## 1 Introduction  
With the expansion of human space travel, rendezvous and docking technology in spacecraft have become indispensable for a variety of space activities [1, 2]. When conducting docking activities in space, active and passive docking mechanisms must attain and maintain high levels of reliability and stability. Inspection and acceptance of the ground test platform should ensure the platform's high dependability and stability [3]. Currently, it is customary to employ a semi-physical simulation test platform to conduct a large number of ground-docking simulation experiments in order to thoroughly examine the entire spacecraft docking process [4]. This method can be used to replicate docking studies involving vehicles with varying initial attitudes and surroundings. In addition, it can be used to test the functioning of each subsystem and device incorporated into the docking procedure, as well as to confirm the initial attitude of the spacecraft during docking to assure the effective completion of the space docking task [5]. The ground-docking simulation test platform is becoming increasingly significant as the major test equipment for developing and evaluating the docking mechanism and space docking technologies. Therefore, its ongoing development and renewal is essential. Even though there are numerous types of semi-physical simulation test platforms, only vertical or horizontal single-mode docking tests can be conducted. The inability to conduct docking experiments with different docking modes on the same test platform hinders the design and development of the docking mechanism. In addition, with only a vertical or horizontal single-mode docking test, a more comprehensive examination of docking technology, which advances research on space docking technology, remains a blind spot [6]. In the study of spacecraft attitude error, corresponding research has been undertaken. The space docking mechanism has drawn the interest of numerous countries doing aerospace-related scientific research. As the linchpin technology of docking and capturing mechanisms, all nations have conducted extensive research on it and attained specific achievements. The docking form adopted by the on-orbit capture device of the UnitedStates' \"Orbit Express\" space autonomous operation system is a trident-shaped docking mechanism. The direct capture technique is distinguished by its light weight, outstanding performance, and strong orbital maneuverability [7]. The United States and Russia utilized the cone-type docking mechanism in their early docking practices, including the lunar landing program, the \"Skylab\" project, and the design of the \"Soyuz\" manned spacecraft. After ongoing development, a relatively finished docking mechanism was created. It is used extensively in significant space equipment, such as the \"Progress\" cargo spacecraft, \"Salute,\" and \"Mir\" space station [8; 9; 10]. In addition to the docking mechanisms listed above, there are numerous configurations of docking mechanisms, such as the end of the Japanese-developed actuators ERA and ARH being equipped with a variety of sensors, which can greatly enhance the safety and flexibility of docking and perform precise operations such as fuel filling and module maintenance [11; 12; 13]. The Canadian-developed dexterous hand SPDM motion manipulator is mounted on the space station remote control manipulator system (SSRMS) [14; 15; 16; 17]. ESA's three-degrees-of-freedom horizontal docking simulation test bench consists of an active test platform, a gravity balance mechanism, and a docking mechanism [18; 19; 20], etc. In most cases, a collision will result in a linkage reaction mechanism, and the dynamic performance parameters are obtained via the multiple buffer feedback devices arranged in [21]. The equipment is primarily used in the research center [22; 23; 24] to simulate various typical state changes during the docking and separation process, such as collision and stability regression.