## 1 Introduction  
In recent decades, as the demand for ocean exploration has increased, an increasing number of Autonomous Underwater Vehicles (AUVs) have been developed to expand the boundary of human knowledge [1; 2]. Research on controlling these AUVs has received considerable attention from the robotics and marine research communities [3; 4; 5]. Based on the density of a given vehicle, AUVs can be classified as one of three types: positive buoyancy, neutral buoyancy, and negative buoyancy [6; 7]. Compared with positive and neutral AUVs, negative buoyancy AUVs have the advantages of high energy efficiency, high speed, and a long cruising range. For the development of a previous version of the Negative-buoyancy Tri-tilt-rotor AUV (NTAUV), the attitude-stabilization control system was designed based on Immersion and Invariance (I and I) methodology [8; 9]. However, when the NTAUV changes its mode from hover to transition, its asymmetric arrangement of rotors caused disturbance torque to impact the attitude control. To overcome this disadvantage, a negative-buoyancy quad-tilt-rotor AUV (NQTAUV) is proposed in this paper with the design of a disturbance-rejection attitude-tracking system. The NQTAUV has many advantages. The symmetric arrangement of rotors makes attitude stabilization more convenient, and this structure provides the NQTAUV with the capability of rotor-failure recovery. In the case of one or two of its rotors failing, it retains the ability to hover using the remaining rotors [10; 11]. The other advantage of the NQTAUV is that it maintains a level body attitude while moving forward, producing minimum extra hydrodynamic torque and reducing drag force. Quad-tilt rotors provide AUV pitch control within 0\(\sim\)10\({}^{\circ}\) without horizontal motion [12]. Attitude-tracking performance under disturbance is essential for rigid-body vehicles [13]. When the NQTAUV is deployed in water, its attitude control is affected by ocean currents, waves [14; 15; 16], and the motion of its rotors, and they produce disturbance torques that affect the attitude. To reduce the influence of this disturbance, a number of methodologies have been studied. [PERSON] designed a robust depth controller for AUVs in the presence of hydrodynamic-parameter uncertainties and disturbances [17]. [PERSON] designed a sliding-mode controller for combined steering, diving, and speed-control functions based on a six-degree-of-freedom model for the maneuvering of an underwater vehicle [18]. [PERSON] designed an adaptive neural-network controller for the problem of trajectory tracking under external disturbances, control input nonlinearities, and model uncertainties [19]. [PERSON] designed a PID back-stepping controller with the help of a particle-swarming optimization approach in optimizing performance [20]. [PERSON] designed a Lyapunov-based model predictive controller for AUVs to utilize computational resources (online optimization) to improve trajectory-tracking performance [21]. Disturbance rejection has attracted wide attention in recent years, for which disturbance-observer design is a widely studied core concept. A disturbance observer is an artificial system that can estimate the complex disturbances acting on a nominal system, and its controller design procedure can be enumerated in three steps: (1) Designing a controller for the nominal system to achieve stability and other performance improvements under the assumption that the disturbance is measurable; (2) designing a nonlinear disturbance observer to estimate the disturbance; (3) integrating the disturbance observer with the controller by replacing the disturbance in the control law with its estimation yielded by the disturbance observer [22; 23]. Based on disturbance-observer methodology, [PERSON] designed a guidance controller for a small unmanned aerial vehicle (UAV) to achieve a path following the presence of wind disturbances [24]. [PERSON] derived a nonlinear disturbance observer to compensate for the friction of two-link robotic manipulators [22].