## 1 Introduction  
AUV is a kind of marine equipment that plays a major role to improve the human life, such as marine environment exploration, marine resource monitoring, pelagic survey, seabed resource exploitation, military mission, and so forth [1; 2; 3]. It is increasingly becoming a hot topic for research in the world. Limited by its own energy consumption and endurance, AUV is mostly used to carry sensors for ocean exploration. The research object of this paper is an underactuated AUV, and, based on the analysis, the horizontal planar motion model is established by hypothesis and simplification.  
For now, three different types of control technologies play a crucial role in the development of AUVs: set-point control, trajectory tracking control and path following control [4]. Set-point control enables AUV to reach the target point as a desired attitude without any requirements for the path. Trajectory tracking control enables AUV to track the time parameterized reference path. Path following control enables AUV to converge and follow the desired path without any time specification. The motion control system of AUV is susceptible to external disturbances. Obviously, path following control is more robust and more practical. [PERSON] presents that path following is the most basic function of autonomous navigation [5], and the research problem of this paper is path following of AUV.  
In recent years, many path following control methods have been well verified in theory, such as fuzzy control [6; 7], backstepping control [8; 9], sliding mode control [10; 11], etc., [12; 13]. Specifically, an adaptive fuzzy control method is presented to stabilize the underactuated surface vessel (USV) to the desired position [14]. However, the fuzzy method can not adapt to the change of a controlled object and has poor robustness. An adaptive nonlinear second order sliding mode controller is designed in [15], and a lake experiment verified the effect of the method under linear tracking. However, it does not apply to curve tracking. Backstepping is mostly used for three-dimensional path following, and its control law is usually characterized by multiple parameters adjustment. Considering the complexity of the whole control system of AUV in practical application, the simple design of the control law with less parameters adjusting is more suitable. LOS guidance for underactuated ship path following is presented in [16], which is often used in a way-point ship control practice. Now, the most classic and stable method of path following is LOS guidance law combined with heading controller, which has been verified in practice and applied to the path following of AUV, remotely operated vehicle (ROV), USV and other intelligent machines. The guidance law aims at calculating the desired heading. The control law is introduced to make the current heading reach the desired heading. Hence, the effect of path following is closely related to the guidance law and the control law [17], especially the former. The reason is that this special guidance law exploits the geometry relationships to generate a yaw angle known as the approaching angle, which is fed into the control system. In other words, the control system tracks the reference yaw angle signal together with the specified velocity tracking [18]. In this paper, the path following controller of AUV is designed based on the classical LOS, which aims at realizing precise tracking of arbitrary curves.  
The remainder of this paper is organized as follows: Section 2 concludes the literature review, introduces the methods in the paper and presents the contributions. In Section 3, the model of AUV is given. Section 4 introduces the problem statement and some preliminaries. In Section 5, the designed guidance law and the controller are deduced. At the same time, the stability analysis is given by a _Lyapunov_ theorem. In Section 6, simulations and experiments validate the previous analyses of the method. Section 7 summarizes the conclusions of this work.