SLAM: Simultaneous Localization and Mapping

Autonomous Mobile Robots

Autonomous Systems LabZürich

SLAM: Simultaneous Localization and Mapping

"Position"

Global Map

Perception Motion Control

Cognition

Real WorldEnvironment

Localization

PathEnvironment Model

Local Map

© R. Siegwart, D. Scaramuzza and M. Chli, ETH Zurich - ASL

Today‟s lecture

Section 5.8 + some extras…

One of the fundamental problems in robotics: SLAM

EKF SLAM

Particle filter SLAM

GraphSLAM

Look into MonoSLAM

Lec.122

12 – Simultaneous Localization And Mapping


Simultaneous Localization and Mapping

The SLAM problem:

How can a body navigate in a previously unknown environment while constantly building and updating a map of its workspace using

on board sensors only?

When is SLAM necessary?

When a robot must be truly autonomous (no human input)

When there is no prior knowledge about the environment

When we cannot place beacons (also in GPS-denied environments)

When the robot needs to know where it is


Lec.123


Simultaneous Localization and Mapping

SLAM is significantly more difficult than all robotics problems discussed so far:

More difficult than pure localization: the map is unknown and has to be estimated along the way.

More difficult than mapping with known poses: the poses are unknown and have to be estimated along the way.

SLAM: one of the greatest challenges in probabilistic robotics


Lec.124

12 3.5

By hand: hard & costly(e.g. large environment) Automatic Map Building:

More challenging, but:

Automatic

The robot learns its environment

Can adapt to dynamic changes


Features for SLAM

Can we track the motion of a camera/robot while it is moving?

Pick natural scene features to serve as landmarks (in most modern SLAM systems)

Range sensing (laser/sonar): line segments, 3D planes, corners

Vision: point features, lines, textured surfaces.

Key: features must be distinctive & recognizable from different viewpoints

Lec.125


Courtesy of Andrew J. Davison


Map Building

1. Map Maintenance: Keeping track of

changes in the environment

e.g. disappearing

cupboard

- e.g. measure of belief of each

environment feature

- Generally assume static environment

2. Representing and Propagating Uncertainty

position of robot -> position of wall

position of wall -> position of robot

probability densities for feature positions

Map can become inconsistent due to

erroneous measurements / motion drift

?


Lec.126


How to do SLAMLec.12

7


Use internal representations for

the positions of landmarks (: map)

the camera parameters

Assumption: Robot‟s uncertainty at starting position is zero

A

B C

Start: robot has zero uncertainty


Lec.128


On every frame:

Predict how the robot has moved

Measure

Update the internal representations

Start: camera has zero uncertaintyFirst measurement of feature A

How to do SLAM

A

B C


Lec.129


On every frame:


Measure


The robot observes a feature which is mapped with an uncertainty related to the exteroceptive sensor error model(aka measurement model)

How to do SLAM

A

B C


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Robot moves forwards: uncertainty grows

On every frame:


Measure


As the robot moves, its pose uncertainty increases (obeying the robot‟s motion model)

How to do SLAM

A

B C


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Robot makes first measurements of B & C

On every frame:


Measure


Robot observes two new features.

How to do SLAM

A

B C


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On every frame:


Measure


Their position uncertainty results from the combination of the measurement error with the robotpose uncertainty.

map becomes correlated with the robot position estimate.

How to do SLAM

Robot makes first measurements of B & C

A

B C


Lec.1213


Robot moves again: uncertainty grows more

On every frame:


Measure


How to do SLAM

Robot moves again and its uncertainty increases (motionmodel)

A

B C


Robot moves again: uncertainty grows more

A

B C

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Robot re-measures A: “loop closure”

On every frame:


Measure


Robot re-observes an old feature Loop closure detection

How to do SLAM


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Robot re-measures A: “loop closure”uncertainty shrinks

On every frame:


Measure


Robot updates its position: the resulting position estimate becomes correlated with the feature location estimates.

