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arXiv · 1909.05569

Refined Analysis of Asymptotically-Optimal Kinodynamic Planning in the State-Cost Space

Michal Kleinbort·Edgar Granados·Kiril Solovey·Riccardo Bonalli·Kostas E. Bekris·Dan Halperin
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Abstract

We present a novel analysis of AO-RRT: a tree-based planner for motion planning with kinodynamic constraints, originally described by Hauser and Zhou (AO-X, 2016). AO-RRT explores the state-cost space and has been shown to efficiently obtain high-quality solutions in practice without relying on the availability of a computationally-intensive two-point boundary-value solver. Our main contribution is an optimality proof for the single-tree version of the algorithm---a variant that was not analyzed before. Our proof only requires a mild and easily-verifiable set of assumptions on the problem and system: Lipschitz-continuity of the cost function and the dynamics. In particular, we prove that for any system satisfying these assumptions, any trajectory having a piecewise-constant control function and positive clearance from the obstacles can be approximated arbitrarily well by a trajectory found by AO-RRT. We also discuss practical aspects of AO-RRT and present experimental comparisons of variants of the algorithm.

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Michal Kleinbort, Edgar Granados, Kiril Solovey, Riccardo Bonalli, Kostas E. Bekris, Dan Halperin. 2019-09-12. Refined Analysis of Asymptotically-Optimal Kinodynamic Planning in the State-Cost Space. https://arxiv.org/abs/1909.05569

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