Formation Control with Feedback Nash Strategy for Multiple Unmanned Aerial Vehicles in Unknown Environments

In the paper, the formation control problem in unknown environments for networked multi-unmanned aerial vehicle systems (UAVSs) is resolved under a nonlinear differential game (NL-DDG) framework. The main challenge of this framework is how to obtain feedback Nash strategies, which typically overly rely on global information and cannot ensure the existence of Nash strategies in unknown environments. Toward this goal, we initially design collision avoidance rules to ensure the safety of each UAV. Subsequently, we utilize an inverse optimal control method to construct the NL-DDG that incorporates both formation control and collision avoidance costs, enabling the derivation of analytical forms of Nash strategies relying solely on local information and minimizing performance metrics. In addition, the existence of feedback Nash strategy can be guaranteed with an undirected and connected information topology, which represents the optimality for the UAVSs. Moreover, we analyze the stability of the closed-loop system. Finally, the simulation results validate the effectiveness of the proposed scheme.