Robot‟s uncertainty shrinks and so does the uncertainty in the rest of the map

How to do SLAM

A

B C


SLAM: Probabilistic Formulation

Robot pose at time t : xt Robot path up to this time: {x0, x1,…, xt}

Robot motion between time t-1 and t : ut (control inputs / propriocept. sens.

readings) Sequence of robot relative motions: {u0, u1,…, ut}

The true map of the environment: {m0, m1,…, mN}

At each time t the robot makes measurements zi

Set of all measurements (observations): {z0, z1,…, zk}

The Full SLAM problem: estimate the posterior

p(x0:t ,m0:n | z0:k ,u0:t )

The Online SLAM problem: estimate the posterior

p(xt ,m0:n | z0:k ,u0:t )

Lec.1216



z13z0 z1 z2 z3 z4 z5 z6 z7 z8 z9z12

z15z14 z16z10 z11

SLAM: graphical representationLec.12

17


m0 m1 m2 m3 m4 m5 m6 m7 m8

x0 x1 x2 x3 . . .

u0 u1 u2 u3


Approaches SLAM

Full graph optimization (bundle adjustment)

Eliminate observations & control-input nodes and solve for the constraints between poses and landmarks.

Globally consistent solution, but infeasible for large-scale SLAM

If real-time is a requirement, we need to sparsify this graph

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m0 m1 m2 m3 m4 m5 m6 m7 m8

x0 x1 x2 x3


Approaches SLAM

Filtering

Eliminate all past poses: „summarize‟ all experience with respect to the last pose, using a state vector and the associated covariance matrix

We‟re going to look at filtering in more detail…

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m0 m1 m2 m3 m4 m5 m6 m7 m8

x3x0 x1 x2


Approaches SLAM

Key-frames

Retain the most „representative‟ poses (key-frames) and their dependency links optimize the resulting graph

Example: PTAM [Klein & Murray, ISMAR 2007]

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m0 m1 m2 m3 m4 m5 m6 m7 m8

x0 x1 x2 x3

http://www.robots.ox.ac.uk/~gk/publications/KleinMurray2007ISMAR.pdf


PTAM: Parallel Tracking and MappingLec.12

21


http://www.youtube.com/watch?v=Y9HMn6bd-v8

http://www.youtube.com/watch?v=Y9HMn6bd-v8


The Three SLAM paradigms

Some of the most important approaches to SLAM:

Extended Kalman Filter SLAM (EKF SLAM)

Particle Filter SLAM (FastSLAM)

GraphSLAM


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EKF SLAM: overview

Like the standard EKF for robot localization

EKF SLAM summarizes all past experience in an extended state vector yt

comprising of the robot pose xt and the position of all the features mi in the map, and an associated covariance matrix Pyt:

If we sense 2D line-landmarks, the size of yt is 3+2n

(and size of Pt : (3+2n)(3+2n) )

3 variables to represent the robot pose and

2n variables for the n line-landmarks with state components

Hence,

As the robot moves and makes measurements, yt and Pyt are updated using the standard EKF equations

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Lec.1223


The predicted robot pose at time-stamp t is computed using the estimated pose at time-stamp t-1 and the odometric control input

During this step, the position of the features remains unchanged.

EKF Prediction Equations:

EKF SLAM: Prediction

b

SSb

SSSSb

SSSS

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X

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lr

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Lec.1224

tx̂

1tx },{ rlt SSu

Based on the example of Section 5.2.4

: distance travelled by the left and right wheels resp.

: distance between the two robot wheels

rl SS ;

bOdometryfunction

Jacobians of f

Covariance at previous time-stamp

Covariance of noise associated to the motion


EKF SLAM: Comparison with EKF localization

EKF LOCALIZATION

The state is ONLY the robot

configuration:

The prediction function is:

),(ˆ1 ttt uxfx

b

SSb

SSSSb

SSSS

Y

X

Y

X

lr

lrt

lr

lrt

lr

t

t

t

t

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t

)2

sin(2

)2

cos(2

ˆ

ˆ

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1

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1

1

1

EKF SLAM

The state comprises of the robot

configuration and that of each feature :

The prediction function is:

T

tttt YXx ],,[

),(ˆ1 ttt uyfy

0

0

...

0

0

)2

sin(2

)2

cos(2

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nntttt rrYXy ],,...,,,,,[ 1100


Lec.1225

txtx

tyim


EKF SLAM: Measurement prediction & Update

The application of the measurement model is the same as in EKF localization. The predicted observation of each feature is:

After obtaining the set of actual observations z0:n-1 the EKF state gets

updated:

where

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Lec.1226

im

We need the predicted new pose to predict where each feature lies in measurement space

Jacobian of h Measurement noise

Kalman Gain Innovation Covariance


EKF SLAM: Correlations

At start, when the robot makes the first measurements, the covariance matrix is populated by assuming that these (initial) features are uncorrelated off-diagonal elements are zero.

