Discrete Partitioning and Coverage Control With Gossip Communication

Abstract

In this paper we propose distributed algorithms to automatically deploy a group of robotic agents and provide coverage of a discretized environment represented by a graph. We present a discrete coverage algorithm which converges to a centroidal Voronoi partition while requiring only pairwise "gossip" communication between the agents. Our theoretical analysis is based on a dynamical system on partitions of the graph's vertices. We also establish bounds on the computational requirements of the algorithm and demonstrate its functionality with simulations.

Pairwise optimal discrete coverage control for gossiping robots

“…The problem domain and goal we are considering is the same as that in [14]: given a group of N robotic agents with limited sensing and communication capabilities, and a discretized environment, we want to apportion the environment into smaller regions and assign one region to each agent. The goal is to optimize the quality of coverage, as measured by a cost functional which depends on the current partition and the positions of the agents.…”

“…This paper is organized as follows. Section II defines the domain and goal of our algorithm, while III contains a review of Lloyd-type gossip algorithms from [14]. Section IV presents our new algorithm and its properties, while in VI we detail its computational requirements.…”

Communication-Free Distributed Coverage for Networked Systems

“…In some studies, distributed coverage control was studied on discrete spaces represented as graphs (e.g., [17], [18], [19], [20]). One possible approach is to achieve a centroidal Voronoi partition of the graph via pairwise gossip algorithms (e.g., [17]) or via asynchronous greedy updates (e.g., [18] Alternatively, distributed coverage control on discrete spaces can be studied in a game theoretic framework (e.g., [19], [20]). Game theoretic methods have been used to solve many cooperative control problems such as vehicle-target assignment (e.g., [21]), dynamic vehicle routing (e.g.…”

Discrete Partitioning and Coverage Control for Gossiping Robots

“…In response to this issue, in [18] the authors have shown how a group of robotic agents can optimize the partition of a convex bounded set using a Lloyd algorithm with gossip communication. A Lloyd algorithm with gossip communication has also been applied to optimizing partitions of non-convex environments in [19], the key idea being to transform the coverage problem in Euclidean space into a coverage problem on a graph with geodesic distances.Distributed Lloyd methods are built around separate partitioning and centering steps, and they are attractive because there are known ways to characterize their equilibrium sets (the so-called centroidal Voronoi partitions) and prove convergence. Unfortunately, even for very simple environments (both continuous and discrete) the set of centroidal Voronoi partitions may contain several sub-optimal configurations.…”

“…In response to this issue, in [18] the authors have shown how a group of robotic agents can optimize the partition of a convex bounded set using a Lloyd algorithm with gossip communication. A Lloyd algorithm with gossip communication has also been applied to optimizing partitions of non-convex environments in [19], the key idea being to transform the coverage problem in Euclidean space into a coverage problem on a graph with geodesic distances.…”