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

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