Collision Detection or Nearest-Neighbor Search? On the Computational Bottleneck in Sampling-based Motion Planning

Michal Kleinbort*, Oren Salzman, Dan Halperin

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

The complexity of nearest-neighbor search dominates the asymptotic running time of many sampling-based motion-planning algorithms. However, collision detection is often considered to be the computational bottleneck in practice. Examining various asymptotically optimal planning algorithms, we characterize settings, which we call NN-sensitive, in which the practical computational role of nearest-neighbor search is far from being negligible, i.e., the portion of running time taken up by nearest-neighbor search is comparable to, or sometimes even greater than the portion of time taken up by collision detection. This reinforces and substantiates the claim that motion-planning algorithms could significantly benefit from efficient and possibly specially-tailored nearest-neighbor data structures. The asymptotic (near) optimality of these algorithms relies on a prescribed connection radius, defining a ball around a configuration q, such that q needs to be connected to all other configurations in that ball. To facilitate our study, we show how to adapt this radius to non-Euclidean spaces, which are prevalent in motion planning. This technical result is of independent interest, as it enables to compare the radial-connection approach with the common alternative, namely, connecting each configuration to its k nearest neighbors (K-NN). Indeed, as we demonstrate, there are scenarios where using the radial connection scheme, a solution path of a specific cost is produced ten-fold (and more) faster than with K-NN.

Original languageEnglish
Title of host publicationSpringer Proceedings in Advanced Robotics
PublisherSpringer Science and Business Media B.V.
Pages624-639
Number of pages16
DOIs
StatePublished - 2020

Publication series

NameSpringer Proceedings in Advanced Robotics
Volume13
ISSN (Print)2511-1256
ISSN (Electronic)2511-1264

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