## 3 Experimental Results
### Experiment on the Accuracy of the Pose Estimation System
Figure 11 confirms that the error of the translation axis ranges between 0.825 and 9.834 mm and 0.825-5.810%, and the average error is 5.417 mm and 4.850% for the \(X\)-axis, 4.001 mm and 3.513% for the  
Figure 10: Building reference point cloud models of each 6-DoF pose for estimating measured clouds of the dynamic workpiece in the (**a**) i-axis, (**b**) \(Y\)-axis, (**c**) \(Z\)-axis, (**d**) \(RX\)-axis, (**e**) \(RY\)-axis, and (**f**) \(RZ\)-axis. Figure 9: Setup of standard rotation angles for different estimation poses of the dynamic workpiece using the professional laser rangefinder of BOSCH. \(Y\)-axis, and 1.570 mm and 2.214% for the \(Z\)-axis. The trend of Figure 11a points out that in the \(X\) and \(Y\) axes, the larger the distance between the reference and the measured points, the higher the error of the system. On the contrary, a smaller distance will lead to a higher error percent in the system. The same trend appears in the error of the \(Z\)-axis (Figure 11b). Figure 12 demonstrates the rotation error of the system. For the \(RX\) and \(RY\) axes (Figure 12a), and the \(RZ\)-axis (Figure 12b), the errors are small if the real angle differences are small, but the error percent will increase when the angle differences decrease. The error and error percentage of the rotation axis range 0.13\({}^{\circ}\)-2.67\({}^{\circ}\) and 0.37-16.40%, respectively. The average error and error percentage of the \(RX\)-axis are 1.36\({}^{\circ}\) and 6.38%, respectively, the average error and error percentage of the \(RY\)-axis are 1.01\({}^{\circ}\) and 6.01%, respectively, and the average error and error percentage for the \(RZ\)-axis are 1.21\({}^{\circ}\) and 2.59%, respectively. The second sub-experiment was conducted to examine the repetition accuracy of the pose estimation system. The setup of this sub-experiment is similar to the above experiments (as shown in Figures 8 and 9). First, the workpiece is placed in the reference position, then it is moved to the new position that needs to be measured. However, in this experiment, the workpiece will be repositioned in all 6 axes. The measured position will be  
Figure 11: Translation errors of workpiece modeling at different estimated poses for the (**a**) \(XY\)-axis and the (**b**) \(Z\)-axis. Figure 12: Rotation errors of workpiece modeling at different estimated poses for (**a**) the \(RX\) and \(RY\) axes and (**b**) the \(RZ\)-axis. estimated 10 times; later, the data will be analyzed to find the repetition error of the pose estimation system. As shown in Figure 12(a), the translation error ranges 0.024-8.563 mm, which is 0.080-9.937%. The rotation error ranges 0.094\({}^{\circ}\)-2.908\({}^{\circ}\), which is 0.314-9.923% (Figure 12(b)). The average error percentages of each axis are 3.905%, 3.182%, 5.087%, 6.013%, 6.189%, and 5.523% for the X, Y, Z, RX, RY, and RZ axes, respectively. The error values which were measured were all less than 10% and 9 mm. For the purpose of researching and developing, the pose estimation repetition error is adequate for the robot system to successfully pick up the object. All the measurements were performed independently; hence, each time, measuring repetition errors will result in a different set of errors and do not relate to any of the previous sets of measurements.