Trajectory Planning for Unmanned Surface Vessels in Confined Waters

This paper presents a novel trajectory planning method for unmanned surface vessels (USVs) operating in confined waters. The proposed approach formulates the planning problem as an optimal control problem, considering the vessel's dynamics and environmental constraints. Obstacle avoidance is formulated as a separation problem using the hyperplane separation theorem, while collision avoidance with boundaries is modeled as a containment problem using smooth, differentiable constraints. This formulation allows for efficient solving using gradient-based optimization algorithms. A geometry-based method for initializing auxiliary variables is introduced to improve computational performance. The method is validated through a simulated case study of USV docking in a confined port with static and dynamic obstacles. Results demonstrate the ability to generate optimal, collision-free trajectories that satisfy dynamic constraints and navigate complex environments.