## 1 Introduction  
With the increasing demand for marine equipment over the past decades, different types of marine vehicles have been developed to expand human exploration capabilities [1] from the surface to the bottom of the ocean. Underwater vehicles perform various missions, such as collecting samples [2], acquiring data [3], and repairing marine structures [4]. In accordance with the level of autonomy for self-driving vehicles, underwater vehicles can be classified into remotely operated underwater vehicles (ROV) [5], autonomous underwater vehicles (AUV) [6; 7], and human occupied vehicles (HOV) [8]. ROV consist of a cable that is used for power supply and as a communication line, which is used by the operator to remotely control the ROV [2; 9]; an AUV is autonomous, and it performs motion control and mission planning [10; 11; 12]; an HOV has a life support system, and a pilot inside the vehicle controls the movement of the HOV for precise movement. ROV and AUV are unmanned underwater vehicles, and therefore, they have the advantages of no risk to life and long operation time. However, the densities of these vehicles are similar to that of the water owing to the buoyancy of the material used [13; 14]. This increases the size and drag force, which considerably slows down the speed of the vehicle [15]. In some scenarios, a high-speed underwater vehicle is required to perform time-sensitive missions. Moreover, with the development of deep sea mining [16], a spot hover is a necessary capability for missions such as recharging and payload transition. Traditional underwater vehicles have a cylindrical shape or an open frame. Cylindrical-shaped underwater vehicles have the advantage of a low drag force. They are propelled using fixed thrusters,and some of these vehicles are equipped with vertical and horizon thrusters to provide extra control forces. An ocean glider is an autonomous underwater vehicle used for ocean science [15; 17]; it uses a small change of buoyancy in order to ascend and descend. A fixed wing converts the vertical motion to horizontal motion [18], thus acting like a saw tooth pattern [19]. The energy effect is so high that the glider can continually glide over hundreds of kilometers for months. Open frame vehicles such as an ROV can operate at one spot with the help of multiple rotors [20]; the AUV cannot achieve this [21]. However, the cable connecting the ROV to the mother ship limits the work range of the ROV [2]. A kind of negative buoyancy vehicle is designed to achieve high speed and long cruise range, it is more efficient than traditional AUV at high speed. However, it has to fly in the water to maintain depth, besides, spot hover capability is not achieved [22]. The design and control of an underwater vehicle involves many problems such as the nonlinearity of the model [13; 21; 23], underactuation [24], and the influence of the ocean current, waves, and turbulence [25]. In this paper, we present a negative-buoyancy tri-tilt-rotor autonomous underwater vehicle (NTAUV) to achieve the capability of spot hover and high-speed motion. The NTAUV is illustrated in Figure 1. The NTAUV is heavier than water, has negative buoyancy, and it balances the weight by buoyancy and lift force generated by the fixed wing or thrusters. Further, it operates under three modes: hover, horizontal motion, and transition between them. The NTAUV can hover or slowly cruise by controlling the rotor speed and the tail rotor angle in the hover mode. The hover motion control of NTAUV uses a hierarchical control scheme. The outer layer is position control, and the inner layer is attitude control. Attitude control is the fundamental function of the underactuated system. This paper focuses on hover mode modeling and control, especially attitude control. We design an adaptive nonlinear attitude controller using the immersion and invariance (I&I) methodology. The article is structured as follows.