# Quadrotor Stabilization and Tracking Using Nonlinear Surface Sliding Mode Control and Observer
## 1 Introduction  
Recently, unmanned aerial vehicles (UAVs) have attracted considerable research attention. A quadrotor that is one of the most widely used UAVs in various industrial fields is classified as a rotorcraft since it takes off vertically using four motors. Many researchers have studied quadrotors for various purposes, such as swarming, parcel delivery, exploration, and vehicles [1; 2; 3; 4; 5; 6]. In various studies, the basic technology for quadrotor stabilization and movement is attitude control based on proportional-integral-derivative (PID) or sliding mode control (SMC) as general controllers. PID, which has the advantage of simple control structure, is a widely used maneuvering algorithm in controller design [7; 8; 9; 10; 11; 12]. However, PID has a disadvantage against disturbances and is limited for precision control. Meanwhile, SMC shows strong, robust performance in the presence of disturbances and model uncertainties [13; 14; 15; 16; 17; 18; 19]. A quadrotor system is sensitive to parameter uncertainties and external disturbances. To solve this problem, we propose an augmented system that adopts correction variables (\(z_{i}\)). When the state converges to the sliding surface, the trajectory becomes less sensitive to disturbances during the sliding phase. The stability of the control system is proved by following the Lyapunov stability theorem. However, in spite of the robust characteristic to disturbances or model uncertainties, sliding mode control has drawbacks of chattering phenomena and time delay for attitude stabilization. Even if the state converges to the sliding surface, a discontinuous control value with high frequency switching action is induced so that it causes unnecessary noises and switching stress in the system. As a solution, we propose a nonlinear sliding surface in SMC to reduce the error between thedesired value and the measured value. Moreover, the proposed nonlinear sliding surface reduces the response time of the controller. The control input is derived to satisfy the stability condition of the Lyapunov function with the sliding surface. Sliding mode observer (SMO) is widely used to improve the state estimation performance [20; 21; 22; 23; 24]. In SMO, we estimate the unmeasured state and use a saturation function to set up the correction variable with the estimated and the measured data. To improve tracking performance, SMC has been applied in various controller design problems [25]. A quadrotor is a nonlinear system with four independent inputs and six coordinate outputs. A novel SMC based on a nonlinear disturbance observer was proposed in [26] wherein the disturbance estimation was included to attenuate the mismatched uncertainties. The control algorithm in [27] was a hybrid of SMC and backstepping to stabilize the attitude and was widely adapted in various control applications. To achieve sensorless control of a permanent magnet synchronous motor, a sliding mode observer was proposed in [28] according to the back electromotive force model. By estimating the capacitor voltages from measurement of the load current, an adaptive gain second-order sliding mode observer for a multi-cell power converter system was designed in [29]. The capacitor voltages were estimated under the input sequences using the observability concept. In this paper, we propose an SMC- and SMO-based control method for the position tracking and attitude stabilization of a quadrotor system. We set up the quadrotor dynamic model and design the augmented quadrotor dynamics with correction variables obtained by SMO. In general, there are two approaches to derive the quadrotor motion dynamics: Newton-Euler and Euler-Lagrange methods. Newton-Euler formalism gives physical insights through the derivation. Euler-Lagrange formalism provides the linkage between the classical framework and the Lagrangian or Hamiltonian method [30]. In this paper, the dynamics of the quadrotor is formulated based on Newton-Euler approach.