## 4 Experiment and Analysis  
In order to further verify the hand-eye calibration algorithm described above, an experiment was conducted on a real dual-arm hand-eye robot system, which contains a dual-arm robot SDA5F and two monocular cameras. The SDA5F is a kind of humanoid robot made by Yaskawa Electric for scientific research, and the two monocular cameras were used for mimicking the different views of a human being. Both of the cameras were calibrated in the experiment. As shown in Figure 6, the two cameras were fixed near the rotational axis of the dual-arm robot base, and both of them were monocular RGB cameras. Camera 1 looked up at an angle from the horizon plane in order to mimic the upward view of a human being, and camera 2 looked down at an angle from the horizontal plane in order to mimic the downward view of a human being. The two monocular cameras have the ability to sense the body, and the main properties of them are RGB image acquisition functions with adjustable frequencies. During the experiment, the software platforms were running in the Windows operating system, and C++ was used to carry out the secondary development of the robot control programs, including the hand-eye calibration and result analysis of the dual-arm robot. The model of the robot control cabinet is FS100, which is a type of processing center manufactured by Yaskawa Electric Co., Ltd. in Kitakyushu, Fukuoka, Japan. The control cabinet can connect to the PC in order to obtain the predetermined instructions from the host computer. The hand-eye calibration algorithm proposed in this paper mainly considers the identification of the external parameters of the cameras and requires multiple pictures with the known two-dimensional board as the target. Figure 7 shows the setup of the hand-eye calibration of the dual-arm hand-eye robot system during the experiment, and the external parameters of the two cameras were identified. Figure 7a shows the calibration setup of the left arm of the SDA5F robot and camera 1. Figure 7b shows the calibration setup of the right arm of the SDA5F robot and camera 2. It is necessary to calibrate the two arms and cameras to describe them in a unified coordinate system at last. The data extracted from the pictures describe the movement of the target that is useful for further processing such that that the two-dimensional board is fixed at the end-effector of one arm of the dual-arm robot, and its orientation is close to that of the end-effector coordinate. Although the simulation of the MDQ algorithm proposed could obtain better results with added random noise, it is also affected by the accuracy of the poses or other factors which would be difficult to model in this experiment. Therefore, in order to make the adverse effects on the observed data as acceptable as possible, it was necessary to use a calibration board with a flat surface and a suitable accuracy so that more groups of experimental data for calibration could be collected and conveniently processed. In order to obtain better experimental results, approximately random poses of each end-effector were selected in different areas of the robot workspace. The cameras captured multiple sets of pictures and collected reasonable data. For the comparison, the  
Figure 6: Setup of the two cameras in the dual-arm hand–eye robot system. same data were identified by the method mentioned in the reference [21]. The two arms of the dual-arm robot and the two cameras were calibrated in the experiment, and the results were processed with the same set of the measurements as the two arms have the same structure. Figure 8 shows some pictures of the calibration board captured by the two cameras in the experiment, and each camera was calibrated separately.