Optimal Transport for Time-Varying Multi-Agent Coverage Control

Abstract

Coverage control has traditionally focused on static target densities, where agents are deployed to match a fixed spatial distribution optimally. However, many real-world applications require tracking densities that evolve over time. 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. In this talk, I present a recent optimal transport approach to time-varying coverage, in which a finite set of agents evolves to minimize the instantaneous Wasserstein distance to a continuously changing target density. This formulation leads to a simple dynamical system governing both agent locations and the associated partition of space (i.e., generalized Voronoi regions), with explicit solutions in one dimension. Finally, I show how this framework can be extended to settings in which the target density is not prescribed a priori but must be computed to address multiscale leader-follower systems, where a small number of controlled agents influence a large, uncontrolled population.

Biography

Italo Napolitano (i.napolitano@ssmeridionale.it) is a third-year Ph.D. student at the Scuola Superiore Meridionale (Naples, Italy). He received his M.Sc. in Automation and Robotics Engineering from the University of Naples Federico II in October 2023, where he completed a research thesis on learning-based strategies for multi-agent shepherding control problems. His current research focuses on the control of multi-agent systems (e.g., robotic swarms) using learning-based methods and optimal transport techniques for controlling populations from microscopic to macroscopic scales.