Traditional control methods designed for the trajectory tracking problem of under-actuated vehicles often aim to directly stabilize the tracking-error system of differential equations to the origin. This often results in complex control algorithms. This paper introduces a simplified control method for the trajectory tracking problem of an under-actuated Unmanned Surface Vehicle (USV). The proposed method consists of a guidance law for intermediate variables, which are the pseudo yaw angle and the pseudo surge velocity, and a Proportional-Integral (PI) controller. The control term for surge velocity is designed to be bounded, which reduces undesired instability. A model is built based on linear dynamics equations and parameters of an USV. The proposed tracking method is applied to the model to track different trajectories in simulations. The simulation results show that the proposed method effectively tracks different trajectories under various initial conditions. The control term for surge velocity remains stable despite the relatively large initial tracking-error condition.
