1. NUS CS 5247 David Hsu Sampling Narrow Passages

2. NUS CS 5247 David Hsu2 Narrow passages

3. NUS CS 5247 David Hsu3 Narrowness connected by a tube: (n-1)-dim narrow connected by a tube: 1-dim narrow n-dim hypercube

4. NUS CS 5247 David Hsu4 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. NUS CS 5247 David Hsu5 Key elements of PRM  Sampling strategy Distribution e.g., uniform, Gaussian Source e.g., pseudo-random, quasi-random, lattice distribution source  Connection strategy

6. NUS CS 5247 David Hsu6 Difficulty PSAPCE-hard random sampling narrow passages

7. NUS CS 5247 David Hsu7 Dilating free space original free space dilated free space

8. NUS CS 5247 David Hsu8 Sampling near obstacle boundaries OBPRMGaussian Sampler

9. NUS CS 5247 David Hsu9 What is the problem here?

10. NUS CS 5247 David Hsu10 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 