# Segmented Hybrid Impedance Control for Hyper-Redundant Space Manipulators
## 6 Simulation Analysis
### First Scenario  
This scenario sketched in Figure 6 and depicted in Figure 7 is created to validate the new segmented hyper-impedance controller, focusing mainly on the impedance behavior of the manipulator with both the non-cooperative object and the base treated as fixed rigid bodies and the manipulator segmented into two segments. This case can be compared in the real world to a manipulator wrapping around a truss structure to achieve a better end-effector position and velocity error. In the second scenario, our experimental set-up mirrors the challenges encountered in orbital debris removal missions. The diverse nature of space debris, varying in geometry, mass distribution, and material composition, presents a complex manipulation challenge that validates the adaptability of our control approach. The controller's ability to maintain stable impedance characteristics while handling objects demonstrates its potential application in space debris removal operations. This flexibility is particularly valuable as debris can range from defunct satellites with regular geometries to fragmented components with unpredictable mass distributions. \begin{table}
\begin{tabular}{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]\({}^{\mathrm{T}}\) & 11 & [0 0 1]\({}^{\mathrm{T}}\) & 19 & [0 1 0]\({}^{\mathrm{T}}\) \\ \(4\) & [0 0 1]\({}^{\mathrm{T}}\) & 12 & [0 0 1]\({}^{\mathrm{T}}\) & 20 & [0 0 1]\({}^{\mathrm{T}}\) \\ \(5\) & [1 0 0]\({}^{\mathrm{T}}\) & 13 & [0 0 1]\({}^{\mathrm{T}}\) & 21 & [1 0 0]\({}^{\mathrm{T}}\) \\ \(6\) & [0 0 1]\({}^{\mathrm{T}}\) & 14 & [0 0 1]\({}^{\mathrm{T}}\) & 22 & [0 0 1]\({}^{\mathrm{T}}\) \\ \(7\) & [0 0 1]\({}^{\mathrm{T}}\) & 15 & [1 0 0]\({}^{\mathrm{T}}\) & 23 & [1 0 0]\({}^{\mathrm{T}}\) \\ \(8\) & [0 0 1]\({}^{\mathrm{T}}\) & 16 & [0 0 1]\({}^{\mathrm{T}}\) & 24 & [0 0 1]\({}^{\mathrm{T}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Rotation axis of the joints in scenario one. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Physical Quantity** & **Value** & **Physical Quantity** & **Value** \\ \hline Robot surface elastic modulus (\(\mathrm{E}_{\mathrm{\tiny{I}}}/\mathrm{MPa}\)) & 7.84 & Target surface elastic modulus (\(\mathrm{E}_{\mathrm{\tiny{2}}}/\mathrm{GP}_{\mathrm{\tiny{2}}}\)) & 70 \\ Robot surface Poisson’s ratio (\(\mathrm{\
u}_{\mathrm{\tiny{1}}}\)) & 0.47 & Target surface Poisson’s ratio (\(\mathrm{\
u}_{\mathrm{\tiny{2}}}\)) & 0.3 \\ Force coefficient (\(\mathrm{n}\)) & 1.5 & Recovery coefficient (\(\mathrm{C}_{\mathrm{\tiny{I}}}\)) & 0.7 \\ Dynamic friction coefficient (\(\mathrm{\mu}_{\mathrm{d}}\)) & 0.2 & Static friction coefficient (\(\mathrm{\mu}_{\mathrm{\tiny{8}}}\)) & 0.4 \\ Stribeck model index (\(\mathrm{\xi}_{\mathrm{\tiny{8}}}\)) & 2 & Stribeck speed (\(\mathrm{\xi}_{\mathrm{\tiny{8}}}/\mathrm{(m}/\mathrm{s})\)) & 0.1 \\ Robot surface elastic modulus (\(\mathrm{E}_{\mathrm{\tiny{1}}}/\mathrm{MPa}\)) & 7.84 & Target surface elastic modulus (\(\mathrm{E}_{\mathrm{\tiny{2}}}/\mathrm{GP}_{\mathrm{\tiny{2}}}\)) & 70 \\ Robot surface Poisson’s ratio (\(\mathrm{\
u}_{\mathrm{\tiny{1}}}\)) & 0.47 & Target surface Poisson’s ratio (\(\mathrm{\
u}_{\mathrm{\tiny{2}}}\)) & 0.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Rotation axis of the joints in scenario two.