# Optimal Attitude Determination for the CR200 Underwater Walking Robot
## 3 Results
### Downforce Prediction  
This section aims to examine the effect of changes in posture defined by the predetermined parameters on downforce. The CFD simulation results for the nine predefined cases \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Minimum** & **Maximum** \\ \hline \(\alpha\) (\({}^{\circ}\)) & 10 & 14 \\ \(\mu\) (m) & 0.10 & 0.14 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The parameters of attitude determination and their respective ranges. Figure 6: Visualization of posture-defining parameters: (**a**) the pitch angle between the inflow and the CG; (**b**) the distance from the seabed to the CG and height. Figure 7: Computational mesh systems around the CR200 according to simulation cases defined by attitude parameters \((\alpha,\hat{\alpha})\). Total number of meshes: (**a**) 4.47 \(M\); (**b**) 4.76 \(M\); (**c**) 4.82 \(M\); (**d**) 4.41 \(M\); (**e**) 4.63 \(M\); (**f**) 4.98 \(M\); (**g**) 4.45 \(M\); (**h**) 4.89 \(M\); (**i**) 5.03 \(M\). All renderings are captured from the same perspective, illustrating variations in angle and distance from the seabed, depending on the robot’s posture. are presented, allowing for the identification and comparison of the optimal posture that maximizes downforce with the suboptimal attitude that minimizes it. Table 3 shows the magnitude of downforce acting in each posture. The results indicate that the downforce does not exhibit a simple proportional relationship with the increase or decrease in the posture-determining parameters. This suggests the presence of complex fluid dynamic phenomena, which will be further examined. Figure 8 visualizes the results of downforce magnitude acting on the surface based on the main body posture. Figure 9 shows the pressure distribution along the longitudinal section of the CR200. Due to the reduced distance from the seabed, an adverse pressure gradient region occurs on the lower surface of the CR200, while positive pressure acts on the upper surface. As a result, the downforce derived from the net pressure distribution across the surface is generated on the CR200 in all postures. Figure 10 illustrates the streamlines aligned with the incoming flow direction around the CR200. The effect of downforce generation is most dramatically indicated by the upward deviation of the streamlines behind the robot body. The streamline deviation is particularly significant near the optimal posture, as shown in Figure 10e, compared to the sub-optimal posture in Figure 10g. An additional feature related to the attitude change can be observed around the wake pattern behind and below the aft part of the body. Unlike the smooth flow along the upper surface, the lower surface shows the development of boundary layer separation as it approaches the aft part of the lower surface. This results in reverse flow, moving opposite to the freestream and downforce direction, leading to a loss of downforce. Additionally, when the amplitude of downforce is large, vortex formation occurs, causing the streamlines in the wake region to rise higher. In contrast, when the downforce is smaller, the wake formation contributing to the downforce is less pronounced. Figure 8: Downforce response surface with respect to the attitude pitch angle \(\alpha\) and the seafloor clearance \(\hat{\pi}\). The red markers indicate the original data points used for constructing the response surface. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Downforce (\(N\))**} & \multicolumn{4}{c}{\(\hat{\pi}\) (\(m\))} \\ \cline{2-5}  & **0.10** & **0.12** & **0.14** \\ \hline \multirow{3}{*}{\(\alpha\) (\(\circ\))} & 10 & 804.58 & 746.57 & 690.69 \\  & 12 & 253.93 & 848.37 & 793.53 \\ \cline{1-1}  & 14 & 130.14 & 235.80 & 763.22 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Magnitude of downforce acting on the surface based on the defined posture. The primary cause of downforce generation is the pressure distribution on the surface of the body.