## 1 Introduction  
In recent decades, with the continuous development of marine resources across the world, countries have made important progress in the research and development of intelligent marine robotic technologies and developed various types of marine equipment, such as ocean observation buoys [1], underwater gliders (UGs) [2], unmanned surface vehicles (USVs) [3], unmanned underwater vehicles (UUVs) [4], and ocean unmanned aerial vehicles (UAVs) [5]. However, the main function of traditional marine robots is to realize surface water and underwater rescue operations, sampling, hydrological monitoring, intelligence gathering, and reconnaissance. It is impossible to realize the joint task of aerial, surface water, and underwater operations on the same platform. In order to realize multi-domain tasks, the common choice at present is the cooperative operation of different platforms,which not only wastes a large number of resources but also reduces the reliability of the whole system [6]. In recent years, scholars from various scientific research institutions have developed a new kind of ocean robot, the hybrid aerial underwater vehicle (HAUV) [7]. Combining the advantages of a UUV and a UAV, an HAUV is a new type of marine robot capable of performing various tasks in both water and air media, and research on HAUVs has gradually become a popular research topic in marine exploration equipment. The concept of HAUVs can be traced back to the LPL flying submarine project proposed by Soviet engineer [PERSON] in 1934 [8]. Since the LPL project, researchers have put forward a variety of different ideas for trans-medium vehicle schemes for different mission backgrounds and operational requirements. At present, many researchers focus on the structural design of HAUVs and attempt to explore practical and feasible solutions. According to the different structural forms of HAUVs, the existing research results can be roughly classified into three categories: fixed-wing design, multi-rotor design, and bionic design. In addition to these three main types, there is also a new type of HAUV designed to combine the benefits of both UAVs and UUVs [9]. HAUVs based on multi-rotor design are gradually winning the favor of researchers all over the world because of their significant advantages in vertical takeoff and landing and handling stability. In addition, the other most important factor is that a multi-rotor HAUV can navigate autonomously based on a set closed-loop control system. Due to the comprehensive advantages of multi-rotor HAUVs in terms of kinematic stability and maneuverability in the two media, HAUVs based on multi-rotor configurations are increasingly appearing. At present, research on multi-rotor HAUVs mainly focuses on new configuration design, cross-medium system modeling analysis, and robust control system design and development. In 2014, [PERSON] et al. conducted modeling and application scenario simulation research on their double-layer propeller HAUV [10]. In the initial study, the team used a simple gain-switching PD controller to verify the effectiveness of the modeling method through simulation. Researchers from Rutgers, the State University of New Jersey, designed a PID controller for their HAUV navigator that could adjust parameters based on the operating environment and verified the scheme through simulations and a pool test [11]. To circumvent the singular problems of Euler modeling, the team modeled the navigator's attitude using the quaternion method and successfully performed high-mobility operations [12]. Researchers from the University of Auckland designed a PD controller for the Loon Copter and successfully implemented maneuvers for underwater navigation, underwater attitude adjustment, and taking off and landing across the water [13]. In 2016, a team at the China Air Force Engineering University proposed an active disturbance rejection control (ADRC) algorithm to achieve attitude control of a quadrotor HAUV operating near a water surface while considering ground effect [14].