# Pursuit-Evasion Problem of Unmanned Surface Vehicles in a Complex Marine Environment
## 4 Simulation and Analysis  
In order to validate the effectiveness of intercepting escaping targets under the guidance strategy proposed in this paper, a simulation experiment was carried out for the algorithm. The ship model used in the simulation is the scale model of CyberShip II (CS2) [21], which is the test tool of the Marine Cybernetics Laboratory (MCLab). The hydrodynamic parameters are also taken from the parameters of the well-known surface vehicle CS2. In order to test the robustness of the proposed control algorithm to external disturbances, it is assumed that there is an error of 10% between the nominal value and the actual value of the motion parameters. \(\widehat{\bullet}\) indicates the nominal value and the specific nominal value of hydrodynamic parameters, which can be found in the literature [21]. The actual values of the motion parameters are shown in Table 1.  
The parameter model of USV was taken as a constant disturbance and summed up in the disturbance model for external wind, waves, and currents. The environmental disturbance model is defined as follows:  
\[\left\{ \begin{array}{l l l}\tau_{uu}=(h(s)w_{u}(s)+\xi_{uu})m_{11}\\ \tau_{avv}=(h(s)w_{v}(s)+\xi_{uv})m_{22}\\ \tau_{ur}=(h(s)w_{r}(s)+\xi_{ur})m_{33}\end{array} \right. \tag{32}\]  
with  
\[h(s)=\frac{K_{\omega}s}{s^{2}+2\zeta\omega_{0}s+\omega_{0}^{2}} \tag{33}\]  
where \(w_{u}\), \(w_{v}\), and \(w_{r}\) are Gaussian white noise; \(\xi_{uu}\), \(\xi_{uv}\), and \(\xi_{ur}\) are the uncertainty error coefficient of the model. \(\zeta=0.3\), \(K_{\omega}=0.25\), \(\sigma_{m}=0.4\), \(\omega_{0}=0.8\), and \(k_{wu}=k_{wp}=k_{ur}=0.1\). The maximum values of \(\tau_{cu}/m_{11}\), \(\tau_{cv}/m_{22}\), and \(\tau_{cr}/m_{33}\) are 0.1 m/s\({}^{2}\), 0.1 m/s\({}^{2}\), and 0.5 m/s\({}^{2}\), respectively. The recommended values of parameters in the controller in the simulation are shown in Table 2.  
The initial state of the pursuer is cruising. When the escaping target enters its sensing range, the pursuer adjusts its state and begins its pursuit. The escaping target moves along a curved path. The curved path can be parameterized as follows:  
\[\left\{ \begin{array}{l l l}(x_{E},y_{E})=(0.4\omega+10\,,\,0.6\omega+10)&,0 \leq\omega<100\\ (x_{E},y_{E})=(0.6\omega-10,\,20\sin(0.2(\omega/25-4))+70)\,,\,\omega\geq 100 \end{array} \right. \tag{34}\]  
where the path parameter is \(\omega=V_{E}/\sqrt{{x_{E}^{\prime}}^{2}+{y_{E}^{\prime}}^{2}}\). Within the range of simulation time \(t=0\)-170 s, the trajectories of the pursuer and evader are shown in Figure 3.  
Set the parameters in the filter as the parameters in the actual observer to maintain the consistent performance for the actual observer. \(H\) is the measurement vector of the sensor, which is the coordinate value obtained through the UWB in this system. As the source of the systematic observation data, the UWB positioning equipment has a coordinate accuracy of 0.1 m, so the element value in matrix \(R\) was taken as 0.1. The element value in matrix \(Q\) was taken as 0.1. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Value** & **Parameters** & **Value** \\ \hline \(m_{11}\) & \(1.1\hat{m}_{11}\) & \(d_{11}\) & \(1.1\hat{d}_{11}+0.2\hat{d}_{11}|u|\) \\ \(m_{22}\) & \(1.1\hat{m}_{22}\) & \(d_{22}\) & \(1.1\hat{d}_{22}+0.2\hat{d}_{22}|v|\) \\ \(m_{23}\) & \(1.1\hat{m}_{23}\) & \(d_{23}\) & \(1.1\hat{d}_{23}\) \\ \(m_{33}\) & \(1.1\hat{m}_{33}\) & \(d_{33}\) & \(1.1\hat{d}_{33}+0.2\hat{d}_{33}|r|\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Actual values of CS2. The observation trajectory obtained by the observation station is obviously oscillating, but the observation noise value of the observer is relatively small, so it is closer to the value of the real trajectory. This measurement value can be directly used for target-locking and interception in the simulation. However, since the actual observer may have abnormal values, it is necessary to determine and discard abnormal values.