# Segmented Hybrid Impedance Control for Hyper-Redundant Space Manipulators
## 6 Simulation Analysis
### First Scenario
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Number** & **Rotation Axis** & **Body Number** & **Rotation Axis** & **Body Number** & **Rotation Axis** \\ \hline \(1\) & [1 0 0]\({}^{\mathrm{T}}\) & 9 & [0 0 1]\({}^{\mathrm{T}}\) & 17 & [1 0 0]\({}^{\mathrm{T}}\) \\ \(2\) & [0 0 1]\({}^{\mathrm{T}}\) & 10 & [0 0 1]\({}^{\mathrm{T}}\) & 18 & [0 0 1]\({}^{\mathrm{T}}\) \\ \(3\) & [1 0 0]\({}^{\mathrm{T}}\The force controller parameters are as follows:  
\[\text{K}_{\text{p\_force}}=15,\text{K}_{\text{i\_force}}=7\]  
\[\text{F}_{\text{d}}=10\;\text{N}\]  
The hybrid position force controller parameters are as follows:  
\[\text{K}_{\text{damp}}=\text{diag}([10\;10\;10\;10\;10\;10])\]  
\[\text{K}_{\text{p\_sec1}}=\text{diag}([10\;10\;\cdots 10\;10]),\text{K}_{\text{d\_sec1}}= \text{diag}([16\;16\;\cdots 16\;16])\]  
The impedance control model parameters for 10 joints (joint 6 to joint 15) are as follows:  
\[\text{M}_{\text{H,d}}=\text{diag}(100\cdots 100),\text{B}_{\text{H,d}}=\text{ diag}(2000\cdots 2000)\]  
Since there will be multiple collisions between the robotic arm and the contact target in a multi-point contact scenario, the motion control error of tracking the trajectory of the  
Figure 6: Sketch of the contact link and two segments in the first scenario. Figure 7: Illustration of the first scenario: (**a**) winding entanglement scene system (0 s time); and (**b**) winding entanglement scene system (20 s time). first segment before the second segment of the robotic arm achieves stable leaning is large, so the winding process needs to be performed at different time periods. In the numerical simulation, the initial position of the manipulator is around the target, but it has not yet made contact with the target. The first stage of the motion process is 0-10 s. The 6-15 joints of the robotic arm converge toward the target according to the designed expected trajectory. After contact and collision with the target, a force/position hybrid impedance controller is used instead to make the 14 th joint track the expected value with a normal contact force of 10 N; the second stage is 10-20 s. Based on the premise that the first segment of the robotic arm achieves stable contact, the second segment performs position control according to the designed desired trajectory shown in Figure 8a,b to complete the desired robotic arm manipulation. We introduce noise to the link 14 normal force sensor, as shown if Figure 9.  
The impedance control is only applied to joints 6 to 15 because they are the section in contact of the first segment of the robotic arm because this can minimize the impact of the first segment's motion on the second segment while ensuring that the first segment of the robotic arm exhibits good impedance characteristics. The simulation results are compared with the situation where after the first segment of the manipulator comes into contact with an external object, no resistance is applied and only force/position hybrid control is used. The impedance model adjusts the manipulator's impedance characteristics, leading to a noticeable reduction in the number of contacts between the manipulator and the object, as shown in Figure 10a,b. This outcome aligns with the design objectives of the impedance  
Figure 8: Desired active joint velocity: (**a**) first segment; and (**b**) second segment. \[\text{K}_{\text{p\_force}}=15,\text{K}_{\text{i\_force}}=7\]0 Normal contact forces at sensor noise link 14.  
controller, addressing the limitations observed in previous work where impedance was not implemented. Fewer contacts result in more robust control of the HRSM, offering better protection from physical damage and ensuring stable multi-point contact. In contrast, Figure 11a,b present the contact collision force response without low-frequency filtering.