1. Motion Planning
CS121 – Winter 2003
Motion Planning

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

3. From Robotics …
Motion Planning

4. … to Graphic Animation …
Motion Planning

5. … to Biology
Motion Planning

6. … to Biology
Motion Planning

7. How Do You Get There? ?
Motion Planning

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

9. Digital Character q q Q(t) Parts DOF L 19 68 H 51 118 1 2 n 3 4n 4 q 2
Parts DOF L H
Joint variables are avars for primary motions.
A Motion clip is a curve parameterized by time in the joint space (C-space).
MPEG4-SNHC standard body description
each hand = 25 DOF
lower body = 21
upper body = 62
global hip position & orientation = 6
Q(t)
Motion Planning

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

11. Hierarchical Collision Checking
Motion Planning

12. Example in 3D
Motion Planning

13. Hierarchical Collision Checking
Motion Planning

14. Hierarchical Collision Checking
Motion Planning

15. Performance Evaluation
Collision checking takes between 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
Motion Planning

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

17. Why It Works
Motion Planning

18. Narrow Passage Issue
Easy
Difficult
Motion Planning

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).
Motion Planning

20. Multi-Query Sampling Strategies
Motion Planning

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

22. Single-Query Sampling Strategiesmb mg
Motion Planning

23. Single-Query Sampling Strategiesmb mg
Diffusion strategies
Adaptive-step strategies
Lazy collision checking
Motion Planning

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

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

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

27. Motion Planning

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

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

30. Single-Query Sampling Strategiesmb mg
Motion Planning

31. Total duration : 40 sec
Motion Planning

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

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
Motion Planning

34. Radiosurgery: Irradiate a Tumor
Motion Planning

35. Mobile Robots: Map Building
Motion Planning

36. Next-Best View
Motion Planning

37. Example
Motion Planning

38. 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
Example of an information state = (1,1,0)
Motion Planning

39. Critical Curve
Motion Planning

40. More Complex Example
Motion Planning

41. Example with Two Robots
(Greedy algorithm)
Motion Planning

42. Surgical Planning
Motion Planning

43. Half-Dome, NW Face, Summer of 2010 …
Motion Planning
Tim Bretl

44. Motion Planning

45. Rock-Climbing Robot
Motion Planning

46. Motion Planning

47. Motion Planning

48. Motion Planning