Asymptotically-Optimal Motion Planning using Lower Bounds on Cost

TL;DR

This paper introduces MPLB, an asymptotically optimal motion planning algorithm that uses lower bounds on cost to efficiently find low-cost paths, reducing collision detection overhead.

Contribution

The paper presents MPLB, a novel sampling-based motion planning algorithm that incorporates lower bounds on cost to improve efficiency and asymptotic optimality.

Findings

MPLB reduces collision detection calls compared to FMT*.

MPLB efficiently produces low-cost paths in complex scenarios.

Simulation results demonstrate improved performance in path quality and computation time.

Abstract

Many path-finding algorithms on graphs such as A* are sped up by using a heuristic function that gives lower bounds on the cost to reach the goal. Aiming to apply similar techniques to speed up sampling-based motion-planning algorithms, we use effective lower bounds on the cost between configurations to tightly estimate the cost-to-go. We then use these estimates in an anytime asymptotically-optimal algorithm which we call Motion Planning using Lower Bounds (MPLB). MPLB is based on the Fast Marching Trees (FMT*) algorithm recently presented by Janson and Pavone. An advantage of our approach is that in many cases (especially as the number of samples grows) the weight of collision detection in the computation is almost negligible with respect to nearest-neighbor calls. We prove that MPLB performs no more collision-detection calls than an anytime version of FMT*. Additionally, we demonstrate in simulations that for certain scenarios, the algorithmic tools presented here enable efficiently producing low-cost paths while spending only a small fraction of the running time on collision detection.