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CS 326A: Motion Planning. Jean-Claude Latombe CA: Aditya Mandayam. Motion planning is the ability for an agent to compute its own motions in order to achieve certain goals. All autonomous robots and digital actors should eventually have this ability. Piano Mover’s Problem. Sense. Plan. - PowerPoint PPT Presentation
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CS 326A: Motion Planning
Jean-Claude Latombe
CA: Aditya Mandayam
Motion planning is the ability for an agent to compute its own motions in order to achieve certain goals. All autonomous
robots and digital actors should eventually have this ability
Piano Mover’s Problem
Plan MoveSense
ARL Robot
Goal
Plan MoveSense
LearnMotion library
Goal of Motion Planning
• Compute motion strategies, e.g.:– geometric paths – time-parameterized trajectories– sequence of sensor-based motion commands
• To achieve high-level goals, e.g.:– go to A without colliding with obstacles– assemble product P– build map of environment E– find object O
Fundamental QuestionAre two given points connected by a path?
Valid region
Forbidden region
Fundamental QuestionAre two given points connected by a path?
Valid region
Forbidden region
E.g.:▪Collision with obstacle▪Lack of visibility of an object▪Lack of stability
Basic Problem Statement:
Compute a collision-free path for a rigid or articulated object among static obstacles
Inputs:•Geometry of moving object and obstacles•Kinematics of moving object (degrees of freedom)•Initial and goal configurations (placements)
Output:Continuous sequence of collision-free robot configurations connecting the initial and goal configurations
Is It Easy?
Tool: Configuration Space
Problems:• Geometric complexity• Space dimensionality
Continuous space
Discretization
Search
C-space
Sampling-based Criticality-based
Extensions of Basic Problem
• Moving obstacles• Multiple robots• Movable objects• Assembly planning• Goal is to acquire
information by sensing– Model building– Object finding/tracking– Inspection
• Nonholonomic constraints
• Dynamic constraints• Stability constraints
• Optimal planning• Uncertainty in model,
control and sensing• Exploiting task
mechanics (sensorless motions, under-actualted systems)
• Physical models and deformable objects
• Integration of planning and control
• Integration with higher-level planning
Some Applications
Humanoid Robots
HRP-2, AIST, Japan
Lunar Vehicle (ATHLETE, NASA/JPL)
Climbing Robot
http://www.youtube.com/watch?v=biSx-aKN690
Dexterous Manipulation
Modular Reconfigurable Robots
Manipulation of Deformable Objects
Topologicallydefined goal
Digital Characters
A Bug’s Life (Pixar/Disney) Toy Story (Pixar/Disney)
Tomb Raider 3 (Eidos Interactive) Final Fantasy VIII (SquareOne)The Legend of Zelda (Nintendo)
Antz (Dreamworks)
Digital Characters
Animation of Crowds
Design for Manufacturing and Servicing
Design for Manufacturing and Servicing
Design for Manufacturing and Servicing
Assembly Sequence Planning
Cable Harness/ Pipe design
Map Building
Where to move next?
Navigation Through Virtual Environments
Virtual Angiography / Bronchoscopy /
Colonoscopy
Radiosurgical Planning
CyberKnife (Accuray)
Building Code Verification
9-inch turning radius24-inch turning radius
Egress Simulation
Primary escape route
Secondary escape route
Potential congesting areas
Transportation of A380 Fuselage through Small
Villages
Kineo
Study of Motion of Bio-Molecules
Inhibitor binding to HIV protease
Goals of CS326A
Present a coherent framework for motion planning problems
Emphasis of “practical” algorithms with some guarantees of performance over “theoretical” or purely “heuristic” algorithms
General Framework
Continuous representation(configuration space and related spaces + constraints)
Discretization(probabilistic sampling, criticality-based decomposition)
Graph searching(blind, best-first, A*)
Practical Algorithms (1/2)
A complete motion planner always returns a solution plan when one exists and indicates that no such plan exists otherwise.
Most motion planning problems are hard, meaning that complete planners take exponential time in # of degrees of freedom, objects, etc.
Practical Algorithms (2/2)
Theoretical algorithms strive for completeness and minimal worst-case complexity. Difficult to implement and not robust.
Heuristic algorithms strive for efficiency in commonly encountered situations. Usually no performance guarantee.
Weaker completeness Simplifying assumptions Exponential algorithms that work in practice
Prerequisites for CS326A
Ability and willingness to complete a significant programming project with graphic interface.
Basic knowledge and taste for geometry and algorithms.
Interest in devoting reasonable time each week in reading papers.
CS326A is not a course in …
Differential Geometry and TopologyKinematics and DynamicsGeometric Modeling
… but it makes use of knowledge from all these areas
Work to Do
A. Attend every classB. Prepare/give two presentations with
ppt slides (20 minutes each)C. For each class read the two papers
listed as “required reading” in advance
D. Complete the programming projectE. Complete two homework
assignments
Programming Project• Navigate in virtual environment
• Simulate legged robot
• Inspection of structures
• Search and escape
Website and Schedule
ai.stanford.edu/~latombe/cs326/2009/index.htm