Command Filter Based Fixed-time Trajectory Tracking Control for Flexible-joint Space Robots

To resolve the susceptibility of flexible-joint free-flying space robots to elastic vibrations during motion owing to external disturbances and model uncertainties, which decrease control accuracy at the end of the manipulator, we propose a nonsingular fixed-time command filtering backstepping control method. Firstly, to avoid the "explosion of complexity" caused by the recursive differentiation of the virtual control law for backstepping, we utilize a fixed-time command filter to obtain the derivative of the desired virtual control law and its derivatives. Furthermore, to eliminate the filtering errors generated by the command filter, we propose a nonsingular fixed-time filtering error compensation algorithm to improve the tracking accuracy of the system. Subsequently, we present a command filtering backstepping tracking controller based on Lyapunov's stability theory, ensuring that the proposed controller can facilitate the convergence of system tracking errors to the origin within a fixed time. The simulation results demonstrate that the designed nonsingular fixed-time command filtering backstepping controller exhibits high convergence speed and tracking accuracy.