# Research and Verification of Trajectory Tracking Control of a Quadrotor Carrying a Load
## 1 Introduction  
The quadrotor is the main type of multi-rotor UAV and is the most used type. Because it can perform rapid vertical takeoff and landing and free hovering in the air and other maneuvers that cannot be performed by ordinary aircraft, it has an increasingly wide range of applications. Initially, it was used in the military field, such as controlling aircraft to perform various tasks in dangerous environments, ensuring the safety of human life and property and even participating in rescue operations [1; 2; 3]. The use of quadrotors for transporting supplies in rescue activities is one of the important directions for quadrotor application research. Currently, most solutions involve transporting loads by using ropes to hang them. Not only does the quadrotor maintain its inherent flexibility during flight, but the quadrotor can hover stationary at a designated target location to facilitate the loading and unloading of loads [4; 5; 6; 7]. Therefore, research on the anti-disturbance control of a quadrotor carrying a load has important theoretical significance and practical applications. A quadrotor carrying a load is a typical underdriven system with four control input signals and eight degrees of freedom, including two swing angles. The control problem is more complex compared to the flight control of a quadrotor. Since a quadrotor carrying a load cannot be controlled directly by the drive, the motion of the load is driven by controlling the motion of the quadrotor, so the motion of the load depends on the quadrotor. At the same time, there are uncertain external disturbances, such as wind fields, during the hanging and transportation of the quadrotor. This problem greatly increases the difficulty of designing quadrotor stability control for hanging loads under external perturbations [8; 9]. Some excellent teams at home and abroad have conducted much research on a quadrotor carrying a load and have achieved good results. A dynamic programming method for aquadrotor carrying a load has been proposed in the literature [10]. The method ensures that the load can follow the quadrotor through narrow boundaries without touching them. However, the literature does not consider the environmental interference of various complex interferences, such as the wind field magnetic field. At the same time, the swing angle of the system is not controlled, and the coupling degree is increased. The literature [11] presents a path planning algorithm for quadrotors that models the payload delivered by a hanging rope as a hybrid dynamical system. The experimental results show that this approach is effective in generating an aggressive hybrid and avoidance maneuver trajectory, including state transitions. However, the literature does not consider the suppression of the swing angle of the rope. In [12], a nonlinear adaptive integral backstepping control method is proposed to reduce the impact of load swing on the flight, aiming at the problem that the stability of quadrotor carrying a load system is easily affected by load swing caused by wind disturbance. However, the research on the influence of wind disturbance is relatively superficial, and the data are few. In [13], the authors propose a nonlinear stable quadrotor and its load controller. However, the literature only simulates the flight simulation of the quadrotor and its hanging load on a two-dimensional plane. In the actual three-dimensional space, the coupling degree of the nonlinear term of the system is deepened, and the design method suitable for a two-dimensional plane cannot be simply extended to a three-dimensional one. Therefore, the extension of the control system to a three-dimensional space while preserving the nonlinearity of the system has become the current research direction. In [14], the authors study the control algorithm of a quadrotor which uses rope to carry the load. By using [PERSON]'s matrix method, the literature develops a nonlinear controller that stabilizes the system through the linear part of the quadrotor.