Multi-agent Coverage Control: From Discrete Assignments to Continuous Multi-agent Distribution Matching

TL;DR

The note surveys multi-agent spatial coverage problems across static, discrete, and continuum deployment settings, anchored by a stationary area-priority density $\phi$ and a unifying objective $H(P,\bar{\mathcal{W}})$. It presents three complementary frameworks: (i) Voronoi-/power-diagram-based concurrent area partitioning for fixed agents, (ii) a two-step discrete PoI extraction and optimal assignment pipeline using GMM/$K$-means/SVGD and bipartite matching, and (iii) continuum distribution matching for large swarms based on the $p$-Wasserstein distance $W_p$ and distributed transport algorithms. Key insights include linking the locational cost to Wasserstein transport in the large-scale limit, leveraging submodular optimization for PoI selection, and enabling distributed implementations that respect microscopic sensing and communication constraints. The work provides a unifying perspective and practical guidance for scalable, heterogeneous multi-agent coverage with potential integration of learning and decentralized control.

Abstract

The multi-agent spatial coverage control problem encompasses a broad research domain, dealing with both dynamic and static deployment strategies, discrete-task assignments, and spatial distribution-matching deployment. Coverage control may involve the deployment of a finite number of agents or a continuum through centralized or decentralized, locally-interacting schemes. All these problems can be solved via a different taxonomy of deployment algorithms for multiple agents. Depending on the application scenario, these problems involve from purely discrete descriptions of tasks (finite loads) and agents (finite resources), to a mixture of discrete and continuous elements, to fully continuous descriptions of the same. Yet, it is possible to find common features that underline all the above formulations, which we aim to illustrate here. By doing so, we aim to point the reader to novel references related to these problems. The short article outline is the following: Static coverage via concurrent area partitioning and assignment; Static coverage as a discrete task assignment; and Continuum task assignment for large-scale swarms.

Figures (4)

• Figure 1: Weighted Voronoi-based deployment based on minimizing \ref{['eq::power_diagram']}. The contour plot in the background shows the area priority density distribution function $\phi$. The agents final deployment positions shown by red dots and their power disks shown with dashed circles. Plots (a), (b) and (c) show respectively, deployment results for four, three and two heterogeneous agents. Figure courtesy of Donipolo Ghimire.
• Figure 2: Extracting PoIs from $K$-means and GMM clustering. PoIs are shown by filled red dots.
• Figure 3: Schematic illustration of the multi-agent assignment as an optimal bipartite matching problem, where red dots denote PoIs.
• Figure 4: A swarm of agents evolve under the distributed transport algorithm of VK-SM:18-cdc to reconfigure into an image. Figure courtesy of Vishaal Krishnan.