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Motion Planning

Motion Planning. CS121 – Winter 2003. Basic Problem. Are two given points connected by a path?. From Robotics …. … to Graphic Animation …. … to Biology. … to Biology. How Do You Get There?. ?. Configuration Space. Approximate the free space by random sampling. Problems:

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Motion Planning

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  1. Motion Planning CS121 – Winter 2003

  2. Basic Problem Are two given points connected by a path?

  3. From Robotics …

  4. … to Graphic Animation …

  5. … to Biology

  6. … to Biology

  7. How Do You Get There? ?

  8. Configuration Space Approximate the free space by random sampling • Problems: • Geometric complexity • Number of dimensions of space • How to discretize the free space?

  9. q q q q q q 2 1 3 0 n 4 Parts DOF L 19 68 H 51 118 Digital Character Q(t)

  10. Configuration Space Approximate the free space by random sampling • Problems: • Geometric complexity • Number of dimensions of space • How to discretize the free space?

  11. Hierarchical Collision Checking

  12. Example in 3D

  13. Hierarchical Collision Checking

  14. Hierarchical Collision Checking

  15. Performance Evaluation • 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

  16. local path milestone mg mb Probabilistic Roadmap (PRM) free space

  17. Why It Works

  18. Easy Narrow Passage Issue Difficult

  19. Probabilistic Completeness Under the generally satisfied assumption that the free space is expansive, the probability that a PRM finds a path when one exists goes to 1 exponentially in the number of milestones (~ running time).

  20. Multi-Query Sampling Strategies

  21. Multi-Query Sampling Strategies • Multi-stage strategies • Obstacle-sensitive strategies • Narrow-passage strategies

  22. mg mb Single-Query Sampling Strategies

  23. mg mb Single-Query Sampling Strategies • Diffusion strategies • Adaptive-step strategies • Lazy collision checking

  24. Examples Nrobot = 3,000; Nobst = 50,000 Tav = 0.17 s Nrobot = 5,000; Nobst = 83,000 Tav = 4.42 s

  25. Design for Manufacturing/Servicing General Motors General Motors General Electric [Hsu, 2000]

  26. Modular Reconfigurable Robots Casal and Yim, 1999 Xerox, Parc

  27. Humanoid Robot [Kuffner and Inoue, 2000] (U. Tokyo) Stability constraints

  28. Space Robotics robot obstacles air thrusters gas tank air bearing [Kindel, 2000] Dynamic constraints

  29. mg mb Single-Query Sampling Strategies

  30. Total duration : 40 sec

  31. Autonomous Helicopter [Feron, 2000] (AA Dept., MIT)

  32. Other goals The goal may not be to attain a given position, but to achieve a certain condition, e.g.: - Irradiate a tumor - Build a map of an environment - Sweep an environment to find a target

  33. Radiosurgery: Irradiate a Tumor

  34. Mobile Robots: Map Building

  35. Next-Best View

  36. Example

  37. 0 : the target does not hide beyond the edge 1 : the target may hide beyond the edge Information State Example of an information state = (1,1,0)

  38. Critical Curve

  39. More Complex Example

  40. Example with Two Robots (Greedy algorithm)

  41. Surgical Planning

  42. Half-Dome, NW Face, Summer of 2010 … Tim Bretl

  43. Rock-Climbing Robot

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