# Position Tracking Control of 4-DOF Underwater Robot Leg Using Deep Learning
## 6 Conclusions  
In this study, we proposed the hybrid controller to enhance the position-tracking performance of the robot leg. Our approach relies on a deep learning neural network, eliminating the need for explicit modeling and computation of non-linear dynamic characteristics, including fluid effects. The efficacy of the hybrid controller was verified using an actual 4-DOF underwater robot leg. Leveraging the capabilities of deep learning, particularly linear regression, trajectories not directly used for learning were employed for verification. To ensure accurate testing, experiments were conducted with two sets of PD control gains applied to both forward and lateral motions. The result demonstrated a substantial improvement in position accuracy when comparing the hybrid controller to the single task-space PD controller, even with similar torque outputs across nearly all conditions. Quantitative analysis revealed that the position error in the task-space was reduced by about 60.96% in air and about 42.7% in water on average. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Env.** & **PD Gain** & **Method** & **Joint 1** & **Joint 2** & **Joint 3** & **Joint 4** \\ \hline \multirow{4}{*}{Air} & \multirow{2}{*}{Low} & PD only & 0.1797 * & 0.1300 & 0.4039 * & 0.1611 * \\  & & Hybrid & 0.1945 & 0.1287 * & 0.4375 & 0.1678 \\ \cline{2-6}  & \multirow{2}{*}{High} & PD only & 0.2532 * & 0.4075 & 0.4525 * & 0.1806 \\  & & Hybrid & 0.2636 & 0.2711 * & 0.4773 & 0.1606 * \\ \hline \multirow{4}{*}{Water} & \multirow{2}{*}{Low} & PD only & 0.2583 * & 0.1803 * & 0.5089 * & 0.3429 \\  & & Hybrid & 0.2871 & 0.1912 & 0.5216 & 0.2893 * \\ \cline{1-1} \cline{2-6}  & \multirow{2}{*}{High} & PD only & 0.2907 * & 0.2610 & 0.5286 * & 0.3098 \\ \cline{1-1}  & & Hybrid & 0.3276 & 0.1699 * & 0.5781 & 0.3021 * \\ \hline \hline \end{tabular}  
* is a lower number.  
\end{table} 
Table 6: RMS joint torque of forward motion. (unit: [Nm]). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Env.** & **PD Gain** & **Method** & **X** & **Y** & **Z** \\ \hline \multirow{4}{*}{Air} & \multirow{2}{*}{Low} & PD only & 0.0030 & 0.0044 & 0.0150 \\  & & Hybrid & 0.0009 * & 0.0024 * & 0.0047 * \\ \cline{2-6}  & & \multirow{2}{*}{High} & PD only & 0.0028 & 0.0037 & 0.0120 \\  & & Hybrid & 0.0011 * & 0.0018 * & 0.0036 * \\ \hline \multirow{4}{*}{Water} & \multirow{2}{*}{Low} & PD only & 0.0058 & 0.0051 & 0.0174 \\  & & Hybrid & 0.0035 * & 0.0031 * & 0.0080 * \\ \cline{1-1} \cline{2-6}  & & \multirow{2}{*}{High} & PD only & 0.0046 & 0.0037 & 0.0139 \\  & & Hybrid & 0.0024 * & 0.0030 * & 0.0061 * \\ \hline \hline \end{tabular}  
* is a lower number.  
\end{table} 
Table 5: RMSE of forward motion. (unit: [m]). These findings suggest the potential of overcoming non-linearity by learning the dynamic characteristics of motors and robots in both air and water. Therefore, this study makes notable contributions by considering non-linear dynamics factors, adapting to various environments, enhancing utility through the combination of PD control, and achieving lower torque output with higher position accuracy. When controlling the lateral motion of the robot leg, it was observed that the RMSE in water was smaller than that in air, indicating better control performance underwater. This improvement could be attributed to the relatively low fluid force due to the simple movement in the lateral direction motion within a two-dimensional plane. We presumed that buoyancy acted as reduced gravity compensation, likely contributing to the overall enhanced performance. However, in the case of forward-direction motion, it is evident that position-tracking performance was further degraded. For three-dimensional movements like walking, various fluid forces such as drag and lift, in addition to buoyancy, were more generated compared to the two-dimensional movement of the lateral direction motion. This increased complexity seems to have adversely affected control performance.