###### Abstract
Other control techniques in AUVs can include a constrained self-tuning controller for the heading and diving motions [20], and a unified receding horizon optimization scheme for the integrated path-planning and tracking control [21]. Additionally, [PERSON] et al. [22] addressed a three-dimensional (3D) path-following control for underactuated AUVs with parameter uncertainties and external disturbances. Coverage path-planning (CPP) determines a path that moves through all points of a certain area or volume of interest while bypassing obstacles [23]. This procedure allows for several applications, such as mine-countermeasure missions, search and rescue missions, seabed explorations, or offshore inspections. Classical methods include the exact cellular decomposition that divides the free space into simple, non-overlapping regions called cells. These cells, without obstacles inside, provide easy coverage and allow for robot sweeping with simple motions. One of the most used methods in the research field is the Boustrophedon cellular decomposition [24]. Nonetheless, this is defined as an offline method, as it assumes previous knowledge of the area and the polygonal obstacles. Most CPP methods consider the modeling of the environment as a simple planar surface. However, the underwater scenario is inherently 3D and requires a different CPP to cover these surfaces. [PERSON] et al. [25] proposed a novel 3D exploration and coverage methodology for AUVs. [PERSON] et al. [26] presented an online 3D coverage algorithm based on a planar two-dimensional (2D) terrain-covering algorithm. Additionally, [PERSON] and [PERSON] [27] presented an offline 3D CPP algorithm that is suitable for covering seafloor areas, including 3D structure, operating on a bathymetric map. This study continues the work presented in [28] for the design, modeling, and implementation of a path-following algorithm as a GNC architecture for an AUV. The previous work implemented a path-following algorithm for a predefined path, whose waypoints were defined based on a wall-detection algorithm. However, the dynamic coefficients of the vehicle were not accurate, and the mathematical model needed an improvement, with the necessary model validation. Moreover, the control system included a fixed yaw angle of the AUV equal to the slope of the detected wall. This paper develops a four DOFs mathematical model for the AUV using offline parameter estimation procedures based on field test data. This paper also validates an LOS-based, path-following algorithm with the experimental results from two control scenarios (simulation and field test) using the Girona500 AUV platform. First, the model validation allows for the estimation of the hydrodynamic coefficients in the AUV mathematical model. Then, this study advances the path-following algorithm presented in [28] by adding an LOS-based guidance system, which provides the required course angle for the path-following algorithm, allowing for continuous path operation. However, the motion control system does not compensate for environmental forces due to waves and ocean currents that affect the AUV's performance to simplify the vehicle implementation. The path-following scenario is enhanced with additional waypoints, and is tested in both a water tank and a sea environment. This manuscript does not include the wall-detection algorithm developed in the previous work. Nonetheless, the AUV can incorporate it due to the modular architecture of the system. This article proposes a path-following algorithm based on a GNC architecture for an AUV. In Section II, the AUV modeling and simulation are introduced based on the parameter estimation method to determine the four DOFs mathematical model of the vehicle. Then, in Section III, the control design is developed using a LOS-based guidance system with a series of position PID controllers. Additionally, this section defines the path-following waypoints based on a predefined planar coverage area.