Multi-Agent Distributed Optimal Control for Tracking Large-Scale Multi-Target Systems in Dynamic Environments

This article considers the problem of motion coordination for a multiagent (MA) network whose goal is to track a large-scale multitarget (MT) system in a region populated by dynamic obstacles. We first characterize a density path which corresponds to the expected evolution of the macroscopic state of the MT system, which is represented by the probability density function (PDF) of a time-varying Gaussian mixture (GM). We compute this density path by using an adaptive optimal control method which accounts for the distribution of the (possibly moving) obstacles over the environment described by a time-varying obstacle map function. We show that each target of the MT system can find microscopic inputs that can collectively realize the density path while guaranteeing obstacle avoidance at all times. Subsequently, we propose a Voronoi distributed motion coordination algorithm which determines the individual microscopic control inputs of each agent of the MA network so that the latter can track the MT system while avoiding collisions with obstacles and their teammates. The proposed algorithm relies on a distributed move-to-centroid control law in which the density over the Voronoi cell of each agent is determined by the estimated macroscopic state evolution of the MT system. Finally, simulation results are presented to showcase the effectiveness of our proposed approach.