HPRM: a hierarchical PRM

We introduce a hierarchical variant of the probabilistic roadmap method for motion planning. By recursively refining an initially sparse sampling in neighborhoods of the obstacle boundary, our algorithm generates a smaller roadmap that is more likely to find narrow passages than uniform sampling. We analyze the failure probability and computation time, relating them to path length, path clearance, roadmap size, recursion depth, and a local property of the free space. The approach is general, and can be tailored to any variety of robots. In particular, we describe algorithmic details for a planar articulated arm.