## 1 Introduction  
USV is a kind of intelligent offshore platform equipment, which has the characteristics of small volume and fast speed. It can perform tasks in harsh or dangerous environments, which can reduce unnecessary casualties [1]. Travel speed is one of the most important factors to describe the performance level of ships. Many literature works have proven that the propulsion efficiency of the pod is higher than the ordinary propeller-rudder, which can significantly improve the maneuverability and the speed of ships [2; 3]. The research object of this paper is a podded propulsion USV, and based on the analysis, the thrust of the pod and the force acting on the ship hull, the three-DOF planar motion model is established by hypothesis and simplification. The biggest advantage of USV comes from its ability for independent, autonomous travel. Meanwhile, path following is the most basic function of autonomous navigation [4]. For now, the most popular navigation algorithm to implement path following is look-ahead LOS [5; 6]. The main principle of the LOS guidance algorithm is to imitate the behavior of a helmsman, which steers the vehicle towards a lookahead distance (\(\Delta\)) ahead of the projection point of the vehicle along the path. The characteristics of the LOS algorithm lie in that it is light in computation and easy to implement. However, the traditional LOS guidance algorithm has two shortcomings: in the path-following process, the sideslip angle will be generated due to the effects of ocean disturbances; the value of \(\Delta\) is a constant, which cannot be adjusted adaptively. To compensate for the adverse effects of sideslip angle, many efforts have been made by scholars from all over the world. Generally speaking, the simplest way is to measure the sideslip angle directly. In [7], the sideslip angle was calculated by measuring the surge and sway velocities. However, not only are the corresponding measuring instruments (sensors, etc.) expensive, but also the measured data are noisy. Another way is that an integral term was added into the classic LOS guidance algorithm, proposing integral LOS (ILOS) to alleviate the effect of sideslip angle [8]. [PERSON] et al. proved that the \(\kappa\)-exponentially stable ILOS guidance algorithm was derived for curved paths [9]. In addition, [PERSON] et al. treated the sideslip angle as an unknown constant and identified its value with an online adaptive approach [10]. Meanwhile, a novel predictor-based LOS (PLOS) guidance law for the path following of the underactuated marine surface vehicle was proposed [11]. The proposed navigation strategy not only inherited the simplicity of the traditional LOS, but also ensured the fast convergence of the marine surface vehicle sideslip angle. For the issue of time-varying \(\Delta\), [PERSON] et al. presented a nonlinear model predictive control (MPC) approach, which can adjust its value online to achieve smaller overshoot and faster convergence speed compared with the constant \(\Delta\)[12]. A function to adjust \(\Delta\) according to the cross-track error was given in [13]. In [10], only the cross-track was considered, but in this note, both cross-track error and along-track error are taken into account, which is more universal. Besides, the fuzzy algorithm is adopted to optimize the value of \(\Delta\). Due to its small size and high speed, USV is more susceptible to external disturbances. Therefore, both cross-track error and the differential of cross-track error are taken into account when tuning \(\Delta\). The role of the differential of cross-track error is to provide an early judgment, which can enhance the robustness of the system. Modeling, guidance and motion control are three essential elements of path following. There is very much literature investigating the design of the path following controller, and different algorithms are introduced into it, such as classic and variant PID control [13; 14], fuzzy control [15], sliding mode control [16], backstepping control [17], and so on.