## 4 System Verification with Full-Vehicle Simulation
### Results and Discussions  
Figure 13 shows examples of the time history of vehicle motion (\(V_{obj}\) = 50 km/h, \(D_{obj\_offset}\) = 16 m). It also shows the simulation results of velocity, acceleration, and system brake pedal stroke for AEBS only and for both PBS and AEBS cases, respectively. The red dotted line in Figure 13a indicates when the collision occurred, and the green dotted line in Figure 13b indicates the safe velocity \(V_{safe}\). Figure 13a,b show that the vehicle initially decelerated the vehicle at about \(-\)0.3 m/s\({}^{2}\) for both systems because the driver did not operate the pedals. Regarding the system response, Figure 13a shows that AEBS increased the brake pedal stroke from 0% to 100% after detecting a darting out, and the vehicle suddenly decelerated to a stop. However, since the ego vehicle entered the object's driving corridor, the collision could not be avoided. On the other hand, as shown in Figure 13b, the PBS decelerated the vehicle in advance so that the vehicle velocity became lower than the safe velocity. Therefore, when darting out occurred, the vehicle was able to stop before entering the conflict area without activating AEBS, and the collision did not occur. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Definition** & **Symbol** & **Value** & **Unit** \\ \hline Acc. for mild deceleration & \(a_{b}\) & \(-\)2.94 & m/s\({}^{2}\) \\ System activation delay time & \(T_{d}\) & 0.1 & s \\ Prediction time & \(T_{p}\) & 2.0 & s \\ Post Encroachment Time & _PET_ & 1.0 & s \\ Virtual darting-out velocity & \(V_{vir}\) & 50 & km/h \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Driving condition parameters. Figure 12: Definition of vehicle position conditions. To verify the degree of collision risk at the time instant the on-board sensor detected a darting out, the time to conflict area of the ego vehicle and the darting-out object was compared. Figure 14 shows a representative example of the time history of \(T_{ego\_in}\), \(T_{ego\_out}\), \(T_{obj\_in}\), and \(T_{obj\_out}\) described in Section 4.1. In Figure 14, we extracted the simulation condition where collisions in neither the case of AEBS-equipped vehicle nor the case of PBS-AEBS-equipped vehicle occurred (\(V_{obj}\) = 40 km/h, \(D_{obj\_offset}\) = 12 m). The black dotted vertical line indicates the time instant when the object was detected, and the red dotted vertical line indicates the time instant when the system was activated in Figure 14. In addition, the blue shaded area corresponds to the time zone in which the ego vehicle body will occupy the space in the conflict area in the future, and the red shaded area corresponds to the time zone in the case of the darting-out object. If these two time zones overlap, it means that a collision will occur at a certain horizon time if both vehicles maintain their current velocity. Figure 14a shows that the time zones in which the ego vehicle and object occupy the conflict area overlapped when the on-board sensor detected the object. Therefore, although AEBS was able to avoid a collision under this driving condition, the collision risk was high, and it was near-miss a situation. On the other hand, Figure 14b shows that PBS started decelerating 2.7 s before the darting-out detection, moving to a state in which the time zones of the conflict area occupancy did not overlap. As a result, since the occupied time zones no longer overlapped (\(T_{ego\_in}-T_{obj\_out}\) = 0) at the time of darting-out detection, it was not considered to be a near-miss situation. Figure 14: Time history of \(T_{ego\_in}\), \(T_{ego\_out}\), \(T_{obj\_in}\), and \(T_{obj\_out}\) (\(V_{obj}\) = 40 km/h, \(D_{obj\_offset}\) = 12 m). (a) AEBS; (b) PBS and AEBS. Figure 13: Time history of the ego vehicle in the simulation (\(V_{obj}\)= 50 km/h, \(D_{obj\_offset}\) = 16 m). (a) AEBS; (b) PBS and AEBS. To analyze the time margin for deceleration at the time of darting-out detection, the Safety Cushion Time (SCT) as an index of situational risk assessment proposed by [PERSON] et al.