For autonomous underwater vehicle (AUV) systems with actuator failures, external disturbances and model uncertainties, a robust adaptive trajectory tracking error constrained control strategy based on the fully actuated system (FAS) approach is proposed to enable AUV to asymptotically track target signals. First, the error constrained fully actuated system method is proposed by combining the tracking error-related normalization function and the barrier function with the time-varying scale function. Second, radial basis function neural networks (RBFNNs) are combined with the error-constrained fully actuated system method to deal with the uncertainty model in the system. Further, an adaptive compensation mechanism is designed to deal with actuator faults. Again, it is proved that the trajectory tracking error asymptotically converges to zero based on Lyapunov stability theory. Finally, the simulation result verifies the effectiveness of the designed robust adaptive trajectory tracking error constrained controller.