## 2 Materials and Methods
### Multi-USV Aggregation Formation Experiment  
According to Tables 1 and 2, three USV environments were created, and obstacles were added. The reference value of heading control \(\beta^{\prime}\) of the optimization algorithm \(\beta^{\prime}\) was set, and a simulation experiment was conducted for USV aggregation formation. The results are shown in Figures 19-21.  
Figure 19: Simulation of aggregation formation (\(\beta^{\prime}=0^{\circ}\)).  
Figure 20: Simulation of aggregation formation (\(\beta^{\prime}=60^{\circ}\)).  
In Figures 19-21, it is observed that the optimized algorithm provides significant improvements in obstacle avoidance, encounter, and end course uniformity in the environment of the three USVs, achieving ideal results in the simulation environment, by completing more complicated USV aggregation formation tasks.  
Through the above experiments and analysis, the method proposed in Reference [18] is compared with the fusion algorithm in this paper, as shown in Table 3:  
Compared with the method proposed in reference [18], the fusion algorithm in this paper has the following advantages:  
1. By improving the traditional A* algorithm, this paper realizes the function of specifying the terminal course, which is more comprehensive in formation control ability;
2. The algorithm in this paper can be successfully implemented in multi-type environments by setting appropriate parameters. However, the deep reinforcement learning algorithm needs many simulated environments for training, and also needs targeted training according to different types of environments to achieve better results. Therefore, the algorithm proposed in this paper is more adaptable to the environment;
3. A deep reinforcement learning algorithm needs a lot of computing power and takes a long time to obtain an ideal training model, which puts higher demands on the equipment configuration involved in the calculation. The algorithm proposed in this paper is based on traditional A* and DWA algorithms, which have lower complexity and less demand for computing power;
4. The RVO algorithm itself is prone to heading jitter in the navigation process, which puts forward higher requirements for the robot's maneuverability, while the DWA algorithm fully considers the robot's maneuverability and is more suitable for under-actuated systems such as USV.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithm Name** & **Fusion Algorithm of A* and DWA** & **Fusion Algorithm of RVO and DRL** \\ \hline Algorithm core method & Fusion algorithm of Improved A* and traditional DWA & Fusion algorithm of RVO and multiple \\ Number of robots in formation & 3 & 10/16/20 \\ Designated terminal course & Yes & No \\ Acclimatization & Strong & Weak \\ Computing power demand & Low & High \\ Maneuverability requirements of robots & Low & High \\ \hline \hline \end{tabular}
\end{table}
Table 3: Algorithm comparison.  
Figure 21: Simulation of aggregation formation (\(\beta^{\prime}=90^{\circ}\)).  
At the same time, the shortcomings of the algorithm in this paper are that the number of robots in the formation is small, and more complex collision avoidance strategies need to be introduced, which puts forward higher requirements for the efficiency of the algorithm and is more difficult to realize.