# An Automatic Navigation System for Unmanned Surface Vehicles in Realistic Sea Environments
## 6 Simulation Study and Discussion
### Verification in Simulation Environment with Single Moving Target Vessel  
In the first test, the simulation environment is static without any dynamic obstacles. The final result of the simulation is shown in Figure 17, which is depicted in both a binary map and the corresponding potential map. It is clear that both the collision area (in black) and safe area (in white) have been identified. We can see that the USV can travel smoothly and safely into the end area. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Parameter** & **Value** & **Units** \\ \hline \multicolumn{4}{c}{Size of the USV (length, breadth)} \\  & Initial course of the USV & 90.0 & \({}^{\circ}\) \\  & Initial speed of the USV & 0.0 (0.0) & m/s (kn) \\  & Initial thruster speed & 0.0 & r/min \\  & Maximum thruster speed & 66.7 (4000) & r/s (r/min) \\ USV & Change rate of thruster speed & 6.7 & r/s\({}^{2}\) \\  & Discrete thruster speed & 1.7 (100) & r/s (r/min) \\  & Initial propulsion angle & 0.0 & \({}^{\circ}\) \\  & Maximum propulsion angle & 30.0 & \({}^{\circ}\) \\  & Change rate of propulsion angle & 5.0 & \({}^{\circ}\)/s \\  & Discrete propulsion angle & 1.0 & \({}^{\circ}\) \\ \hline \multicolumn{4}{c}{\(Saturation\)} \\  & Search range & 100.0 & m \\ Algorithm & Prediction horizon & 8.0 & s \\  & Control update interval & 1.0 & s \\  & Weight of evaluation function & (1.50, 1.50, 0.01, 2.00) & – \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameter information about the automatic navigation system (ANS) of the unmanned surface vehicle (USV). Then, in order to test the capability of the algorithm to avoid dynamic obstacles, the moving TV1, which has a similar size (7.00, 3.00) m and speed 10 m/s (19.4 kn) to the USV, is added into the simulation environment. Generally, there are three types of situations in which the two vessels encounter each other: overtaking, head-on, and crossing situations. The most dangerous situation is the head-on situation. So, on the premise of removing the motion information of the USV, the path of the target vessel given by the TFMS method reaches a head-on situation with the USV. The simulated target vessel may be hostile or have detection system failure. The simulation results recording the movement sequences of the vessels are represented in Figure 18. Figure 18a-c shows how the USV adjusts the course to the end point. As the initial course of the USV is opposite to the direction of the end point, the planned path of DTFMS method extends a certain distance to the direction of the course. Figure 18d-f illustrates how the USV avoids TV1. The two vessels form a head-on situation and starboard side turning is adopted by the USV in Figure 18d. After 43 s, the USV decelerates gradually and enters the end area in a safe state (Figure 18g,h). In the corresponding safety potential maps, it can be observed that the USV can stay well outside collision area (including static obstacles and the target vessel domain), which proves that the ANS is able to guarantee collision-free navigation of the USV. Figure 18h shows the comparison of the tracks in the dynamic environmental (blue solid curve) and the static environment (blue dashed curve). Evaluations of the USV behavior and algorithm performance in the dynamic and static environments are given in Table 2 and Figure 19. Table 2 describes the results of evaluation index of two tests. Figure 19a-d shows the control behaviors (thruster speed and command propulsion angle) and state output (speed and course) of the USV during the whole process. In Figure 19a,c, the USV and thruster keep at maximum speed during the sailing time, except for a slight decline in collision avoidance, which illustrates that the algorithm can adjust the speed according to the hazard under the premise of rapidity. In Figure 19d, at the beginning and the end of process, it is necessary to adjust the course with the larger command propulsion angle so that the USV can reach the end point.