# Research on Human-Robot Collaboration Method for Parallel Robots Oriented to Segment Docking
## 4 Experimental Verification
### Single-Degree-of-Freedom Experiment  
The effectiveness of the fractional-order admittance control was evaluated on individual degrees of freedom. Due to the different parameter settings for translational and rotational degrees of freedom, experiments were conducted on both Cartesian translational and rotational degrees of freedom. Figure 5 shows a response performance comparison between the conventional admittance control and the fractional-order admittance control. Figure 5a,b show the position/attitude change curves of the Stewart parallel platform under the control of the two controllers after applying a force of \(Fz=20\) N and a moment of \(Tz=2\) Nm to the translational and rotational degrees of freedom of the \(Z\)-axis, respectively. By comparing the curves, it was observed that, in the translational degree of freedom, applying a force of 20 N for 3 s led to a 52.05% increase in response speed and a slight reduction in overshoot when employing fractional-order admittance control. Similarly, during the rotational degree of freedom, applying a torque of 20 Nm for 3 s showcased a 41.28% higher response speed in fractional-order admittance control in contrast to traditional admittance control. These comparative outcomes distinctly highlight the substantial enhancement in response speed achieved through fractional-order admittance control as opposed to traditional methods. Subsequent assembly experiments have shown that this improvement adequately meets the requirement for a fast robot response during cabin segment docking. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \(I_{\text{B}_{x}}/mm\) & \(I_{\text{B}_{y}}/mm\) & \(I_{\text{B}_{x}}/mm\) & \(I_{\text{B}_{y}}/kg\cdot mm\) & \(I_{\text{B}_{z}}/kg\cdot mm\) & \(I_{\text{B}_{z}}/kg\cdot mm\) \\ \hline Value & 50 & 100 & 10 & 0.238 & 0.167 & 0.102 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mass and geometric parameters of the load-bearing props. Figure 5: Tracking curves for dynamics control and dynamics robust control. **(a)** Comparison of response performance in three translational degrees of freedom along the \(Z\)-axis as an example of verification. **(b)** Comparison of the response performance in the three rotational degrees of freedom, verified using the rotational degree of freedom around the \(Z\)-axis as an example. The robustness of the inverse dynamic robust controller against unknown external forces underwent validation via experiments. The experimental results are shown in Figure 6. Tests encompassed both simple dynamic control (Equation (14)) and the resultant inverse dynamics robust control. These experiments entailed applying a 20 N upward force along the \(Z\)-axis for 3 s, followed by a downward force of 20 N on the end-effector of the parallel robot. Upon the generation of interaction forces, it becomes apparent that the tracking error of the controllers gradually increases. Around 5.3 s, both the inverse dynamics controller and the inverse dynamics robust controller contained peak tracking errors. Specifically, the peak tracking error for the inverse dynamic controller was 1.18 cm, whereas for the inverse dynamic robust controller, this remained at only 0.57 cm. In comparison to the simple dynamic controller, the dynamic robust controller consistently produces smaller, bounded errors. Conversely, the simple dynamic controller yields larger errors, potentially causing unexpected robot motion during interaction. Through this experiment, the necessity of introducing robust control in dynamic controllers for achieving high-precision segment  
Figure 6: Tracking error for dynamics control and dynamics robust control. (**a**) Comparison of the tracking of the desired position profile of a Stewart parallel platform in the \(Z\)-axis translational degree of freedom under dynamics control versus dynamics robust control. (**b**) Comparison of tracking error of desired position profile by Stewart parallel platform in \(Z\)-axis translational degree of freedom under dynamics control vs. dynamics robust control.