Discretized optimal control approach for dynamic multi-agent decentralized coverage

This paper presents a novel discrete-time decentralized control law for the Voronoi-based self-deployment of a Multi-Agent dynamical system. The basic control objective is to let the agents deploy into a bounded convex polyhedral region and maximize the coverage quality by computing locally the control action for each agent. The Voronoi tessellation algorithm is employed to partition dynamically the deployed region and to allocate each agent to a corresponding bounded functioning zone at each time instant. The control synthesis is then locally computed based on an optimal formulation framework related to the Lloyd's algorithm but according to the discrete-time agent's dynamics equation. The performance of the discretized optimal solution will be demonstrated via an illustrative example.