تقرير
A Multiscale Analysis of Multi-Agent Coverage Control Algorithms
| العنوان: | A Multiscale Analysis of Multi-Agent Coverage Control Algorithms |
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| المؤلفون: | Krishnan, Vishaal, Martínez, Sonia |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Optimization and Control |
| الوصف: | 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. Comment: 26 pages, 3 figures, 1 table |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2102.11411 |
| رقم الأكسشن: | edsarx.2102.11411 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |