Distributed Large-Scale Swarm Control in Obstacle Environment Based on Random Finite Set Theory

This article investigates the problem of distributed large-scale swarm control using random finite set (RFS) theory. We first formulate an optimization problem for swarm control based on RFS and Gaussian mixture (GM) model assumption. This formulation promotes the efficiency of optimization control for a large-scale swarm via directly optimizing the collective properties of the swarm (e.g., its density distribution at specific locations). A distance function with adaptive parameters and a logarithmic barrier function are developed to guide the swarm autonomously converge to the desired GM distribution in obstacle-rich environment without beforehand destination assignment. The model predictive control (MPC) method with quasi-Newton iteration is then leveraged to find the optimal solution in a distributed way. To support the implementation of the proposed algorithm, a distributed fixed-time observer is designed to guarantee the consensus on the global intensity and the settling time boundary is theoretically proved by the Lyapunov method. Numerical simulations are carried out to demonstrate the RFS-based control method, and the results show the superiority of the obstacle avoidance trajectories and flexible assignment of swarm modeled by GM. The convergence of global information for RFS-based control based on distributed fixed-time observer is also presented.