## 4 Verification Experiment of Impact Force  
In order to analyze the impact of the flexible end-effector and space debris, an impact force identification system was designed, as shown in Figure 5, mainly including an impact test bench, an impact force acquisition device, a data acquisition instrument, a computer, and accessory components. The experimental setup used for the entire impact force measurement process is shown in Figure 6. Details of the main equipment are shown in Table 1. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Species** & **Select** & **Model** & **Remark** & \\ \hline \multirow{2}{*}{Signal amplifier} & KISTLER multichannel charge amplifier & \multirow{2}{*}{5080 A} & \multirow{2}{*}{Fx} & \multirow{2}{*}{-7.5} \\  & KISTLER piezoelectric force gauge & & & \\  & & & & \\  & & & & \\  & & & & \\ Signal acquisition instrument & KISTLER data acquisition system & 5697A1 & & \\  & & & & \\  & & & & \\ Mechanical arm & Eff’s ER10L-C10 articulated robot & ER10L-C10 & & \\  & & & & \\  & & & & \\  & & & & \\  & & & & \\ \end{tabular}
\end{table} 
Table 1: Details of the main equipment. The flexible end-effector with variable pressure is shown in Figure 7. The parameters of its geometric model are shown in Table 2. By inflating the inside of the sphere to change the internal pressure value, the pressure sensor collects numerical signals in real time for feedback. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Inner diameter & 40 mm \\ Outer diameter & 60 mm \\ Poisson\({}^{\prime}\)s ratio & 0.47 \\ Elastic modulus & 0.0078 GPa \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Geometric model parameters. Figure 5: Impact force identification system diagram. Figure 6: Test device of impact. Figure 7: The flexible end-effector with variable pressure. In the experiment, the single variable principle was used. The movement speed of the robot arm was controlled to 0.4 m/s. The impact time \(t\) was 0.27 s. According to the depression amount \(\delta\) and the pressure \(P^{\prime}\) after the impact, the normal impact force was identified using Equations (2), (3), and (7). The initial pressure of the flexible end-effector was changed to 1.0 MPa, 1.5 MPa, 2.0 MPa, and 2.5 MPa, with the experiments performed in sequence. The experimental results are shown in Figure 8. The peak normal impact forces were 48.519 N, 54.669 N, 62.857 N, and 69.183 N, respectively. The actual impact force was loaded and unloaded, which was different from the step signal used in the simulation. The pressure at the impact end-effector was achieved through a pneumatic control system, including an intake pipe, a proportional valve, a check valve, an oil mixer, a filter, and other parts. At the same time, it was difficult to maintain the same pressure for each experiment due to defects in the manufacturing process causing leakage at the impact end-effector. For this reason, 16 sets of data were measured at each pressure point, and the average value was taken as the normal contact force under the pressure; every effort was made to avoid experimental errors. The comparison of the theoretical and experimental values of the normal impact force is shown in Figure 9. The comparative data are shown in Table 3, where the identification error was less than 6.7%. The rationality of the theoretical calculation was clearly proven by the change trend of the experimental data. The friction test device is shown in Figure 10. The initial impact speed was 0.4 m/s and the impact time t was 0.27 s. The inside of the rubber ball was inflated to change the internal pressure by adjusting  
Figure 8: Relationship of normal impact force and pressure.