Trajectory-tracking controller design of underactuated surface vessels

The main difficulty in the control of underactuated mechanical system is that the system has more degrees of outputs to be controlled than the number of independent inputs. For the general ships, there are only main thrusters and rudder equipped with the ship. The problem of using the available control force to control the three degrees motion of ship can be classified into a kind of underactuated problem. In order to solve the problem of the trajectroy-tracking of underactuated vessels and let the controlled vessel track a reference trajectory quickly. A novel trajectory-tracking controller is designed for underactuated surface ships based on backstepping approach combined with Lyapunov´s direct method, which eliminates the condition of yaw velocity being persistently excited, and make the controlled surface ship follows the reference trajectory like straight line and a circle well. Firstly, the mathematical model of underactuated surface ship is established and the error equation group of trajectory-tacking between the virtual ship and the real ship. Secondly, the full-states feedback control law are acquired by the backstepping technology, which constructs the real control input variables. Finally, the numerical simulation experiments are carried out. The simulation results show that underactuated surface ship can follow its object trajectory well under time-varying environmental disturbances induced by wind, wave and ocean-current. Hence, the full-states feedback control law is robust and effective for the trajectroy-tracking of underactuated vessels.