## 5 Experimental Results
### Visual Servo Control without Payload  
Case 1 is the visual servo without a payload mounted on the EEF. The stiffness in X, Y, and RZ of the flexible base is 1.6375 N/mm, 8.158 N/mm, 529 Nm/deg, respectively. The control gains are \(\text{Kp}=(0.032,\,0.048,\,0.05)\) and G = 17,000. The max planned velocity and acceleration of the visual servo are (0.02 m/s, 1 deg/s) and (0.001 m/s\({}^{2}\), 0.05 deg/s\({}^{2}\)). No extra lag compensator is needed due to the small disturbance to the flexible base. The initial distance in the X-direction is 1000 mm, and the intermediate berth is 120 mm. The initial configuration of the wrist, elbow, and shoulder is (39, \(-\)96, \(-\)100) deg. The visual servo control will finish when the tracking errors in X, Y, and Rz are less than (3 mm, 3 mm, 0.3 deg), showing that the manipulator reaches the desired berth position. The experimental results for case 1 are given in Figure 12, in Figure 12,c there is no vibration suppression algorithm, while the right Figure 12b,d is based on FTS feedback. Figure 12a,b show the position error (x-axis and y-axis) and orientation error (Euler angles representation), respectively, with respect to the desired relative position to the HC markers. The visual measure results show that the EEF's motion speeds up and then slows down exponentially, and the visual control is finished normally in each trajectory. The visual errors shown in Table 4 are similar due to the measurement accuracy and resolution limitation. The difference of the trajectory in the x-axis is not obvious because the motion of the EEF is slanted to the y-axis (expressed in the coordinate of BOE). As the stiffness of the base in the y-axis is larger than the x-axis, the higher fundamental frequency is as expected without payload, which means the vibration control does not promote the tracking accuracy under the higher fundamental frequency; the dominant factor is the measurement accuracy and resolution limitation. One can notice that the visual error of the y-axis is significantly suppressed, and the time of the oscillation during each motion is shortened from the initial 8 cycles to about 1 cycle. Similar results of contrast are shown in Figure 12c,d, where the forces (x-axis and y-axis) and torque (Mz) of the base FTS, which is represented in the coordinate of BOE. From the comparison of Mz, it can be seen that the base vibration is quickly suppressed after one period of vibration, the FTS-based suppression works very well. One can notice, the reaction torque of Mz is relevant to the visual tracking errors of the y-axis, the base vibration suppression algorithm can effectively suppress the base disturbance and reduce the measured oscillation period of the EEF. Furthermore, we compare the total VS time under the zero payload condition, as shown in Table 4. It should be mentioned that the total servo time of the four trajectories is not necessarily related to whether or not the vibration control is used. When the servo control stability is guaranteed, the exponential convergence method of the tracking errors is the major contributors to the servo time. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Cases**} & **Vibration** & \multicolumn{2}{c}{**Max Visual Errors**} & \multicolumn{2}{c}{**Vibration**} & \multicolumn{2}{c}{**Total VS**} & \multicolumn{2}{c}{**Torque of**} \\  & **Control** & **X (mm)** & **Y (mm)** & **Rz (deg)** & **Periods** & **Time (s)** & **FTS (Nm)** & **Stability** \\ \hline \multirow{2}{*}{Without payload} & No & 0 & 7 & 0.2 & 8 & 374 & 7.7 & Yes \\  & Yes & 0 & 6 & 0.3 & 1 & 386 & 7.4 & Yes \\
1500 kg payload & No & 12 & 77 & 0.7 & 4 & 530 & 18 & No \\  & Yes & 0 & 77 & 0.8 & 1 & 406 & 13.5 & Yes \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Visual servo results of the two cases. Figure 12: Comparison of the empty load visual servo with or without the base FTS feedback.