A fast streaming spanner algorithm for incrementally constructing sparse roadmaps

Sampling-based probabilistic roadmap algorithms such as PRM and PRM* have been shown to be effective at solving certain motion planning problems, but the large graphs generated to express the connectivity and a metric on the configuration space may require much storage space and be expensive to search. Recent work by Marble and Bekris [14], [19] applied spanner algorithms to PRM* these algorithms prune some edges in a dense graph, while guaranteeably maintaining an approximation to the metric. In this paper, we apply (and improve) a state-of-the-art streaming spanner algorithm to prune PRM* roadmaps. The algorithm we present has the main advantage of computational speed; when applied to PRM*, the processing time per vertex is independent of the number of sampled vertices, n, as compared to O(nlog² nloglogn) in [19]. In practice, the algorithm we present prunes a graph with about 20 million edges in less than 20 seconds on a modern desktop computer; compared to the time required for generating such a roadmap, this additional processing time is essentially trivial. In fact, because the combination of this algorithm with PRM* avoids the need for many collision detections, the combination runs several times faster than PRM*alone.