SEAR: A Polynomial-Time Multi-Robot Path Planning Algorithm with Expected Constant-Factor Optimality Guarantee

TL;DR

This paper introduces SEAR, a polynomial-time multi-robot path planning algorithm with expected constant-factor optimality guarantees, suitable for continuous 2D and 3D domains without obstacles, and validated through theoretical analysis and hardware experiments.

Contribution

The paper presents a novel polynomial-time algorithm for multi-robot path planning with probabilistic optimality guarantees and practical efficiency, extending the state of the art in scalable multi-robot coordination.

Findings

Algorithm guarantees constant-factor optimality in expectation.

Efficient implementation computes near-optimal solutions quickly.

Hardware experiments confirm practical applicability.

Abstract

We study the labeled multi-robot path planning problem in continuous 2D and 3D domains in the absence of obstacles where robots must not collide with each other. For an arbitrary number of robots in arbitrary initial and goal arrangements, we derive a polynomial time, complete algorithm that produces solutions with constant-factor optimality guarantees on both makespan and distance optimality, in expectation, under the assumption that the robot labels are uniformly randomly distributed. Our algorithm only requires a small constant factor expansion of the initial and goal configuration footprints for solving the problem, i.e., the problem can be solved in a fairly small bounded region. Beside theoretical guarantees, we present a thorough computational evaluation of the proposed solution. In addition to the baseline implementation, adapting an effective (but non-polynomial time) routing subroutine, we also provide a highly efficient implementation that quickly computes near-optimal solutions. Hardware experiments on the microMVP platform composed of non-holonomic robots confirms the practical applicability of our algorithmic pipeline.