1. A multiscale analysis of multi-agent coverage control algorithms.
- Author
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Krishnan, Vishaal and Martínez, Sonia
- Subjects
- *
EUCLIDEAN algorithm , *PROBABILITY measures , *ALGORITHMS , *CONVEX functions , *DISTRIBUTED algorithms , *MULTIAGENT systems , *PARTICLE swarm optimization - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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