Sampling Narrow Passages

1
Sampling Narrow Passages
2
Narrow passages
3
Narrowness
n-dim hypercube
connected by a tube (n-1)-dim narrow
connected by a tube 1-dim narrow
4
PRM skeleton

• repeat
• Sample a configuration q with a suitable
• sampling strategy.
• if q is collision-free then
• Add q to the roadmap R.
• Connect q to existing milestones.
• Search R for a path.
• return the path if one is found

5
Key elements of PRM

• Sampling strategy
• Distributione.g., uniform, Gaussian
• Sourcee.g., pseudo-random,quasi-random, lattice

• Connection strategy

6
Difficulty
PSAPCE-hard
random sampling
narrow passages
7
Dilating free space
dilated free space
original free space
8
Sampling near obstacle boundaries
OBPRM
Gaussian Sampler
9
What is the problem here?
10
Adaptive sampling

• 1 Initialize the sampling distribution ?.
• 2 repeat
• 3 Sample new milestones according to ?.
• 4 Extract partial knowledge of the
• configuration space. Evaluate the
• current roadmap.
• 5 Update ?