## 4 Validation of The Proposed Approach
### Experimental Results  
In this section, we discuss the results obtained from the experiment. First, the collected data were plotted to determine how the proposed arm movement pattern reformed the variation in the output. The plots of the master controller's positions over time and the histograms of its position on the \(\mathbf{Y}\)-axis in both the conventional approach and the proposed approach as undertaken by a participant are shown in Figure 8.  
With the conventional approach, we can see both inaccuracy and imprecision throughout the blasting line (Figure 8a). The lack of accuracy was caused by the participants' inability to guess the target accurately, whereas with the appropriate velocity, the participants struggled to maintain precision due to an inability to sufficiently control their arm movements, resulting in a high level of variance in the line. In Figure 8b, the histogram corresponding to Figure 8a clearly shows a low level of accuracy (the mean is far away from the target) and a low level of precision (multiple high-frequency bins), suggesting that the conventional approach is both inconsistent and unable to produce low variation in the output. For the proposed approach, the plots of the master controller's positions and the filtered output (Figure 8c) are represented by dash lines and solid lines, respectively. It can be seen that when the participants try to imitate the guideline under a constraint, i.e., appropriate velocity, human arm movement error appears as a variation in wavelength and amplitude. Focusing on the upper and lower boundaries, we can see that the participants failed to navigate the master controller to accurately and precisely touch and stay in contact with the guideline. Given the limits of human ability, this result was expected. Figure 8: \(Cont.\)  
However, this characteristic of the wave line is suited to the Kalman filter because the error causes the data to form a bell-shaped histogram (imitating random noise in the electrical signal), as shown in Figure 8d. On this basis, the accuracy can be improved because when the operator moves the cursor to approximately come close to both boundaries of the path back and forth across the target line, there is a very high chance that the cursor will frequently cross the target line so that the frequency of the positions will be high at the value close to zero. Consequently, the filtered output, represented by the solid line, is straighter and closer to zero than the dash line produced by the conventional approach is, resulting in lower total variation. Table 1 shows metrics describing the variation in the output from the human operator stage. The precision is represented by the mean square error (MSE), and the accuracy is represented by the absolute value of the difference between the mean and the target line. These values from the conventional approach and the proposed approach are compared next. The data obtained from participant 10 were excluded from the analysis since the data were considered as outliers. Figure 8: An example of the master controller’s positions from the experiment and the histograms of its positions on the _Y_-axis: (**a**) plot of the conventional approach and (**b**) the corresponding histogram; (**c**) plot of the proposed approach and (**d**) the corresponding histogram of the positions before filtering. To assess the participants' ability to imitate the guideline of the proposed arm movement pattern, we observed the MSE before filtering (\(Cov[z_{k}{{}^{\prime}}]\)). The average of the MSE from all the participants was 6.9329, whereas the guideline had an MSE of 8.3240. The difference between those MSEs is approximately 16.7%. This number indicates that despite being well trained, each participant created the pattern in accord with his or her preferred amplitude. Most of the participants preferred a lower amplitude than the guideline amplitude, as shown in a plot of individual variance in Figure 8(a).