The formation rendezvous of multiple underwater unmanned vehicles (UUVs) necessitates comprehensive consideration of various complex constraints, including kinematics, collision avoidance, and communication. However, existing methods inadequately address these constraints, making it challenging to meet practical needs. In response to these issues, this paper presents a rendezvous points allocation method and a trajectory planning method for formation rendezvous based on dynamic parameter particle swarm optimization (DPPSO) optimizing polynomial trajectories. First, various constraints involved in the formation rendezvous of UUVs are defined, including state constraints, velocity constraints, distance constraints, and turning radius constraints. Subsequently, considering the turning radius and heading angle constraints, temporary trajectories for UUVs are generated using the Dubins curve in the rendezvous points allocation. An evaluation function that accounts for trajectory length and uniformity is designed, ultimately resulting in the optimal allocation scheme. Ultimately, the polynomial trajectory planning method generates initial trajectory clusters. By integrating constraints into the DPPSO algorithm’s fitness function, the boundary conditions of the polynomial trajectories are iteratively optimized to derive trajectories that satisfy all constraints. In the simulation, the proposed method was used for rendezvous point assignment in the desired rectangular formation. The simulation results demonstrate that the proposed method provides a rendezvous point assignment solution that meets the design requirements. Furthermore, based on the rendezvous point assignment for the rectangular formation, the method proposed in this paper was applied to trajectory planning for formation rendezvous. The simulation results show that the generated trajectory successfully achieves the formation rendezvous while satisfying multiple constraints.
