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A multiscale analysis of multi-agent coverage control algorithms
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DOI：10.1016/j.automatica.2022.110516.png)
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Abstract
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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. (C) 2022 Elsevier Ltd. All rights reserved.
Keywords:
Multi-agent systems
Coverage control
Multiscale analysis
Proximal descent
Lloyd's algorithm
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