## 6 Conclusions  
This paper addresses the process of cooperative search and target capture by multi-AUV formations in unknown waters. The formation traversal mode in the array-type obstacle domain is analyzed, and the position changes of each robot during the formation transformation are effectively described using the formation parameter information matrix. For the optimal transformation problem of the formation, an FCC model that balances the convergence time, transformation distance and load energy consumption is proposed to realize the formation avoidance of array-shaped obstacles in the cooperative search phase. The FCC model is introduced to the genetic algorithm to solve the capture position assignment problem. The INSOM algorithm is proposed to realize the path-planning in the capture process, and the feasibility of the proposed scheme in different types of obstacle environments is verified by simulation experiments. In summary, the proposed scheme can provide different robot navigation states according to the different formation and obstacle domains, and can also be combined with the assignment and planning in the target capture process to improve the efficiency of robot deployment while ensuring safety. The formation transformation scheme proposed in this article takes natural terrain such as submarine gullies and protrusions as application scenarios, and lacks research on depth-direction transformation. Therefore, the proposed scheme has strict usage conditions for caves, pipelines, and more complex array obstacles that are made manually, and further research is needed to improve the applicability of the method. Conceptualization, X.H. and Y.C. ; Data curation, Y.S. ; Formal analysis, X.H. and G.B. ; Funding acquisition, Y.C. ; Investigation, G.B. ; Methodology, X.H. ; Project administration, Y.C. ; Resources, Y.C. ; Software, Y.S. ; Supervision, Y.C. ; Validation, Y.S. and G.B. ; Visualization, Y.S. ; Writing-original draft, Y.S. ; Writing-review & editing, X.H. All authors have read and agreed to the published version of the manuscript. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**State**} & **Selection** & **Transformation** & **Energy** & **Convergence** & **Total Length of** & **Combine with** & **Target** \\  & **Criteria** & **Scheme** & **Consumption** & **Time** & **Paths** & **Capture?** \\ \hline \multirow{2}{*}{\(v_{g}=4\)} & FCC model & 571 & \(0.7076\times 10^{4}\) & 11.5244 & 138.4584 & Yes \\  & Fixed column & - & \(1.1334\times 10^{4}\) & 16.2500 & 280.1635 & No \\  & formation [6] & 551 & \(0.7274\times 10^{4}\) & 11.5244 & 150.8191 & No \\ \multirow{2}{*}{\(p_{0}=70.3\)} & FCC model [11] & 1371 & \(0.7121\times 10^{4}\) & 11.8585 & 132.4342 & No \\ \hline \multirow{2}{*}{\(v_{g}=5\)} & FCC model & 1371 & \(0.7312\times 10^{4}\) & 9.4868 & 132.4342 & Yes \\  & Fixed column & - & \(0.9963\times 10^{4}\) & 12.9732 & 280.1635 & No \\ \multirow{2}{*}{\(p_{0}=70.3\)} & FCC model [11] & 551 & \(0.7659\times 10^{4}\) & 9.2195 & 150.8191 & No \\  & FEC model [11] & 1371 & \(0.7312\times 10^{4}\) & 9.4868 & 132.4342 & No \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of different formation transformation schemes. **Funding:** This work is supported by Jilin Province Key Science and Technology R&D project under Grant, No:20210203175 SF; Foundation of Education Bureau of Jilin Province under Grant, No:JJKH2020988 KJ; Marine Defense Innovation Found, No:JJ-2022-701-07; Aeronautical Science Foundation of China under Grant, No:2019 ZA0R4001; National Natural Science Foundation of China under Grant, No:51505174; Interdisciplinary integration innovation and cultivation project of Jilin university under Grant, No:JLUXKJC2020105. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** Not applicable. **Acknowledgments:** The opinions expressed in this research are the opinions of all the authors. The research was completed at Jilin University.