Robust Control of a Quadrotor using EKBF State Vector Estimation

This paper presents the design of an optimal nonlinear controller for trajectory tracking of a quadrotor helicopter based on the well-known sliding mode control method (SMC). To this end, the Lyapunov law analysis has been used regarding nonlinear equations of the quadrotor. The proposed control method is characterized by its robustness against disturbances and aerodynamic effects. One of the main targets of this study is to develop a nonlinear observer based on extended kalmanbucy filter (EKBF) to estimate unmeasured states of the system. In order to optimize the parameters in proposed control method, the paper utilizes the genetic algorithm. Finally, simulation results indicate that quadrotor UAV with the proposed controller ensures good tracking of a desired trajectory and its robustness against aerodynamic effects is better than the other previously presented works. Keywords— Quadrotor, Sliding Mode Control, Genetic Algorithm, State Estimation, Extended KalmanBucy Filter INTRODUCTION The quadrotor is an unmanned aerial vehicle (UAV) which has four propellers attached to four motors placed on a fixed body to create six strongly coupled output coordinators [1,2]. Nowadays, these UAVs are vastly used in various applications at minimal cost and without endangering any risk to human life. UAVs are generally suitable for military applications, cartography, surveillance and acquisition of targets. In [3,4] authors describe the aerodynamic forces and moments on rotor dynamic of helicopter by synthesizing momentum with blade element theory. In [6] the SMC has been applied extensively to control quadrotors. A robust second order sliding mode control (SMC) for controlling a quadrotor with uncertain parameters presented based on high order sliding mode control (HOSMC) for trajectory tracking of a quadrotor helicopter. [7] presents the sliding mode control of a class of under actuated systems regarding the quadrotor as a sample model. In [8] the authors use a continuous sliding mode control method based on feedback linearization applied to a quadrotor UAV. [9] gives a new robust backstepping‐based controller that induces integral sliding modes for the under actuated dynamic model of a quadrotor subject to smooth bounded disturbances, consisted of wind gust and aerodynamics effects. In [10‐11] the authors present a design method for attitude control of a quadrotor based on sliding mode control method in which all sliding surfaces are designed using the Lyapunov stability theory. Other methods have also been attempted to achieve good performance [12‐14]. In a specific problem of a continuous‐time stochastic system, inorder to improve the results, state estimation with a nonlinear filter such as Extended Kalman‐Bucy Filter (EKBF) is used which constitutes the basis for [15]. [16] designed an EKBF for accurate and robust tracking of targets in an air combat scenario. A comparative study on applying modern techniques such as Genetic Algorithm (GA) for parameter optimization of controllers is presented in [17]. In [18‐20] the effectiveness of this technique has been shown in position control and path generation of robotic systems. In [21] parameter optimization was obtained for a small helicopter based on GA focusing on stability of the system. In this paper, we utilize the EKBF method along with nonlinear dynamics of the quadrotor as an efficient solution to estimate unmeasured states of the quadrotor dynamics. Finally, a nonlinear robust controller is developed with optimized control parameters adjusted by GA for decreasing the impact of aerodynamic effects on modeling and control of the system. The paper is organized as follows: Section 2 presents the dynamic model of a quadrotor. In section 3 the presentedEKBF is described. Section 4 proposes the developed sliding mode control technique for the quadrotor along with an optimal method using Genetic