Dubins-CPSO: A Hybrid Static–Dynamic Method for Coordinated Trajectory Planning of Multiple UAVs

For the problem of multi-UAV cooperative trajectory planning, this study proposes an integrated static–dynamic trajectory optimization method based on a Dubins-CPSO algorithm. An improved Dubins static path planning method utilizing virtual “Intermediate Points” is introduced, and the reference trajectory generated by this method is employed to design the fitness function for the CPSO algorithm. Within the CPSO-based dynamic optimization framework, real-time local trajectory adjustments are performed by incorporating the UAV’s current state and multi-dimensional physical constraints. This approach combines the high reliability and low command variation rate of conventional algorithms with the flexibility and strong disturbance robustness of intelligent algorithms, achieving complementary advantages. The result is a flight trajectory planning method that is more compatible with the physical mechanisms of the aircraft while possessing a degree of autonomy and intelligence. The simulation results demonstrate that the proposed algorithm can adapt to uncertain initial conditions in the studied scenarios. Furthermore, under interference, it exhibits superior real-time regulation capability compared with traditional algorithms alone and greater robustness and practicality than standalone intelligent algorithms. This provides a more implementable trajectory planning solution for UAVs with strict physical constraints in engineering applications.