Pareto optimal multi-robot motion planning

TL;DR

This paper introduces a novel numerical algorithm for multi-robot coordination that efficiently finds Pareto optimal solutions, balancing individual robot travel times while avoiding collisions, demonstrated through experiments and simulations.

Contribution

It proposes a new algorithm for multi-robot motion planning that guarantees Pareto optimality and provides a consistent approximation method using set-valued numerical analysis.

Findings

Algorithm quickly returns feasible control policies.

The algorithm improves policy optimality over time.

Experiments validate the anytime property of the method.

Abstract

This paper studies a class of multi-robot coordination problems where a team of robots aim to reach their goal regions with minimum time and avoid collisions with obstacles and other robots. A novel numerical algorithm is proposed to identify the Pareto optimal solutions where no robot can unilaterally reduce its traveling time without extending others'. The consistent approximation of the algorithm in the epigraphical profile sense is guaranteed using set-valued numerical analysis. Experiments on an indoor multi-robot platform and computer simulations show the anytime property of the proposed algorithm; i.e., it is able to quickly return a feasible control policy that safely steers the robots to their goal regions and it keeps improving policy optimality if more time is given.