## 4 System Verification with Full-Vehicle Simulation
### Results and Discussions
[30] was calculated. SCT is the time margin for the driver to avoid a collision when an object crosses the road from a blind area in front of the ego vehicle. SCT at the time of object detection is expressed by the following equation:  
\[SCT=\frac{\left\{D_{ego\_in}(t^{*})+\frac{V_{ego}(t^{*})^{2}}{2t_{max}}\right\}}{ V_{ego}(t^{*})}-\tau \tag{10}\]  
where \(t^{*}\) is the time when the object is detected, \(a_{max}\) (= \(-6\) m/s\({}^{2}\)) is the maximum acceleration achievable during the avoidance action phase, and \(\tau\) (=0.25 s) is the required time for the vehicle to decelerate after the driver initiates the brake action. SCT results of the simulation are shown in Figure 15. The vehicle equipped with PBS decelerated without using AEBS under all simulation conditions. Figure 15 shows that all the SCT for the vehicle equipped with AEBS were lower than 1.2 s, whereas those with PBS were higher than 1.6 s. Therefore, PBS provided a larger time margin for collision avoidance than AEBS. Next, SCT was classified into three criticality levels according to the previous study [30]. The classification method of criticality level and the percentage results for each level are shown in Table 2. Most of the situations for vehicles equipped with AEBS were near-miss situations, as 98.6% of cases were classified as high-level critical events. On the other hand, the criticality level of PBS was split between middle level and low level, and there were no high-level events. Therefore, compared to the case of AEBS only, additional braking control by the proposed PBS was able to significantly reduce the near-miss situations (critical situations) when darting-out was detected. Next, Figure 16a,b show the results of the collision/non-collision as well as the DCPA for each driving condition. The smaller the value of DCPA, the higher the collision risk. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Criticality Level** & **AEBS** & **PBS and AEBS** \\ \hline High level (SCT \(<\) 1 s) & 98.6\% & 0\% \\ Middle level (1 s \(\leq\) SCT \(\leq\) 2 s) & 1.4\% & 51.7\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Percentage of criticality level. Figure 15: Comparison of Safety Cushion Time as a risk index. The magnitude of the DCPA was indicated by red-to-white gradation shading. In addition, the red cells with a black dot indicate collision cases and the blue cells indicate the cases where the ego vehicle turns right before coming into contact with the darting-out object. Figure 16a,b show that the PBS reduced the number of collision cases from 143 to 0 compared to AEBS. In Figure 16a, there were 133 cases where the DCPA was less than 1 m for vehicles equipped with AEBS, excluding collision cases. Furthermore, in some cases, the DCPA was less than 20 cm. These results indicate that although no collisions occurred in the simulation cases, the safety margin was small, and the collision risk was considered to be high. On the other hand, with the additional braking by the proposed PBS, the DCPA could be extended to exceed 1 m in all simulation cases. Therefore, it can be concluded that PBS was able to calculate a stop position with a low risk of collision and then stop the controlled vehicle in a safe space. To compare the previous system with the new system, simulations were performed in representative cases. The previous system PBS\({}_{\text{f}}\) was reproduced with \(a_{b}=7.85\) m/s\({}^{2}\) and the on-board sensor mounted at the middle of the front end of the vehicle, based on the theory proposed by [PERSON] et al. [24]. Figure 17 shows the simulation result of the previous system (PBS\({}_{\text{f}}\) and AEBS) and the new system (PBS and AEBS). As shown in Figure 17, the previous system decelerated with AEBS, but the collision occurred because the ego vehicle entered the object's driving corridor, i.e., the stop position of the ego vehicle is inside the predicted conflict area. On the other hand, the new system stopped before entering the conflict area and avoided a collision.