# Free Space Detection Algorithm Using Object Tracking for Autonomous Vehicles
## 3 Results  
Figure 8 is a pictorial representation of the results of Figure 9a. In Figure 8, green is the free space that the vehicle can drive in. In the figure, red is a space in which the vehicle is completely unable to drive, and orange is a space in which the vehicle is unable to drive. The dotted line represents the grid map range, and the yellow represents the obstacle. The direction in which the obstacle moves is represented by an arrow, and the static obstacle is represented by a square dot. The driving target point is indicated by a gray circle. Paths are generated only in free space cells, and the generated paths are indicated by blue lines. By referring to this pictogram, the execution result screen of Figure 9 can be grasped. \begin{table}
\begin{tabular}{c c} \hline \hline
**Specifications** & **Value** \\ \hline Channel & 16 channels \\ Measuring range & 100 m \\ Accuracy & Max \(\pm\)3 cm \\ Field of view (vertical) & +15.0\({}^{\circ}\) to \(-\)15.0\({}^{\circ}\) \\ Field of view (horizontal) & 360\({}^{\circ}\) \\ Angular resolution (vertical) & 2.0\({}^{\circ}\) \\ Angular resolution (horizontal/azimuth) & 0.1–0.4\({}^{\circ}\) \\ Rotation speed & 5–20 Hz \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Velodyne VLP-16 specifications. \begin{table}
\begin{tabular}{c c} \hline \hline
**Constant** & **Value** \\ \hline \(a\) & 0.46 \\ \(b_{1}\) & 6 \\ \(b_{2}\) & 2 \\ \(c\) & 4.3 \\ \(d\) & 2 \\ \(e\) & 0.1 \\ \(f\) & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Constant values of Equations (1)–(4). Figure 7: LiDAR sensor on the vehicle. Figure 8: Pictorial result of path generation based on FSD of two methods in case Figure 9a. Figure 9: _Cont._  
Figure 9 show the execution screen of generating a path based on the FSD of the two methods in six cases. Figure 9 and Table 6 are the FSD results in cases (a)-(f). Case (a) shows one dynamic obstacle moving in opposite directions and two static obstacles. Case (b) has one dynamic obstacle moving in the same direction and one static obstacle. Case (c) is a case with two dynamic obstacles moving in opposite directions and two static obstacles. Case (d) has one dynamic obstacle moving in the same direction and one static obstacle. Case (e) is a case with three static obstacles. Case (f) is a case with two dynamic obstacles moving in opposite directions and two static obstacles. Figure 9 are the results of the comparison between the cases of FSD without obstacle speed information in the circular grid map and the case of FSD by dividing areas with \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{**Case**} & \multicolumn{1}{c}{**CR**} \\ \multicolumn{1}{c}{**FSD without Speed Information**} & \multicolumn{1}{c}{**FSD with Speed Information**} \\ \hline (a) & 21.21 & 18.97 \\ (b) & 89.60 & 14.56 \\ (c) & 75.97 & 68.95 \\ (d) & 11.95 & 5.84 \\ (e) & 23.31 & 21.57 \\ (f) & 107.89 & 54.43 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Collision risk (CR) in cases (a)-(f). Figure 9: Generated path comparison of FSD without speed information in circular grid map and FSD with speed information in trapezoid grid map in cases (a)–(f). speed information of obstacles in the trapezoidal grid map. In Figure 9, the white point is the vehicle driving target point, and the red line represents the generated path according to the free space. As a result of FSD without speed information, it can be seen that a path with a collision risk is created even though there is an obstacle moving in the direction opposite to the vehicle direction. In the result of FSD with speed information, it is determined that the area where the obstacle is moving in the opposite direction to the vehicle's driving direction is an impossible area, and it is divided into red areas to indicate that a safe path is created in the space, not in the driving direction of the obstacle. Table 6 is a quantitative representation of the comparison results of the two cases. As a result of the calculation, the results shown in Table 6 were obtained.