Modeling and Adaptive Tracking Control of a Quadrotor UAV

The dynamics of UAV’s have special features that can complicate the process of designing a trajectory tracking controller. In this paper, after modelling the quadrotor as a VTOL UAV, a nonlinear adaptive controller is designed to solve trajectory tracking problem in the presence of parametric and nonparametric uncertainties. This controller doesn’t need knowing any physical parameters of the quadrotor, and there isn’t need to retune the controller for various payloads. In this approach, the control of a quadrotor is performed by using decentralized adaptive controllers in the inner (attitude control) and outer (translational movement control) loops. The outer loop generates the instantaneous desired angles for inner loop. The inner loop stabilizes the orientation of the vehicle. Inverse kinematic of robot is used to convert outputs of the outer loop to inputs of the inner loop. The controller needs some unknown physical parameter to generate control signals. A robust parameter identiier estimates the required parameters for the outer control loops. Simulations are carried out to illustrate the robustness and tracking performance of the controllers. DOI: 10.4018/ijimr.2012100105 International Journal of Intelligent Mechatronics and Robotics, 2(4), 58-81, October-December 2012 59 Copyright © 2012, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. as wind gust are some of the basic difficulties associated with the control of such systems. Therefore, an advanced control strategy is required to achieve good performance of the controller. Many researchers have solved the trajectory tracking problem for UAV’s in different ways. Das, Lewis, and Subbaro (2009) used backstepping approach for controlling a UAV. In this study aerodynamic forces and moments are estimated by neural networks as a method for handling unknown nonlinearities. A nonlinear adaptive controller for the quadrotor was proposed in Madani and Benallegue (2008). This controller which is based on backstepping technique is combined with neural networks. Huang, Xian, Diao, Yang, and Feng (2010) presented a backstepping based techniques to design a nonlinear adaptive controller which can compensate for the mass uncertainty of the vehicle. Michini and How (2009) developed an L1 adaptive output feedback control design process. This controller has robustness to time delay and actuators failure. However, only linear methods are applied in this paper. In Dierks and Jagannathan (2010), output feedback control of a quadrotor UAV using neural networks is performed. Nicol, Macnab, and Ramirez-Serrano (2011) proposed a new adaptive neural network control to stabilize a quadrotor helicopter against modeling error and considerable wind disturbance. The new method is compared to both dead zone and emodification adaptive techniques. Roberts and Tayebi (2011) presented an adaptive positiontracking control scheme is proposed for a UAV for a set of bounded external disturbances. Raffo, Ortega, and Rubio (2010) used an integral predictive and nonlinear robust control strategy to solve the path following problem for a quadrotor. Aerodynamic disturbances and parametric uncertainties are considered in this paper. In Mhammed and Hicham (2009) a high gain observer and sliding mode controller is designed which allows on-line estimation of the roll and pitch angles as well as all the linear and angular velocities of the vehicle. Under the restriction that only the inertial coordinates and yaw angle are available for measurement. Das, Lewis, and Subbaro (2009) apply dynamic inversion to the inner loops, which yields internal dynamics that are not necessarily stable. Instead of redesigning the output control variables to guarantee stability of the internal dynamics, a robust control approach is used to stabilize the internal dynamics. In Lee, Kim, and Sastry (2009) two types of nonlinear controllers for an autonomous Quadrotor helicopter are presented. A feedback linearization controller, which involves high-order derivative terms, and the second type involves a new approach to an adaptive sliding mode controller using input augmentation. In Benallegue, Mokhtari, and Fridman (2008) a feedback linearization based controller with a high-order sliding mode observer running parallel is applied to a VTOL unmanned aerial vehicle. Zhang, Quan, and Cai (2011) discussed the attitude control of a quadrotor aircraft subject to a time varying and non-vanished disturbances and stabilized using a feedback controller with a sliding mode term. Efe (2011) presented different control architectures; a robust control scheme that can alleviate disturbances. A Proportional Integral and Derivative (PID) type controller with noninteger order derivative and integration is proposed as a remedy. A neural network is used to train to provide the coefficients. Zemalache and Maaref (2009) applied a fuzzy controller based on on-line optimization of a zero order Takagi–Sugeno fuzzy inference system, which is tuned by a back propagationlike algorithm, for a drone. It is used to minimize a cost that prevents an excessive growth of parameters. In this paper some uncertainties are considered. Orsag, Poropat, and Bogdan (2010) used an innovative method to solve the quadrotor control problem, which is based on a discrete automaton. This automaton combines classical PID and more sophisticated LQ controllers to create a hybrid control system. Fahimi and Saffarian (2011) presented an innovative 60 International Journal of Intelligent Mechatronics and Robotics, 2(4), 58-81, October-December 2012 Copyright © 2012, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. approach that uses the spatial three-dimensional coordinates of a point on the helicopter’s local coordinate frame other than its centre of gravity, called the