A Cooperative Trajectory Planning Method for Multi-Aircraft Thunderstorm Avoidance Based on Optimal Control and Game Equilibrium

This paper presents a cooperative trajectory planning method for multiple aircraft avoiding thunderstorms, formulated within a game-theoretic optimal control framework. We model the multi-aircraft system as a non-cooperative game and employ an Iterative Best Response (IBR) algorithm to decompose the coupled planning problem into a series of single-agent, nonlinear optimal control subproblems. Each subproblem is solved using the CasADi framework, enabling the continuous and simultaneous optimization of both aircraft velocity and heading. This approach directly generates smooth, dynamically feasible 4D trajectories that satisfy strict on-time arrival constraints at each waypoint, addressing a key limitation of many existing methods. Our simulations show that the framework not only ensures safe separation from thunderstorms and other aircraft but also effectively manages arrival times, with errors on the order of seconds. These results demonstrate the method’s capability to produce safe, efficient, and punctual trajectories for complex multi-aircraft encounters in dynamic weather.