Phased berthing trajectory planning method based on Bezier curves for inland vessels

To handle the berthing trajectory planning problem for inland vessels, this paper proposes a phased berthing trajectory planning method based on Bezier curves with multiple constraints and uncertainties. A maneuvering model group (MMG) model for twin-propeller twin-rudder inland vessels is built with considering the influence of current and wind. Then, a trajectory planning method accounting for multiple constraints is proposed. Bezier curves are used to plan the berthing trajectory waypoints, and the least squares fitting method is applied to convert the discrete waypoints into a continuous and differentiable reference trajectory. By combining the vessel kinematic characteristics with a speed assignment mechanism, the berthing trajectory is divided into multiple segments, with each segment assigned an appropriate speed. The trajectory is further endowed with time, heading, and speed. Finally, Wuhan Yangluo Port is used as a simulation environment to compare the effectiveness of the proposed berthing trajectory planning method with the traditional path planning method by using a proportional integral derivative (PID) control method. The simulation results show that the proposed method can control the vessel heading error to within 10° and the berthing residual speed to below 0.03 m/s when the vessel is stabilizing, demonstrating a certain advantage over traditional methods.