## 3 Simulation Studies
### Comparison of Different Algorithms  
In order to further validate the performance of the proposed algorithm, it is compared with potential field (PF) algorithm. The comparison studies involve six AUVs, two targets, and some obstacles with environments scale of \(120\times 120\) (m\({}^{2}\)). The target locations, AUVs and obstacles are randomly deployed. The both algorithms are applied to the multi-AUVs that are directed to hunt all the targets. In these conditions, the both algorithms simulation experiments of cooperative hunting were completed 50 times respectively. To make a clear distinction between the two algorithms, Table 1 lists the mean and standard deviation statistics of total path length and hunting time by both algorithms. It is reasonable to conclude that the integrated algorithm of IPF performs better than the PF in each item of simulation results. Hence, it distinguishes itself with the shorter path length and time. By analysis, the PF algorithm doesn't have the function of cooperation for AUVs. However, IPF can not only perform the target hunting, but also it can better complete the task in the environment filled with obstacles.  
\begin{table}
\begin{tabular}{c c c} \hline
**Algorithm** & **Total Path Length (m)** & **Hunting Time (s)** \\ \hline IPF & \(845.3\pm 52.1\) & \(681.9\pm 30.5\) \\ PF & \(992.7\pm 75.6\) & \(807.6\pm 57.3\) \\ \hline \end{tabular}
\end{table}
Table 1: Performance comparison between improved potential field (IPF) and potential field (PF).  
Figure 6: Search process when two AUVs break down. (**a**) The first AUV break down; (**b**) The second AUV breaks down; (**c**) Final trajectories of the whole hunting process.  
In order to further validate the performance of the proposed algorithm, comparison studies with the particle swarm optimization (PSO) algorithm will be carried out. The PSO algorithm plans a path by iteratively improving a candidate solution with regard to the fitness function. The comparison studies involve one target locations, four AUVs, and some obstacles with environments scale of 120 \(\times\) 120 (m\({}^{2}\)). The target locations, AUVs and obstacles are randomly deployed. Different algorithms are used to arrange the multi-AUVs to hunt target. Figure 7 shows the search process with four different algorithms. According to the result of Figure 7, the proposed algorithm completes the target hunting task. However, the PSO algorithm failed to hunt the target because R1 hits an obstacle.  
In order to ensure the accuracy of the experiments, we conducted the experiments many times. In each experiment, the positions of the obstacles, targets, and AUVs are reset. The success rate of performing 50 times of target hunting using two different algorithms is depicted in Figure 7.  
It is very clear to see that the proposed IPF algorithm reaches 100% success rate under a large number of experiments in Figure 8. It means that the most tasks are successfully executed. However, the PSO algorithm only reaches 100% success rate for a few experiments. In some special cases, the success rate of PSO algorithm is only 80%. By comparison, it is found that under certain circumstances, the success rate of the proposed IPF algorithm is below 100%, but it is still superior to the PSO algorithm. By analysis, the PSO algorithm only provides optimum solution under no obstacle conditions. However, IPF works properly for obstacle avoidance, therefore it deserves a high success rate in the environments filled with obstacles.  
Figure 8: Success rate comparison between IPF and PSO algorithms.  
Figure 7: Hunting path with two different algorithms. (**a**) PSO algorithm; (**b**) IPF algorithm.