Multi-Agent Shape Control with Optimal Transport

TL;DR

This paper presents MASCOT, a novel optimal control method for multi-agent systems that uses optimal transport to achieve shape, formation, and density constraints efficiently.

Contribution

It introduces a new approach combining optimal control with Earth Mover's Distance to handle complex shape and distribution constraints in multi-agent control.

Findings

Successfully computes optimal agent distributions respecting shape constraints

Minimizes collision risks through density control

Efficiently assigns agents to destinations using optimal transport

Abstract

We introduce a method called MASCOT (Multi-Agent Shape Control with Optimal Transport) to compute optimal control solutions of agents with shape/formation/density constraints. For example, we might want to apply shape constraints on the agents -- perhaps we desire the agents to hold a particular shape along the path, or we want agents to spread out in order to minimize collisions. We might also want a proportion of agents to move to one destination, while the other agents move to another, and to do this in the optimal way, i.e. the source-destination assignments should be optimal. In order to achieve this, we utilize the Earth Mover's Distance from Optimal Transport to distribute the agents into their proper positions so that certain shapes can be satisfied. This cost is both introduced in the terminal cost and in the running cost of the optimal control problem.