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

7. How Do You Get There? ?

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

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

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

11. Hierarchical Collision Checking

12. Example in 3D

13. 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. Probabilistic Roadmap (PRM) free space mbmbmbmb mgmgmgmg milestone local path

17. Why It Works

18. Narrow Passage Issue Easy 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-stage strategies Obstacle-sensitive strategies Narrow-passage strategies

22. Single-Query Sampling Strategies mbmbmbmb mgmgmgmg

23. mbmbmbmb mgmgmgmg Diffusion strategies Adaptive-step strategies Lazy collision checking

24. Examples N robot = 5,000; N obst = 83,000 T av = 4.42 s N robot = 3,000; N obst = 50,000 T av = 0.17 s

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

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

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

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

30. Single-Query Sampling Strategies mbmbmbmb mgmgmgmg

31. Total duration : 40 sec

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

33. 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

34. Radiosurgery: Irradiate a Tumor

35. Mobile Robots: Map Building

36. Next-Best View

37. Example

38. Scout Robot: Find an Evasive Target

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

40. Critical Curve

41. More Complex Example

42. Example with Two Robots (Greedy algorithm)

43. Surgical Planning

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

46. Rock-Climbing Robot