Optimal path planning of multi-agent cooperative systems with rigid formation

TL;DR

This paper develops an optimal path planning method for multi-agent robotic systems with rigid formations, demonstrating that individual agent control can be simplified by focusing on the system's center of mass, supported by theoretical proofs and simulations.

Contribution

It introduces a novel approach linking individual agent control to the system's center of mass, simplifying multi-agent path planning with theoretical validation.

Findings

Optimal control for each agent is equivalent to the control of the center of mass.

Theoretical proof of control equivalence using analytical mechanics.

Simulation results validate the proposed control strategy.

Abstract

In this article, we consider the path-planning problem of a cooperative homogeneous robotic system with rigid formation. An optimal controller is designed for each agent in such rigid systems based on Pontryagin's minimum principle theory. We found that the optimal control for each agent is equivalent to the optimal control for the Center of Mass (CoM). This equivalence is then proved by using some analytical mechanics. Three examples are finally simulated to illustrate our theoretical results. One application could be utilizing this equivalence to simplify the original multi-agent optimal control problem.