I. Introduction
GREAT attention has been paid to the development of surface vessels over the past decades due to its wide applications in rescue, search, exploration, and reconnaissance missions. Since the surface vessel is a system with nonholonomic constraints that is not able to be stabilized by a continuous time-invariant feedback [1], [2], various nonlinear control schemes have been proposed for the vessel's motion control [3] –[17]. Interested readers may refer to [18] or [19] for a comprehensive literature review of vessel design and control. In this paper, we list some of the recent results related to the path following control of a vessel in a predefined geometric trajectory that is time independent [20]. In [21], together with the Serret–Frenet equations, a backstepping path following controller using the rudder deflection was proposed for a surface vessel. By including the sideslip angle in the control design for the desired heading angle, a robust composite path following controller for the surface vessel under ocean disturbances was presented in [22]. A dynamical virtual ship guidance and path following method was developed in [23], where feedforward approximation, dynamic surface control, and robust neural damping techniques were used to overcome the uncertainties and disturbances. In addition, saturated path following [6], [24] and coordinated path following controls [7], [8], [25] for vessels were respectively investigated. An effective and popular path following method for surface vessel that has been vastly explored due to its simplicity and intuitiveness is the line-of-sight (LOS) guidance [26]–[29]. This method implements a lookahead distance mimicking an experienced sailor, generates the path parameter update law, and computes the desired heading angle to be fed into the inner dynamics loop. Furthermore, extensions to LOS, namely, adaptive LOS [30]–[32], integral LOS [33], [34], and error constraint LOS [35], [36] methods, were developed to alleviate the effects of uncertainties and sideslip angle.