## 1 Introduction  
Nearly two-thirds of the Earth is covered by oceans but only a few areas have been thoroughly explored. Unmanned marine vehicles are suitable for developing marine resources. Over the past decade, the increasing worldwide interest in military reconnaissance, homeland security, shallow-water surveys, environmental monitoring, and commercial and scientific issues associated with oceans has resulted in the increase in demand for the development of unmanned surface vehicles (USVs) with advanced control capabilities [1]. USVs are usually controlled remotely by humans; thus, an effective and reliable guidance, navigation, and control system for the autonomous sailing of USVs is important. Trajectory tracking is a typical motion control problem for USVs, which is considered with the design of control schemes that force a USV to reach and follow a time parameterized reference trajectory. In the past few decades considerable research efforts have been devoted to the trajectory tracking problem of ships or USVs. [PERSON] and [PERSON] [2] transformed a model into a triangular-like form through a coordinate transformation to use integrator backstepping in developing a tracking control law for an underactuated ship. In [3], the authors presented a solution based on previous work by [PERSON] and [PERSON] to the problem of combined trajectory tracking and path following for fully actuated autonomous marine vehicles with non-negligible dynamics. A multivariable sliding-mode control (SMC) law was proposed for the trajectory tracking problem on the basis of nonlinear horizontal motion dynamics of a class of marine vessels in [4]; the ship positions and yaw angle were simultaneously tracked well. In [5], the USV could track desired arbitrary trajectoriesusing a nonlinear robust model-based sliding mode approach; experiments demonstrated that the method was effective. In [6], the authors designed a novel trajectory tracking robust controller through a vectoral backstepping technique with an observer to provide an estimation of unknown disturbances; the proposed trajectory tracking control scheme could provide good transient and steady-state performance for the considered ship system. To realize the trajectory planning and tracking of a USV, the trajectory tracking control law in [7] was based on an SMC approach, and the trajectory of the USV finally converged into the desired target trajectory well. The hydrodynamic coefficients of the surface ship at high speed are difficult to be accurately estimated first; thus, in [8], the author proposed an adaptive output feedback controller based on neural network feedback-feedforward compensator in controlling a surface ship at high speed to track a desired trajectory. A novel trajectory following controller for underactuated surface vessels based in Active Disturbance Rejection Control (ADRC) technique was proposed in [9]. The accurate straight line and curve trajectory tracking for USV were realized using this controller. In order to implement high-speed trajectory tracking tasks for USVs, the authors in [10] put forward a line of sight (LOS) guidance algorithm based on the SF (Serret-Frenet) coordinates framework (SFLOS) and bio-inspired algorithm. In [11], the authors used the non-singular terminal sliding mode control technique and a robust homogeneous differentiator to propose a finite-time trajectory tracking control approach for an USV with unknown dead-zones and unknown disturbances. Using the method, the USV can reduce chattering and track the desired trajectory effectively. In [12], addressed through an integral sliding mode control and homogeneous disturbance observer, a finite-time trajectory tracking control of USV is proposed, considering input saturations and unknown disturbances. Using this control scheme, the actual trajectory can track precisely the desired trajectory and tracking errors can be rendered to zero in a finite time.