A multiscale analysis of multi-agent coverage control algorithms. (November 2022)

• Record Type: Journal Article
• Authors: Krishnan, Vishaal; Martínez, Sonia
• Is Part Of: Automatica. Volume 145(2022)
• Publication Date: 2022-11
• Subjects: Multi-agent systems -- Coverage control -- Multiscale analysis -- Proximal descent -- Lloyd's algorithm; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2022.110516
• Languages: English
• ISSNs: 0005-1098

Abstract

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 L 2 -Wasserstein space. Our analysis exploits the generalized geodesic convexity of the coverage objective function, proving convergence in the L 2 -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.