## 5 Experimental Results
### Experiments on Position/Orientation Error  
To evaluate the performance of the proposed system, we compared the calculated amount of movement of the robot to the actual amount of movement. The amount of robot movement can be easily calculated using Equation (13). In this error evaluation process, 686 data samples were used for neural network training, and 200 data samples were used for testing the neural network. The test results are shown in Figure 11. Although the actual results are not as good as the results from the simulation environment, they have reduced the position/orientation error sufficiently. The after compensation value of mean error-position in each direction as shown in Table 5 are \(e_{t_{x}}=-1.3897\) (mm), \(e_{t_{y}}=-2.4289\) (mm), and \(e_{t_{z}}=1.554\) (mm), for which the error was reduced by 50.3% on average. In Table 6, the standard deviation for position/orientation errors after compensation are greatly reduced: \(e_{t_{x}}=0.6998\) (mm), \(e_{t_{y}}=0.8826\) (mm), and \(e_{t_{z}}=0.4484\) (mm), approximately 69% of error reduction on average. The proposed method showed good performance as a result of the experiment. In Figure 11, the after-compensation error (red line) is smaller and smoother than the before compensation error (blue line) when applying the error compensation technique. This illustrates that the absolute position error of the robot's end-effector is improved. Considering the calculated data from the simulation and experiment as shown in Tables 3-6, respectively, the compensation improvement of the experimental cases is smaller than the result of the simulation cases. The main reason is that it is really difficult in the real experiment to consider all factors that lead to the absolute position error of the robot's end-effector such as tolerances, eccentricities, wear-out, payload, temperature and insufficient knowledge of model parameters for the transformation between robot poses, etc. [5]. However, our algorithm did reduce the absolute position error in real experiments by 50.3%, which can verify the proposed compensation algorithm to be utilized successfully in the real application. Figure 10: Setup for training robot. Comparing the compensation performance the other works, [PERSON] et al. [27] proposed an improved method for the pose accuracy of the robot manipulator by using a multiple-sensor combination measuring system (MCMS). In their experiments, the pose accuracy of the manipulator is improved by 67.3%, to 3.379 mm on average with the Kamal filter (KF) and by 38.2%, to 1.286 mm on average with multi-sensor optimal information fusion algorithm (MOIFA). [PERSON] et al. [2] proposed a method of robot end-effector pose accuracy improving using joint error mutual compensation, the improved value of positioning accuracy for the robot end-effector from 2% to two times, to \(\Delta L=2.39\) mm on \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Measurement**} & \multicolumn{4}{c}{**Standard Deviation Error**} \\ \cline{2-7}  & \multicolumn{2}{c}{**Translation/mm**} & \multicolumn{4}{c}{**Rotation/rad**} \\ \cline{2-7}  & \(e_{t_{s}}\) & \(e_{t_{\gamma}}\) & \(e_{t_{s}}\) & \(e_{\theta_{s}}\) & \(e_{\theta_{s}}\) & \(e_{\theta_{s}}\) \\ \hline Before & 2.2461 & 2.3726 & 1.7413 & 0.0019 & 0.0036 & 0.0010 \\ \hline After & 0.6998 & 0.8826 & 0.4484 & 0.0010 & 0.0018 & 0.00055 \\ \hline Reduced \% & 68.84\% & 62.80\% & 74.25\% & 47.37\% & 50\% & 45\% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Standard deviation error. Figure 11: Comparison between before and after compensation in the experiment environment.