**A Hierarchical Tracking Controller for Quadrotor Without Linear Velocity Measurements**

Yassine Jmili, Nuradeen Fethalla, Jawhar Ghomam and Maarouf Saad

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/62442

#### **Abstract**

[11] Khalil H.K., Grizzle J.W. Nonlinear Systems. 3rd ed. New Jersey: Prentice‐ Hall; 2001.

[12] da Silva Jr. J.M.G., Tarbouriech S. Antiwindup design with guaranteed regions of stability: an LMI‐based approach. IEEE Transactions on Automatic Control. 2005;50(1):

[13] Qi X., Qi J., Theilliol D., Song D., Zhang Y., Han J. Self-healing control design under actuator fault occurrence on single-rotor unmanned helicopters. Journal of Intelligent

[14] Qi X., Theilliol D., Song D., Han J. Invariant‐set‐based planning approach for obstacle avoidance under vehicle dynamic constraints. In: 2015 International Conference on

[15] Boyd S., Ghaoui E.L., Eric F., Venkataramanan B. Linear Matrix Inequalities in Systems

[16] Hu T., Lin Z., Qiu L. An explicit description of null controllable regions of linear systems with saturating actuators. Systems & Control Letters. 2002;47(1):65–78. DOI: 10.1016/

& Robotic Systems. 2016;online first,1–15. DOI: 10.1007/s10846‐016‐0341‐4

Robotics and Biomimetics, IEEE, Zhuhai, China, 6–9 December,; 2015.

and Control Theory. Philadelphia: SIAM; 1994. 205 pp.

750 pp.

136 Recent Progress in Some Aircraft Technologies

106–111. DOI: 10.1109/TAC.2004.841128

S0167‐6911(02)00176‐7

This chapter deals with the position control of quadrotor unmanned aerial vehicle (UAV) when quadrotor's linear velocity is unavailable. We propose a hierarchical tracking controller for quadrotor UAV. The proposed controller does not require measurements of linear velocity of quadrotor. A nonlinear filter that avoids the need for measurements of linear velocity has proposed such that a global stability result is obtained for the position tracking error. However, backstepping based on barrier Lyapunov function has been used for the attitude controller. The control design is achieved by means of the hierarchical control, that is, design the position controller and attitude controller separately. This allows us to choose different nonlinear techniques for each controller.

**Keywords:** Quadrotor UAV, Tracking Control, Nonlinear Filter, Backstepping, Un‐ known linear velocity measurement

### **1. Introduction**

In recent years, multirotor unmanned aerial vehicles (UAVs) have attracted many researchers and became a growing interest in the academic and industrial research. In this chapter, our study focuses on quadrotor UAVs due to its ability to fly in restricted areas. The quadrotor has four rotors controlled by four rotors. Quadrotors have specific characteristics that allow the execution of applications that would be difficult or complex compared with other flying machines. A key issue in making multirotor UAV vehicles feasible and efficient is the control design, consist‐ ing of a navigation system, position and attitude control. This chapter concerns the nonlinear‐

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ity character of the UAV vehicles and focuses on the position and attitude controllers. One of scenarios that could be achieved by the quadrotor is autonomous navigation. Implementing such a mission requires the measurement of the components of vehicle state (position, linear velocity,orientationanglesandangularvelocity)fromGPSsensors.Mostofthe control schemes that have been introduced in the literature rely on the available full state of feedback using definitionofanobserverorrelyontheestimationofvelocityofthevehiclebymeansofderivation of the successive measurements from the used sensors such GPS, etc. [1–3]. However, an additional disturbance may occur in the control loop as a result of the use of the observer. It is also important to validate first convergency of the observer. In addition, the stability of closed loop of complete system controlled by observer has to be assured through checking the compatibility of observerfrequency andcontrollerfrequency [4].In this estimation method,the errors produced by GPS may approach several meters, and in reality, velocity measurement error is growing fast by the induced measurement noise along with numerical integration. Few researchers have solved the problem of linear velocity estimation without the use of GPS, and some of them considered combination and artificial vision and the inertial sensors [5, 6].

In [7], the authors proposed a global exponential observer with a complete order to ensure a continued trajectory of a helicopter (VTOL). To reduce the size of the estimated state vector, a reduced observer introduced in [8], the linear velocity of the quadrotor has been estimated using a complete or partial measure of the acceleration such that the asymptotic stability of the error is obtained. Some other forms of observers have been introduced such as adaptive observer [9], and this approach provided an estimation of the velocity of quadrotor UAV from acceleration measurements calculated by the inertial system, but this method has disadvan‐ tages of slow convergence of the estimated parameters. While the sliding mode observer used in [10] has shown not only the ability to estimate the velocity of quadrotor but also showed its robustness against the external disturbances. The other technique used in the literature to estimate the linear velocity is the filters, and one of these filters is extended Kalman filter that widely applied to nonlinear dynamical systems. In this case, the principle is to use the standard equations of Kalman filter for nonlinear model linearized by Taylor formula of first order and the states of systems can be estimated from the noise measurements. These kinds of filters have been used to estimate the states of quadrotor [11].

In this paper, we propose an approach to solve the problem of position tracking of quadrotor UAV when the linear velocity measurements are unavailable. The proposed controller provides a hierarchical design of the system using assign inner loop for position control and outer loop for attitude control. Each loop has its own control algorithm. The resulting outer control loop, which is based on backstepping, has a simple structure. The inner control loop is based on nonlinear filter-based control design with the aim of estimating the linear velocity of quadrotor.

This paper is organized as follows. In Section 2, the dynamic model of quadrotor UAV is introduced. Section 3 presents the design of position controller based on the nonlinear dynamic model using nonlinear filter-based approach. In Section 4, the attitude controller of rotational system is presented. In Section 5, the overall closed loop system stability is analysed, and simulation results are shown in Section 6.
