# Model-Free-Based Single-Dimension Fuzzy SMC Design for Underactuated Quadrotor UAV
###### Abstract  
The underactuated quadrotor unmanned aerial vehicle (UAV) is one of the nonlinear systems that have few actuators as compared to the degree of freedom (DOF); thus, it is a strenuous task to stabilize its attitude and positions. Moreover, an induction of unmodelled dynamic factors and uncertainties make it more difficult to control its maneuverability. In this paper, a model-free based single-dimension fuzzy sliding mode control (MFSDF-SMC) is proposed to control the attitude and positions of underactuated quadrotor UAV. The paper discusses the kinematic and dynamic models with unmodelled dynamic factors and unknown external disturbances. These unmodelled factors and disturbances may lead the quadrotor towards failure in tracking specific trajectory and may also generate some serious transient and steady-state issues. Furthermore, to avoid the problem of gimbal lock, the model is amalgamated with hyperbolic function to resolve the singularity issues dully developed due to [PERSON]'s dynamic modeling. The simulation results performed for MFSDF-SMC using MATLAB software R2020a are compared with conventional sliding mode control, fuzzy-based sliding control and single-dimension fuzzy-based sliding mode control without a model-free approach. The design and implementation of the model-free single dimension-based fuzzy sliding mode control (MFSDF-SMC) with an updated Lyapunov stability theorem is presented in this work. It is observed that MFSDF-SMC produces robust trajectory performance therefore, and the manuscript suggests the experimental setup to test the proposed algorithm in a noisy environment keeping the same conditions. The verification of the equipment used and its effective demonstration is also available for the reader within the manuscript. model-free approach; quadrotor; single-dimension fuzzy; sliding mode control; unmodelled dynamics; underactuated system +
Footnote †: journal: Computer Science and Engineering  
0000-0001-910  
unknown external disturbances, but still there are some limitations as discussed in [3]. In addition to this, one may see various model-based control designs, i.e., linearized model-based control strategies [4; 5; 6; 7; 8; 9; 10] and nonlinear model-based control techniques [11; 12; 13; 14; 15; 16; 17; 18]. The fuzzy-logic-based self-tuning of proportional integral derivative (F-PID) control is proposed for attitude and position control with the linear dynamic model [4; 5]. In this scheme, the gains of proportional integral and derivative (PID) are tuned to acquire the robust performance. Researchers have proposed Kalman filter scheme to estimate the attitude with different data sets acquired from the inertial measurement unit (IMU) [6]. One may also see the different configurations of proportional (P), integral (I), and derivative (D), in either cascaded or parallel form. The double-gain PD scheme is also proposed for regulating linear attitude dynamics [6]. Similar linear dynamic model is opted in [7], where a linear-quadratic and regulator (LQR) controller is designed with full-state linear observer design. In the previous proposed research works, the sliding mode control (SMC) technique was applied to improve the same attitude and positions of underactuated quadrotor but with linear Newton Euler dynamics [8]. One may see the trend of hybridizing these control and observer design schemes with adaptive techniques to overcome the parametric uncertainties and unmodelled dynamic factors [9]. So far, researchers have proposed various strategies to acquire more realistic real-world dynamic models such as using a continuous predictor-based identification approach. This approach uses the matrix inequality concept for tuning the gains for an underactuated quadrotor [10]. The stability is achieved in all these control algorithms but around the equilibrium conditions using Jacobian method. Thus, researchers later consider the nonlinear models.