for mobile robot perception and navigationrdquo Em Computer 226 (1989) pp 46ndash57
2669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
2969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
3269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
ldquoTesla confirmed that when it stated that Automatic EmergencyBraking will operates only when driving between 5 mph (8 kmh)and 85 mph (140 kmh) but that the vehicle will not automaticallyapply the brakes or will stop applying the brakes ldquoin situationswhere you are taking action to avoid a potential collisionrdquo
bull For examplebull You turn the steering wheel sharplybull You press the accelerator pedalbull You press and release the brake pedalbull A vehicle motorcycle bicycle or pedestrian is no longer detectedaheadrdquo
1669
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
3 Basic Problems in MobileRobotics
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimation in Mobile Robotics
bull An autonomous mobile robot should be able to move in anenvironment to fulfill its tasks which demands that the robotknows its location along with the location of nearby obstacles
bull In realistic scenarios such information is not directly available andthe robot must use its sensors which carry only partial and noisyinformation about the scenario state6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016231969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimationx robotrsquos pose m map zobservations ucontrols
Graphical model
hellip
hellip
1 2 3 hellip
1 2 3 t0
1 2 3 t
t
2069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
3 Basic Problems in Mobile Robotics
31 Mapping
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectory
bull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actions
bull Observationsbull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Mapsbull For environments with locally distinguishable featuresfeature-based (or landmark-based) maps have been extensively used
bull The map is just a set of objects each one with a specific coordinate
(a) Example of a mobile robot mapping a set of stone rocks(b) The image depicts the path and the estimated landmark positions (marked by circles)
Figure extracted from 7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_452369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
2469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Method 8 9 that represents the environment by a discrete grid offixed-size cells
bull Very useful for robots equipped with range-based sensorsbecause the range values of each sensor combined with the absoluteposition of the robot can be used directly to update the cells
bull Each cell has an occupancy value to indicate if it is an obstacle orpart of free space
bull the value 0 indicates that the cell has not been ldquohitrdquo yet thereforeit is likely free space
bull if the cellrsquos value is above a certain threshold (due to several rangingstrikes) the cell is deemed to be an obstacle
8A Elfes ldquoSonar-based real-world mapping and navigationrdquo Em IEEE Journal on Robotics and Automation 33 (1987)
pp 249ndash2659A Elfes ldquoUsing occupancy grids for mobile robot perception and navigationrdquo Em Computer 226 (1989) pp 46ndash57
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
2969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
3 Basic Problems in MobileRobotics
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimation in Mobile Robotics
bull An autonomous mobile robot should be able to move in anenvironment to fulfill its tasks which demands that the robotknows its location along with the location of nearby obstacles
bull In realistic scenarios such information is not directly available andthe robot must use its sensors which carry only partial and noisyinformation about the scenario state6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016231969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimationx robotrsquos pose m map zobservations ucontrols
Graphical model
hellip
hellip
1 2 3 hellip
1 2 3 t0
1 2 3 t
t
2069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
3 Basic Problems in Mobile Robotics
31 Mapping
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectory
bull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actions
bull Observationsbull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Mapsbull For environments with locally distinguishable featuresfeature-based (or landmark-based) maps have been extensively used
bull The map is just a set of objects each one with a specific coordinate
(a) Example of a mobile robot mapping a set of stone rocks(b) The image depicts the path and the estimated landmark positions (marked by circles)
Figure extracted from 7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_452369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
2469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Method 8 9 that represents the environment by a discrete grid offixed-size cells
bull Very useful for robots equipped with range-based sensorsbecause the range values of each sensor combined with the absoluteposition of the robot can be used directly to update the cells
bull Each cell has an occupancy value to indicate if it is an obstacle orpart of free space
bull the value 0 indicates that the cell has not been ldquohitrdquo yet thereforeit is likely free space
bull if the cellrsquos value is above a certain threshold (due to several rangingstrikes) the cell is deemed to be an obstacle
8A Elfes ldquoSonar-based real-world mapping and navigationrdquo Em IEEE Journal on Robotics and Automation 33 (1987)
pp 249ndash2659A Elfes ldquoUsing occupancy grids for mobile robot perception and navigationrdquo Em Computer 226 (1989) pp 46ndash57
2669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
2969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
3269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
3 Basic Problems in MobileRobotics
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimation in Mobile Robotics
bull An autonomous mobile robot should be able to move in anenvironment to fulfill its tasks which demands that the robotknows its location along with the location of nearby obstacles
bull In realistic scenarios such information is not directly available andthe robot must use its sensors which carry only partial and noisyinformation about the scenario state6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016231969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimationx robotrsquos pose m map zobservations ucontrols
Graphical model
hellip
hellip
1 2 3 hellip
1 2 3 t0
1 2 3 t
t
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
3 Basic Problems in Mobile Robotics
31 Mapping
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectory
bull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actions
bull Observationsbull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Mapsbull For environments with locally distinguishable featuresfeature-based (or landmark-based) maps have been extensively used
bull The map is just a set of objects each one with a specific coordinate
(a) Example of a mobile robot mapping a set of stone rocks(b) The image depicts the path and the estimated landmark positions (marked by circles)
Figure extracted from 7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_452369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
2469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Method 8 9 that represents the environment by a discrete grid offixed-size cells
bull Very useful for robots equipped with range-based sensorsbecause the range values of each sensor combined with the absoluteposition of the robot can be used directly to update the cells
bull Each cell has an occupancy value to indicate if it is an obstacle orpart of free space
bull the value 0 indicates that the cell has not been ldquohitrdquo yet thereforeit is likely free space
