Optimal Transport for Time-Varying Multi-Agent Coverage Control

TL;DR

This paper introduces an optimal transport-based framework for multi-agent coverage control in dynamic environments, enabling agents to adaptively track evolving target densities with improved performance.

Contribution

It extends static coverage control to time-varying scenarios using a rigorous optimal transport formulation, including a closed-form solution in one dimension.

Findings

Enhanced tracking accuracy over existing methods

Analytical solution in 1D offers computational efficiency

Numerical results validate improved coverage performance

Abstract

Coverage control algorithms have traditionally focused on static target densities, where agents are deployed to optimally cover a fixed spatial distribution. However, many applications involve time-varying densities, including environmental monitoring, surveillance, and adaptive sensor deployment. Although time-varying coverage strategies have been studied within Voronoi-based frameworks, recent works have reformulated static coverage control as a semi-discrete optimal transport problem. Extending this optimal transport perspective to time-varying scenarios has remained an open challenge. This paper presents a rigorous optimal transport formulation for time-varying coverage control, in which agents minimize the instantaneous Wasserstein distance to a continuously evolving target density. The proposed solution relies on a coupled system of differential equations governing agent positions and the dual variables that define Laguerre regions. In one-dimensional domains, the resulting system admits a closed-form analytical solution, offering both computational benefits and theoretical insight into the structure of optimal time-varying coverage. Numerical simulations demonstrate improved tracking performance compared to quasi-static and Voronoi-based methods, validating the proposed framework.