Polkadot JAM Slides - Token2049 - By Dr. Gavin Wood
Toward Optimal Configuration Space Sampling
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
?