bull if the cellrsquos value is above a certain threshold (due to several rangingstrikes) the cell is deemed to be an obstacle
8A Elfes ldquoSonar-based real-world mapping and navigationrdquo Em IEEE Journal on Robotics and Automation 33 (1987)
pp 249ndash2659A Elfes ldquoUsing occupancy grids for mobile robot perception and navigationrdquo Em Computer 226 (1989) pp 46ndash57
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
2969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practicebull In 20165 an executive of Mercedez-Benz said that they autonomous cars will
prioritize saving the people they carryldquoIf you know you can save at least one person at least save that one Savethe one in the car If all you know for sure is that one death can beprevented then thatrsquos your first priorityrdquo
bull The company later insisted hersquod been misquoted since it would be illegal ldquotomake a decision in favor of one person and against anotherrdquo
ldquoWe believe this ethical question wonrsquot be as relevant as people believetoday There are situations that todayrsquos driver canrsquot handle that wecanrsquot prevent today and automated vehicles canrsquot prevent either rdquo
bull In 2017 september Sebastian Thrun who founded Googlersquos self-driving carinitiative told Bloomberg that the cars will be designed to avoid accidents butthat
ldquoIf it happens where there is a situation where a car couldnrsquot escape itrsquollgo for the smaller thingrdquo
5T Spangler Self-driving cars programmed to decide who dies in a crash https
wwwusatodaycomstorymoneycars20171123self-driving-cars-programmed-decide-who-dies-crash891493001
Accessed 2018-02-265 20171769
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
3 Basic Problems in MobileRobotics
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimation in Mobile Robotics
bull An autonomous mobile robot should be able to move in anenvironment to fulfill its tasks which demands that the robotknows its location along with the location of nearby obstacles
bull In realistic scenarios such information is not directly available andthe robot must use its sensors which carry only partial and noisyinformation about the scenario state6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016231969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimationx robotrsquos pose m map zobservations ucontrols
Graphical model
hellip
hellip
1 2 3 hellip
1 2 3 t0
1 2 3 t
t
2069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
3 Basic Problems in Mobile Robotics
31 Mapping
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectory
bull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actions
bull Observationsbull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Mapsbull For environments with locally distinguishable featuresfeature-based (or landmark-based) maps have been extensively used
bull The map is just a set of objects each one with a specific coordinate
(a) Example of a mobile robot mapping a set of stone rocks(b) The image depicts the path and the estimated landmark positions (marked by circles)
Figure extracted from 7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_452369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
2469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Method 8 9 that represents the environment by a discrete grid offixed-size cells
bull Very useful for robots equipped with range-based sensorsbecause the range values of each sensor combined with the absoluteposition of the robot can be used directly to update the cells
bull Each cell has an occupancy value to indicate if it is an obstacle orpart of free space
bull the value 0 indicates that the cell has not been ldquohitrdquo yet thereforeit is likely free space
bull if the cellrsquos value is above a certain threshold (due to several rangingstrikes) the cell is deemed to be an obstacle
8A Elfes ldquoSonar-based real-world mapping and navigationrdquo Em IEEE Journal on Robotics and Automation 33 (1987)
pp 249ndash2659A Elfes ldquoUsing occupancy grids for mobile robot perception and navigationrdquo Em Computer 226 (1989) pp 46ndash57
2669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
2969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
3269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
3 Basic Problems in MobileRobotics
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimation in Mobile Robotics
bull An autonomous mobile robot should be able to move in anenvironment to fulfill its tasks which demands that the robotknows its location along with the location of nearby obstacles
bull In realistic scenarios such information is not directly available andthe robot must use its sensors which carry only partial and noisyinformation about the scenario state6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016231969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimationx robotrsquos pose m map zobservations ucontrols
Graphical model
hellip
hellip
1 2 3 hellip
1 2 3 t0
1 2 3 t
t
2069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
3 Basic Problems in Mobile Robotics
31 Mapping
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectory
bull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actions
bull Observationsbull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Mapsbull For environments with locally distinguishable featuresfeature-based (or landmark-based) maps have been extensively used
bull The map is just a set of objects each one with a specific coordinate
(a) Example of a mobile robot mapping a set of stone rocks(b) The image depicts the path and the estimated landmark positions (marked by circles)
Figure extracted from 7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_452369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
2469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Method 8 9 that represents the environment by a discrete grid offixed-size cells
bull Very useful for robots equipped with range-based sensorsbecause the range values of each sensor combined with the absoluteposition of the robot can be used directly to update the cells
bull Each cell has an occupancy value to indicate if it is an obstacle orpart of free space
bull the value 0 indicates that the cell has not been ldquohitrdquo yet thereforeit is likely free space
bull if the cellrsquos value is above a certain threshold (due to several rangingstrikes) the cell is deemed to be an obstacle
8A Elfes ldquoSonar-based real-world mapping and navigationrdquo Em IEEE Journal on Robotics and Automation 33 (1987)
pp 249ndash2659A Elfes ldquoUsing occupancy grids for mobile robot perception and navigationrdquo Em Computer 226 (1989) pp 46ndash57
2669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
2969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
3269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics2 Intelligent Robots
Real dilemmas in practice
bull Summing up the official statement from Daimler AG (owners ofMercedes-Benz) says
bull The main goal is to focus on completely avoiding dilemma situationsby for example implementing a risk-avoiding operating strategy inthe vehicles
bull It must follow the principle of providing the highest possible level ofsafety for all road users
For this we must learn how to best solve the problems of mobilerobotics (the goal of this class)
1869
3 Basic Problems in MobileRobotics
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimation in Mobile Robotics
bull An autonomous mobile robot should be able to move in anenvironment to fulfill its tasks which demands that the robotknows its location along with the location of nearby obstacles
bull In realistic scenarios such information is not directly available andthe robot must use its sensors which carry only partial and noisyinformation about the scenario state6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016231969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimationx robotrsquos pose m map zobservations ucontrols
