# Study on Path Planning Method for Imitating the Lane-Changing Operation of Excellent Drivers
## 2 Acquisition of Ideal Path
### Data Processing  
Owing to the data recoded by GPS being longitude, latitude and elevation, it is difficult to directly reflect the vehicle's actual running path in the geodetic coordinate system. In geographic coordinate system, the origin of the coordinates lies in the centroid of the carrier, and its \(X_{g}\) axis, \(Y_{g}\) axis and \(Z_{g}\) axis are the east, north and sky directions, respectively, of the carrier's location. To accurately describe the travel path, it is necessary to transform the coordinates of the geodetic coordinate system into the geographic coordinate system. However, a direct conversion of coordinates between the geodetic coordinate system and the geographic coordinate system is hard to process. Therefore, the Earth Cartesian coordinate system is introduced into the transformation. The relationships between the geodetic coordinate system, the geographic coordinate system and the Earth Cartesian coordinate system are shown in Figure 3.  
The coordinates of the point \(P\) is (\(L\), \(\lambda\), \(h\)) in geodetic coordinate system. The coordinates of the point \(P\) (\(x_{e}\), \(y_{e}\), \(z_{e}\)) in the Cartesian coordinate system can be obtained from Equation (1).  
\[\left\{\begin{array}{l}x_{e}=(R_{N}+h)\cos L\cos\lambda\\ y_{e}=(R_{N}+h)\cos L\sin\lambda\\ z_{e}=[R_{N}(1-e)^{2}+h]\sin L\end{array}\right. \tag{1}\]  
where \(R_{N}\) is the radius of curvature of the ellipsoid, \(R_{N}=R_{e}(1+e\text{sin}2L)\). \(e\) is eccentricity of ellipsoid, \(e=(R_{e}-R_{p})/R_{e}\). \(R_{e}\) is the long radius of the ellipse and \(R_{p}\) is the short radius of the ellipsoid.  
The travel path of the vehicle is a spatial curve connected by many spatial points in geodetic coordinate system. The spatial curve needs to be projected to the \(x_{g}-y_{g}\) plane in the geographic  
\begin{table}
\begin{tabular}{c c c c} \hline
**Driver Number** & **Gender** & **Age** & **Driving Age (Years)** \\ \hline Driver 1 & Female & 55 & 33 \\ Driver 2 & Male & 28 & 10 \\ Driver 3 & Male & 53 & 31 \\ Driver 4 & Male & 46 & 22 \\ Driver 5 & Male & 53 & 21 \\ \hline \end{tabular}
\end{table}
Table 1: Information of drivers.  
Figure 3: Relationships between the three different coordinate systems.  
coordinate system. To facilitate the analysis of the driving path, the coordinate origin of the geographical coordinate system is set at the initial record point of the driving track. Thus, the coordinates of each sampling point in the Earth Cartesian coordinate system needs to be transformed by Equation (2).  
\[\left\{\begin{array}{l}\Delta x(yz)_{e1}=x(yz)_{e1}-x(yz)_{e1}\\ \Delta x(yz)_{e2}=x(yz)_{e2}-x(yz)_{e1}\\ \Delta x(yz)_{e3}=x(yz)_{e3}-x(yz)_{e1}\\ \ldots\ldots\\ \Delta x(yz)_{en}=x(yz)_{en}-x(yz)_{e1}\end{array}\right. \tag{2}\]  
Then, the coordinates of the Earth Cartesian coordinate system are transformed into the coordinates of the geographic coordinate system using Equation (3).  
\[\left[\begin{array}{cc}x_{gi}&y_{gi}&z_{gi}\end{array}\right]=\left[\begin{array} []{cc}\Delta x_{ei}&\Delta y_{ei}&\Delta z_{ei}\end{array}\right]\left[ \begin{array}{cc}-\sin\lambda&\cos\lambda&0\\ -\sin L\cos\lambda&-\sin L\sin\lambda&\cos L\\ \cos L\cos\lambda&\cos L\sin\lambda&\sin L\end{array}\right] \tag{3}\]  
With the above transformations, the driving path can be shown accurately in two-dimensional plane of the geographic coordinate system using the coordinate \((x_{g},y_{g})\).