Robust Attitude Tracking Control for a Quadrotor Based on the Uncertainty and Disturbance Estimator

In this paper, a robust control method based on the uncertainty and disturbance estimator (UDE) is developed to achieve the attitude tracking control for a quadrotor. To facilitate the control design, the coupled terms in the roll, pitch and yaw dynamics are lumped into the uncertainty term and the remained dynamics can be regarded as decoupled subsystems. As a result, for each subsystem, the lumped uncertainty term contains all the coupled terms, uncertainties and disturbances, then the UDE method is applied for the uncertainty compensation. Compared with the existing UDE control works, the introduced filtered tracking error dynamics simplifies the controller design and implementation. Furthermore, the stability analysis of the closed-loop system is established and experimental studies are carried out to illustrate the effectiveness of the developed control method. INTRODUCTION As a promising autonomous system, the quadrotor is designed to fly in complex environments to complete specific missions while offering great autonomy, like rescue and search, remote inspection, surveillance, military applications [1]. The quadrotor has advantages of small size, light weight and ability of vertically taking off and landing. Thus, it holds high maneuverability and has attracted much attention from the research communities. In order to achieve the desired performance, there are usually two sub-problems in the control for the quadrotor : (a) the at∗Address all correspondence to this author. titude control; (b) the position control [2]. The dynamics analysis shows that the position and attitude subsystems of the quadrotor are cascade interconnected [2, 3]. Since the position controller generates a reference attitude set points for the attitude controller, the control problem mainly focuses on the attitude control [4–6]. Furthermore, the complex working environment, various payloads, lacking of accurate model knowledge will generate internal uncertainties and external disturbances. The uncertainties and disturbances compensation is an challenging problem in engineering applications. In this paper, the quadrotor attitude control problem in the presence of coupled dynamics, modeling uncertainties and external disturbances is considered. The quadrotor attitude control has been investigated using various control methods [4, 7–13]. The effectiveness of classical PID (proportional-integral-derivative) controller and LQ (linear quadratic) were investigated in [4]. However, these linear controllers are not easy to deal with the highly nonlinearities. Since the model-based controllers, such as feedback linearization [7], dynamic inversion [8], require the exact knowledge of the model, they cannot handle the uncertainties. The sliding mode control is robust to the large uncertainties, but its switching logic will lead to the chattering phenomenon [9, 10]. The robust methods in frequency domain like H2, H∞ control methods introduced in [12, 13] work well only within a frequency bandwidth limit. In this paper, in order to achieve the attitude control of the quadrotor in the presence of internal uncertainties and external disturbances, a control method based on the uncertainty and disturbance estimator (UDE) is adopted. The UDE method, which was proposed in [14], has many advantages in both design and 1 Copyright c © 2015 by ASME implementation respects and its excellent performance in handling the uncertainty and disturbance yet with very easy tuning and implementation has been demonstrated in recent years through both theories (including extensions to both linear [14,15] and nonlinear systems [16–20], systems with delays [15,17] etc.) and wide applications (covering mechatronics and robotics [21], electrical machines and drives [14, 20], renewable energy [22], aerospace and automotive systems [23,24] etc). The basic idea of the UDE method is that in the frequency domain an engineering signal (the lumped system uncertainty and external disturbance) can be approximated by putting it through a filter with the appropriate bandwidth. The main contributions of this paper are as follows: 1) Extending the UDE method to the decoupling control. The key idea is that lumping the coupled dynamics into an uncertainty term, such that the remained dynamics can be regarded as decoupled subsystems. For each subsystem, the UDE method can be applied individually for the uncertainties compensation. 2) Compared with the existing UDE control works, the filtered tracking error dynamics is introduced to simplify the controller design and implementation. The rest of this paper is organized as follows. Section 2 illustrates the preliminaries about the quadrotor dynamics. Section 3 is devoted to system decoupling and Section 4 presents the attitude tracking controller design. The stability analysis of the closed-loop system is presented in Section 5 and the experiment results are shown in Section 6. Finally, Section 7 gives the conclusions. PROBLEM FORMULATION AND PRELIMINARY As shown in Fig.1, the quadrotor has six degree of freedoms which are controlled by four rotors installed in its arms. The rotation of these propellers generates upward lifting forces and torques along their spinning axes. Two of these propellers rotate clockwise and the remaining rotate anticlockwise. The quadrotor adjusts its height, position, yaw, pitch, roll and completes taking-off, landing actions by changing the speeds of four rotors. The dynamic model is under those assumptions: the structure of quadrotor is supposed to be rigid and symmetric, thrust and drag are supposed to be proportional to the square of rotor speed and the origin of the body frame is fixed at the center of mass. The thrust and torque generated by each propeller is defined by fk = bωk (1) τk = dωk , k = 1,2,3,4 (2) where ωk is the angular speed of kth motor, b is the positive thrust constant, and d is the positive drag constant. The torques τφ τθ