# Study on Oscillatory and Undulatory Motion of Robotic Fish
## 4 Conclusions  
This research uniquely concentrates on a detailed examination of fish motion, particularly highlighting the intricacies of undulating and oscillatory movements, distinguishing itself from current studies. The emphasis shifts towards utilizing kinematic equations of motion control for fluid dynamic calculations. The design, created using Rhino 6 software, incorporates precise fluid resistance computations via Ansys Fluent 19, investigating flow velocities spanning from 1 to 4 m/s.  
As flow velocity linearly increases, the drag force exhibits an inverse variation in tail flap frequency between oscillation and undulation. Using this information, optimization of the motion control equation is necessary for attaining maximum thrust under various tail flapping frequencies causing a resistance to surge. Remarkably, at high tail flapping frequencies, a decreasing trend in drag force is observed (746 N at 1 m/s and 456 N at 4 m/s). The integration of kinematic equations of motion control has facilitated the discovery of this intriguing phenomenon. This research has contributed to analyzing the development of fish shape and motion control to generate thrust under various flapping frequencies from 2 Hz to 5 Hz and under various flow velocities from 1 m/s to 4 m/s.  
Conceptualization, P.H.N.A.; formal analysis, J.H., R.Z. and J.K.; funding acquisition, P.H.N.A.; investigation, J.H., R.Z. and J.K.; methodology, H.-S.C. and P.H.N.A.; project administration, H.-S.C. and P.H.N.A.; resources, P.H.N.A.; supervision, H.-S.C.; writing--original draft, P.H.N.A.; writing--review and editing, H.-S.C. and P.H.N.A. All authors have read and agreed to the published version of the manuscript.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **Flow** \\ **Velocity** \\ **(m/s)** \\ \end{tabular} } & \multicolumn{4}{c}{**Flapping Frequency \(f_{\theta}\)=2 Hz**} & \multicolumn{4}{c}{**Flapping Frequency \(f_{\theta}\)=5 Hz**} \\ \cline{2-10}  & \multirow{2}{*}{**St**} & \multicolumn{2}{c}{**Oscillation**} & \multicolumn{2}{c}{**Undulation**} & \multirow{2}{*}{**St**} & \multicolumn{2}{c}{**Oscillation**} & \multicolumn{2}{c}{**Undulation**} \\ \cline{3-10}  & & & \(C_{D}\) & \(F_{D}\) **(N)** & & & \(C_{D}\) & \(F_{D}\) **(N)** & & \(C_{D}\) & \(F_{D}\) \\ \hline
1.0 & 0.300 & 1.812 & 47.931 & 4.497 & 73.343 & 0.750 & 16.228 & 429.269 & 28.196 & 745.845 \\
2.0 & 0.150 & 0.450 & 47.635 & 0.693 & 112.677 & 0.375 & 3.993 & 422.462 & 5.874 & 621.566 \\
3.0 & 0.100 & 0.314 & 74.845 & 0.516 & 118.954 & 0.250 & 1.830 & 422.292 & 2.283 & 543.528 \\
3.6 & 0.083 & 0.296 & 101.434 & 0.486 & 166.652 & 0.208 & 1.232 & 422.245 & 1.430 & 490.055 \\
4.0 & 0.075 & 0.291 & 123.065 & 0.473 & 218.566 & 0.188 & 0.969 & 409.942 & 1.077 & 455.868 \\ \hline \hline \end{tabular}
\end{table}
Table 4: The drag coefficient and drag force for each type of motion depending on the flow velocity.  
Figure 15: The comparison of the drag force between the results of oscillation and undulation.  
**Funding:** This work was supported by the Korea Research Institute for Defense Technology Planning and Advancement (KRIT) grant funded by the Korea government (DAPA, Defense Acquisition Program Administration) (KRIT-CT-23-008, Development of a biomimetic underwater robot platform, 2023).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Data is contained within the article.  
**Conflicts of Interest:** The authors declare no conflicts of interest.