# Position Tracking Control of 4-DOF Underwater Robot Leg Using Deep Learning
## 5 Performance Evaluation
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**Env.** & **PD Gain** & **Method** & **Joint 1** & **Joint 2** & **Joint 3** & **Joint 4** \\ \hline \multirow{4}{*}{Air} & \multirow{2}{*}{Low} & PD only & 0.0852 & 0.1042 & 0.3226 * & 0.1391 * \\  & & Hybrid & 0.0637 * & 0.0794 * & 0.3516 & 0.1484 \\ \cline{2-6}  & \multirow{2}{*}{High} & PD only & 0.1556 & 0.2725 & 0.4072 * & 0.1635 * \\  & & Hybrid & 0.1127 * & 0.1735 * & 0.4533 & 0.1843 \\ \hline \multirow{4}{*}{Water} & \multirow{2}{*}{Low} & PD only & 0.0625 * & 0.1343 & 0.2394 & 0.1181 \\  & & Hybrid & 0.0659 & 0.0837 * & 0.2386 * & 0.1142 * \\ \cline{1-1} \cline{2-6}  & \multirow{2}{*}{High} & PD only & 0.1300 & 0.1602 * & 0.3905 & 0.1349 \\ \cline{1-1}  & & Hybrid & 0.1107 * & 0.1975 & 0.3422 * & 0.1259 * \\ \hline \end{tabular}
* is a lower number.  
\end{table} 
Table 4: RMS joint torque of lateral motion. (unit: [Nm]). \begin{table}
\begin{tabular}{c c c c c c} \hline
**Env.** & **PD Gain** & **Method** & **X** & **Y** & **Z** \\ \hline \multirow{4}{*}{Air} & \multirow{2}{*}{Low} & PD only & 0.0006 & 0.0030 & 0.0153 \\  & & Hybrid & 0.0005 * & 0.0016 * & 0.0037 * \\ \cline{2-6}  & & \multirow{2}{*}{High} & PD only & 0.0017 & 0.0024 & 0.0102 \\  & & Hybrid * & 0.0013 * & 0.0018 * & 0.0027 * \\ \hline \multirow{4}{*}{Water} & \multirow{2}{*}{Low} & PD only & 0.0006 & 0.0023 & 0.0096 \\  & & Hybrid & 0.0004 * & 0.0013 * & 0.0034 * \\ \cline{1-1} \cline{2-6}  & & \multirow{2}{*}{High} & PD only & 0.0003 * & 0.0019 & 0.0060 \\ \cline{1-1}  & & Hybrid & 0.0004 & 0.0012 * & 0.0020 * \\ \hline \end{tabular}
* is a lower number.  
\end{table} 
Table 3: RMSE of lateral motion. (unit: [m]). Figure 27: RMS torque output of lateral motion with high PD gain. Figure 31: RMS torque output of forward motion with high PD gain. Figure 28: RMSE of forward motion with low PD gain. Figure 30: RMS torque output of forward motion with low PD gain. Figure 29: RMSE of forward motion with high PD gain. An analysis of the bar graphs and tables reveals that, across nearly all conditions, the RMSEs for the reference trajectories of the hybrid controller are significantly lower, irrespective of the control gain magnitude. In the case of forward motion with high control gains, the RMSE decreased by approximately 69.96% on the \(X\)-axis, 45.07% on the \(Y\)-axis, and 68.94% on the \(Z\)-axis in air. And in water, the RMSE decreased by about 39.83% on the \(X\)-axis, 40.48% on the \(Y\)-axis, and 54.07% on the \(Z\)-axis. Additionally, the RMS torque graph shows no significant difference in the joint torque output between the two controllers. The biggest torque difference occurs in the pitch joint during forward motion in the air with high PD control gains, and the difference is approximately 0.1364 Nm, which is at a very small level. This observation indicates that, even with a similar level of torque output, much higher position accuracy was achieved. Furthermore, the RMS joint torque output of each joint increases proportionally with the increase in PD control gains, suggesting a decrease in compliance with disturbance. Therefore, using the hybrid controller can simultaneously satisfy both high position accuracy and joint compliance.