## 3 Path Planning  
### Potential Field Algorithm  
The autonomous driving algorithm is divided into upper control and lower control elements. In the upper control element, a path is generated by processing GPS/INS and LiDAR sensor signals, whereas, in the lower control element, steering control is performed to follow the created path. The potential field [21; 22] algorithm was used for path generation, while the pure pursuit [23] algorithm was used for path tracking. A flow chart of the system is shown in Figure 3.  
The location of obstacles is identified by fusion of distance information obtained from LiDAR and INS information. After creating a global path in a straight line from the current position to the waypoint with the waypoint received from the control system as the target point, a local path that can avoid obstacles is generated using the potential field algorithm.  
\[U(q)=U_{att}(q)+U_{rep}(q). \tag{1}\]  
\[U_{rep}=\begin{cases}\min\left[\begin{array}{cc}U_{rep,max}\;,&k\left(\frac{ 1}{D}-\frac{1}{Q}\right)^{2}\end{array}\right]&if\;D<Q\\ 0&else\end{cases} \tag{2}\]  
\[U_{att}=C\times l^{2}. \tag{3}\]  
In Equation (1), \(q\) is a point in space, \(U_{att}\) is the attractive potential, \(U_{rep}\) is the repulsive potential, and \(U_{rep,max}\) is the maximum value of repulsive potential. \(D\) is the distance to the nearest obstacle, and \(k\) is the gain for calculating the repulsive potential. In order to consider only obstacles within the distance \(Q\) and to make the potential continuous, an equation is defined in the form of Equation (2). In Equation (3), \(C\) is the gain for calculating the attractive potential, and \(l\) is the perpendicular distance from \(q\) to the shortest path to  
Figure 3: Flow chart of autonomous driving algorithm.  
the goal. When the global path is in the \(x\)-direction and there is an obstacle at (10, 0), the shape of the potential field is as shown in Figure 4.  
A potential field is calculated at regular intervals in the direction perpendicular to the global path at regular intervals created using waypoints. At this time, \(U_{att}\) was defined to have a high potential in proportion to the square of the distance away from the path, and it moved along the point with the lowest potential.  
The potential field algorithm generally calculates the path after calculating the potential for all points in the domain. However, when the potential was calculated for all points in the domain in the DCS of the developed system, the operation time was intermittently exceeded. Since the developed electric vehicle featured rear-wheel driving and front-wheel steering, the area where the vehicle could reach the next time step was limited. Using this fact, instead of calculating the potential for all grids around the vehicle, the calculation was reduced by calculating only the potential in the reachable area, as shown in Figure 5[25].  
In the existing potential field, the global path is given as \(G=\{g_{1},g_{2},\ldots g_{n}\}\), and, in each \(g_{i}\), there are \(Q(g_{i})=\{q_{i1},q_{i2},\ldots q_{im}\}\) to calculate the \(Potential(Q(g_{i}))\). Furthermore, \(\arg\,q_{min}\,Potential(Q(g_{i}))\) is selected as the \(i\)-th local path \(LP(i)\). At this time, instead of calculating all of the \(Potential(Q(g_{i}))\) for \(Q(g_{i})\), the calculation time can be reduced by calculating the potential only for \(Q(g_{i})\) within a certain range from \(LP(i-1)\). It is desirable to determine this range by considering the maximum steering angle of the vehicle and path_interval, which is the interval of the global path. In this paper, the ratio of the range and path_interval is expressed as potential_dist_ratio, and the simulations and experiments were performed for a value of 2.  
Figure 4: Potential field algorithm [24].  
Figure 5: Efficient potential field calculation method [25].