Trajectory Planning Method for Multi-UUV Formation Rendezvous in Obstacle and Current Environments

Formation rendezvous is a critical phase during the deployment or recovery of multiple unmanned underwater vehicles (UUVs) in cooperative missions, and represents one of the core problems in multi-UUV cooperative planning. In practical marine environments with obstacles and currents, multiple constraints must be simultaneously satisfied, including obstacle avoidance, inter-UUV collision prevention, kinematic limitations, and specified initial and terminal states. These requirements make energy-optimal trajectory planning for multi-UUV formation rendezvous highly challenging. Traditional integrated cooperative planning methods often struggle to obtain optimal or even feasible solutions due to the complexity of constraints and the vastness of the solution space. To address these issues, a dual-layer planning framework for multi-UUV formation rendezvous trajectory planning in environments with obstacles and currents is proposed in this paper. The framework consists of an initial individual trajectory planning layer and a secondary cooperative planning layer. In the initial individual trajectory planning stage, the Grey Wolf Optimization (GWO) algorithm is employed to optimize high-order terms of polynomial curves, generating initial trajectories for individual UUVs that satisfy obstacle avoidance, kinematic constraints, and state requirements. These trajectories are then used as inputs to the secondary cooperative planning stage. In the cooperative stage, a Self-Adaptive Particle Swarm Optimization (SAPSO) is introduced to explicitly address inter-UUV collision avoidance while incorporating all individual constraints, ultimately producing a cooperative rendezvous trajectory that minimizes overall energy consumption. To validate the effectiveness of the proposed method, a simulation environment incorporating vortex flow fields and real-world island topography was constructed. Simulation results demonstrate that the proposed hierarchical trajectory planning method is capable of generating energy-optimal formation rendezvous trajectories that satisfy multiple constraints for multi-UUV systems in environments with obstacles and ocean currents, highlighting its strong potential for practical engineering applications.