Safe formation and path planning method for unmanned surface vessels in restricted navigation environments

This paper investigates safe formation control and path planning for multiple unmanned surface vessels (USVs) operating in restricted and obstacle-constrained waters. A cooperative control framework is proposed by integrating nonlinear model predictive control (NMPC), an adaptive virtual-obstacle replanning strategy, and a trajectory-prioritised formation-transformation strategy. When the reference trajectory repeatedly loses progress near a narrow obstacle gap, the virtual-obstacle diameter and rollback distance are increased iteratively until a collision-free replanned trajectory is obtained or the prescribed iteration limit is reached. For narrow-waterway navigation, the formation is reconfigured from a lateral arrangement to a longitudinal or compact sequential arrangement before entering the restricted region and is restored after passage. A first-order Markov process is used to generate time-varying generalised disturbances, and the resulting trajectory and tracking errors are compared with the nominal condition. MATLAB simulations evaluate local-difficulty escape, narrow-waterway formation transformation, moving-obstacle avoidance, and extensions to a four-USV formation. Real-USV experiments further demonstrate the implementation of the formation-transformation procedure. The results support the feasibility of the proposed framework under the tested constrained-water conditions.