## 1 Introduction  
Due to advancements in microprocessors and sensors, quadrotors have recently received much attention, playing an increasingly important role in unmanned aerial vehicles (UAVs). Now, quadrotors can easily hover indoors or outdoors and fly fast with global positioning system (GPS) devices or tiny cameras. Generally, changing the velocities of rotors [1; 2] can generate lift and steering torque to control the attitude and position of the quadcopter. Scholars and engineers have proposed several methods to solve the control problem for a quadrotor. These methods can be divided into: PID control [3; 4; 5], feedback linearization [6], optimal control [7], back-stepping [8; 9], SMC [10; 11; 12; 13], robust control [14], neural control [15; 16], and nonlinear control [17]. To handle uncertainty systematically, researchers have extensively applied SMCs to address the robust control problem of quadrotors. The super-twist control algorithm [18; 19; 20], a second-order SMC, has been studied to alleviate harmful chattering and maintain the robust capability of first-order SMCs. The studies in [21; 22; 23] demonstrate the stability and finite-time convergence of the super-twist control algorithm for single-variable systems through a Lyapunov stability analysis. For instance, [PERSON] et al. [11] studied an adaptive terminal sliding mode for a quadrotor attitude control with specified capability and input saturation. In addition, [PERSON] et al. [12] proposed an observer-based SMC to address model uncertainty and wind perturbation. The recent work in [24; 25] introduced the perturbation observer incorporating enhanced SMC for application in quadrotor UAV control. Recently, several control methods have been proposed to solve the localization or following problem of under-actuated quadrotors, but these methods are still insufficient and have many shortcomings. For example, if the actuator fails or the rotor is damaged, the quadrotor will crash due to a lack of actuator redundancy to restore attitude and position. Tilt-rotor quadrotors [26] can increase the degree of control freedom and provide control redundancy. Compared with under-actuated quadrotors, full-drive quadrotors have more flexibility than under-actuated quadrotors and have recently attracted the research community's attention. [PERSON] et al. [27] proposed a modeling approach for an overdrive quadrotor UAV. They provide a dynamic linearization control that uses higher-order derivatives of the measured output. [PERSON] et al. [28] studied the control of vertical take-off and landing (VTOL) vehicles with bank thrust angle limitation. The proposed control can achieve the primary and secondary goals of asymptotically stabilizing position and direction. Recently, [PERSON] et al. [29] reviewed various UAV designs with fully actuated multi-rotors, in the literature. They introduced the control allocation matrix to categorize the proposed hardware framework and discussed the criteria for optimizing the UAV design. [PERSON] et al. [30] introduced the hardware design of an experimental tilt-rotor drone that uses linear servo motors to control the tilt mechanism. The authors also implemented and tested their PD-based translation and attitude control scheme on the fully actuated prototype quadrotor. To control the hovering and fixed-wing flight of a tilt-rotor UAV and the transition between them, [PERSON] et al. [31] proposed a control scheme, which includes a low-level angular rate controller and a variable mixer, and an LQR following control  
We propose a TRQ model based on translational and rotational dynamics, perturbation, and model uncertainty. Note that the SMC presented for an under-actuated quadrotor cannot be directly applied to a tilt-rotor quadrotor. We propose an SMC scheme with control allocation, exploiting the structural features of rotational dynamics and avoiding chattering in translational dynamics to further enhance the robustness and capability of TRQ systems.