## 5 Results and Discussion
### Simulation Results  
#### 5.1.1 Scenario1: Only Ocean Current Information  
As mentioned above, the ocean current has a significant influence on the navigation of AUVs, affecting navigation accuracy and energy consumption. Therefore, if the planned path can go in the direction of the ocean current, the ocean current will be used to improve the navigation performance of the AUV. In this part, this study analyzed the planning effect of the SHH algorithm for the scenario that only contained ocean current information. The results of the SHH were compared with the path planning results using two heuristic algorithms, PSO and FFA. The solid line in Figure 7 was the planning result using the SHH algorithm without considering the influence of the ocean current. Since there was no danger area, the planning result was a straight line with the shortest path. The dashed line was the result after considering the influence of ocean current information. It is evident that the planning path has obvious bending under the influence of the ocean current. Under the condition of ensuring smoothness, the direction of planned path tried to follow the direction of the ocean current as near as possible, which proved that the ocean current constraint in the optimization cost function influenced the planning result. Figure 8 is a comparison of the results of PSO, FFA and SHH algorithms in the case of only ocean current information. The solid line was the result of the PSO; the dash-dot line described the result of the FFA algorithm, and the dashed line was the running result of the SHH algorithm. All of the three algorithms were planning a bending route because of the influence of ocean currents. The results show that all algorithms can generate the local paths that basically conform to ocean current information in scenario 1. Figure 7: Comparison of the path planning results of the SHH algorithm without and with the ocean current information. The results of the three algorithms running 200 times under the same conditions were analyzed. Table 2 is the result comparison of the PSO, FFA, and SHH in the scenario only containing ocean current information. The data in the table were the average values obtained after repeatedly running 200 times under the same conditions. The computing time refers to the interval time from the entry to the completion of the algorithm iteration. The average computing time of PSO, FFA and SHH were 2.2815 s, 1.1834 s, and 0.6214 s respectively. It appeared that the SHH algorithm had the shortest average computing time compared with the PSO and FFA algorithms because the swarm operations of the three algorithms were different. The FFA operation was only the darkness individual moving towards the bright individual. This operation needs to traverse all other individuals when operating one individual. This process is time-consuming. In addition to the operations of following the better individual which need to traverse all other individuals, the other operations can be done in constant time, so it is easily understandable that the SHH algorithm has high computing efficiency. The total cost value of the final optimization of PSO, FFA, and SHH were 998.8257, 701.4505, and 624.668 respectively. The cost functions of the three algorithm evaluation paths were consistent. Therefore, the results obtained by the SHH algorithm had the best cost value. It is visible that the SHH algorithm using multiple operation sets has more advantages in solving the proposed path planning problem. In addition, although the path length obtained by the SHH is longer, it is smoother and more suitable for ocean current constraints. \begin{table}
\begin{tabular}{c c c c} \hline  & **PSO** & **FFA** & **SHH** \\ \hline Computing time & 2.2815s & 1.1834s & 0.6214s \\ Final total cost & 998.8257 & 701.4505 & 624.6680 \\ Time cost & 171.2734 & 173.3448 & 176.5915 \\ Curvature cost & 73.0122 & 153.6648 & 150.5598 \\ Ocean current cost & 754.5393 & 374.4410 & 297.5167 \\ \hline \end{tabular}
\end{table}