When the robot starts moving & making new measurements, both the robot pose and features start becoming correlated.

Accordingly, the covariance matrix becomes dense.

11

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Lec.1227

T

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EKF SLAM: Correlations

Correlations arise as

the uncertainty in the robot pose is used to obtain the uncertainty of the observed features.

the feature measurements are used to update the robot pose.

Regularly covisible features become correlated and when their motion is coherent, their correlation is even stronger

Correlations very important for convergence: The more observations are made, the more the correlations between the features will grow, the better the solution to SLAM.


Lec.1228

Chli & Davison, ICRA 2009

Features moving coherently

Features moving incoherently


Feature Based SLAM (ETH - ASL)

3D laser on board

corner features extracted from lines and corners attached to structures


Lec.1229

[Weingarten & Siegwart, IROS 2006]


Feature Based SLAM (ETH - ASL)


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[Weingarten & Siegwart, IROS 2006]

3D laser on board

corner features extracted from lines and corners attached to structures


Drawbacks of EKF SLAM

The state vector in EKF SLAM is much larger than the state vector in EKF localization

Newly observed features are added to the state vector The covariance matrix grows quadratically with the no. features computationally expensive for large-scale SLAM.

Approach to attack this: sparsify the structure of the covariance matrix (via approximations)


Lec.1231

Chli & Davison, ICRA 2009

http://www.doc.ic.ac.uk/~mchli/videos/ICRA2009video2.avi


Particle Filter SLAM

Particle filters: mathematical models that represent probability distributions as a set of discrete particles which occupy the state space.

Particle = a point estimate of the state with an associated weight(all weights should add up to 1)

Steps in Particle Filtering:

Predict:Apply motion prediction to each particle

Make measurements

Update: for each particle:

• Compare the particle‟s predictions of measurements with the actual measurements

• Assign weights such that particles with good predictions have higher weight

Normalize weights of particles to add up to 1

Resample: generate a new set of M particles which all have equal weights 1/M reflecting the probability density of the last particle set.


Lec.1232

},{ iti wypi


Particle Filter SLAM

FastSLAM approach [Montemerlo et al., 2002]

• Solve state posterior using a Rao-Blackwellized Particle Filter

• Each landmark estimate is represented by a 2x2 EKF.

• Each particle is “independent” (due the factorization) from the others and maintains the estimate of M landmark positions.


Lec.1233


FastSLAM example


Lec.1234

[Montemerlo et al., 2002]

http://www.mobilerobots.ethz.ch/videos/Thrun_Mapping.AVI


GraphSLAM [Thrun and Montemerlo, IJRR 2006]


Lec.1235

GraphSLAM basic idea: SLAM can be interpreted as a sparse graph of nodes and constraints between nodes.

nodes: robot locations and map-feature locations

edges: constraints between

consecutive robot poses (given by the odometry input u) and

robot poses and the features observed from these poses.


Key property: constraints are not to be thought as rigid constraints but as soft constraints constraints acting like springs

Solve full SLAM by relaxing these constraints get the best estimate of the robot path and

the environment map by computing the state of minimal energy of this network


Lec.1236 GraphSLAM [Thrun and Montemerlo, IJRR 2006]


In GraphSLAM style techniques

the update-time is constant and

the required memory is linear with the no. features

… while in EKF SLAM, both the update-time and the storage of the covariance matrix scales quadratically with the no. features

However, the final graph optimization can be computationally very costly if the robot path is long.


