## 1 Introduction  
In recent years, the control scheme design of vertical take-off and landing (VTOL) unmanned aerial vehicles (UAVs) has become a significant research topic. As exemplified by quadrotors, this is partly due to the growing interest in the development of the technology for these robots. Quadcopters are most well known for being small aircrafts with multiple rotors, with under-actuated, nonlinear, and coupled systems. However, these characteristics lead to great control challenges. By controlling the velocity, and consequently, the thrust of each rotor, a translational motion in three directions (\(x\), \(y\), and \(z\)) and a rotation around three axes (roll, pitch, and yaw) are generated. The under-actuated property of quadcopters leads to strong coupling between translational and rotary motions. Therefore, it is an arduous task to control the position or the trajectory tracking of the quadcopter. To deal with this dilemma, the hierarchical control strategy has demonstrated positive performances and it has been widely used to solve trajectory-tracking problems. Since the introduction of quadcopters to the robotic community, numerous projects have been devoted to model and control these platforms,as simple as projects based on linear methods and as complex as nonlinear techniques. In the relevant literature, a great number of controllers have been proposed. Among them, a hierarchy controller for the quadcopter has been developed in [1]. This study uses, a compensated proportional-derivative (PD) control, contributing stable attitude control and accurate position tracking. In [2], a second-order sliding mode controller is developed for the translational dynamic to deal with external negative signal while avoiding the undesired chattering effect. Another nonlinear adaptive hierarchical sliding mode control approach for quadrotors has been developed in [3]. To accomplish trajectory-tracking missions, two controllers have been investigated to solve the problem of the under-actuated nature of the system. Furthermore, a global stability analysis and control design based on the cascade theory has been studied in [4]. The complete closed-loop system was divided into two reduced-order subsystems to deal with the coupling property. The backstepping approach and sliding mode control method has been used in [4] as well. In [5], authors addressed the problem of designing and experimentally validating a controller for steering a quadcopter along a trajectory, while rejecting constant force disturbances. The proposed controller was investigated using the nonlinear adaptive state feedback technique. Other approaches have been widely used in trajectory tracking control, such as the backstepping technique and the adaptive control algorithm. For instance, a flight controller with a disturbance observer was designed using the backstepping technique, which can be seen in [6]. In [7], a nonlinear adaptive algorithm was used for a trajectory tracking control problem for a quadcopter with parametric uncertainty. Combined with the neural network algorithm, the adaptive control algorithm was applied to elaborate a controller for the trajectory tracking for a quadcopter in [8]. In addition, in [9], the adaptive algorithm was used in addition to an adaptive sliding mode observer for fault diagnosis in the quadcopter's actuator. All of the aforementioned control approaches have proven to be successful in simulation. Some approaches have proven to be successful in experimental environments too, but only under specific operating conditions. Hence, the dynamic properties of the quadcopter are often neglected, which implies that the overall quadcopter dynamics are not represented for effective control. The use of intelligent approaches could be a solution to this conflict. For example, in [10], the fuzzy logic control technique was employed to implement a fuzzy hitting control law, in order to reduce the chattering phenomena on a conventional backstepping sliding mode controller.