Ship Course Planning and Course Keeping in Close Proximity to Banks Based on Optimal Control Theory

Ship navigation safety in restricted water areas is of great concern to crew members, because ships proceeding in close proximity to banks will undertake a powerful influence from the so-called ship-bank interaction. The purpose of this paper is to apply the optimal control theory to help helmsmen plan ships’ trajectory and maintain the expected course in restricted waters. To achieve this objective, the motion of a very large crude carrier (VLCC) close to a bank is modeled with the linear equations of manoeuvring and the influence of bank effect on the ship hydrodynamic force is considered in the model. State-space framework is cast in a Multiple-Input Multiple-Output (MIMO) system, where the scheme of model predictive control (MPC) is designed for course planning and the linear quadratic regulator (LQR) is used for course keeping. Simulation results show that the control methods effectively work in ship trajectory planning and course keeping with varying ship-bank distances. And the advantage of adopting speed variation as the second control input is obvious.