To comply with the process of a space robot capturing a spacecraft and the subsequent auxiliary docking operation， precise control of the output force and position of the spacecraft docking device was studied herein. A spring damper buffer device was added between the joint motor and manipulator to prevent the joint from being damaged under the huge impact force generated during contact and impact. First， by combining Newton's third law， velocity constraints of the capture points， and closed-chain system geometric constraints， a dynamic model of the hybrid system after capture was obtained， and the impact effect and force were estimated based on momentum conservation. Then， the impedance model during docking was established through the kinematics of the spacecraft docking device relative to the base coordinate system. Subsequently， a robust adaptive-double-layer sliding-mode control strategy was developed. Combined with impedance control， this strategy employed a force load servo control system to accurately control the position and output force of the docking device to reduce the impact force during contact and impact. The control strategy featured a double-layer sliding-mode structure， with the first layer ensuring convergence of the hybrid system in finite time and the second layer being used to solve the high-gain problem of the controller. Finally， the stability of the system was proved using the Lyapunov theorem， and the effectiveness of the proposed strategy was verified through a numerical simulation. The simulation results indicate that the buffer device can reduce the impact force by 46.78% of the maximum at the given velocities. Moreover， the control accuracy of the output force is better than 0.5 N， while the accuracies of the position and attitude are better than 10^-3 m and 0.5°， respectively.