## 5 Simulation Analysis
### Operational Results of Robot Formations  
For a clearer representation of the search, formation transformation and hunting processes, this section provides a detailed description of the transformation process by taking any of the robot navigation states in Table 4 as an example. When \(v_{g}\)= 5 and \(p_{0}\) = 70.3, the transformed energy consumption of different formations is shown in Figure 10. From the results in Table 4, the FCEC model is selected as the 1371 st formation transformation scheme, and this scheme is the one with a less integrated energy consumption under the premise of smoothly passing the obstacle domain that corresponds to Figure 10.  
The whole operational effect of the multi-AUV formation in the current motion state is shown in Figure 11, and the projection to the XOY coordinate plane is shown in Figure 12. As can be seen from the figure, the proposed scheme in this paper enables the formation of multiple AUVs to accomplish the tasks of area search and target capture in an unknown underwater 3D environment. During the cooperative search process, the formation can lead to an independent obstacle-avoidance strategy according to the detected array-shaped obstacles, determine the optimal traversal solution and complete the formation transformation through the FCC model, and return to the basic wild goose formation after traversing the obstacle domain to continue the search operation. After detecting the target, the task is assigned to the robots in the formation using the improved GA. After each robot determines its own target capture position, it completes the path-planning using the proposed INSOM algorithm and finally successfully achieves the cooperative target hunting. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(v_{g}\) & \(p_{0}\) & \begin{tabular}{c} **Transformation** \\ **Scheme** \\ \end{tabular}  & \begin{tabular}{c} **Convergence** \\ **Time** \\ \end{tabular}  & \ \begin{tabular}{c} **Total Path Length of the** \\ **Transformation** \\ \end{tabular}  & \begin{tabular}{c} **Comprehensive** \\ **Energy** \\ **Consumption** \\ \end{tabular}  \\ \hline
0.5 & 70.3 & 571 & 92.1954 & 138.4584 & 3.8923 \(\times\) 10\({}^{4}\) \\
1 & 70.3 & 571 & 46.0977 & 138.4584 & 1.9582 \(\times\) 10\({}^{4}\) \\
2 & 70.3 & 571 & 23.0489 & 138.4584 & 1.0276 \(\times\) 10\({}^{4}\) \\
4 & 70.3 & 571 & 11.5244 & 138.4584 & 0.7076 \(\times\) 10\Figure 11: 3D panoramic view of cooperative search, formation transformation and hunting operations. Figure 10: Comparison of energy consumption of different formation transformation schemes. Six different colored * represent six robots with different numbers within the formation. Figures 13 and 14 show the formation transformation process for the 3D and 2D (projected to the XOY coordinate plane) cases, respectively. From the beginning to the end of the dynamic formation transformation, the coordinate changes of each robot are shown in Table 5.  
Figure 12: 2D projection view for search, formation transformation and hunting operations. Figure 13: 3D view of dynamic formation transformation. Figure 16: 2D view of the column transformation scheme. Figure 15: 3D operational view of the column transformation scheme. To obtain more obvious comparison results, the simulation results of four schemes with different navigation parameters are given in Table 6 by taking the energy consumption, convergence time and the total length of the paths in the formation transformation process as the judgment criteria. Figure 17: The formation transformation scheme selected by the FCT model. Figure 18: The formation transformation scheme selected by the FEC model.