The space robot will violent collision with satellite in the capture operation. If its fragile joints are not protected, the space robot may be damaged. Therefore, a spring-damper device is added between a joint motor and a manipulator, which can not only digest and absorb the impact energy in the collision process, but also design a compliance strategy matched with the buffer device to realize the calm control of the hybrid system. first, the dynamic modes of dual-arm space robot open-loop system and target satellite system before capturing are established by the Lagrange function. Combined with momentum theorem, velocity constraints, closed-chain geometric constraints and Newton"s third law, the closed-chain dynamic model of hybrid system after capture is obtained, and impact effect and impact force are calculated. After that, in order to control the hybrid system, an integral terminal sliding mode control matched with the buffer device is proposed. The parameters of sliding mode controler are optimized by grey wolf optimizer to reached fast and stable control of the hybrid system. Finally, The stability of the hybrid system is proved by Lyapunov theorem, and the anti-impact performance of the spring-damper device and the effectiveness of compliance strategy are proved by numerical simulation.