Nonlinear model predictive dynamic positioning control with nonlinear thrust allocation for fully actuated vessels under thruster magnitude and rate saturations

A dynamic positioning (DP) system for a fully actuated vessel allows the vessel to maintain its position and heading against external environmental disturbances by means of its own thrusters. For DP of the fully actuated vessel equipped with azimuth thrusters under input magnitude and rate saturations, this paper develops a nonlinear model predictive control (NMPC) scheme with nonlinear thrust allocation (TA). The objective function of the receding horizon optimization problem considers the DP regulating accuracy, thruster power consumption, thruster azimuth rate, vessel velocity limitations, a penalty function of a thruster configuration matrix, and input rate saturation of thrusters. The constraints of the receding horizon optimization problem include the input magnitude saturation of thrusters and nonlinear system dynamics of the fully actuated vessel. The receding horizon optimization problem is solved numerically utilizing the sequential quadratic programming method. The optimal azimuth angles and thrust for the thrusters can be directly adopted to thruster control without separated TA algorithms, which allows the fully actuated vessel under both the input magnitude and rate saturations of thrusters to reject the unknown environmental disturbances and maintain its position and heading at desired values accurately with minimized power consumption and thruster tear-and-wear. Simulations on a fully actuated model vessel named Cybership III are carried out to demonstrate the effectiveness of the developed NMPC scheme for DP of the fully actuated vessel.