Nonlinear Control of Quadrotor for Fault Tolerance: A Total Failure of One Actuator

This paper deals with the problem of a quadrotor experiencing a total failure of one actuator. First, a nonlinear mathematical model for the faulty quadrotor is derived with three control inputs and six outputs, which includes the translational and rotational dynamics. Because of the limited inputs, the controllability of the yaw state is sacrificed, and the control inputs are reallocated to the other three healthy rotors. Second, a nonlinear controller is designed based on the proposed model. This presented controller includes two subcontrollers: 1) a roll angle, pitch angle, and altitude subcontroller and 2) a horizontal position subcontroller. In the controller design, the Moore-Penrose pseudoinverse of the coefficient matrix is applied to overcome the singularity of the roll angle. Third, the stability of both of the designed subcontrollers is verified by the Lyapunov stability theorem, and the convergence of the designed subcontrollers is analyzed. Finally, simulation results are provided to verify the effectiveness of the proposed model and the designed controller.