## 4 Simulation  
In this section, an in-orbit service task as shown in Figure 5 is designed for a free-floating dual-arm space robot, in which one manipulator performs the capture operation on the target object and the other manipulator performs the maintenance operation on the captured object. The parameters of the free-floating dual-arm space robot are shown in Table 1.  
The space robot will inevitably be affected by uncertain dynamic parameters and external disturbance when it performs the in-orbit service task. First, we use the traditional NMPC method to simulate and contrast the trajectory tracking of the space robot under the influence of dynamic parameter uncertainty and external disturbance. The relevant parameter settings of the dynamic parameter uncertainty and external disturbance of the space robot during simulation can be found in Table 1. Taking joint 5 as an example, the traditional NMPC method is used to simulate and compare the actual situation of the free-floating dual-arm space robot affected by parameter uncertainty and external disturbance with the ideal situation that is not affected. The results are shown in Figure 6. It can be seen from Figure 6 that the traditional NMPC method has a good control effect on the robot under ideal conditions, but the control effect of the robot under actual conditions with disturbances needs to be improved.  
To show the advantages of the proposed improved NMPC method, we next build two controllers based on the traditional NMPC method and the proposed improved NMPC method, respectively. The relevant parameter settings of these two controllers can be found in Table 1. We use these two controllers to simulate the trajectory tracking of the two arms of the free-floating dual-arm space robot under the influence of uncertain dynamic parameters and external disturbances. Figure 7 shows the tracking comparison of each joint of the left arm based on these two controllers to the desired trajectory. As shown in Figure 7, compared with the traditional NMPC controller, the proposed improved NMPC controller is more accurate in tracking the desired trajectory, and can keep the error within the target range, showing an excellent control effect.  
Unlike the ground fixed manipulator, the attitude of the base of the free-floating dual-arm space robot needs to be controlled stably; otherwise, it will seriously affect the operation accuracy of the two arms, resulting in the failure of the operation task. Therefore, we finally use these two controllers to simulate the stable control of the base attitude of the free-floating dual-arm space robot. In order to further demonstrate the advantages of the designed improved NMPC controller, we increase the amplitude of the external disturbance of the robot base attitude simulation experiment to five times the original to increase the uncertainty of the system to verify the performance of the proposed controller. Figure 8 shows the error comparison of the base attitude stabilization control of the free-floating dual-arm space robot based on these two controllers. It can be seen from Figure 8 that compared with the traditional NMPC controller, the designed improved controller obtains a more stable base attitude. The proposed controller shows excellent stability in conditions of strong disturbance.  
Figure 6: Simulation comparison of traditional NMPC with and without disturbance. (**a**) Comparison of desired trajectory tracking for joint 5. (**b**) Error comparison of desired trajectory tracking for joint 5.  
Figure 7: Simulation comparison between traditional NMPC and proposed improved NMPC. (**a**) Comparison of desired trajectory tracking for joint 4. (**b**) Error comparison of desired trajectory tracking for joint 4. (**c**) Comparison of desired trajectory tracking for joint 5. (**d**) Error comparison of desired trajectory tracking for joint 6. (**f**) Error comparison of desired trajectory tracking for joint 6.