Sparsification of motion-planning roadmaps by edge contraction

Roadmaps constructed by the recently introduced PRM∗ algorithm for asymptotically-optimal motion planning encode high-quality paths yet can be extremely dense. We consider the problem of sparsifying the roadmap, i.e. reducing its size, while minimizing the degradation of the quality of paths that can be extracted from the resulting roadmap. We present a simple, effective sparsifying algorithm, called roadmap sparsificationby edgecontraction (RSEC). The primitive operation used by RSEC is edgecontraction - the contraction of a roadmap edge (v',v'') to a new vertex v' and the connection of the new vertex v to the neighboring vertices of the contracted edge's vertices (i.e. to all neighbors of v' and v'). For certain scenarios, we compress more than 97% of the edges and vertices of a given roadmap at the cost of degradation of average shortest path length by at most 4%.