Asymptotically Optimal Planning by Feasible Kinodynamic Planning in State-Cost Space

TL;DR

This paper introduces a meta-algorithm transforming feasible kinodynamic planning into asymptotically optimal planning in state-cost space, applicable broadly without steering functions, and demonstrates superior performance on benchmarks.

Contribution

It establishes an equivalence between feasible and optimal kinodynamic planning, enabling the creation of an asymptotically optimal planner using existing feasible planners as subroutines.

Findings

Meta-algorithm is proven asymptotically optimal.

The approach does not require steering functions or boundary-value solvers.

Demonstrates superior or comparable performance on benchmark problems.

Abstract

This paper presents an equivalence between feasible kinodynamic planning and optimal kinodynamic planning, in that any optimal planning problem can be transformed into a series of feasible planning problems in a state-cost space whose solutions approach the optimum. This transformation gives rise to a meta-algorithm that produces an asymptotically optimal planner, given any feasible kinodynamic planner as a subroutine. The meta-algorithm is proven to be asymptotically optimal, and a formula is derived relating expected running time and solution suboptimality. It is directly applicable to a wide range of optimal planning problems because it does not resort to the use of steering functions or numerical boundary-value problem solvers. On a set of benchmark problems, it is demonstrated to perform, using the EST and RRT algorithms as subroutines, at a superior or comparable level to related planners.