## 5 Simulation Analysis
Therefore, for the fully flexible space robot system, the control schemes mainly include the following two categories: (1) IFSM control and IFSM-NV control and (2) ISM control and ISM-NV control. Figure 3 shows the base attitude trajectory tracking curve of the fully flexible space robot under two control conditions, and Figure 4 shows the 1 joint trajectory tracking curve of the fully flexible space robot under two control conditions. Figure 5 is the 2 joint trajectory tracking curve of fully flexible space robot under two control conditions. From Figure 3a, it can be seen that with IFSM, the error between the base attitude angle and the desired base attitude angle of the fully flexible space robot is 0.0199 rad at 3.2 s, while with IFSM-NV, the desired trajectory can be tracked by 6.8 s, but the base trajectory has a tendency of irregular motion at 7 s. As can be seen from Figures 4a and 5a, with IFSM, the error between the actual trajectory of the 1 joint and the desired trajectory is 0.0199 rad at 3 s, the error of the 2 joint is 0.0199 rad at 2.2 s; When IFSM-NV is used, both 1 joint and 2 joint tend to track the desired trajectory, but the tracking trend of 2 joint is not obvious, and both joints deviate from the desired trajectory at 7 s. As can be seen from Figures 3b, 4b and 5b, with ISM, the base attitude and joints of the fully flexible space robot can accurately track the desired trajectory. When the convergence time of the base and joint are 4 s, 3.3 s and 2.5 s, respectively, the error reaches 0.0199 rad; When ISM-NV is used, the base tends to track the desired trajectory before 2.5 s and the joint tends to track the desired trajectory before 2 s, but the joint deviates from the desired trajectory after 2 s. The simulation results show that both IFSM and ISM can control the base attitude and joint movement of the fully flexible space robot according to the expected trajectory. IFSM-NV and ISM-NV can only make the fully flexible space robot move according to the desired trajectory, or track the desired trajectory for a short time, and finally all diverge. It is verified that the rigid controller controls the fully flexible system with low control accuracy and easy to cause control failure. In addition, under IFSM control, the system convergence time is less than 5.6 s, while under ISM control, the system convergence time is less than 6 s. According to Equation (35), the fixed time of IFSM convergence is 3.8958 s; therefore, compared with ISM, the controller proposed in this paper meets the requirements of convergence in a fixed time. Figure 4: Trajectory tracking curve of the fully flexible space robot, 1 joint under two controls. **(a)** IFSM, **(b)** ISM. Figure 3: Trajectory tracking curve of the fully flexible space robot base attitude under t controls. **(a)** IFSM, **(b)** ISM. In order to visually observe the flexible vibration suppression effect of the flexible vibration suppressor proposed in this paper on the system base and joint, the following simulation is carried out. Figure 6 is the flexible vibration curve of the base of the fully flexible space robot under two control conditions, and Figure 7 is the flexible vibration curve of the 1 joint of the fully flexible space robot under two control conditions. Figure 8 shows the flexible vibration curves of 2 joints of fully flexible space robot under two control conditions. Figure 5: Trajectory tracking curve of the fully flexible space robot, 2 joint under two controls. (**a**) IFSM, (**b**) ISM. Figure 6: Elastic vibration curve of the fully flexible space robot base under two controls. (**a**) IFSM, (**b**) ISM. According to Figure 6a,b, the flexible vibration of the base can be suppressed within 0.015 m by using IFSM and ISM controllers. For space robots with large volume and heavy load, the vibration of the base truss guide rail meets the scope of aerospace applications.