## 2 Modeling
### Path Planning Environment Modeling  
Establishing a real ocean environment model is essential so that unmanned surface vehicles can perceive the external environment before path planning. Binarization processing is applied to build environment model via binarize remote sensing satellite is the majority of path planning [7; 17; 19; 26; 30]. Nevertheless, the depth of water is not considered, thus navigation along the planned path may be stranding. Vector electronic navigation chart, shown as Figure 4a, supports a variety of intelligent functions and provides water depth information with advantages of minute storage, swift display speed and high accuracy. It is suitable for marine environment modeling and processing for further development [15; 20]. Raster data has a simpler data structure than other environmental modeling methods and can contain terrain cost information, such as elevation [16]. In this paper, Vector electronic navigation Chart is applied to describe the real marine environment information. Uniform square grid is selected to process the electronic chart, and global static obstacle and depth of water extracted. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Mesh** & **Mesh 1** & **Mesh 2** & **Mesh 3** \\ \hline Number of meshs & 774,921 & 1,373,495 & 1,925,630 \\ \(E=\left\lvert 1-\overline{C}_{d,i}/\overline{C}_{d,3}\right\rvert\) & \(1.13\times 10^{-3}\) & \(4.35\times 10^{-3}\) & – \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Mesh independency study. Figure 3: Mesh Generation and Distribution. (**a**) Three-dimensional Mesh Generation; (**b**) Grid Distribution Around the Wall. In vector electronic navigation charts, spatial objects, such as land area, island reef, and navigation aids, are stored and expressed in the form of point, line and area features. In this paper, feasible space [25] is obtained by selecting objects which could risk on navigation. Obstacle region \(O_{bs}\subset R^{2}\) is calculated by Equation (9):  
\[O_{bs}=O_{Aera}\cup O_{Line}\cup O_{Point}, \tag{9}\]  
in which, \(O_{Aera},O_{Line},O_{Point}\) represent surface, line and point obstacles respectively. Feasible space is calculated by Equation (10),  
\[O_{f}=\Omega_{D}-O_{bs}, \tag{10}\]  
where, \(\Omega_{D}\subset R^{2}\) is the two-dimensional configuration space represented by \"DEPARE\" coverage in S57 ENC file stands for the area covered with water shown as Figure 5c, where free space \(\Omega_{f}\) is obtained by Formula (10) in the form of a polygon. According to the ship maneuverability standard, the minimum turning radius of large ships is equal to five times of the ship length, and that of small ships is three times of the ship length [10]. Considering the size of the vessel (3.2 m), localization error (5 m), buffer zone distance (5 m) and error of electronic navigation chart (5 m), the grid size is set to 25 m \(\times\) 25 m. The mesh size partition considers the kinematics constrictions of unmanned surface vehicles fully, so that unmanned surface vehicles can make starboard and port side turns up to 180 degrees within a grid cell. Non-feasible space and feasible space can be obtained by (9) and (10) as shown in Figure 5c. The hazard cost of water depth of blocked grids is set to 1. In electronic navigation charts, water depth is stored and expressed in the form of depth point, depth contour and depth area. The depth contour interval extracted from a chart of various plotting scale is different, as shown in Table 5.  
In order to obtain the water depth information of the planned sea area, we extract water depth point, contour and depth area coverage shown as Figure 5d from S57 vector electronic navigation chart shown as Figure 5a. As shown in Figure 5b, because the depth information is only in the discrete depth area, shown in Table 5, the depth risk of each grid cannot be evaluated more accurately. Therefore,  
Figure 4: S57 Environmental Modeling Map (**a**) Study Area of S57 Electronic Chart.