# Fuzzy Risk Evaluation and Collision Avoidance Control of Unmanned Surface Vessels
## 3 Design of Smart Collision Avoidance Control System for USVs
### Scenario 1: Crossing Situations  
In this scenario, a crossing situation that a target ship appears in region B of Figure 2 and heads to the controlled USV is adopted. According to Table 1, the controlled USV is a give-way ship that shall take action to avoid the collision, and the target ship is a stand-on ship and just keeps on her course and speed.  
The testing conditions for scenario 1 is listed in Table 4.  
The simulation result of scenario 1 without the collision avoidance treatment is shown in Figure 18. Obviously, a collision will occur between point 12 and point 13 if no evasion action is taken. For solving this collision problem, the proposed smart collision avoidance control system is used, and the simulation result with the aid of this proposed method is displayed in Figure 19. In Figure 19, the black line is the optimal collision avoidance trajectory which was generated by using (45)-(49) and (51) of the proposed smart collision avoidance control system. As to the blue line, it represents the tracking trajectory of the controlled USV which is guided by using the optimal nonlinear control law \(\tau_{\eta 2}\) = T\({}_{2}\)(**e**,_t_) + \(\rho_{2}\)\({}^{-1}\)**u\({}_{2}\)**'(**e**,_t_) in (54). The red line is the sailing trajectory of the target ship. Figure 20 is the enlarged figure of the red dash block in Figure 18 for showing the detailed position and attitude of these two encountered vessels (the controlled USV and the incoming ship) during the crossing situation. From Figures 18 and 20, they reveal the fact that no collision occurs in this crossing situation after an effective evasion was taken. In this scenario, the controlled USV took a right turn by following COLREGs rules. This achievement strongly relies on the precisely trajectory tracking ability of the optimal nonlinear control law because it guides the controlled USV to sail along the no collision trajectory with a pinpoint accuracy. This promising property can be easily found from the tracking errors of \(x\)-axis, \(y\)-axis, and heading angle \(e_{x}\), \(e_{y}\) and \(e_{\psi}\) shown in Figures 21-23, respectively. In these figures, \(e_{x}\), \(e_{y}\), and \(e_{\psi}\) converge to nearly zero due to an effective trajectory tracking performance delivered by the optimal nonlinear control law.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **USV** & **Target Ship** \\ \hline Start point (m) & (3, \(-\)6) & (\(-\)9.6, 275.7) \\ End point (m) & (70.3, 253.5) & (\(-\)79.9, 22.1) \\ Heading angle (deg) & 92 & 210 \\ Initial velocity (m/s) & 0 & 0 \\ Final velocity (m/s) & 2.565 & 2.565 \\ Length (m) & 1.72 & 1.5 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Testing conditions for Scenario 1.  
Figure 19: History for the testing condition in Scenario 1 without the collision avoidance treatment.  
Figure 20: The position and attitude of two ships during the crossing situation.  
Figure 18: History for the testing condition in Scenario 1 without the collision avoidance treatment.  
Figure 23: Tracking error \(e_{\phi}\) in heading angle.  
Figure 21: History of the tracking error \(e_{x}\) in \(x\)-axis.  
Figure 22: Tracking error \(e_{y}\) in \(y\)-axis.  
Figure 24, a \(\mu_{CRI}\) > 0.8 can be found after 30 s. If no collision avoidance action is taken, an inevitable collision will occur about 75 s (\(\mu_{CRI}\) = 1 and the relative distance = 0, black dash line). To avoid this collision, an effective decision: taking a right turn at 52 s, which satisfies COLREGs rules, is made by this proposed collision avoidance system for the controlled USV. From the blue solid line of Figures 24 and 25, the collision risk index \(\mu_{CRI}\) decreases rapidly and a minimum positive relative distance of 10.6 m > the required total distance \(L_{S}\) = \(1.5L_{O}\) + \(0.5L_{T}\) in (9) can be obtained after applying the smart collision avoidance control system, and this implies that no collision will occur in this crossing situation.