An Asymptotically-Optimal Sampling-Based Algorithm for Bi-directional Motion Planning

TL;DR

This paper introduces BFMT*, a bi-directional, sampling-based algorithm that extends FMT* to improve motion planning success and convergence rates while maintaining asymptotic optimality.

Contribution

It presents the first bi-directional, asymptotically optimal motion planner that combines lazy search with bidirectional sampling-based methods.

Findings

BFMT* outperforms unidirectional FMT* in success rates.

BFMT* demonstrates faster convergence to optimal solutions.

Numerical experiments show advantages over other state-of-the-art planners.

Abstract

Bi-directional search is a widely used strategy to increase the success and convergence rates of sampling-based motion planning algorithms. Yet, few results are available that merge both bi-directional search and asymptotic optimality into existing optimal planners, such as PRM*, RRT*, and FMT*. The objective of this paper is to fill this gap. Specifically, this paper presents a bi-directional, sampling-based, asymptotically-optimal algorithm named Bi-directional FMT* (BFMT*) that extends the Fast Marching Tree (FMT*) algorithm to bi-directional search while preserving its key properties, chiefly lazy search and asymptotic optimality through convergence in probability. BFMT* performs a two-source, lazy dynamic programming recursion over a set of randomly-drawn samples, correspondingly generating two search trees: one in cost-to-come space from the initial configuration and another in cost-to-go space from the goal configuration. Numerical experiments illustrate the advantages of BFMT* over its unidirectional counterpart, as well as a number of other state-of-the-art planners.