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We propose a distributed control algorithm for a multi-agent network whoseagents deploy over a cluttered region in accordance with a time-varyingcoverage density function while avoiding collisions with all obstacles theyencounter. Our algorithm is built on a two-level characterization of thenetwork. The first level treats the multi-agent network as a whole based on thedistribution of the locations of its agents over the spatial domain. In thesecond level, the network is described in terms of the individual positions ofits agents. The aim of the multi-agent network is to attain a spatialdistribution that resembles that of a reference coverage density function(high-level problem) by means of local (microscopic) interactions of its agents(low-level problem). In addition, as the agents deploy, they must avoidcollisions with all the obstacles in the region at all times. Our approachutilizes a modified version of Voronoi tessellations which are comprised ofwhat we refer to as Obstacle-Aware Voronoi Cells (OAVC) in order to enablecoverage control while ensuring obstacle avoidance. We consider two controlproblems. The first problem which we refer to as the high-level coveragecontrol problem corresponds to an interpolation problem in the class ofGaussian mixtures (no collision avoidance requirement), which we solveanalytically. The second problem which we refer to as the low-level coveragecontrol problem corresponds to a distributed control problem (collisionavoidance requirement is now enforced at all times) which is solved byutilizing Lloyd's algorithm together with the modified Voronoi tessellation(OAVC) and a time-varying coverage density function which corresponds to thesolution of the high-level coverage control problem. Finally, simulationresults for coverage in a cluttered environment are provided to demonstrate theefficacy of the proposed approach.

Distributed Coverage Control of Multi-Agent Networks with Guaranteed Collision Avoidance in Cluttered Environments