An Efficient Motion Planner Based on Random Sampling

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An Efficient Motion PlannerBased on Random
Sampling

• Jean-Claude Latombe
• Computer Science DepartmentStanford University

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Main Collaborators

• Lydia Kavraki (Rice U.)
• David Hsu (U. of North Carolina, Chapel Hill)
• Gildardo Sanchez (ITESM, Mexico)
• James Kuffner (U. of Tokyo)
• Rajeev Motwani (Stanford U.)

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Goal of Motion Planning

• Answer queries about the connectivity of a space

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Possible Constraints

• Collision-free
• Kino-dynamic

• Stability
• Visibility

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The Beginning
Shakey (Nilsson, 1969) Visibility graph
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Configuration Space
Represent the robot as a point in a parameter
space
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Why Sampling-Based Planning?

• Computing an explicit representation of the
  collision-free space is extremely time consuming
  and impractical
• There exist fast collision-checking algorithms to
  test whether any given configuration or short
  path is collision-free, or not (0.001 sec or less)

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Outline

• General Approach
• Specific Planner
• Experimental Results
• Other Applications

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Probabilistic Roadmap (PRM)
admissible space
Kavraki, Svetska, Latombe,Overmars, 95
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Relation to Art-Gallery Problems
Kavraki, Latombe, Motwani, Raghavan, 95
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Narrow Passage Issue
Difficult
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Probabilistic Completeness

• Under generally satisfied assumptions, if a
  solution path exists, the probability that a PRM
  planner fails to find one goes to 0 exponentially
  in the number of milestones.

Full completeness ? Too costly
Heuristic ? Too unreliable
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Key Techniques

• Collision checking / Distance computation
• Sampling strategies

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Key Techniques

• Collision checking / Distance computation
• Hierarchical approach
• Feature-based approach
• Sampling strategies

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Hierarchical Collision Checking
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Three-Dimensional Case
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Collision Checking
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Collision Checking
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Performance

• Collision checking takes between 0.0001 and .002
  seconds for 2 objects of 500,000 triangles each
  on a 1-GHz Pentium III
• Collision checking is faster when objects collide
  or are far apart, and gets slower when they get
  closer without colliding
• Overall collision checking time grows roughly as
  the log of the number of triangles

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Key Techniques

• Collision checking / Distance computation
• Sampling strategies
• Multi-stage strategies
• Obstacle-sensitive strategies
• Multiple vs. single query strategies
• Configuration vs. control sampling
• Single vs. bi-directional sampling
• Lazy collision checking
• Probabilistic biases (e.g., medial axis transform)

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Outline

• General Approach
• Specific Planner
• Experimental Results
• Other Applications

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SBL Planner

• Single-query
• Does not pre-compute a roadmap Hsu, Latombe,
  Motwani, 1997
• Bi-directional sampling
• Constructs a roadmap by growing two trees of
  milestones rooted at the input query
  configuration Hsu, 2000
• Lazy collision checking
• Postpone collision-checking operations until
  absolutely needed Bohlin and Kavraki, 2000

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SBL Planner
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SBL Planner
m
m is picked at random among the milestones with a
probabilistic distribution inverse to the local
density of sampling
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SBL Planner
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SBL Planner
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SBL Planner
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SBL Planner
X
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SBL Planner
The collision-checking work is memorized
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Why Postponing Collision Checking?

• The a priori probability that a short edge be
  collision-free is rather large

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Why Postponing Collision Checking?

• The a priori probability that a short edge be
  collision-free is rather large
• The test of an edge is most expensive when it is
  actually collision-free
• Most edges of a roadmap do not end up in a
  solution path

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Path Optimization
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Outline

• General Approach
• Specific Planner
• Experimental Results
• Other Applications

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Single-Robot Examples
nrob 3,000 and nobs 50,000
nrob 5,000 and nobs 21,000
nrob 5,000 nobs 83,000
nrob 3,000 nobs 50
nrob 3,000 and nobs 100
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Videos
nrobot 5,000 nobst 21,000 Tav 0.6 s
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Videos
nrobot 5,000 nobst 83,000 Tav 4.42 s
nrobot 3,000 nobst 50,000 Tav 0.17 s
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Videos
nrobot 3,000 nobst 100 Tav 6.99 s
nrobot 3,000 nobst 50,000 Tav 4.45 s
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Experimental Data on One Example
nrob 5,000 nobs 21,000
(1 GHz Pentium III processor)
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Average Performance
Averages over 100 runs
(1GHz Pentium III processor)
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Convergence of SBL
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Impact of Lazy Collision Checking
Average performance with lazy collision checking
Average performance without lazy collision
checking
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Multi-Robot Spot Welding
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Typical Problem
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Video
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Average Running Times
(1 GHz processor)
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Centralized vs. Decoupled Planning
Averages over 20 runs
 
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Outline

• General Approach
• Specific Planner
• Experimental Results
• Other Applications

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Design for Manufacturing/Servicing
General Motors
General Motors
General Electric
Hsu, 2000
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Radio-Surgical Planning
Cyberknife System (Accuray, Inc.)
CARABEAMER Planner
Tombropoulos, Adler, and Latombe, 1997

Visibility constraints
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Radio-Surgical Planning
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Radio-Surgical Planning
50 Isodose Surface
80 Isodose Surface
Conventional systems plan
CARABEAMERs plan
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Cyberknife Systems
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Modular Reconfigurable Robots
Casal and Yim, 1999
Xerox, Parc
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Humanoid Robot
Kuffner and Inoue, 2000 (U. Tokyo)
Stability constraints
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Space Robotics
robot
obstacles
air thrusters
gas tank
air bearing
Kindel, Hsu, Latombe, and Rock, 2000
Dynamic constraints
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Total duration 40 sec
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Autonomous Helicopter
Feron, 2000 (AA Dept., MIT)
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Interacting Nonholonomic Robots
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Map Building
Gonzalez, 2000
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Next-Best View Computation
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Map Building
Gonzalez, 2000
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Map Building
Gonzalez, 2000
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Graphic Animation of Digital Actors
The MotionFactory
Koga, Kondo, Kuffner, and Latombe, 1994
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Prediction of Molecular Motions
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Outline

• General Approach
• Specific Planner
• Experimental Results
• Other Applications
• Conclusion

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Conclusion

• Probabilistic Roadmaps provide an efficient and
  reliable computational approach to motion
  planning
• PRM planners are rather easy to implement
• They have been experimented on very different
  problems

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Remaining Issues

• Relatively large standard deviation of planning
  time
• No rigorous termination criterion when no
  solution is found
• New challenging applications

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Optimal Touring of Multiple Goals
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Surgical Planning with Soft Tissue
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Planning Nice-Looking Motions
A Bugs Life (Pixar/Disney)
Toy Story (Pixar/Disney)
Antz (Dreamworks)
Tomb Raider 3 (Eidos Interactive)
Final Fantasy VIII (SquareOne)
The Legend of Zelda (Nintendo)
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1,000s of Degrees of Freedom
Protein folding
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The End
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