Scalable Optimal Motion Planning for Multi-Agent Systems by Cosserat Theory of Rods

TL;DR

This paper introduces a scalable motion planning method for large multi-agent systems using Cosserat rod theory, formulating the problem as a PDE-based optimal control and solving it via Bernstein polynomial discretization.

Contribution

It presents a novel continuum-based optimal control framework for multi-agent systems that remains scalable regardless of formation size, utilizing Bernstein surface polynomials for discretization.

Findings

Effective handling of large formations demonstrated through numerical examples

Scalability achieved as problem complexity is independent of the number of agents

Bernstein surface polynomials facilitate efficient discretization and solution

Abstract

We address the motion planning problem for large multi-agent systems, utilizing Cosserat rod theory to model the dynamic behavior of vehicle formations. The problem is formulated as an optimal control problem over partial differential equations (PDEs) that describe the system as a continuum. This approach ensures scalability with respect to the number of vehicles, as the problem's complexity remains unaffected by the size of the formation. The numerical discretization of the governing equations and problem's constraints is achieved through Bernstein surface polynomials, facilitating the conversion of the optimal control problem into a nonlinear programming (NLP) problem. This NLP problem is subsequently solved using off-the-shelf optimization software. We present several properties and algorithms related to Bernstein surface polynomials to support the selection of this methodology. Numerical demonstrations underscore the efficacy of this mathematical framework.