This document discusses sampling algorithms for quickly sampling in high-dimensional configuration spaces. It introduces configuration space and roadmaps, describes two main ideas for improving sampling, and presents a utility-guided multi-query sampling algorithm evaluated in experiments.

1. T O C S S
B B  O B
Hannes Schulz
University of Freiburg, ACS
Feb 2008

2. O
1 I: C S  R
2 T M I  U G S
Idea 1: Use Config Space Structure
Idea 2: Increase Connectivity
3 S A
4 E: C  S S
5 C  C

3. O
1 I: C S  R
2 T M I  U G S
Idea 1: Use Config Space Structure
Idea 2: Increase Connectivity
3 S A
4 E: C  S S
5 C  C

4. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
C S
World Space Configuration Space
http://ford.ieor.berkeley.edu/cspace

5. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
C S
World Space Configuration Space
http://ford.ieor.berkeley.edu/cspace

6. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
C S
World Space Configuration Space
http://ford.ieor.berkeley.edu/cspace

7. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
C S
World Space Configuration Space
http://ford.ieor.berkeley.edu/cspace

8. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
C S
World Space Configuration Space
http://ford.ieor.berkeley.edu/cspace

9. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
C S
World Space Configuration Space
http://ford.ieor.berkeley.edu/cspace

10. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
C S
World Space Configuration Space
http://ford.ieor.berkeley.edu/cspace

11. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
C S
World Space Configuration Space
http://ford.ieor.berkeley.edu/cspace

12. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
C S
World Space Configuration Space
http://ford.ieor.berkeley.edu/cspace

13. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
R M
Config Space
w/ Obstacles

14. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
R M
Config Space
w/ Obstacles
and Samples

15. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
R M
Config Space Visibility Road Map
w/ Obstacles
and Samples

16. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
R M
Config Space Visibility Road Map
w/ Obstacles Planned Path
and Samples

17. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
R M
Config Space Visibility Road Map
w/ Obstacles Planned Path
and Samples
How to sample quickly in high-dimensional Config Space?

18. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
S A
S
G
Uniform

19. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
S A
S S
G G
Uniform Wavefront
single query

20. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
S A
S S
G G
Uniform Wavefront Model- Guided
single query multi-query

21. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
S A
S S
G G
Uniform Wavefront Model- Guided
single query multi-query

22. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
S A
S S Entropy-guided,
Model-guided,
Bridge-Sampling,
G G ...
Uniform Wavefront Guided
single query multi-query

23. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
S A
S S Entropy-guided,
Model-guided,
Bridge-Sampling,
G G ...
Uniform Wavefront Guided
single query multi-query
In this paper:
?
“utility-guided”
multi-query

24. O
1 I: C S  R
2 T M I  U G S
Idea 1: Use Config Space Structure
Idea 2: Increase Connectivity
3 S A
4 E: C  S S
5 C  C

25. O
1 I: C S  R
2 T M I  U G S
Idea 1: Use Config Space Structure
Idea 2: Increase Connectivity
3 S A
4 E: C  S S
5 C  C

26. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
U C S S F A L

27. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
U C S S F A L
Obstacle Sample
Free Space Sample

28. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
U C S S F A L

29. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
U C S S F A L
Function Approximator: Approximate Model of Config Space
Use Model to select next free sample
Using all known samples aids active learning

30. O
1 I: C S  R
2 T M I  U G S
Idea 1: Use Config Space Structure
Idea 2: Increase Connectivity
3 S A
4 E: C  S S
5 C  C

31. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
D  “U”   S
Component 1
Obstacle
Component 2
Entropy: Probability that random sample is in visibility region of
particular component

32. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
D  “U”   S
Component 1
Obstacle
Component 2
Red Sample: Entropy unchanged, Zero information gain

33. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
D  “U”   S
Component 1
Obstacle
Component 2
Entropy: Probability that random sample is in visibility region of
particular component

34. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
D  “U”   S
Obstacle
Just 1 Component left
Red Sample: Less Entropy, Large information gain, high Utility

35. O
1 I: C S  R
2 T M I  U G S
Idea 1: Use Config Space Structure
Idea 2: Increase Connectivity
3 S A
4 E: C  S S
5 C  C

36. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
E C U M  C
Component 1
Obstacle
Component 2
Application Idea 2: Try to increase connectivity

37. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
E C U M  C
Component 1
Obstacle
Component 2
Application Idea 2: Try to increase connectivity

38. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
E C U M  C
Component 1
Obstacle
Component 2
Center Point

39. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
E C U M  C
Component 1
Obstacle
Component 2

40. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
W  P S  M
Component 1
Obstacle
Component 2
Application Idea 1: Exploit model of config space

41. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
W  P S  M
Component 1
Obstacle
Component 2
Application Idea 1: Exploit model of config space

42. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
W  P S  M
Component 1
Obstacle
Component 2

43. O
1 I: C S  R
2 T M I  U G S
Idea 1: Use Config Space Structure
Idea 2: Increase Connectivity
3 S A
4 E: C  S S
5 C  C

44. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
R
3 or 4 Joints with 3 DOF Mobile base (2 DOF)
each 2 Joints with 1 / 2 DOF each
9 DOF / 12 DOF 4 DOF / 6 DOF
Compare only Sampling strategy until path found
Difficulty: Analyzing Overhead of Model, Utility Evaluation

45. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
R
Runtimes: 4-DOF mobile manipulator

46. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
R
Fraction of Config Space covered: 9-DOF arm

47. O
1 I: C S  R
2 T M I  U G S
Idea 1: Use Config Space Structure
Idea 2: Increase Connectivity
3 S A
4 E: C  S S
5 C  C

48. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
A P P  U-G S?
Goal Start
Initially, just two Samples at start and goal, respectively. What
happens?

49. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
A P P  U-G S?
Goal Start
Line between two clusters

50. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
A P P  U-G S?
Goal Start
Sample candidates around mitpoint

51. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
A P P  U-G S?
Goal Start
Model does not provide information, choose any.

52. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
A P P  U-G S?
Goal Start
Green: New model. Suppose same nodes chosen again. What
happens?

53. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
A P P  U-G S?
Goal Start
New points cluster around previous points

54. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
A P P  U-G S?
Goal Start
“Worst case” scenario

55. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
C
Burns & Brock introduced a sampling algorithm
for multi-query planning
uses active learning
maximizes utility
outperforms other algorithms
not thoroughly evaluated
may have strong dependency on parameters/environment

56. Intro Two Main Ideas Sampling Algorithm Experiments Comments and Conclusion
D
?