Distributed Circumferential Coverage Control in Non-Convex Annulus Environments

TL;DR

The paper addresses distributed coverage control for a team of agents operating in a non-convex annulus, aiming to balance workload without relying on a common reference point. It introduces a distributed partition law using a virtual bar sliding along the inner boundary and builds a Riemannian metric on subregions to enable collision-free navigation toward local subregion optima. Theoretical results, including a Lyapunov-based analysis and key lemmas, prove exponential convergence of workload distribution and asymptotic convergence of agents to subregion centroids, with guarantees of boundary avoidance. A case study demonstrates effective partitioning and convergence in a complex, hole-containing environment. The approach has practical implications for robust, scalable deployment of multi-agent systems in challenging geometries.

Abstract

It has long been a prominent challenge in multi-agent systems to achieve distributed coverage of non-convex annulus environments while ensuring workload equalization among agents. To address this challenge, a distributed circumferential coverage control formulation is developed in this note by constructing a Riemannian metric for the navigation in the non-convex subregion while avoiding collisions with the region boundary. In addition, a distributed partition law is designed to balance the workload on the entire coverage region by endowing each agent with a virtual partition bar that slides along the inner boundary of coverage region. Theoretical analysis is conducted to ensure the exponential convergence of workload partition and asymptotic convergence of each agent towards the local optimum in its subregion. Finally, a case study is presented to demonstrate the effectiveness of the proposed coverage control approach.

Figures (2)

• Figure 1: The nonconvex annulus coverage region for multi-agent system. The blue lines denote the virtual partition bars, and the blue solid ball stands for the position of agent. The red triangle represents the optimal position for minimizing local coverage cost.
• Figure 2: Snapshots illustrating the simulation results of the MAS, showing the region partitions, subregion centroids, and agent positions. The mobile agents are marked by black points, the centroids of the subregions are represented by red stars.

Theorems & Definitions (17)

• Lemma 1
• proof
• Lemma 2
• proof
• Lemma 3
• proof
• Lemma 4
• proof
• Lemma 5
• proof