Density regulation of large-scale robotic swarm using robust model predictive mean-field control

Abstract

This paper studies the density regulation problem for a large-scale robotic swarm with homogeneous agents. A novel robust model predictive mean-field control method is proposed to significantly improve the control performance and the algorithm scalability with the population size. To that end, a top-down control philosophy is first employed, under which the physical space is divided into finite disjoint bins and the actual density distribution (ADD) over these bins is taken as the macrostate. The system dynamics of ADD is then established by including a stochastic disturbance in the mean-field model, which describes the evolution process of each agent’s probability density distribution over the bins. Next, an optimization-based model predictive control method is developed to efficiently overcome the performance degradation raised by the disturbance term. Furthermore, the conditions ensuring the algorithm feasibility are strictly developed. We also prove that the actual swarm density converges to the target one in probability. Finally, simulation and comparison studies illustrate the effectiveness and advantages of the proposed algorithm over the existing results.