Lec.1237 GraphSLAM vs. EKF SLAM

Autonomous Mobile Robots

Autonomous Systems LabZürich

Example of EKF SLAM

MonoSLAM: Real-Time Single Camera SLAM

[Davison, Reid, Molton and Stasse. PAMI 2007]

http://www.doc.ic.ac.uk/~ajd/Publications/davison_etal_pami2007.pdf


Single Camera SLAMLec.12

39


• Images = information-rich snapshots of a scene

• Compactness + affordability of cameras

• HW advances

Visionfor SLAM

SLAM using a single, handheld camera:

• Hard but … (e.g. cannot recover depth from 1 image)

• very applicable, compact, affordable, …

Image Courtesy of G. Klein


From SFM to SLAM


Lec.1240

P1

P2

P3

Structure from Motion (SFM):

Take some images of the object/scene to reconstruct

Features (points, lines, …) are extracted from all frames and matched among them

Process all images simultaneously

Optimisation to recover both: camera motion and 3D structureup to a scale factor (similar to GraphSLAM)

Not real-time

[Agrawal et al., ICCV 2009]

http://www.youtube.com/watch?v=HrgHFDPJHXo&feature=player_embedded


MonoSLAMLec.12

41


camera view internal SLAM map

Can we track the motion of a hand-held camera while it is moving?i.e. online

SLAM using a single camera, grabbing frames at 30Hz

Ellipses (in camera view) and Bubbles (in map view) represent uncertainty


http://www.doc.ic.ac.uk/~ajd/Movies/kitchen.mp4.avi

http://www.doc.ic.ac.uk/~ajd/Movies/kitchen.mp4.avi


Representation of the world

The belief about the state of the world x is approximated with a single,

multivariate Gaussian distribution:

Lec.1242


Mean(state vector)

Covariance matrix

Camera state

: Position [3 dim.]

: Orientation using quaternions [4 dim.]

: Linear velocity [3 dim.]

: Angular velocity [3 dim.]

Landmark’s statee.g. 3D position for

point-features


Motion & Probabilistic Prediction

How has the camera moved from frame t-1 to frame t?

The camera is hand-held no odometry or control input data

Use a motion model

But how can we model the unknown intentions of a human carrier?

Davison et al. use a constant velocity motion model:

Lec.1243


“on average we expect undetermined accelerations occur with a Gaussian profile”

),(ˆ1 ttt uxfx

T

utu

T

ytyt FQFFPFP 1ˆ


Constant Velocity Model

The constant velocity motion model, imposes a certain smoothness on the camera

motion expected.

In each time step, the unknown linear and angular accelerations (characterized by

zero-mean Gausian distr.) cause an impulse of velocity:


Lec.1244


Motion & Probabilistic Prediction

Based on the predicted new camera pose predict which known features will be visible and where they will lie in the image

Use measurement model h to identify the predicted location of each

feature and an associated search region (defined in the corresponding diagonal block of )

Essentially: project the 3D ellipsoids in image space

Lec.1245


),ˆ(ˆitii yxhz

RHPH T

tIN ˆ


Measurement & EKF update

Search for the known feature-patches inside their corresponding search regions to get the set of all observations

Update the state using the EKF equations

where:

Lec.1246


T

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)),ˆ((ˆ1:01:01:0

1)(ˆ

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Application: HPR-2 Humanoid at JRL, AIST, Japan


Lec.1247

• Small circular loop within a large room

• No re-observation of „old‟ features until closing of large loop


http://www.doc.ic.ac.uk/~ajd/Movies/hrploopclose.mpg

http://www.doc.ic.ac.uk/~ajd/Movies/CircleHRP2.mpg


Real-time Single Camera SLAM systemsLec.12

48


MonoSLAM is computationally expensive with increasing no. features

not ready yet to leave the lab & perform everyday tasks

MonoSLAM[Davison et al. 2007]

PTAM[Klein, Murray 2008]

Graph-SLAM[Eade, Drummond 2007]


SLAM challengesLec.12

49


• Handle larger amounts of data more effectively

• Competing goals:

PRECISIONEFFICIENCY

• Fast motion

• Large scales

• Robustness

• Rich maps

• Low computation for embedded apps

Ishikawa Komuro Lab.

http://www.youtube.com/watch?v=UCqpFA-tyH0&feature=related


Essential components of a scalable SLAM systemLec.12

50


Map management &optimisation

1

2 3

Mapping & loop-closure

detection

Robust local motion estimation


Live Dense ReconstructionLec.12

51


During live camera tracking, perform dense per-pixel surface reconstruction

Relies heavily on GPU processing for dense image matching

[Newcombe, Davison CVPR 2010 ]

http://www.doc.ic.ac.uk/~ajd/Movies/olderReconstruction09.avi

Documents

SLAM: Simultaneous Localization and Mapping