Distributed hierarchical MPC based on evolutionary game for formation control with collision and obstacle avoidance

In this paper, we present a distributed hierarchical model predictive control (MPC) algorithm based on evolutionary game for formation control of multi-agent systems in environments with static obstacles. This algorithm is in a strategic-tactical structure for each agent’s decision making. At the strategic level, the leader agent uses a predictive controller to obtain the optimal control input in the consideration of obstacle avoidance constraints. At the tactical level, by describing the formation problem in the framework of evolutionary game, each follower agent is capable of predicting its state by using distributed density-dependent smith dynamics with the guarantee of asymptotic stability of the Nash equilibrium point. The predicted positions are then sent to its neighbors, so that all the follower agents can make decisions simultaneously. Real-time collision avoidance between agents is addressed at the tactical level by including predicted neighbors’ future position as a constraint in the optimisation problem. Finally, a numerical simulation is provided to verify the efficacy of the proposed algorithm in terms of both obstacle avoidance and collision avoidance.