Is Limited Information Enough? An Approximate Multi-agent Coverage Control in Non-Convex Discrete Environments

TL;DR

This work tackles distributed coverage control in non-convex discrete environments under limited information by extending a prior 1D result to general dimensions. It proposes a neighborhood-optimal algorithm that coordinates small coalitions through a communication tree, achieving convergence to a neighborhood optimum with an approximation ratio of 2 despite restricted information. The method preserves scalability by fixing a small neighborhood and introduces a potential function to guarantee progress, and it demonstrates improved performance over state-of-the-art benchmarks in simulations. The approach offers practical implications for medium-scale multi-agent sensing and robotic deployment where full information sharing is impractical.

Abstract

Conventional distributed approaches to coverage control may suffer from lack of convergence and poor performance, due to the fact that agents have limited information, especially in non-convex discrete environments. To address this issue, we extend the approach of [Marden 2016] which demonstrates how a limited degree of inter-agent communication can be exploited to overcome such pitfalls in one-dimensional discrete environments. The focus of this paper is on extending such results to general dimensional settings. We show that the extension is convergent and keeps the approximation ratio of 2, meaning that any stable solution is guaranteed to have a performance within 50% of the optimal one. The experimental results exhibit that our algorithm outperforms several state-of-the-art algorithms, and also that the runtime is scalable.

Figures (14)

• Figure 1: Coverage example with 6 agents: Circles in grey are agents. A number in a white circle shows the Manhattan distance to the closest agent.
• Figure 2: The environment of Example \ref{['ex:cov']} with Voronoi partitions and the corresponding neighborhood graph
• Figure 3: Agent $e$ would contribute to $G(x)$ the most from the addition of an agent (depicted as '+') in her region
• Figure 4: (Left): the neighborhood graph in Example \ref{['ex:cov']}. The numbers represent utilities. (Right): a communication tree in convergence. In this case, agent 'a' is $i_{\min}$ and therefore the root of the tree.
• Figure 5: A pathological non-convex discrete example. Different from grid spaces, nodes are connected by edges. Left: Voronoi partition. Middle: A move of agent $a$ changes partitions outside of the neighborhood. Right: Changes in $\mathcal{P}$ are confined inside the neighborhood.

Theorems & Definitions (13)

• Example 1
• Theorem 1: from marden2016role
• Example 2
• Theorem 2: Convergence with Performance guarantee
• Example 3
• Example 4
• Theorem 3
• Lemma 1
• Lemma 2
• Lemma 3