# Estimation of Hand Motion from Piezoelectric Soft Sensor Using Deep Recurrent Network
## 4 Result and Discussion
### Angle Value Estimation  
Based on good network performance for predicting \(m_{p}\), we show the ability for joint angle estimation by utilizing \(m_{p}\) in this subsection. For demonstration, we compared the result for the methods used in our earlier studies [18; 19]. In [18], we assumed that the offset \(O_{a}\) as average value of sensor data without using moving state. In [19], we estimated the moving state heuristically and determined the offset \(O_{h}\). In this experiment, we assumed that the offset values were determined for the predicted moving state \(O_{p}\), as the average of the recent 200 data for \(m_{p}=0\).  
For joint angle calculation, we applied offsets \(O_{a}\), \(O_{h}\), and \(O_{p}\) in Equation (10). The calculated joint angles were compared to the joint angles measured by the leap motion controller, and the criteria are defined as the difference between the degrees.  
Table 4 shows the average values of the angle difference in degrees between the joint angle from the leap motion controller and the calculated joint angles. Table 5 shows the standard deviation of the degree difference for each location. Figures 9 and 10 show the graph for examples of angle value comparisons between the joint angles in each location.  
Figure 8: Experimental results for moving state predicted by learning networks of index3 when the clenching fist motion except for the thumb shown in Figure 7c is repeated six times: (**a**) piezoelectric voltage; (**b**) joint angle calculated by leap motion controller; (**c**) comparison of the moving state of the joint angle from leap motion controller and predicted by the proposed network; and (**d**) moving state predicted with the heuristic method.  
\begin{table}
\begin{tabular}{l c c c c c c} \hline  & **thumb1** & **thumb2** & **thumb3** & **index1** & **index2** & **index3** \\ \hline proposed method & 6.79\({}^{\circ}\) & 5.64\({}^{\circ}\) & 9.40\({}^{\circ}\) & 8.92\({}^{\circ}\) & 12.88\({}^{\circ}\) & 13.75\({}^{\circ}\) \\ average method & 13.28\({}^{\circ}\) & 10.72\({}^{\circ}\) & 12.16\({}^{\circ}\) & 9.94\({}^{\circ}\) & 16.04\({}^{\circ}\) & 20.91\({}^{\circ}\) \\ heuristic method & 6.28\({}^{\circ}\) & 7.07\({}^{\circ}\) & 17.23\({}^{\circ}\) & 11.76\({}^{\circ}\) & 25.66\({}^{\circ}\) & 25.91\({}^{\circ}\) \\ \hline \end{tabular}
\end{table}
Table 4: Average of angle degree difference between calculated angles and joint angles from leap motion controller.  
\begin{table}
\begin{tabular}{l c c c c c} \hline  & **thumb1** & **thumb2** & **thumb3** & **index1** & **index2** & **index3** \\ \hline proposed method & 5.92 & 4.97 & 7.73 & 7.02 & 10.01 & 10.83 \\ average method & 9.61 & 7.69 & 9.46 & 7.64 & 11.50 & 14.75 \\ heuristic method & 5.62 & 5.21 & 13.10 & 8.99 & 18.82 & 19.19 \\ \hline \end{tabular}
\end{table}
Table 5: Standard deviation of the degree difference.  
Figure 9: Graph for the angle value of the thumb when the hand is bending the thumb shown in Figure 7b. Graph for: (**a**) thumb1; (**b**) thumb2; and (**c**) thumb3.  
From the results, the averages and standard deviations for degree differences facilitate the lowest value of the joint angle calculated using \(O_{p}\). In addition, as shown in Figures 9 and 10, the angle estimation based on the proposed method shows the most similar value compared to the ground-truth data. The result demonstrates that a good estimation of the moving state leads to a good result for angle estimation. One notable result is the joint angle calculated using \(O_{h}\) is very stable occasionally but does not always exhibit good result for angle estimation compared to using \(O_{a}\). This means that incorrect estimation of the moving state can lead to poor results for angle estimation. Therefore, we demonstrate the importance of precise estimation of moving state via two results: good estimation of joint angle using \(O_{p}\) and some estimation of joint angle using \(O_{h}\).