## 5 Experiment and Validation Results
### Experimental Calibration Results  
In this experiment, a robot calibration system consists of a Hyundai HH800 robot (6 degree of freedom (d.o.f)) that has one closed-loop actuating mechanism, a 3D point sensing device (API Laser Tracker, measurement accuracy of 0.01 mm/m, repeatability of +/-0.006 mm/m), and an accompanying laser reflector. The reflector is fixed at a particular location of the robot end-effector. The system is arranged as shown in Figure 5.  
In order to acquire suitable measurement data for robot parameter identification and IWO-NN training, the robot moves its end-effector to positions such that they entirely cover the workspace. The three-dimensional coordinates of the end points are measured by the Laser Tracker and saved in a computer. At the same time, the associated robot joint readings also are recorded.  
These measurements are grouped as follows: A set of 40 robot configurations (Q1) is used for parameter identification and collected over all the workspaces. By using the SKCM method, the kinematic and joint compliance parameters are identified. These parameters are presented in Tables 2 and 3, including four joint compliance parameters and 29 kinematic parameters. Another set (Q2) of 50 robot configurations is also randomly selected to determine the weights and biases of the neural network that has five hidden nodes, six inputs, and three outputs. The reason why we use a different set (Q2) from the first set (Q1) is that the neural network compensator has more general error compensation capability over the entire robot workspace. A set of 50 arbitrary endpoints (Q3) for robot accuracy validation is collected over all the workspaces.  
Figure 5: Calibration setup of the Hyundai HH800 robot.  
In this calibration progress, the HH800 robot is used to apply four different calibration algorithms. Table 4 and Figure 6 demonstrate the results of these calibration methods. Figure 6 provides a visual result of the absolute position errors of each calibration pose using four calibration methods, including the conventional kinematic calibration method (KM), as well as the simultaneous identification of joint compliance and kinematic parameters method (SKCM), and the combination of NN compensator and SKCM method (NN-SKCM). It shows that the position errors generated by the proposed method are the lowest and better converging in comparison with the other methods. By using the IWO-NN SKCM, the mean of errors is reduced from 0.5961 to 0.3450 mm by as much as 42.12% compared to the KM method. This mean of errors is also decreased as much as 31.52% in comparison to the SKCM method (0.5038 mm).  
Figure 6: Absolute position error of the HH800 robot after calibration.  
Figure 7: Absolute position error of the HH800 robot after validation.  
\begin{table}
\begin{tabular}{c c c c} \hline  & **Mean (mm)** & **Max. (mm)** & **Std. (mm)** \\ \hline Before calibration & 4.4266 & 6.2749 & 0.6772 \\ KC & 0.5981 & 1.4293 & 0.285 \\ SKC & 0.5458 & 1.0078 & 0.2142 \\ NN-SKC & 0.5187 & 1.0532 & 0.2642 \\ IWO-NN-SKCM & 0.4662 & 0.6538 & 0.1333 \\ \hline \end{tabular}
\end{table}
Table 5: Absolute position accuracy of the HH800 robot (validation).  
By using the proposed method, the mean of errors is reduced from 0.5981 to 0.4662 mm by as much as 22.07% better in comparison to the KM method. The mean of errors is also decreased by as much as 26.72% in comparison to the SKCM method (0.5458 mm), and there is a 10.14% decline from the mean of errors by using the NN-SKCM method (0.5187 mm). The proposed method also generates the lowest maximum position error (0.6538 mm) and standard deviation (0.1333 mm).