1. Sampling Techniques for Probabilistic Roadmap Planners
Roland Geraerts and Mark Overmars
IAS-8
March 2004

2. Overview Probabilistic roadmaps Test scenes PRM choices Sampling
Variation of running times
Conclusions
Important choices
Collision checking
Node adding
Sampling
Uniform
Advanced

3. Probabilistic Roadmap Method
Free space
Construction (G =V,E )
Loop
c  a free sample
add c to the vertices V
Nc  a set of nodes
for all c’ in Nc in increasing distance
if c’ and c are not connected in G then
if local path between c and c’ exists then
add the edge c’c to E
Forbidden space
Sample
Local path
Colliding path c c’ c c c’ c c c’

4. Probabilistic Roadmap Method
Free space
Construction (G =V,E )
Loop
c  a free sample
add c to the vertices V
Nc  a set of nodes
for all c’ in Nc in increasing distance
if c’ and c are not connected in G then
if local path between c and c’ exists then
add the edge c’c to E
Query
connect sample s and g to roadmap
Dijkstra’s shortest path
Forbidden space
Sample
Local path
Start / goal
Shortest path

5. Test Scenes
Comparison of techniques

6. Experimental Setup Environment Preprocessing method
Single system
SAMPLE
Same computer
Pentium IV 2.66GHz, 1GB memory
Same test scenes
Cage, clutter, hole, house, rooms, wrench
Preprocessing method
but single query
Average time (s) over 30 runs

7. PRM choices Collision checking on local path Neighbor selecting
Incremental
Binary
Rotate-at-s
Neighbor selecting
Nearest-k
Component-k
Visibility

8. Collision Checking
Rotate-at-s
Incremental
Binary

9. Collision Checking – Results
incremental
binary
rotate-at-s
cage
2.4
1.9
2.7
clutter
1.8
1.3
3.1
hole
431.9
422.3
1206.7
house
6.4
4.9
47.1
rooms
0.5
0.4
1.1
wrench
0.9

10. Neighbor Selecting
Nearest-k
Component-k
Component
Visibility

11. Neighbor Strategy Nearest-k Component Component-k Visibility
Nearest k neighbors
Component
Nearest 1 neighbor in each connected component
Component-k
Nearest k neighbors in each connected component
Visibility
Only useful nodes, add node/connection only if:
Node cannot be connected to other nodes
Node can be connected to 2 (or more) connected components

12. Neighbor Strategy – Results
nearest-k
comp.
comp.-k
visibility
cage
1.9
3.4
1.6
3.0
clutter
1.3
1.4
2.3
hole
409.5
7428.2
7554.4
102.5
house
4.9
13.0
45.5
rooms
0.4
0.2
6.3
wrench
0.5

13. Uniform Sampling
Random
Grid

14. Uniform Sampling
Cell
Halton (variants)

15. Uniform Sampling – Results
halton, seed:
random
grid
cell
cage
2.3
3.2
1.9
2.0
2.8
clutter
1.2
3.4
1.3
1.5
1.4
hole
433.9
370.4
422.3
201.4
279.5
house
78.7
4.9
10.4
10.0
rooms
0.7
0.8
0.4
wrench
0.5

16. Advanced Sampling
Gaussian
Bridge test

17. Advanced Sampling
Obstacle based
Nearest contact

18. Advanced Sampling
Medial axis

19. Advanced Sampling – Results
gaussian
bridge
obstacle NC MA
rnd halton
cage
7.3
3.1
5.3
5.4
215.9
2.0
clutter
2.8
2.6
7.1
620.4
1.5
hole
8.8
47.5
2.3
7.7
201.4
house
18.0
20.7
13.0
15.7
199.3
10.4
rooms
0.5
0.4
3.5
0.7
wrench
2.7
0.9
1.9
3.8
11.0

20. Variation of Running Times
min
avg
max
st dev
without restart
0.03
1.01
60.81
2.32
with restart
0.05
0.88
8.20
1.00

21. Conclusions Many claims could not be confirmed Local planner
Rotate-at-s is worse than binary collision checking
Node adding
Component-k seems to work best
Visibility sampling didn’t perform as well as expected

22. Conclusions
Sampling
Small difference between uniform methods
Halton didn’t outperform uniform sampling but may be preferred (deterministic)
Advanced sampling is only useful in scenes with large open areas and some narrow passages
It is not necessarily true that a combination of good techniques is good
Reduction of variance is desirable

23. Questions
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