A Mixed-Integer Trajectory Optimization Method for Unpowered Aerial Vehicles Formation Reconfiguration

In examining the formation reconfiguration problem for unpowered aerial vehicles, it’s crucial to note that formation position assignment significantly affects performance indices. Traditional trajectory optimization methods that rely on continuous variables often struggle to model this assignment process accurately. To generate a trajectory that optimizes swarm energy for reconfiguration, this paper introduces a method based on mixed-integer programming. First, the configuration position assignment is modeled using integer variables. This discrete assignment is then integrated with continuous trajectory optimization, forming a mixed-integer optimal control problem. This problem is subsequently transformed into a convex one through processes of convexification and discretization. To address this, we design an iterative mixed-integer convex optimization algorithm rooted in sequential convex programming. Numerical simulations validate that our approach efficiently supports multiple unpowered vehicles in their formation configuration. Furthermore, it ensures the position assignments made by the method achieve global optimality.