# Vision-Based Path Guidance to Achieve Dies-Free Roller Hemming Process
## 3 Verification and Results
### Hemming Experiment and Results
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & & \multicolumn{8}{c}{**Unit: mm**} \\ \hline  & \multicolumn{2}{c}{**Robot Pose**} & & & **Part** & **Part** & **Part** & **XYZ Offset** & **Distance** \\  & \multicolumn{2}{c}{} & & & & **A** & **B** & **C** & **among 3 Parts** & **Error \(\varepsilon\)** \\ \hline \multirow{3}{*}{P1} & X & 1215.305 & W & \(-\)179.887 & X & \(-\)10.073 & \(-\)8.826 & \(-\)7.456 & dX & 2.617 & \multirow{3}{*}{3.017} \\  & Y & \(-\)393.498 & P & \(-\)0.474 & Y & 0.222 & 0.220 & 0.220 & dY & 0.002 & 3.017 \\  & Z & 589.524 & R & \(-\)9.634 & Z & \(-\)4.278 & \(-\)4.517 & \(-\)5.780 & dZ & 1.502 & \multirow{3}{*}{2.729} \\ \hline \multirow{3}{*}{P2} & X & 1300.716 & W & \(-\)179.886 & X & \(-\)9.779 & \(-\)8.975 & \(-\)7.712 & dX & 2.067 & \multirow{3}{*}{3.017} \\  & Y & 103.561 & P & \(-\)0.473 & Y & 0.222 & 0.220 & 0.212 & dY & 0.010 & 2.729 \\  & Z & 550.759 & R & 20.929 & Z & \(-\)4.396 & \(-\)4.379 & \(-\)2.614 & dZ & 1.782 & \multirow{3}{*}{2.171} \\ \hline \multirow{3}{*}{P3} & X & 1275.583 & W & \(-\)179.887 & X & \(-\)10.160 & \(-\)9.843 & \(-\)9.186 & dX & 0.974 & \multirow{3}{*}{2.171} \\  & Y & \(-\)451.610 & P & 0.475 & Y & 0.219 & 0.219 & 0.222 & dY & 0.003 & 2.171 \\  & Z & 568.554 & R & 32.942 & Z & \(-\)3.095 & \(-\)3.594 & \(-\)5.035 & dZ & 1.940 & \multirow{3}{*}{4.245} \\ \hline \multirow{3}{*}{P4} & X & 1377.169 & W & \(-\)179.888 & X & 0.177 & 0.178 & 0.183 & dX & 0.006 & \multirow{3}{*}{4.245} \\  & Y & \(-\)560.232 & P & 0.473 & Y & \(-\)1.192 & \(-\)1.892 & \(-\)3.282 & dY & 2.090 & 4.245 \\ \cline{1-1}  & Z & 641.432 & R & \(-\)77.453 & Z & 2.664 & 1.646 & \(-\)1.031 & dZ & 3.695 & \multirow{3}{*}{4.245} \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The scanned data and errors of the car hood sheet metal parts. For visualization of real-time compensation of the hemming path, relevant software has been developed, and a screenshot of the software is shown in Figure 17. In this software, the 3D surface reconstruction and position correction functions of the sheet metal are based on random sample consensus (RANSAC) [15], in which iterative closest points (ICP) [16] are used for point cloud features. The algorithm is adopted to match the reconstructed 3D surface of the sheet metal with the point cloud of the CAD model as a position correction. To demonstrate how the hemming process is performed, two 180 mm wide, 0.8 mm thick galvanized steel (SS41) flat metal sheets with either a 9 mm or 10 mm flange height were used for the 90\({}^{\circ}\) \(\rightarrow\) 0\({}^{\circ}\)  hemming test as schematically illustrated in Figure 18a. With the previously described calibration process, the robot follows the path generated by the proposed visual path guidance model to perform hemming of these two flat steel sheets. The flange is progressively hemmed from 90\({}^{\circ}\) to 45\({}^{\circ}\) and then from 45\({}^{\circ}\) to finally 0\({}^{\circ}\), during which process the upper rollers with different taper angles, as shown in Figure 2b, are interchanged.