Distributed MPC for formation of multi-agent systems with collision avoidance and obstacle avoidance

The paper is concerned with the problem of distributed model predictive control (DMPC) for formation of multiple linear second-order agents with collision avoidance and obstacle avoidance. All the agents are permitted to implement optimization simultaneously at each time step. The assumed input trajectory and state trajectory are introduced to obtain a computationally tractable optimization problem in a distributed manner. As a result, a compatibility constraint is required to ensure the consistency between each agent׳s real operation and its plan and to establish the agreement among agents. The terminal ingredients are tailored by making use of the specific form of the system model and the control objective. The terminal set is ensured to be positively invariant with the designed terminal controller. The collision avoidance constraint and the obstacle avoidance constraint are satisfied for any state in the terminal set. The weighted matrix of the terminal cost is determined by solving a Lyapunov equation. Moreover, recursive feasibility of the resulting optimization problem is guaranteed and closed-loop stability of the whole system is ensured. Finally, a numerical example is given to illustrate the effectiveness of the proposed algorithm.