## 1 Introduction  
The technical advances of GPS, navigation equipment, battery system, electrical power unit, as well as global trends such as complex urban transportation and climate change have accelerated research on unmanned aerial vehicles (UAVs). In particular, the movement to utilize UAVs for logistics and urban delivery centering around the megacorporation of Amazon and UPS has fundamentally changed the conventional automotive-based delivery system. With recent advancements in both hardware and software, multi-rotor UAVs quadrotors have become much smaller, lighter, and computationally rich. They have significant maneuverability, long flight times, and fast on-board computation. They enjoy almost all the capabilities of any ground vehicle with an added advantage in various 3-D motions [1, 2]. UAVs have been applied to agricultural management, in the response to forest fires and fields of disaster, aerial cinematography, and pollutant material measurement and removal in place of human beings. Quadrotor UAVs have garnered even more interest owing to their simple design, small size, light weight, and efficient maneuverability. However, stable and credible maneuverability of the quadrotor UAVs is essential because they can fall or crash, and their high rotation speed can cause severe accidents. The main control constraints of the quadrotor UAVs are attributed to the underactuated navigation in a 6-degree configuration space with four actuators, a highly nonlinear dynamic problem, and uncertainty problems, including environmental disturbances and unknown varying loads. Therefore, an effective and robust controller is required to obtain safe and reliable flight performance of the quadrotor UAVs [3, 4, 5]. Linear control schemes [6; 7; 8; 9; 10; 11; 12; 13; 14] initially applied for the navigation task of the quadrotor UAVs have often undergone application limits because the widely used feedback linearization control cancels the useful nonlinear dynamics and some linear controls cannot cope with the properly excessive perturbations of the quadrotor UAVs. To conserve the high control performance of the quadrotor UAVs, nonlinear backstepping control (BSC) [15; 16; 17] is generally utilized to address the aforementioned coupled higher-order nonlinearities for quadrotor UAVs [18; 19; 20; 21; 22; 23]. However, the conventional BSC method has some drawbacks, despite its popular approach and advantage for nonlinearities. The first issue is the repeated high-order differentiation problem of a virtual stabilizing control designed in the recursive steps that causes complexities in the whole control system. As a potential solution to this issue, tracking differentiator methods [24; 25; 26; 27; 28] have recently been studied. Furthermore, a second-order finite-time tracking differentiator [29; 30; 31; 32] was designed to obtain finite-time convergent performance of the tracking differentiator adopted in the previous BSC system. However, high gains of the BSC system to guarantee the robustness to the uncertainty result in excessive control input in the actuators, which can generate actuator failure. Therefore, as another solution to the uncertainty issue without high increase of the actuator input, several disturbance observers to estimate unknown uncertainties have been developed [33; 34; 35; 36; 37]. A disturbance observer studied in [33; 34] was designed under the assumption of a slow variation of uncertainties. Therefore, the application of this observer to the real application can be limited. The extended state observer (ESO) [35] has the problem of long time-integration errors that can influence the position information. This further causes degradation of the estimation accuracy of the observers. Recently, advanced disturbance observers that utilize the structure of tracking differentiators were developed [36; 37]. However, a slower convergence rate of the observer state of this observer degrades the estimation performance of the observer.