## 1 Introduction  
Quadrotor unmanned aerial vehicles (UAVs) are well-suited to various applications, including vertical takeoff and landing [1] and flexible trajectory tracking [2]. Consequently, they have garnered significant attention from developers worldwide, stimulating extensive research in this field. Consequently, quadrotor UAVs have found extensive utilization across various civilian domains [3; 4; 5; 6; 7]. Nevertheless, the design of a UAV flight control system, be it for autonomous or non-autonomous flight, often presents challenges concerning sensor technology, hardware, and software design. The quadrotor UAV represents a highly complex nonlinear control system that has garnered considerable interest among researchers in the field of automatic control. Trajectory tracking control has consistently been a focal point of research in the autonomous flight control of quadrotor UAVs. Among the commonly utilized control methods, linear control strategies [8] offer simplicity and ease of design and implementation. However, the inherent nonlinear and strongly coupled characteristics of quadrotor UAV dynamics impose numerous limitations on the effectiveness of these linear control strategies. Moreover, quadrotor UAVs are consistently exposed to external and internal disturbances during autonomous flight operations in complex scenarios, rendering the existing linear control strategies challenging to apply in practical settings. To address the limitations of linear control strategies, previous studies have proposed various nonlinear control strategies [9; 10; 11; 12; 13; 14]. Robust nonlinear control techniques, in general, enhance flight stability, ensuring satisfactory performance even in the face of unpredictable environmental changes. They enable flexible maneuverability and precise trajectory tracking. Initially, nonlinear control techniques were employed to govern the vertical takeoff and landing (VTOL) of three-degrees-of-freedom helicopters [15]. Controller design for quadrotor UAVs poses greater challenges due to the inherent strong coupling between the body frame dynamics and the yaw, pitch, and roll motion, in contrast to helicopters. Numerous studies have explored different nonlinear controllers for diverse autonomous flight control tasks of quadrotor UAVs, including backstepping controllers [10; 11], sliding mode controllers [12; 13], and other related adaptive nonlinear controllers [14]. The pioneering work of Reference [16] introduced a nonlinear controller for quadrotor aircraft. The authors developed a dynamic feedback controller for hovering flight, utilizing a technique known as exact feedback linearization. The simulation results presented in the paper demonstrated acceptable performance, even in the presence of external disturbances. However, the design of controllers using feedback linearization necessitates an exact model with stable zero dynamics to compensate for the nonlinear terms. However, in practice, the dynamic uncertainty and external disturbances that are inherent in quadrotor flight pose challenges in achieving accurate model predictions, rendering the feedback linearization control strategy infeasible for real-time trajectory tracking control. Consequently, to apply this feedback linearization control strategy in practical applications, it should be augmented with another control strategy that incorporates quadrotor model prediction, as suggested in Reference [17]. The backstepping control strategy [11] is widely employed in robot control as one of the most commonly used methods. Its fundamental principle involves recursively stabilizing a closed-loop backstepping system. Analysis and design of this strategy can be carried out using Lyapunov stability theory. When designing controllers for quadrotor unmanned aerial vehicles using the backstepping control strategy [18], the design of control laws is dependent on the tracking error. Consequently, a significant tracking error leads to a substantial speed jump in the control signal.