A fast online spanner for roadmap construction

This paper introduces a fast weighted streaming spanner algorithm WSS that trims edges from roadmaps generated by robot motion planning algorithms such as Probabilistic Roadmap PRM and variants e.g. k-PRM* as the edges are generated, but before collision detection; no route in the resulting graph is more than a constant factor larger than it would have been in the original roadmap. Experiments applying WSS to k-PRM* were conducted, and the results show our algorithm's capability to filter graphs with up to 1.28 million vertices, discarding about three-quarters of the edges. Due to the fact that many collision detection steps can be avoided, the combination of WSS and k-PRM* is faster than k-PRM* alone. The paper further presents an online directed spanner algorithm that can be used for systems with non-holonomic constraints, with proof of correctness and experimental results.