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

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Algorithmic Foundations of Robotics XII

Part of the book series: Springer Proceedings in Advanced Robotics ((SPAR,volume 13))

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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.

This work has been supported in part by the Israel Science Foundation (grant no. 825/15), by the Blavatnik Computer Science Research Fund, and by the Hermann Minkowski–Minerva Center for Geometry at Tel Aviv University. O. Salzman has been also supported by the National Science Foundation IIS (#1409003), Toyota Motor Engineering & Manufacturing (TEMA), and the Office of Naval Research. Part of this work was carried out while O. Salzman was a student at Tel Aviv University.

M. Kleinbort and O. Salzman contributed equally to this paper.

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Correspondence to Michal Kleinbort .

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Kleinbort, M., Salzman, O., Halperin, D. (2020). Collision Detection or Nearest-Neighbor Search? On the Computational Bottleneck in Sampling-based Motion Planning. In: Goldberg, K., Abbeel, P., Bekris, K., Miller, L. (eds) Algorithmic Foundations of Robotics XII. Springer Proceedings in Advanced Robotics, vol 13. Springer, Cham. https://doi.org/10.1007/978-3-030-43089-4_40

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