Graphical model
hellip
hellip
1 2 3 hellip
1 2 3 t0
1 2 3 t
t
2069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
3 Basic Problems in Mobile Robotics
31 Mapping
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectory
bull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actions
bull Observationsbull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Mapsbull For environments with locally distinguishable featuresfeature-based (or landmark-based) maps have been extensively used
bull The map is just a set of objects each one with a specific coordinate
(a) Example of a mobile robot mapping a set of stone rocks(b) The image depicts the path and the estimated landmark positions (marked by circles)
Figure extracted from 7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_452369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
2469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Method 8 9 that represents the environment by a discrete grid offixed-size cells
bull Very useful for robots equipped with range-based sensorsbecause the range values of each sensor combined with the absoluteposition of the robot can be used directly to update the cells
bull Each cell has an occupancy value to indicate if it is an obstacle orpart of free space
bull the value 0 indicates that the cell has not been ldquohitrdquo yet thereforeit is likely free space
bull if the cellrsquos value is above a certain threshold (due to several rangingstrikes) the cell is deemed to be an obstacle
8A Elfes ldquoSonar-based real-world mapping and navigationrdquo Em IEEE Journal on Robotics and Automation 33 (1987)
pp 249ndash2659A Elfes ldquoUsing occupancy grids for mobile robot perception and navigationrdquo Em Computer 226 (1989) pp 46ndash57
2669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
2969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
3269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
3 Basic Problems in MobileRobotics
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimation in Mobile Robotics
bull An autonomous mobile robot should be able to move in anenvironment to fulfill its tasks which demands that the robotknows its location along with the location of nearby obstacles
bull In realistic scenarios such information is not directly available andthe robot must use its sensors which carry only partial and noisyinformation about the scenario state6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016231969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimationx robotrsquos pose m map zobservations ucontrols
Graphical model
hellip
hellip
1 2 3 hellip
1 2 3 t0
1 2 3 t
t
2069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
3 Basic Problems in Mobile Robotics
31 Mapping
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectory
bull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actions
bull Observationsbull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Mapsbull For environments with locally distinguishable featuresfeature-based (or landmark-based) maps have been extensively used
bull The map is just a set of objects each one with a specific coordinate
(a) Example of a mobile robot mapping a set of stone rocks(b) The image depicts the path and the estimated landmark positions (marked by circles)
Figure extracted from 7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_452369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
2469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Method 8 9 that represents the environment by a discrete grid offixed-size cells
bull Very useful for robots equipped with range-based sensorsbecause the range values of each sensor combined with the absoluteposition of the robot can be used directly to update the cells
bull Each cell has an occupancy value to indicate if it is an obstacle orpart of free space
bull the value 0 indicates that the cell has not been ldquohitrdquo yet thereforeit is likely free space
bull if the cellrsquos value is above a certain threshold (due to several rangingstrikes) the cell is deemed to be an obstacle
8A Elfes ldquoSonar-based real-world mapping and navigationrdquo Em IEEE Journal on Robotics and Automation 33 (1987)
pp 249ndash2659A Elfes ldquoUsing occupancy grids for mobile robot perception and navigationrdquo Em Computer 226 (1989) pp 46ndash57
2669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
2969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimation in Mobile Robotics
bull An autonomous mobile robot should be able to move in anenvironment to fulfill its tasks which demands that the robotknows its location along with the location of nearby obstacles
bull In realistic scenarios such information is not directly available andthe robot must use its sensors which carry only partial and noisyinformation about the scenario state6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016231969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimationx robotrsquos pose m map zobservations ucontrols
Graphical model
hellip
hellip
1 2 3 hellip
1 2 3 t0
1 2 3 t
t
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
3 Basic Problems in Mobile Robotics
31 Mapping
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectory
bull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actions
bull Observationsbull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Mapsbull For environments with locally distinguishable featuresfeature-based (or landmark-based) maps have been extensively used
bull The map is just a set of objects each one with a specific coordinate
(a) Example of a mobile robot mapping a set of stone rocks(b) The image depicts the path and the estimated landmark positions (marked by circles)
Figure extracted from 7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_452369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
2469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Method 8 9 that represents the environment by a discrete grid offixed-size cells
bull Very useful for robots equipped with range-based sensorsbecause the range values of each sensor combined with the absoluteposition of the robot can be used directly to update the cells
bull Each cell has an occupancy value to indicate if it is an obstacle orpart of free space
bull the value 0 indicates that the cell has not been ldquohitrdquo yet thereforeit is likely free space
bull if the cellrsquos value is above a certain threshold (due to several rangingstrikes) the cell is deemed to be an obstacle
8A Elfes ldquoSonar-based real-world mapping and navigationrdquo Em IEEE Journal on Robotics and Automation 33 (1987)
pp 249ndash2659A Elfes ldquoUsing occupancy grids for mobile robot perception and navigationrdquo Em Computer 226 (1989) pp 46ndash57
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
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3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
State Estimationx robotrsquos pose m map zobservations ucontrols
Graphical model
hellip
hellip
1 2 3 hellip
1 2 3 t0
1 2 3 t
t
2069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
3 Basic Problems in Mobile Robotics
31 Mapping
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectory
bull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actions
bull Observationsbull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Mapsbull For environments with locally distinguishable featuresfeature-based (or landmark-based) maps have been extensively used
bull The map is just a set of objects each one with a specific coordinate
(a) Example of a mobile robot mapping a set of stone rocks(b) The image depicts the path and the estimated landmark positions (marked by circles)
Figure extracted from 7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_452369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
