## 1 Introduction  
Space robots are rootless multi-body systems used to perform exploration, assembly, construction, service, repair, or assist astronauts in extravehicular missions in the special space environment, and play an integral role in the space exploration process, and have been the focus of research by space workers [1, 2, 3, 4, 5]. Space missions are complex and diverse, and space robots have different configurations [7]. For space robots with small size, low slow speed, and low control accuracy requirements, they are generally modelled and controlled according to multi-rigid body systems. In recent years, as the research on space robotics has intensified, various studies on space robotics under the assumption of rigid model have been relatively mature, and the obtained results can better solve various problems including system dynamics modelling, motion planning and trajectory tracking. However, the existing space robots are typical flexible multi-body systems, and their base, links and joints are subject to flexible vibration phenomena. For example, the joint device that drives the motion of the links of a space robot will be flexible due to reasons such as a lightweight drive motor [8]. The link is generally made of lightweight materials due to factors such as launch cost and structural design, and is designed as a slender rod-like structure, which is prone to vibration when performing tasks [9]. Moreover, the length of the space robot link is limited by constraints such as the size and structure of the launch vehicle. Moreover, due to the constraints of launch vehicle size and structure, the length of the space robot link is limited, so it is easy to fail to reach the working area during the construction or maintenance of large solar power panels, etc. Considering the space robot with the robot arm fixed to the base, the working range and operational flexibility are much less than the space robot with the robot arm sliding on the base in the same configuration, so the latter is more operable. A space robot arm which can slide on the base is mounted on the base truss rail to cover a larger working area by moving the arm, but the truss rail is prone to vibration under the influence of external forces [10]. From the above analysis, it is clear the space robot structure flexibility is mainly caused by the vibration of three types of components: the base, links and joints. In the non-damped space environment, once the flexible vibration is excited, the decay will be very slow, and the high-frequency tremor not only affects the normal rest and relaxation of astronauts, but also excites each other with the space robot base and joint motion, which in serious cases causes significant shaking of the base of the reserve liquid fuel and even damage to the joint device. In addition, because the space robot motor directly drives the base and joints, and the vibration of the flexible joints and the joint drive torque are coupled with each other, it is easy to cause the vibration of the base, which leads to the difficulty of controlling the base and joints, and then affects the control accuracy of the whole system, and even triggers the control failure. Therefore, considering the flexibility effect of space robot bases, arms, and joints and actively suppressing their vibration is of great importance in improving system control accuracy and ensuring reliability. At present, scholars from various countries have accumulated a great deal of research experience in dealing with the flexibility of space robot arms [11]; they have also achieved certain results in the control and vibration suppression problems of flexible jointed robots [12]; they have also obtained stage results in dealing with the influence of the flexibility of a certain two types of components in the existence of bases, arms and joints of space robots [13]. [PERSON] et al. [14] discussed collision motion control of a flexible two-armed space robot capturing a rotating object. [PERSON] et al.