## 1 Introduction
The five-degrees-of-freedom, rope-type comprehensive docking test bench is mostly utilized for dynamic testing and verification of the actual model. The model is suspended on a three-level hinge suspension rope [25; 26; 27] to maintain its center of mass position. It has been utilized in the \"Apollo\" and \"Soyuz\" docking verification test [28]. The bottom tracking mechanism of the six-degree-of-freedom hybrid comprehensive test bench in the United States is designed with a hydraulic buffer to enable irregular six-degree-of-freedom motion [29; 30; 31]. Its upper platform is fitted with a number of sensors for determining the docking status. On the basis of the theoretical model, this type of test bench can examine various parameter value changes in the actual docking scenario [32], as well as simulate and test the butt joints of asymmetric structures at various temperatures [33; 34]. Harbin University of Technology researchers have proposed a new attitude description method and a representation method of gaze error, which directly takes the angle between the optical axis and the target vector as the error variable, establishes the error kinematics equation, and applies it to agile spacecraft in order to observe more targets [35]. Using hyperbolic tangent function, potential function, and linear sliding mode function, [PERSON] of Harbin University of Technology creates a new sliding mode surface function and designs a collision avoidance tracking controller; the closed-loop system is asymptotically stable [36]. [PERSON], a professor at Northwestern Polytechnic University, uses the sumo/front project of the United States as a backdrop to study the key technical problems related to attitude takeover control after space robot target capture, in order to provide theoretical support for future on orbit services such as satellite life extension, runaway satellite rescue, and orbital waste cleaning [37]. Chinese academics have proposed a robust control algorithm for tracking the attitude of the spacecraft during time-dependent rendezvous, which can ensure the accuracy of the tracking algorithm of the spacecraft during time-dependent rendezvous [38]. Chinese scholars such as [PERSON] expounded the topological structure of the nine degree of freedom motion system and the establishment process of low order body array, analyzed the basic law of the system with error motion, proposed the construction method of adjacent body characteristic matrix, and studied the comprehensive spatial error of the nine degree of freedom motion system based on the characteristics of adjacent bodies. Numerous scholars from several nations have conducted extensive research on collision features [39]. [PERSON] investigated the impact of historical events on the formation process on the collision characteristics of S-shaped structural components. According to the change in thickness, equivalent plastic strain, and residual stress and strain resulting from the stamping operation, the related collision modelswere developed, calculated, and assessed [40]. [PERSON] utilized the \"separation collision\" two-state model and the nonlinear spring damping force function to simulate the collision process between piston rods. He also established the dynamic model of an erecting multi-rigid body system that accounts for collision and simulated the motion process of a multi-stage oil cylinder. The simulation results demonstrate the effect of collision on the stability of large-scale device erection, laying the groundwork for the design of a rapid erection system [41]. Ballistic impact tests were conducted at impact speeds of 75 M/s, 105 M/s, 154 M/s, and 183 M/s using a composite material proposed by [PERSON] and other researchers. Ref. [42] evaluated the energy absorption and damage mitigation properties of the proposed fiber metal elastomer three-layer composites.