## 6 Conclusions  
This paper aims to improve the vibration suppression effect on the cantilever workpiece through configuration optimization. Due to the complex structure and poor stiffness of the robot and the AGV, as well as the approximate closed-loop structure of the ARGW systems, it is difficult to predict the vibration response. For the optimal vibration suppression, the dynamics model of the ARGW system was established based on the MSTMM  
Figure 19: Milling results under different clamping robot configurations. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Group**} & **Non-** & \multirow{2}{*}{**Config. 1**} & \multirow{2}{*}{**Config. 2**} & \multirow{2}{*}{**Config. 3**} & \multirow{2}{*}{**Config. 4**} \\  & **Clamping** & & & & \\ \hline Ra (\(\mu\)m) & 1.684 & 0.921 & 0.801 & 0.611 & 0.576 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Surface roughness of the milling path. considering the robot stiffness changing with configuration, and the configuration optimization was carried out with the workpiece response as the index. Through simulation analysis and experimental results, the following conclusions can be drawn. Through simulation and experimental comparison, it is found that the response obtained from the dynamics model is approximately 1.5% to 3.4% lower than the experiment; however, the overall agreement is good. The comparison results verify the accuracy of the ARGW system dynamics model established in this paper. The influence laws of different clamping robot configurations on the response were simulated based on the dynamics model. According to the simulation results, the closer the robot end is to the base coordinate system, the worse the vibration suppression effect on the workpiece will be. When the gripper clamping the workpiece in \(z_{\text{end}}=1.03\) m, the maximum response obtained using the simulation is located at \(P_{\text{max}}\) point (\(x_{\text{end}}=0.5\) m, \(y_{\text{end}}=0\) m), reaching 67.98 m/s\({}^{2}\). Then, the response of the workpiece was reduced to 44.77 m/s\({}^{2}\) using the configuration optimization method. In the experiments, the workpiece's surface roughness decreases from 0.921 to 0.576 as the response decreases from 62.69 m/s\({}^{2}\) to 46.78 m/s\({}^{2}\) after the configuration optimization of the clamping robot. Although the workpiece vibration response is not linearly related to the surface roughness, optimizing the configuration of the clamping robot based on the workpiece response can effectively improve the machining quality. In fact, in addition to the configuration of the clamping robot, there are many factors that affect the vibration response of the workpiece. In order to further improve the vibration suppression effect of the system in the future research, influence factors such as the gripper position, clamping force, and machining parameters should be considered. In addition, it is necessary to further establish the dynamics model of the dual-robot cooperative machining system and analyze the influence of the milling robot on the machining quality of the workpiece. Furthermore, the mapping relationship between workpiece vibration response and surface roughness can be explored to provide the basis for obtaining the ideal machining quality. Conceptualization, P.W., W.T. and B.L. ; methodology, P.W. and B.L. ; validation, P.W. and B.L. ; formal analysis, P.W. and W.T. ; investigation, P.W. and W.T. ; data curation, P.W. ; writing--original draft preparation, P.W. ; writing--review and editing, P.W., B.L. and Y.M. ; supervision, W.T. and B.L. All authors have read and agreed to the published version of the manuscript. This work was co-supported by the National Key R&D Program of China (No. 2020 YFB170300), the National Natural Science Foundation of China (Nos. 52075256 and 52005254), the Fundamental Research Funds for the Central Universities (No. NT2022016), and the National Defense Basic Scientific Research program of China (No. JCKY2019210B004). Not applicable. The authors declare no conflict of interest.