Efficient sampling-based bottleneck pathfinding over cost maps

TL;DR

This paper presents a sampling-based algorithm called bottleneck tree (BTT) for efficiently finding paths that minimize the maximum cost in a map, outperforming existing methods in multi-agent scenarios.

Contribution

The paper introduces BTT, a novel sampling-based planner for bottleneck pathfinding on cost maps, with theoretical analysis and improved empirical performance.

Findings

BTT outperforms T-RRT* in multi-agent pathfinding tasks.

Theoretical analysis of BTT's asymptotic properties.

Effective handling of monotone trajectory constraints.

Abstract

We introduce a simple yet effective sampling-based planner that is tailored for bottleneck pathfinding: Given an implicitly-defined cost map $\mathcal{M}:\mathbb{R}^d\rightarrow \mathbb{R}$, which assigns to every point in space a real value, we wish to find a path connecting two given points, that minimizes the maximal value with respect to~$\mathcal{M}$. We demonstrate the capabilities of our algorithm, which we call bottleneck tree (BTT), on several challenging instances of the problem involving multiple agents, where it outperforms the state-of-the-art cost-map planning technique T-RRT*. On the theoretical side, we study the asymptotic properties of our method and consider the special setting where the computed trajectories must be monotone in all coordinates. This constraint arises in cases where the problem involves the coordination of multiple agents that are restricted to forward motions along predefined paths.