2469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Method 8 9 that represents the environment by a discrete grid offixed-size cells
bull Very useful for robots equipped with range-based sensorsbecause the range values of each sensor combined with the absoluteposition of the robot can be used directly to update the cells
bull Each cell has an occupancy value to indicate if it is an obstacle orpart of free space
bull the value 0 indicates that the cell has not been ldquohitrdquo yet thereforeit is likely free space
bull if the cellrsquos value is above a certain threshold (due to several rangingstrikes) the cell is deemed to be an obstacle
8A Elfes ldquoSonar-based real-world mapping and navigationrdquo Em IEEE Journal on Robotics and Automation 33 (1987)
pp 249ndash2659A Elfes ldquoUsing occupancy grids for mobile robot perception and navigationrdquo Em Computer 226 (1989) pp 46ndash57
2669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
2969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
3269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
3 Basic Problems in Mobile Robotics
31 Mapping
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectory
bull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actions
bull Observationsbull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Mapsbull For environments with locally distinguishable featuresfeature-based (or landmark-based) maps have been extensively used
bull The map is just a set of objects each one with a specific coordinate
(a) Example of a mobile robot mapping a set of stone rocks(b) The image depicts the path and the estimated landmark positions (marked by circles)
Figure extracted from 7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_452369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
2469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Method 8 9 that represents the environment by a discrete grid offixed-size cells
bull Very useful for robots equipped with range-based sensorsbecause the range values of each sensor combined with the absoluteposition of the robot can be used directly to update the cells
bull Each cell has an occupancy value to indicate if it is an obstacle orpart of free space
bull the value 0 indicates that the cell has not been ldquohitrdquo yet thereforeit is likely free space
bull if the cellrsquos value is above a certain threshold (due to several rangingstrikes) the cell is deemed to be an obstacle
8A Elfes ldquoSonar-based real-world mapping and navigationrdquo Em IEEE Journal on Robotics and Automation 33 (1987)
pp 249ndash2659A Elfes ldquoUsing occupancy grids for mobile robot perception and navigationrdquo Em Computer 226 (1989) pp 46ndash57
2669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
2969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
3269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Markov assumptionbull The Markov assumption (or complete state assumption)postulates that past and future data are independent if one knowsthe current state xt
bull With the Markov assumption we compute the state belief at time t
based only on the belief at time tminus 1 while considering the lastaction and last observation made by the robot
bull In other words we assume that the previous state belief issufficient to represent the past history of the robot
bull Note that the Markov assumption in robotics is only anapproximation due to unmodeled dynamics and other inaccuraciesYet as shown in the literature is very robust in practice6
6S Thrun W Burgard e D Fox Probabilistic Robotics Intelligent robotics and autonomous agents 2005 url
httpwwwamazoncomexecobidosredirecttag=citeulike07-20amppath=ASIN02622016232169
3 Basic Problems in Mobile Robotics
31 Mapping
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectory
bull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actions
bull Observationsbull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Mapsbull For environments with locally distinguishable featuresfeature-based (or landmark-based) maps have been extensively used
bull The map is just a set of objects each one with a specific coordinate
(a) Example of a mobile robot mapping a set of stone rocks(b) The image depicts the path and the estimated landmark positions (marked by circles)
Figure extracted from 7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_452369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
2469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Method 8 9 that represents the environment by a discrete grid offixed-size cells
bull Very useful for robots equipped with range-based sensorsbecause the range values of each sensor combined with the absoluteposition of the robot can be used directly to update the cells
bull Each cell has an occupancy value to indicate if it is an obstacle orpart of free space
bull the value 0 indicates that the cell has not been ldquohitrdquo yet thereforeit is likely free space
bull if the cellrsquos value is above a certain threshold (due to several rangingstrikes) the cell is deemed to be an obstacle
8A Elfes ldquoSonar-based real-world mapping and navigationrdquo Em IEEE Journal on Robotics and Automation 33 (1987)
pp 249ndash2659A Elfes ldquoUsing occupancy grids for mobile robot perception and navigationrdquo Em Computer 226 (1989) pp 46ndash57
2669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
2969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
3269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
3 Basic Problems in Mobile Robotics
31 Mapping
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectory
bull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actions
bull Observationsbull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Mapsbull For environments with locally distinguishable featuresfeature-based (or landmark-based) maps have been extensively used
bull The map is just a set of objects each one with a specific coordinate
(a) Example of a mobile robot mapping a set of stone rocks(b) The image depicts the path and the estimated landmark positions (marked by circles)
Figure extracted from 7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_452369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
2469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Method 8 9 that represents the environment by a discrete grid offixed-size cells
bull Very useful for robots equipped with range-based sensorsbecause the range values of each sensor combined with the absoluteposition of the robot can be used directly to update the cells
bull Each cell has an occupancy value to indicate if it is an obstacle orpart of free space
bull the value 0 indicates that the cell has not been ldquohitrdquo yet thereforeit is likely free space
bull if the cellrsquos value is above a certain threshold (due to several rangingstrikes) the cell is deemed to be an obstacle
8A Elfes ldquoSonar-based real-world mapping and navigationrdquo Em IEEE Journal on Robotics and Automation 33 (1987)
pp 249ndash2659A Elfes ldquoUsing occupancy grids for mobile robot perception and navigationrdquo Em Computer 226 (1989) pp 46ndash57
2669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
2969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
3269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectory
bull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actions
bull Observationsbull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Mapsbull For environments with locally distinguishable featuresfeature-based (or landmark-based) maps have been extensively used
bull The map is just a set of objects each one with a specific coordinate
(a) Example of a mobile robot mapping a set of stone rocks(b) The image depicts the path and the estimated landmark positions (marked by circles)
Figure extracted from 7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_452369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
