Efficient high-quality motion planning by fast all-pairs r-nearest-neighbors
This work addresses efficiency issues in motion planning for robotics or autonomous systems, but it is incremental as it builds on existing RTG methods.
The paper tackles the computational bottleneck of nearest-neighbor queries in sampling-based motion-planning algorithms by employing randomly transformed grids (RTG) as an application-specific data structure, resulting in faster convergence to high-quality solutions and a speedup by a factor of two to three in construction times for batched-PRM variants.
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.