状態コスト空間における漸近最適キノダイナミック計画の精緻な解析
Refined Analysis of Asymptotically-Optimal Kinodynamic Planning in the State-Cost Space
キノダイナミック制約付き運動計画のためのAO-RRTについて、単一木版の最適性をコスト関数とダイナミクスのリプシッツ連続性のみを仮定して証明し、実用的な比較実験も行った論文。
著者: Michal Kleinbort, Edgar Granados, Kiril Solovey, Riccardo Bonalli, Kostas E. Bekris, Dan Halperin
分類: cs.RO
原文アブストラクト
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.
