Trajectory tracking is a key step for a free-floating space robot (FFSR) system to complete a space operation. However, the flexibility of links and deadzone in joint input torque decrease the system's trajectory tracking accuracy. The angle tracking for the multi-flexible-link FFSR was discussed to suppress the vibrations of the flexible links and prevent the influence of the deadzone. First, the dynamic equation of the FFSR system was derived. Second, the FFSR system was decomposed into the slow and fast subsystems. Then, for the slow subsystem, a robust control method based on a nominal model and a deadzone estimation compensator were proposed. For the fast subsystem, a linear quadratic regulator optimal method was used to actively suppress vibrations. Finally, experiments were carried out to verify that the FFSR is capable of effectively tracking the desired trajectory. The simulation results show the robustness of the control scheme. It effectively suppressed the vibrations as the vibration modes of the links convergent to zero. This study provides a control scheme for improving the trajectory tracking accuracy of FFSR, which is of practical importance.

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