Fault-Tolerant Adaptive Control for Trajectory Tracking of a Quadrotor Considering State Constraints and Input Saturation

A fault-tolerant trajectory tracking controller is proposed for a quadrotor. Usually, the effect of actuator faults is mainly regarded as an external disturbance, which makes it difficult to properly respond to time-varying loss of effectiveness faults or input saturation under state constraints. Adaptive control based on the Nussbaum-type function provides robust control performance for the unknown time-varying control effectiveness. However, numerical instability is the biggest obstacle to applying Nussbaum-type functions to fault-tolerant control, especially for state-constrained problems due to the large feedback from tracking errors. In this study, an adaptive control scheme utilizing the Nussbaum-type function is proposed to address the problems of input saturation and numerical instability. The Nussbaum-type gain is assigned to each rotor directly to consider the independent faults and saturation of each rotor. The quadrotor position control structure is redesigned to properly update the Nussbaum-type gains by passing the total thrust command from the position control loop to the attitude control loop. A nonlinear mapping is also proposed to constrain the states as well as to address the numerical instability of the Nussbaum-type function by exploiting a gradient modifier in the nonlinear mapping. The stability analysis shows that all the closed-loop signals are uniformly ultimately bounded under mild assumptions. Numerical simulations demonstrate that the proposed method has satisfactory trajectory tracking performance under various fluctuating loss of effective faults and input saturation while satisfying state constraints.