Two-Level Control of Multiagent Networks for Dynamic Coverage Problems

We propose a two-level coverage control framework for a multiagent network whose members have to deploy over a given region in accordance with a (possibly time-varying) coverage density function. Our approach is based on a two-level description of the multiagent network. The first level corresponds to the probability density function of the agents' locations over a given region, in which the multiagent network is treated as one unit (macroscopic description), whereas in the second level, the network is described in terms of the collection of all individual positions of its agents (microscopic description). The goal of the multiagent network is to attain a spatial distribution that (approximately) matches the reference coverage density function (high-level coverage control problem) through local interactions of the agents of the network at the individual level (low-level coverage control problem). We address the high-level control problem by associating it with an interpolation problem in the class of Gaussian mixtures. Furthermore, we address the low-level control problem by utilizing a variation of Lloyd's algorithm with a time-varying coverage density function, which is updated at each step based on the distribution of the agents' locations. Because the high-level and the low-level coverage control problems are inherently coupled to each other, we propose an iterative scheme that combines their solutions in order to address the deployment problem in a holistic way. Finally, a set of simulation results is provided to show the effectiveness of the proposed approach.