control point, and the helicopter’s yaw angle as four control outputs. With this choice of control outputs, the helicopter’s input–output model becomes a square control system. Vision based control of UAVs is discussed in Guenard, Hamel, and Mahony (2008); Mahony, Corke, and Hamel (2008); Bourquardez, Mahony, Guenard, Chaumette, Hamel, and Eck (2009); García Carrillo, Rondon, Sanchez, Dzul, and Lozano (2011) and Eberli, Scaramuzza, Weiss, and Siegwart (2011). In Tarhan and Altug (2011), catadioptric systems in UAVs to estimate vehicle attitude using parallel lines that exist on many structures in an urban environment was used. In order to increase the estimation and control speed an Extended Kalman Filter (EKF) was used. Most of these control schemes don’t consider parametric and nonparametric uncertainties in their models. In addition most of them were ignoring important practical issues such as dynamics of actuators and battery discharging during flight time. It is important also to note that he quadrotor structure and its mass are constant but quadrotor payload can change in every mission. Therefore, mass properties of quadrotor are changing and a time-invariant feedback control could not provide a satisfying performance. The contribution of this paper is to describe a clear, comprehensive and step by step modelling procedure. On the other hand a controller of proper structure having a feasible attitude control inner loop and a practical position control outer loop is designed. This uses inverse kinematic instead of small angle approximation to achieve better accuracy. An online robust parameter estimation to cope with parametric uncertainty is the explicit part of this controller. The proposed non-linear adaptive controller doesn’t depend on the physical parameter of the UAV such as mass or moment of inertia tensor. Furthermore the proposed controller works well with various payloads. Also in designing this controller both of the parametric and nonparametric uncertainties are considered. In this paper the general dynamics of VTOL UAV’s is obtained by Lagrange-Euler formalism. These dynamic equations are specified for a quadrotor UAV configuration. Then an adaptive controller is designed to solve trajectory tracking problem in the presence of all mentioned problems. In this approach the control of the UAV is performed in two inner and outer control loops. The outer control loop, which controls the translational movements, generates the instantaneous desired angles as a reference trajectory to an inner control loop. In addition, translational forces are produced in the outer loop. The inner loop as attitude control stabilizes the orientation of the vehicle according to the desired angles which are generated by an outer loop. Decentralized adaptive controllers are used in both inner and outer control loops to cope with uncertain dynamics of the system. Inverse kinematics of the robot is used to convert outputs of the outer loop to inputs of the inner loop. Controller needs some physical parameters of UAV, like total mass, to generate appropriate control signals. A robust parameter identifier estimates the required parameters for the controller. Finally, the proposed controller is developed for the quadrotor and simulations are carried out to illustrate the robustness and tracking performance of the controller. Comparing with the other adaptive controllers that used to trajectory tracking control of the quadrotor, which most of them are based on the backstepping technique and neural networks, the proposed controller unlike backstepping based controllers has a simple and clear structure, and unlike neural network based controllers doesn’t need training. It is important to note that the training a neural network in order to identify a non-linear multi-input multi-output system such International Journal of Intelligent Mechatronics and Robotics, 2(4), 58-81, October-December 2012 61 Copyright © 2012, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. as quadrotor is not easy at all. The suggested decentralized adaptive controller doesn’t need to a high speed microprocessor as a control unit because it is not a high computing controller. The reminder of the paper presents the general model of a UAV, as well as a quadrotor is introduced as rotary wing UAV. Next the control strategy and decentralized adaptive controller is described. Simulation results are presented in next. Finally, the major conclusions of the paper are provided. UAV MODELLING Having mathematical dynamic model of a vehicle is essential for designing a good controller. Nevertheless a UAV model always includes some uncertainties. As the model becomes simpler the controller becomes more complicated. A model with more details leads to a more efficient controller. But modelling with all details is an expensive task and needs the special apparatus such as a wind tunnel and hardware in the loop (HIL) facilities. UAV modelling procedure includes the following steps: • Determining the dynamic equations of the vehicle; • Determining the structure of uncertain dynamics; • Determining the relationship between control inputs and outputs of the actuators for a specified UAV; • Determining the actuators dynamics. Dynamics Equation of Rigid Body For obtaining the dynamic equations of 6DOF rigid body, two frames should be defined. The inertial frame and the body frame. Let B B B B = { , , } 1 2 3 be the body fixed frame and E Ex Ey Ez = { , , } be the inertial frame. The inertial frame is considered fixed with respect to the Earth (Figure 1). The vector ξ = [ , , ] x y z T is the position of UAV in inertial frame and the vector η θ ψ = [ , , ] φ T is the orientation of body frame with respect to a fixed frame, and referred to as Euler angles. These angles are bounded as follows: roll pitch yaw : : : − < < − < < − < < 