A multiscale analysis of multi-agent coverage control algorithms

Vishaal Krishnan and Sonia Martínez
Automatica, 145 (2022) 110516 2545-2550

Abstract:

This paper presents a theoretical framework for the design and analysis of gradient descent-based algorithms for coverage control tasks involving robot swarms. We adopt a multiscale approach to analysis and design to ensure consistency of the algorithms in the large-scale limit. First, we represent the macroscopic configuration of the swarm as a probability measure and formulate the macroscopic coverage task as the minimization of a convex objective function over probability measures. We then construct a macroscopic dynamics for swarm coverage, which takes the form of a proximal descent scheme in the L2-Wasserstein space. Our analysis exploits the generalized geodesic convexity of the coverage objective function, proving convergence in the L2-Wasserstein sense to the target probability measure. We then obtain a consistent gradient descent algorithm in the Euclidean space that is implementable by a finite collection of agents, via a "variational" discretization of the macroscopic coverage objective function. We establish the convergence properties of the gradient descent and its behavior in the continuous-time and large-scale limits. Furthermore, we establish a connection with well-known Lloyd-based algorithms, seen as a particular class of algorithms within our framework, and demonstrate our results via numerical experiments.

File: (ArXiv version)

Bib-tex entry:

@article{VK-SM:22-auto,
author = {V. Krishnan and S. Mart{\'\i}nez},
title = {A multiscale analysis of multi-agent coverage control algorithms },
journal= {Automatica},
pages = {1246--1256},
doi = {110516},
year = {2022}
}