# Segmented Hybrid Impedance Control for Hyper-Redundant Space Manipulators
## 6 Simulation Analysis
### Second Scenario  
The simulated scenario is sketched in Figure 15 and illustrated in Figure 16, where the manipulator wraps around an obstacle with a configuration stated in Table 4, grasps it, and  
Figure 14: End-effector linear velocity tracking error: (**a**) end-effector velocity without impedance control; and (**b**) end-effector velocity with impedance control. Figure 12: Normal contact force: (**a**) normal contact force link 14 without impedance control; and (**b**) normal contact force link 14 with impedance control. Figure 13: End-effector position tracking error: (**a**) end-effector position without impedance control; and (**b**) end-effector position with impedance control. manipulates it along a planned trajectory while avoiding additional obstacles. Initially, the manipulator is positioned near the target but has not yet established contact. In this case, the manipulator is treated as a single segment (joint 1 to joint 24) and the desired force is applied by the end-effector. The designed desired trajectory shown in Figure 17a,b describe the desired robotic arm manipulation. Figure 18a,b shows the number of contacts between the manipulator and the object where we can notice a significant reduction of contact separation. During the first simulation phase, the motion planning is coupled with a force controller to ensure secure object grasping. The end-effector applies a consistent force of 5 N to maintain a stable grip, as shown in Figures 19a,b and 20a,b. Impedance control is employed by the virtual end  
Figure 16: Illustration of the second scenario: (**a**) manipulation scene system (0 s time); and (**b**) manipulation scene system (30 s time). Figure 17: Desired active joints velocity: (**a**) joint velocity (0–10 s); and (**b**) joints velocity (10–30 s). Figure 15: Sketch of the contact link and manipulator. effector (joint 15 to joint 24) to ensure compliance during the contact and mitigate forces exerted by the obstacle. After securing the object, the manipulator initiates its movement. The Euclidean position error of the object (Figure 21a,b) remains within permissible bounds, given the manipulator's width and the obstacle's size. We introduce noise to  
Figure 19: Normal unfiltered contact force: (**a**) normal contact force link 24 without impedance control; and (**b**) normal contact force link 24 with impedance control. Figure 20: Normal contact force: (**a**) normal contact force link 24 without impedance control; and (**b**) normal contact force link 24 with impedance control. the end-effector contact sensor, as shown if Figure 9. The system stability is evaluated by verifying that the sum of the external forces and torques remains within acceptable limits, as demonstrated in Figures 22a,b and 23a,b. The base's Euler angles also exhibit a negligible influence on the system efficiency (Figure 24a,b). Figure 23: Non-cooperative object sum of external torques: (**a**) sum of external torques without impedance control; and (**b**) sum of external torques with impedance control. Figure 12:0 Non-cooperative object position error: (**a**) object position error without impedance control; and (**b**) object position error with impedance control. Finally, base attitude control plays a critical role in counteracting destabilizing external forces. This integration of trajectory tracking, force control, and stability assessment highlights the system's capability to manage complex dynamic tasks effectively. The force controller parameters are as follows:  
Figure 12:1  
Figure 12:2  
The hybrid position force controller parameters are as follows:  
Figure 12:3  
Figure 12:4  
The impedance control model parameters for 11 joints (joint 14 to joint 24) are as follows:  
Figure 12:5