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

TL;DR

This paper introduces an efficient implementation of random transformed grids (RTG) for motion planning, significantly speeding up nearest-neighbor queries and improving solution quality in sampling-based algorithms.

Contribution

It demonstrates how RTG can be effectively employed in motion planning, leading to faster convergence and reduced construction times compared to traditional methods.

Findings

RTG enables faster convergence to high-quality solutions.

RTG significantly reduces construction times for batched-PRM.

RTG outperforms common NN data structures in motion planning contexts.

Abstract

Sampling-based motion-planning algorithms typically rely on nearest-neighbor (NN) queries when constructing a roadmap. Recent results suggest that in various settings NN queries may be the computational bottleneck of such algorithms. Moreover, in several asymptotically-optimal algorithms these NN queries are of a specific form: Given a set of points and a radius r report all pairs of points whose distance is at most r. This calls for an application-specific NN data structure tailored to efficiently answering this type of queries. Randomly transformed grids (RTG) were recently proposed by Aiger et al. as a tool to answer such queries and have been shown to outperform common implementations of NN data structures in this context. In this work we employ RTG for sampling-based motion-planning algorithms and describe an efficient implementation of the approach. We show that for motion-planning, RTG allow for faster convergence to high-quality solutions when compared with existing NN data structures. Additionally, RTG enable significantly shorter construction times for batched-PRM variants; specifically, we demonstrate a speedup by a factor of two to three for some scenarios.