2469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Method 8 9 that represents the environment by a discrete grid offixed-size cells
bull Very useful for robots equipped with range-based sensorsbecause the range values of each sensor combined with the absoluteposition of the robot can be used directly to update the cells
bull Each cell has an occupancy value to indicate if it is an obstacle orpart of free space
bull the value 0 indicates that the cell has not been ldquohitrdquo yet thereforeit is likely free space
bull if the cellrsquos value is above a certain threshold (due to several rangingstrikes) the cell is deemed to be an obstacle
8A Elfes ldquoSonar-based real-world mapping and navigationrdquo Em IEEE Journal on Robotics and Automation 33 (1987)
pp 249ndash2659A Elfes ldquoUsing occupancy grids for mobile robot perception and navigationrdquo Em Computer 226 (1989) pp 46ndash57
2669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
2969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
3269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectory
bull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actions
bull Observationsbull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Mapsbull For environments with locally distinguishable featuresfeature-based (or landmark-based) maps have been extensively used
bull The map is just a set of objects each one with a specific coordinate
(a) Example of a mobile robot mapping a set of stone rocks(b) The image depicts the path and the estimated landmark positions (marked by circles)
Figure extracted from 7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_452369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
2469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Method 8 9 that represents the environment by a discrete grid offixed-size cells
bull Very useful for robots equipped with range-based sensorsbecause the range values of each sensor combined with the absoluteposition of the robot can be used directly to update the cells
bull Each cell has an occupancy value to indicate if it is an obstacle orpart of free space
bull the value 0 indicates that the cell has not been ldquohitrdquo yet thereforeit is likely free space
bull if the cellrsquos value is above a certain threshold (due to several rangingstrikes) the cell is deemed to be an obstacle
8A Elfes ldquoSonar-based real-world mapping and navigationrdquo Em IEEE Journal on Robotics and Automation 33 (1987)
pp 249ndash2659A Elfes ldquoUsing occupancy grids for mobile robot perception and navigationrdquo Em Computer 226 (1989) pp 46ndash57
2669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
2969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
3269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
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3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectory
bull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actions
bull Observationsbull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Mapsbull For environments with locally distinguishable featuresfeature-based (or landmark-based) maps have been extensively used
bull The map is just a set of objects each one with a specific coordinate
(a) Example of a mobile robot mapping a set of stone rocks(b) The image depicts the path and the estimated landmark positions (marked by circles)
Figure extracted from 7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_452369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
2469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Method 8 9 that represents the environment by a discrete grid offixed-size cells
bull Very useful for robots equipped with range-based sensorsbecause the range values of each sensor combined with the absoluteposition of the robot can be used directly to update the cells
bull Each cell has an occupancy value to indicate if it is an obstacle orpart of free space
bull the value 0 indicates that the cell has not been ldquohitrdquo yet thereforeit is likely free space
bull if the cellrsquos value is above a certain threshold (due to several rangingstrikes) the cell is deemed to be an obstacle
8A Elfes ldquoSonar-based real-world mapping and navigationrdquo Em IEEE Journal on Robotics and Automation 33 (1987)
pp 249ndash2659A Elfes ldquoUsing occupancy grids for mobile robot perception and navigationrdquo Em Computer 226 (1989) pp 46ndash57
2669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
2969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
3269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actions
bull Observationsbull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Mapsbull For environments with locally distinguishable featuresfeature-based (or landmark-based) maps have been extensively used
bull The map is just a set of objects each one with a specific coordinate
(a) Example of a mobile robot mapping a set of stone rocks(b) The image depicts the path and the estimated landmark positions (marked by circles)
Figure extracted from 7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_452369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
2469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Method 8 9 that represents the environment by a discrete grid offixed-size cells
bull Very useful for robots equipped with range-based sensorsbecause the range values of each sensor combined with the absoluteposition of the robot can be used directly to update the cells
bull Each cell has an occupancy value to indicate if it is an obstacle orpart of free space
bull the value 0 indicates that the cell has not been ldquohitrdquo yet thereforeit is likely free space
bull if the cellrsquos value is above a certain threshold (due to several rangingstrikes) the cell is deemed to be an obstacle
8A Elfes ldquoSonar-based real-world mapping and navigationrdquo Em IEEE Journal on Robotics and Automation 33 (1987)
pp 249ndash2659A Elfes ldquoUsing occupancy grids for mobile robot perception and navigationrdquo Em Computer 226 (1989) pp 46ndash57
2669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
2969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
3269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Mapsbull For environments with locally distinguishable featuresfeature-based (or landmark-based) maps have been extensively used
bull The map is just a set of objects each one with a specific coordinate
(a) Example of a mobile robot mapping a set of stone rocks(b) The image depicts the path and the estimated landmark positions (marked by circles)
Figure extracted from 7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_452369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
2469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Method 8 9 that represents the environment by a discrete grid offixed-size cells
bull Very useful for robots equipped with range-based sensorsbecause the range values of each sensor combined with the absoluteposition of the robot can be used directly to update the cells
bull Each cell has an occupancy value to indicate if it is an obstacle orpart of free space
bull the value 0 indicates that the cell has not been ldquohitrdquo yet thereforeit is likely free space
bull if the cellrsquos value is above a certain threshold (due to several rangingstrikes) the cell is deemed to be an obstacle
8A Elfes ldquoSonar-based real-world mapping and navigationrdquo Em IEEE Journal on Robotics and Automation 33 (1987)
pp 249ndash2659A Elfes ldquoUsing occupancy grids for mobile robot perception and navigationrdquo Em Computer 226 (1989) pp 46ndash57
2669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
2969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Mapsbull For environments with locally distinguishable featuresfeature-based (or landmark-based) maps have been extensively used
bull The map is just a set of objects each one with a specific coordinate
