Sparsification of motion-planning roadmaps by edge contraction

Abstract

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 [Formula: see text] 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 [Formula: see text][Formula: see text] (RSEC). The primitive operation used by RSEC is [Formula: see text]—the contraction of a roadmap edge ( v′, v″) to a new vertex [Formula: see text] and the connection of the new vertex [Formula: see text] to the neighboring vertices of the contracted edge’s vertices (i.e. to all neighbors of [Formula: see text] and [Formula: see text]). 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%.