Control of Quadrotor Using Sliding Mode Disturbance Observer and Nonlinear H∞

International Journal of Robotics, Vol. 4, No. 1, 38-46 (2015) / Gh. Alizadeh, K. Ghasemi 39 The remainder of this paper is then organized as follows. fIGThe control strategy is exposed in Section III; in this section, two approaches of nonlinear robust control design are proposed: the SMDO control for translational movements and the nonlinear H∞ control for the rotational subsystem. Section IV is devoted to simulation results. 2. Quadrotor Dynamics In this section, model of the quadrotor rotorcraft is presented. Quadrotor platform has the shape of the cross (+) with a motor and propeller placed on each one of the four ends of the axes. Two propellers rotate counter clockwise and the others rotate clockwise such that the total torque of the system is balanced (approximately canceling gyroscopic effects and aerodynamic torques in stationary trimmed flight). Vertical motions of the quadrotor are generated by varying the rotor speeds of all four motors. The helicopter tilts towards the direction with lower lift rotor and accelerates along that direction. The basic model of an unmanned quadrotor is shown in Fig. 1. Pitch movement is obtained by increasing (reducing) the speed of the rear motor and reducing (increasing) the speed of the front motor. The roll movement is obtained similarly using the lateral motors. The yaw movement is obtained by increasing (decreasing) the speed of the front and rear motors and decreasing (increasing) the speed of the lateral motors (Fig. 2). Fig. 1: The quadrotor helicopter configuration with roll-pitch-yaw Euler angles. Move left Rotate clockwise Rotate counterclockwise Move right Fig. 2: The quadrotor motion description, the arrow width is proportional to propeller rotational speed [14]. The dynamics of the four rotors are relatively faster than the main system and thus it can be neglected here. . Earth fixed frame and body fixed frame are represented by E={e1I,e2I,e3I} and B={e1B,e2B,e3B}, respectively. The generalized coordinates of the rotorcraft are q=(x,y,z,φ,θ,ψ), where (x,y,z) represents the absolute mass center position of the quadrotor with respect to an internal frame. (φ,θ,ψ) are the three Euler angles ( 2 2; 2 2; )                   representing the orientation of the rotorcraft, namely rollpitch-yaw of the vehicle. The translational and rotational coordinates are assumed in the form ζ=(x,y,z)Tε R3 and η=(φ,θ,ψ) ε S3. Considering the quadrotor as a single rigid body with 6 DOFs and neglecting the ground effect, the equation of motion for the rigid body is obtained in Newton-Euler formalism. The equations of motion for the helicopter can be written as follow [7]: