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

TL;DR

This paper provides a rigorous proof of asymptotic optimality for the single-tree AO-RRT motion planner, demonstrating its effectiveness in kinodynamic planning under mild assumptions, and compares its variants experimentally.

Contribution

The paper offers the first optimality proof for the single-tree AO-RRT algorithm under Lipschitz conditions, expanding theoretical understanding of kinodynamic motion planning.

Findings

AO-RRT is asymptotically optimal under mild assumptions.

The single-tree version of AO-RRT can approximate any feasible trajectory.

Experimental results compare different AO-RRT variants.

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.