# An Automatic Navigation System for Unmanned Surface Vehicles in Realistic Sea Environments
## 6 Simulation Study and Discussion
### Verification in Realistic Sea Environment with Multiple Moving Target Vessels  
A more complex simulation is done in a realistic sea environment (shown in Figure 8a) with multiple moving TVs. Under the same algorithm parameter conditions, the USV first starts to sail in the static sea area and the final result is shown in Figure 20. It can be seen that the USV travels into the harbor in the safe area and eventually reaches the end area. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Environment** & **Index** & \begin{tabular}{c} **Speed of the** \\ **USV (m/s)** \\ \end{tabular} & \begin{tabular}{c} **Thruster** \\ **Speed (r/min)** \\ \end{tabular} & \begin{tabular}{c} **Propulsion** \\ **Angle (\({}^{\circ}\))** \\ \end{tabular} & \
\begin{tabular}{c} **Computation** \\ **Time (s)** \\ \end{tabular} &
\begin{tabular}{c} **Distance** \\ **(m)** \\ \end{tabular} \\ \hline \multirow{3}{*}{static} & maximum & 11.0 & 4000 & 0.0 & 0.63 & 100.0 \\  & minimum & 0.0 & 0 & \(-\)30.0 & 0.11 & 19.8 \\  & average & 7.5 & 3109 & \(-\)10.8 & 0.25 & 51.1 \\ \hline \multirow{3}{*}{dynamic} & maximum & 10.9 & 4000 & 3.0 & 0.61 & 86.8 \\  & minimum & 0.0 & 0 & \(-\)30.0 & 0.11 & 10.4 \\  & average & 7.2 & 3059 & \(-\)10.5 & 0.26 & 35.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results of evaluation index comprised of two tests in the simulation environment. USV: unmanned surface vehicle. Figure 19: Evaluation results in the simulation environment. (**a**) Speed of the unmanned surface vehicle (USV); (**b**) Course of the USV; (**c**) Thruster speed; (**d**) Command propulsion angle; (**e**) Computation time; (**f**) Distance between the USV and collision area. Now, three virtual TVs are added into the environment, traveling at 10 m/s (TV1), 7 m/s (TV2), and 5 m/s (TV3) respectively. The size (7.00, 3.00) m of TV1 and TV2 is similar to the USV, and TV3 measures (20.00, 8.00) m. In the same way, their path is also generated by the TFMS method without regard for other vessels. The movement sequences are expressed in Figure 21, which includes both the original binary maps as well as the potential maps. The potential maps show the vessel domain of three TVs based on their velocities. In addition, the system is verified in three encounter situations. Figure 21a,b plots the USV moving from the initial state to the harbor. At the entrance of the harbor, the USV encounters TV1 and forms a head-on situation. Next, Figure 21b-d displays the USV evasion process. After moving away from TV1, a crossing situation is made up of USV and TV2 in Figure 21e-g. When TV1 and TV2 are successfully avoided, the USV begins to overtake TV3. From Figure 21h-j, it is observed that the USV completed the task of overtaking, although TV3 changes its course in the process. The process of entering the end area is depicted in Figure 21k,l. Figure 21l shows the contrast of the final tracks of the USV in the two tests. Figure 21: _Cont._  
Figure 20: The simulation final result in static sea environment. **(a)** The binary map; **(b)** The potential map. same except for distance. Compared to the two tests, the speeds of the USV and thruster are largely the same and can maintain a maximum during the sail time in Figure 22a,c. In Figure 22d, the propulsion angle is completely consistent before collision avoidance. During the collision avoidance, the size of command propulsion angle is less than \(5^{\circ}\), similar to the static environment at less than \(4^{\circ}\). Figure 22e displays the computation time of the FCS-MPC. In the real environment, the DTFMS method time is 3.6 s which is far longer than the FCS-MPC time. The \(T_{upd}\) is selected as 4.00 s. Figure 22f records the distance between the USV and the detected collision area in the two tests. During the collision avoidance, the minimum distances of three situations are respectively 28.2 m, 25.4 m, and 69.3 m, which means that the USV is safe enough to drive.