## 5 Experimental Results
### Visual Servo Control with Large Payload  
Case 2 is the large payload visual servo comparison with and without vibration suppression. In order to verify that the control effect is more significant and robust to different stiffness, the manipulator carries a 1500 kg load at a maximum planning speed of 50 mm/s in free space. A new stiffness in X, Y, and RZ of the flexible base is 1.046 N/mm, 2.3155 N/mm, and 120.91 Nm/deg, respectively. The frequency of the system in the configuration of (\(-\)155, 0, \(-\)90) deg is (0.0875, 0.035) in the X and Y directions, which is expressed in the coordinate of BOE. The control gains are Kp = (0.05, 0.05, 0.05) and G = 17,000. The max planned velocity and acceleration of the visual servo is (0.05 m/s, 0.5 deg/s) and (0.003 m/s\({}^{2}\), 0.05 deg/s\({}^{2}\)). The extra lag compensator is needed, which is \(\frac{s+1}{4s+1}\). The camera of HC is sheltered and the PC is needed, which is mounted in front of the payload. The initial distance in the X direction is 1100 mm, and the intermediate berth is 200 mm. The initial configuration of the wrist, elbow, and shoulder is (\(-\)55, \(-\)102, \(-\)89) deg. The visual servo exit threshold is set to (5 mm, 5 mm, 0.3 deg) due to the different accuracy of the cameras. The experimental results for case 2 are given in Figure 13, the left Figure 13a,c has no vibration suppression algorithm, the right Figure 13b,d is based on FTS feedback. Figure 13a,b show the position error (x-axis and y-axis) and error (Euler angles representation), respectively, with respect to the desired relative position of the tool coordinates of payload to the VM of PC. The vibration reflected in the visual errors in Figure 13a is obvious compared to the empty load condition in Figure 12a, due to the lower fundamental frequency and higher motion speed. One can notice in the first trajectory, in the time from 7 s to 118 s, the servo control stopped abnormally after three swing periods, causing the visual measure errors to fluctuate until 190 s; it is obvious that the VS without vibration control will take a long time to wait for the vibration to fade away, as shown in Table 4. The total servo time of the four trajectories is much longer if there is no vibration suppression. It can be seen that the visual servo without vibration suppression has a large end oscillation at high speed and is difficult to attenuate, which may cause the camera to lose the target, leading to the termination of the visual servo motion, causing unnecessary disturbances, as shown in Table 4. The servo errors in the x-axis are 12 mm beyond the target, as a comparison, the overshoot in the X direction is avoided with the suppression algorithm, and dampen the non-forward direction (y-axis and Rz); thus, the vibration period basically decays from 4 to 1. Naturally, the time cost is lower, for example, it takes only 120 s to finish the first trajectory, reduced by 37%. The vibration suppression-based visual servo algorithm reduces the disturbance torque on the base (Figure 13d) from 18 Nm to 13.5 Nm, decreases the swing frequency of the load, and reduces the magnitude of the lateral swing to a certain extent to ensure that the target is within the field of view of the camera and improves the reliability of the visual servo tracking algorithm. One can notice that the visual error of the y-axis is significantly suppressed and the x-direction is smooth in Figure 13b. It should be noted that the deflection of the visual errors in the first half period of vibration is inevitable, even though the vibration will be damped rapidly, as shown in the Y-axis and Rz-axis. A reasonable interpretation is that the system's natural frequency is low, and the response bandwidth of the manipulator is not enough to instantly compensate for the visual errors, even though the manipulator has one redundant DOF for compensating for different directions of motion.