## 1 Introduction  
Most of the marine resources, such as deep-sea manganese nodules, cobalt-rich hulls, and hydrothermal sulfides, exist on the seabed, so seabed development and exploration are one application trend of underwater robots. As a new disk-shaped autonomous underwater vehicle (AUV), the autonomous underwater helicopter (AUH) is dedicated to subsea operations, with many advantages, such as seabed residence, fixed-point hovering, high maneuverability, and anti-flow stability [1, 2]. As to the work pattern (Figure 1), the AUH generally flies from one subsea docking system (SDS) to another, completing tasks that can include communications, equipment maintenance, and charging. When the AUH needs to upload data to the sea surface or be charged, it approaches the SDS at a low speed [3], and the docking is then performed through the acoustic-optical guiding system. The controller's performance of the AUH significantly affects its stability and success rate of docking onto an SDS. As most AUVs have dynamic characteristics, such as tight coupling, strong nonlinear effects, and parameter uncertainty, there remains a difficulty in obtaining an accurate dynamic model. When considering the uncertainty of model parameters and the influence of unknown external perturbation, robust control methods, including the back-stepping and sliding mode controls, are adopted in AUV motion control. With the three-dimensional path following the error model being established based on the virtual guidance method, [PERSON] [4] proposed a path following a robust control system using command-filtered back-stepping control, neural networks, and adaptive control techniques. Moreover, the authorsfrom [5] proposed a back-stepping controller for tracking the desired depth of the AUV's system, which lies on a vertical surface. At present, sliding mode control [6; 7] has been widely studied and applied due to its simple design and easy implementation. [PERSON] [8] designed a terminal sliding mode variable structure control system with fast convergence speeds, high control precision, and strong robustness. [PERSON] [9] developed a sliding mode heading control system for over-actuated, hover-capable AUVs that operate over a range of forward speeds. The proposed control system was also proven in field trials to enhance robust vehicle performance, even when subjected to external disturbances. The hydrodynamic performance of an autonomous underwater vehicle (AUH) can be greatly affected by various factors, including the flow channel, external communication mechanism, external sensors, and other components. Although many hydrodynamic simulations of AUHs use simplified models [10; 11; 12], these models may not accurately capture the complex interactions between the vehicle and its environment. There is a large gap between the hydrodynamic simulation based on computational fluid dynamics (CFD) technology and the real situation; thus, it is unsuitable to use classical model-based control methods for the accurate control of AUHs [13; 14]. Currently, researchers have gradually applied data-driven control methods to underwater vehicle control, such as model-free adaptive control (MFAC) [15], active disturbance rejection control (ADRC) [16], and fuzzy control [17] due to their advantages of having simple parameter adjustments and no model parameter limitations. Strictly speaking, the motion control of the AUH is a nonlinear system, and the system parameters will vary with the working depth and cruising speed. The authors currently use a neuroadaptive learning algorithm [18] and two new integral robust algorithms to deal with the nonlinear system with disturbance [19]. Furthermore, the authors introduced a global differentiator based on higher-order sliding modes (HOSM) and dynamic gains to solve the trajectory tracking problem [20] and proposed an improved active disturbance rejection control method for the output tracking of uncertain plants with unknown control directions [21]. For the docking of AUHs, its accurate low-speed motion control is the basis.