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DISCRETE PARTITIONING AND COVERAGE CONTROL WITH GOSSIP COMMUNICATION Joseph W Durham Paolo Frasca Francesco Bullo Ruggero Carli Istituto per le Applicazioni del Calcolo Department of Mechanical Engineering Department of Mechanical Engineering Consiglio Nazionale delle Ricerche University of California University of California Rome Italy Santa Barbara California 93106 Santa Barbara California 93106 paolo frasca gmail com bullo engineering ucsb edu joey carlirug engineering ucsb edu 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 1 INTRODUCTION This paper deals with distributed partitioning and coverage control problems for a network of robotic agents in a potentially non convex environment The distributed partitioning problem for robotic networks consists of designing control and communication laws to divide an environment into territories Typically partitioning is done so as to optimize a cost function that measures the quality of the partitions Coverage control algorithms are usually designed in a similar way with an additional criterion of optimizing the placement of the agents In this paper we describe a partitioning and coverage control algorithm which optimizes the configuration of a group of agents in a discrete environment represented by a graph Optimality is defined with reference to a cost function which depends on the locations of the agents and geodesic distances in the graph As with all multiagent coordination applications the challenge comes from

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