The flexibility of the free-floating flexible space manipulator system’s link and joint may affect the control accuracy and cause vibrations. We studied the dynamics modeling, joint trajectory tracking control, and vibration suppressing problem of free-floating flexible-link and flexible-joints space manipulator system with external interference and uncertain parameter. The system’s dynamic equations are established using linear momentum conservation, angular momentum conservation, assumed mode method, and Lagrange equation. Then, the system’s singular perturbation model is established, and a hybrid control is presented. For the slow subsystem, a robust fuzzy sliding mode control is proposed to realize the joint desired trajectory tracking. For the fast subsystem, a speed difference feedback control and a linear-quadratic optimal control are designed to suppress the vibration caused by the flexible joints and the flexible link separately. The simulation comparison experiments under different conditions are taken. The simulate results demonstrate the proposed hybrid control’s validity.

Joint flexibility introduces additional degrees of freedom and vibration modes, thus limiting the performance of the manipulator. To improve control bandwidth, this paper proposes an enhanced two-stage state feedback (SFB) controller, which combines two parts. The first is a SFB loop, which considers the motor position as a virtual control input for the link side dynamics. The second is a disturbance-state observer, which compensates disturbances and reconstructs indirect measurements. Experimental results show the effectiveness of the proposed controller in terms of position tracking, link vibration, and rejection of the kinematic error from the joint’s harmonic drive reducer.