Abstract: The buffer and compliant control for space robot to avoid joint damage during on-orbit capture non-cooperative satellite are studied. For the reason, a compliant mechanism is mounted between the joint motor and space manipulator, its functions are: first, the deformation of internal spring in compliant mechanism can absorb the impact torque of the captured satellite acting on the joint of the space robot; second, the joint impact torque can be limited to a safe range by reasonably designing the buffer and compliant control scheme. First of all, the dynamic models of the space robot system and the target satellite system before capture are derived by multi-body theory. After that, based on the law of conservation of momentum, the constraints of kinematics and the law of force transfer, the integrated dynamic model of the combined system is derived. At the same time, the impact effect and impact force are calculated. For the stabilization control of post-capture unstable combined system, a buffer and compliant control scheme based on dynamic surface is proposed. The proposed control scheme can not only effectively absorb the impact torque generated by the on-orbit capture process, but also timely open or close the joint motor when the impact torque is too large, which can avoid overload and damage of the joint motor. In addition, the dynamic surface control scheme is utilized to avoid calculation expansion caused by backstepping method and to reduce the calculation effectively. The stability of the system is proved by Lyapunov theorem, and numerical simulation verifies the effectiveness of the proposed buffer and compliant control method.