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Sampling-based motion-planning algorithms typically rely on nearest-neighbor(NN) queries when constructing a roadmap. Recent results suggest that invarious settings NN queries may be the computational bottleneck of suchalgorithms. Moreover, in several asymptotically-optimal algorithms these NNqueries are of a specific form: Given a set of points and a radius r report allpairs of points whose distance is at most r. This calls for anapplication-specific NN data structure tailored to efficiently answering thistype of queries. Randomly transformed grids (RTG) were recently proposed byAiger et al. as a tool to answer such queries and have been shown to outperformcommon implementations of NN data structures in this context. In this work weemploy RTG for sampling-based motion-planning algorithms and describe anefficient implementation of the approach. We show that for motion-planning, RTGallow for faster convergence to high-quality solutions when compared withexisting NN data structures. Additionally, RTG enable significantly shorterconstruction times for batched-PRM variants; specifically, we demonstrate aspeedup by a factor of two to three for some scenarios.

Efficient high-quality motion planning by fast all-pairs r-nearest-neighbors