## 9 Conclusions  
In this study, by aiming to enhance the control performance of the USV swarm for research purposes, we introduced a methodology involving the prediction of ocean currents through learning and the implementation of ANN-PID control algorithms. The algorithm proposed in this study learns from measured ocean current data, forecasts future ocean currents, and presents a technique for enhancing controller performance. This is achieved by incorporating the predicted data into the control output as an influencing factor. To implement this approach, we designed an ANN-PID system and developed a USV control system tailored for swarm operations. The controller's gain is dynamically adjusted based on the predicted ocean currents to optimize performance. For verification purposes, a 3-DOF USV model incorporating fluid forces was developed, an algorithm for learning external forces was implemented, and an ANN-PID controller was designed. Furthermore, achieving smooth learning outcomes was facilitated by stable data processing through input data standardization. Optimization and activation functions were employed to enhance learning efficiency through empirical methods. Moreover, we conducted an analysis of the resemblance between the USV model designed to verify the algorithm and the swarm USV path generated by the simulator. This analysis encompassed the behavioral control rules of the USV swarm and the actual path followed by the swarm USVs at sea.  
We confirmed the accuracy of the mathematical model and behavioral control rules for the designed USV. Subsequently, we compared the movement paths of the USV swarm with and without the disturbance learning algorithm, along with the application of the ANN-PID control algorithm in the designed simulator, to assess position error and cluster formation maintenance.  
Conclusively, upon validating the control algorithm implemented for the USV swarm, we observed variations based on the application of predicted external force data. Specifically, there was a 12.4% enhancement in formation maintenance performance and a 14.8% reduction in position error during movement. The external force learning model exhibited an average error which amounted to under 4.2% when compared with the actual measured data.  
In this study, only ocean currents were taken into account as external forces. However, in future research, additional external factors such as waves and wind will be incorporated to learn and predict a comprehensive external force for more effective swarm control.  
S.K.J.: research, software, original draft preparation, investigation, data analysis, and editing: M.K.K.: investigation, software, original draft preparation, and review; H.Y.P.: investigation, original draft preparation, and review; Y.C.K.: investigation, data analysis, and draft preparation; D.-H.J.: conceptualization, investigation, review and editing, and project administration. All authors have read and agreed to the published version of the manuscript.  
This research was a part of the project titled \"Development of smart maintenance monitoring techniques to prepare for disaster and deterioration of port infrastructures\" funded by the Ministry of Oceans and Fisheries.  
Not applicable.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
The authors declare no conflict of interest.