## 1 Introduction  
With the development of space technology, the number of spacecraft launched every year is increasing, thereby generating a series of high-intensity and high-risk space missions, such as on-orbit fuel refueling, on-orbit maintenance, recovery of failed spacecraft, space debris removal [1, 2, 3, 4], etc. As outer space is a harsh environment with high pressure, extreme temperatures, high vacuum and strong electromagnetic radiation, it is very hazardous for astronauts to out of the module to carry out the above mission operations. [PERSON] et al. [5] proposed a dynamics decomposition that decouples the end-effector task from the base force actuator and reduces the use of thrusters. [PERSON] et al. [6] proposed a fuzzy adaptive robust control (FARC) strategy which is adaptive to these model variations for trajectory tracking control of space robots. [PERSON] et al. [7] presented an optimization-based guidance algorithm for onboard implementation and real-time use suitable for space robots. [PERSON] and [PERSON] [8] considered the process of capturing spacecraft by dual-arm clamping and the force/position control of its post-stabilization movement and proposed a fuzzy control scheme based on the passivity theory. Therefore, it is a better choice to use space robots to replace astronauts to complete on-orbit services (OOS) missions. Because the capture and operation ability of space robots is the basic and key technology to realize OOS missions. [PERSON] et al. [9] studied the on-orbit services space robot considering joint friction, based on the [PERSON]'s velocity variation principle and the single direction recursive construction method derived the dynamic equation of the system. [PERSON] and [PERSON] [10] analyzed the dynamic behavior of a tethered satellite system for space debris capture, by using the absolute nodal coordinate formulation established the equations of motion of the tethered satellite system. [PERSON] et al. [11] presented strategies for point-to-point reactionless manipulation of a satellite- mounted dual-arm robotic system for capturing tumbling orbiting objects. [PERSON] et al. [12] studied an impedance-based contact control of a free-flying space robot with respect to the coefficient of restitution. Therefore, the research on capturing operation technology of space robots has become a hot topic in the aerospace field in recent years. The operation process of space robot capturing a non-cooperative spacecraft can be divided into four phases: (1) the observation phase, in this phase, the position and attitude of the target spacecraft are observed; (2) the approaching phase, through trajectory planning and motion control of space robot to reaching the capture area; (3) the capturing operation phase, the space robot uses the end-effector to capture the target spacecraft; (4) stable control phase, considering the post-capture unstable motion which is caused by the collision and impact of the capturing operation phase, design the stability control strategy of the hybrid system formed by the space robot and the target spacecraft. Considering that the space robot will inevitably experience a violent contact and collision with the target spacecraft during phase 3 of the capturing operation process, in this process, the joint of the manipulator arm will be subjected to a great impact moment [13]. If the impact torque affecting the joint is too large, it could cause the impact damage to the joints and lead to the failure of the space mission. At present, there is no effective way to solve the problem except using the minimum relative approaching velocity. Although this method is feasible for cooperative spacecraft, it is basically not applicable to non-cooperative spacecraft. Therefore, in the phases 3 and 4 of the capture of a non- cooperative spacecraft, it is of great exploratory value and significance to take certain measures to avoid the damage to joint actuators caused by such impact and collision.