(a) Example of a mobile robot mapping a set of stone rocks(b) The image depicts the path and the estimated landmark positions (marked by circles)
Figure extracted from 7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_452369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
2469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Method 8 9 that represents the environment by a discrete grid offixed-size cells
bull Very useful for robots equipped with range-based sensorsbecause the range values of each sensor combined with the absoluteposition of the robot can be used directly to update the cells
bull Each cell has an occupancy value to indicate if it is an obstacle orpart of free space
bull the value 0 indicates that the cell has not been ldquohitrdquo yet thereforeit is likely free space
bull if the cellrsquos value is above a certain threshold (due to several rangingstrikes) the cell is deemed to be an obstacle
8A Elfes ldquoSonar-based real-world mapping and navigationrdquo Em IEEE Journal on Robotics and Automation 33 (1987)
pp 249ndash2659A Elfes ldquoUsing occupancy grids for mobile robot perception and navigationrdquo Em Computer 226 (1989) pp 46ndash57
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
2969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Mapping Problem
ldquoWhat does the world look likerdquo
bull Known pose of the robot
bull Modeling of the sensors observationsinto a map representation
bull Input
bull Robot trajectorybull Actionsbull Observations
bull Output
bull Map
mapping
(Makarenko 2002)
2269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Mapsbull For environments with locally distinguishable featuresfeature-based (or landmark-based) maps have been extensively used
bull The map is just a set of objects each one with a specific coordinate
(a) Example of a mobile robot mapping a set of stone rocks(b) The image depicts the path and the estimated landmark positions (marked by circles)
Figure extracted from 7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_452369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
2469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Method 8 9 that represents the environment by a discrete grid offixed-size cells
bull Very useful for robots equipped with range-based sensorsbecause the range values of each sensor combined with the absoluteposition of the robot can be used directly to update the cells
bull Each cell has an occupancy value to indicate if it is an obstacle orpart of free space
bull the value 0 indicates that the cell has not been ldquohitrdquo yet thereforeit is likely free space
bull if the cellrsquos value is above a certain threshold (due to several rangingstrikes) the cell is deemed to be an obstacle
8A Elfes ldquoSonar-based real-world mapping and navigationrdquo Em IEEE Journal on Robotics and Automation 33 (1987)
pp 249ndash2659A Elfes ldquoUsing occupancy grids for mobile robot perception and navigationrdquo Em Computer 226 (1989) pp 46ndash57
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
2969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Mapsbull For environments with locally distinguishable featuresfeature-based (or landmark-based) maps have been extensively used
bull The map is just a set of objects each one with a specific coordinate
(a) Example of a mobile robot mapping a set of stone rocks(b) The image depicts the path and the estimated landmark positions (marked by circles)
Figure extracted from 7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_452369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
2469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Method 8 9 that represents the environment by a discrete grid offixed-size cells
bull Very useful for robots equipped with range-based sensorsbecause the range values of each sensor combined with the absoluteposition of the robot can be used directly to update the cells
bull Each cell has an occupancy value to indicate if it is an obstacle orpart of free space
bull the value 0 indicates that the cell has not been ldquohitrdquo yet thereforeit is likely free space
bull if the cellrsquos value is above a certain threshold (due to several rangingstrikes) the cell is deemed to be an obstacle
8A Elfes ldquoSonar-based real-world mapping and navigationrdquo Em IEEE Journal on Robotics and Automation 33 (1987)
pp 249ndash2659A Elfes ldquoUsing occupancy grids for mobile robot perception and navigationrdquo Em Computer 226 (1989) pp 46ndash57
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
2469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Method 8 9 that represents the environment by a discrete grid offixed-size cells
bull Very useful for robots equipped with range-based sensorsbecause the range values of each sensor combined with the absoluteposition of the robot can be used directly to update the cells
bull Each cell has an occupancy value to indicate if it is an obstacle orpart of free space
bull the value 0 indicates that the cell has not been ldquohitrdquo yet thereforeit is likely free space
bull if the cellrsquos value is above a certain threshold (due to several rangingstrikes) the cell is deemed to be an obstacle
8A Elfes ldquoSonar-based real-world mapping and navigationrdquo Em IEEE Journal on Robotics and Automation 33 (1987)
pp 249ndash2659A Elfes ldquoUsing occupancy grids for mobile robot perception and navigationrdquo Em Computer 226 (1989) pp 46ndash57
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Method 8 9 that represents the environment by a discrete grid offixed-size cells
bull Very useful for robots equipped with range-based sensorsbecause the range values of each sensor combined with the absoluteposition of the robot can be used directly to update the cells
bull Each cell has an occupancy value to indicate if it is an obstacle orpart of free space
bull the value 0 indicates that the cell has not been ldquohitrdquo yet thereforeit is likely free space
bull if the cellrsquos value is above a certain threshold (due to several rangingstrikes) the cell is deemed to be an obstacle
8A Elfes ldquoSonar-based real-world mapping and navigationrdquo Em IEEE Journal on Robotics and Automation 33 (1987)
pp 249ndash2659A Elfes ldquoUsing occupancy grids for mobile robot perception and navigationrdquo Em Computer 226 (1989) pp 46ndash57
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Method 8 9 that represents the environment by a discrete grid offixed-size cells
bull Very useful for robots equipped with range-based sensorsbecause the range values of each sensor combined with the absoluteposition of the robot can be used directly to update the cells
bull Each cell has an occupancy value to indicate if it is an obstacle orpart of free space
bull the value 0 indicates that the cell has not been ldquohitrdquo yet thereforeit is likely free space
bull if the cellrsquos value is above a certain threshold (due to several rangingstrikes) the cell is deemed to be an obstacle
8A Elfes ldquoSonar-based real-world mapping and navigationrdquo Em IEEE Journal on Robotics and Automation 33 (1987)
pp 249ndash2659A Elfes ldquoUsing occupancy grids for mobile robot perception and navigationrdquo Em Computer 226 (1989) pp 46ndash57
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Feature-based Maps
bull The most popular SLAM techniques in the literature can be directlyapplied over feature-based maps
bull Some advantages of feature-based maps are the low memory costsand the simplicity of the map representation
bull A major disadvantage is the requirement of mechanisms forextracting salient features in the environment
bull Also not every environment has enough salient features for a propermapping
bull Usually the only way to circumvent this problem is by addingartificial landmarks to the environment
2569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Method 8 9 that represents the environment by a discrete grid offixed-size cells
