A space manipulator needs to exhibit high stiffness for tracking, and good compliance for capturing a tumbling satellite. However, the elasticity caused by harmonic drives challenges both the highprecision motion and the flexibility of the manipulator. In this paper, we propose a novel control method based on a robust torque-tracking controller to eliminate the unexpected vibration resulting from elasticity and reject the perturbation caused by nonlinear friction of the motor. In order to achieve the high-precision motion of the manipulator with uncertain dynamics, we combined the method with an improved adaptive method. The position-based impedance control, taking both the translational and rotational impedance into account, is added to achieve the soft-capture of a tumbling satellite. The stability of the proposed method has been strictly proven by the Lyapunov method. The space manipulator is mounted on a controlled chaser, forming a free-flying space robot. A loose coordinated control between the chaser and the manipulator is adopted in the task simulation. The simulations for verifying controller performance and the task simulation reveal that the manipulator has high-precision motion performance in the pre-capture phase, achieves soft-capture in the capturing phase and offers a reliable connection between the chaser and the target in the de-tumbling phase. INDEX TERMS Flexible-joint manipulator, capture of tumbling satellite, robust and adaptive control, free-flying space robot.