A First-order Optimization Method for Cooperative Collision-free Trajectory Design for Multiple Unmanned Aerial Vehicles

This paper introduces a novel design method for generating collision-free trajectories for multiple aerial vehicles. Addressing the collision avoidance problem as an optimization challenge with nonconvex constraints presents significant difficulties. Traditionally, such problems have been tackled by linearizing or relaxing constraints. However, in this study, we employed the alternating direction method of multipliers (ADMM) algorithm to directly address the nonconvex optimization problem. The proposed method involves an iterative application of expansive projection steps onto nonconvex feasible sets within each ADMM iteration, ultimately converging the solution to local minima. This iterative process ensures that the resulting trajectories are not only feasible but also optimal in terms of collision avoidance and cooperative movement. We conducted extensive numerical simulations across various scenarios to validate the proposed trajectory design method, and the obtained results consistently demonstrated that the proposed method can effectively generate cooperative, collision-free trajectories for multiple aerial vehicles. Moreover, the converged solutions from the performed simulations confirm the robustness, efficiency, and practical applicability of the proposed approach in real-world situations, highlighting its potential for enhancing UAV coordination in complex environments.