bull Very useful for robots equipped with range-based sensorsbecause the range values of each sensor combined with the absoluteposition of the robot can be used directly to update the cells
bull Each cell has an occupancy value to indicate if it is an obstacle orpart of free space
bull the value 0 indicates that the cell has not been ldquohitrdquo yet thereforeit is likely free space
bull if the cellrsquos value is above a certain threshold (due to several rangingstrikes) the cell is deemed to be an obstacle
8A Elfes ldquoSonar-based real-world mapping and navigationrdquo Em IEEE Journal on Robotics and Automation 33 (1987)
pp 249ndash2659A Elfes ldquoUsing occupancy grids for mobile robot perception and navigationrdquo Em Computer 226 (1989) pp 46ndash57
2669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
2969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
3269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
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Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Method 8 9 that represents the environment by a discrete grid offixed-size cells
bull Very useful for robots equipped with range-based sensorsbecause the range values of each sensor combined with the absoluteposition of the robot can be used directly to update the cells
bull Each cell has an occupancy value to indicate if it is an obstacle orpart of free space
bull the value 0 indicates that the cell has not been ldquohitrdquo yet thereforeit is likely free space
bull if the cellrsquos value is above a certain threshold (due to several rangingstrikes) the cell is deemed to be an obstacle
8A Elfes ldquoSonar-based real-world mapping and navigationrdquo Em IEEE Journal on Robotics and Automation 33 (1987)
pp 249ndash2659A Elfes ldquoUsing occupancy grids for mobile robot perception and navigationrdquo Em Computer 226 (1989) pp 46ndash57
2669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
2969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
3269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Gridbull Occupancy grids are extremely popular in mobile robotics due tothe simplicity of updatingrepresenting real environments
Fixed decomposition (right) of the space (left)Figure extracted from 10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20042769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
2969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
3269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
bull Occupancy grids are not able to represent symbolic entities such asdoors chairs etc
bull Lack of information compression large empty areas or largeobstacles are represented by a large amount of cells
bull They present some problems concerning the granularity scalabilityand extensibility of the map 11
11T Bailey e E Nebot ldquoLocalisation in large-scale environmentsrdquo Em Robotics and autonomous systems 374 (2001)
pp 261ndash2812869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
2969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
3269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Occupancy Grid
5
Example
Example of high-resolution occupancy grid built using laser information
2969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
3269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
11 14
11
14
132121
121
132
322 323
322
323
342
342
Approximate decomposition of an environment using a quadtreeFigure adapted from 12
12J-C Latombe Robot Motion Planning 19913069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
3269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Quadtrees
Another example of approximate decomposition using quadtreesFigure extracted from10
10R Siegwart e I R Nourbakhsh Introduction to Autonomous Mobile Robots 20043169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
3269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Grids vs Quadtrees
Occupancy grid17787 cells
Quadtree2290 cells
3269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
3D Mapping
bull Extensions of occupancy grids to dense 3D occupancy grids havebeen used to model natural environments
bull However in large scale scenarios 3D grids are too costly3369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
bull Elevation grid is a digital elevation map which stores the value of h(height) at discrete locations (xiyi)
bull They are simple data structures and can be generated from sensordata in a relatively straightforward manner
bull They have been used extensively for mobile robots operating innatural environments with no vertical surfaces or overhangs7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Elevation Grids
Example of elevation map built by accumulating 3D data from a range sensorFigure extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
1 a standard elevation map computed from this data setFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
2 an extended elevation map which correctly represents the underpass under the bridgeFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Problem of suspended obstacles
scan (point set) of a bridge
3 a multilevel surface map that correctly represents the height of the vertical objectsFigures extracted from7
7W Burgard M Hebert e M Bennewitz ldquoWorld Modelingrdquo Em Springer Handbook of Robotics Ed por B Siciliano e
O Khatib 2016 pp 1135ndash1152 url httpsdoiorg101007978-3-319-32552-1_453669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Cloudsbull Point Cloud is a collection of nD points (usually n = 3)
bull They preserve all the sensor data in its original distribution
bull There is no restriction on the geometry of the environment
bull They can be generated by different sensorsbull Laser scans (high quality)bull Stereo cameras (dependent on texture)bull Structured light
bull The drawbacks of mapping systems operating on point clouds isthat
bull neither free space nor unknown areas can be modeledbull sensor noise and dynamic objects cannot be dealt with directly
3769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Point Clouds
3869
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
3 Basic Problems in Mobile Robotics
32 Motion Planning
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Map
bull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting location
bull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal location
bull Cost functionbull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
motionplanning
(Makarenko 2002)
ldquoHow can I reach a given locationrdquo
bull Input
bull Mapbull Starting locationbull Goal locationbull Cost function
bull Output
bull Minimun cost path
3969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull The optimal path passes exactly at the border of the obstacles
Start
Goal
4069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Solution computing the path over free-space obtained afterdiscounting the configuration space associated to all obstacles
Start
Goal
4169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion planningbull Traditional approach computing a path described as a sequenceof cells of a grid map (ie cell decomposition of space)
Start
Goal
4269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Traditional planning approach
bull Planning over a discrete mapbull occupancy grid
4369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost
6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
453
6
bull Defining different actions
bull Actionsbull Move forwardbull Move turning leftbull Move turning right
bull Costs all = 1
what is the min cost6 units
4469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min cost
turning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
23243
25
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 units
always turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Planning over gridmap
1
2
143
154
56 7 8
9
1011121316
bull What happens if the cost tomove turning left is veryhigh
bull Actions - Costsbull Move forward - 1bull Move turning left - 20bull Move turning right - 1
What is the min costturning left - 23 unitsalways turning right - 16 units
4569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of Goal
Wavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Uninformed Search of GoalWavefront strategy
1
2
3
4 5
4669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search of Goal
A Algorithmbull Described by Peter Hart Nils Nilsson andBertram Raphael of Stanford ResearchInstitute in 1968
bull They were trying to improve the pathplanning done by Shakey the Robot
bull A is an informed searchbull expands in the direction of the goal
Bertram Raphael
PeterHart
NilsNilsson
4769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search Expansion
Example A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Informed Search ExpansionExample A
4869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
bull The basic idea behind the potential field approaches it to treat therobot as a point particle in the configuration space under theinfluence of an artificial potential field U
bull The field U is constructed so that the robot isattracted to the final configuration qgoalwhile being repelled from obstacles
bull If U is constructed appropriately there will be a single globalminimum of U at qgoal and no local minima
4969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Potential Fields
Configuration space 2Dcontaining two obstacles
Goal rarr generates attractivepotential field
Obstacles rarr generate repulsivepotential field
Resulting Potential field rarrsum of the two potential fields
Negated gradient of thepotential function
Equipotential contours of thepotential Generated path
following the negated gradient
Figures extracted from12 12J-C Latombe Robot Motion Planning 1991
5069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Motion Planning
bull Alternative approach
bull Sampling-based motion planning
bull The main idea is to avoid the explicit construction of theconfiguration space and instead conduct a search that probes thespace with a sampling scheme
5169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Initialization
Start
Goal
5269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Sampling n points (in the example n = 350)
5369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Connecting nearest points of each component of the graph until is fully
connected
5469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Probabilistic Roadmapsbull Compute min cost path over the graph
5569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Analysis of Probabilistic Roadmaps
bull Better roadmaps are obtained when connecting more than a single nearestneighbor
bull Large number of samples generate better roadmaps
n = 50 n = 150 n = 600
5669
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
3 Basic Problems in Mobile Robotics
33 Localization
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Map
bull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actions
bull Observationsbull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Localization ProblemldquoWhere am Irdquo
bull Determine where the robot is basedon the sequences of observations androbot motion
bull Kalman filters
bull Particle filters
bull Input
bull Mapbull Actionsbull Observations
bull Output
bull Robot trajectory
localization
(Makarenko 2002)
5769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Variations of the Localization Problem
bull Local localization problembull Also known as Position trackingbull It assumes that the initial robot pose is knownbull The pose uncertainty is often approximated by a unimodaldistribution (eg a Gaussian)
bull Global localization problembull The initial pose of the robot is unknownbull Unimodal probability distributions are usually inappropriatebull Global localization subsumes the position tracking problem
5869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot location
bull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Possible observations made by the robotDoor No door
bull Possible robot motion left or right
bull What is the initial belief about the robot locationbull Initially the robot can be anywherebull bel(x) uniform distribution
5969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull The first observation is
Door
bull Now we are able to adjust the belief about the robot location
6069
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Unless the observation is wrong (which is very unlikely) we knowthat the robot is in front of a door
bull Knowing the map configuration the robot must be around one ofthe 3 (indistinguishable) doors in the environment with same highprobability
bull With a small non-zero probability the robot might err and actuallynot be next to a door
6169
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Then the robot moves rightbull The belief distribution is shifted right according to the motionbull However it is also smoothed to account for the inherent uncertaintyin robot motion
6269
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull A new observation is made
Door
bull Once again we are able to adjust the belief about the robot location
6369
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
x
p(z|x)
bull Knowing the map and the previous belief about the robot locationand considering that the robot is in front of a door now the robot isquite confident as to where it is
bull After this last observation the localization algorithm places most ofthe probability mass on the location near the second door
6469
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Global Localization example
x
bel(x)
bull Lastly the robot moves right once againbull The belief distribution is shifted right according to the motion andsmoothed
bull At this point the robot knows where it is
6569
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Core of localization strategy
Sense Act(Observation) (Motion)
Initialbelief
Prediction
CorrectionDecreases uncertainty
Increases uncertainty
6669
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Particle Filterbull Approach for dealing with arbitrary distributionsbull Use multiple particles (samples) to represent thembull The more particles fall into a region the higher the probability ofthe region
samples
6769
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
initialization6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
observation6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
weight update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
resampling6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
motion update6869
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Example
measurement6869
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
3 Basic Problems in Mobile Robotics
34 Advanced Problems
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problems
bull SLAM simultaneous localization andmapping
bull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Introduction to Mobile Robotics3 Basic Problems in Mobile Robotics
Advanced Problems in Mobile Roboticsmap
ping
localizationmotion
planning
exploration
INTEGRATEDEXPLORATION
SLAM
active
localizat
ion
(Makarenko 2002)
Combinations of the basic problemsbull SLAM simultaneous localization and
mappingbull hardest problem in mobile roboticsbull chicken-or-egg problem
bull Explorationbull find best motion strategy to solve
mapping
bull Active Localizationbull find best motion strategy to solve
localization
bull Integrated Exploration(or Active SLAM)
bull find best motion strategy to solveSLAM
6969
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
Universidade Federal do Rio Grande do SulInstituto de Informaacutetica
Phi-Robotics Research Group
Introduction to Mobile Robotics
Renan Maffeirqmaffeiinfufrgsbr
2018
INSTITUTODE INFORMAacuteTICAUFRGS
