## 4 Simulation for Case Study  
The safety performance of the proposed motion planner was evaluated through a simulation study. The base algorithm, which was used for the performance comparison with the proposed algorithm, utilized the same driving mode decision and risk management algorithm [42]. However, a proactive motion planner was not applied to the base algorithm. This difference made the autonomous vehicle governed by the base algorithm accelerate to maximum velocity until detection of the target vehicle. In other words, the base algorithm did not have the approach-motion planner. The intersection for the case study was the four-way uncontrolled intersection. Each road of the intersection intersected at 90 degrees. In addition, structures existed at the boundary of the square intersection area, which created a blind spot for other approach branches. This occlusion restricted the FOV of the environment sensors and delayed the target detection timing. The left turn across path (LTAP) scenario was selected as a case study scenario with the initial position and velocity as shown in Figure 6. The driving routes of the host and target vehicle are marked as a blue and red solid line, respectively. In this simulation, the target vehicle came from the right branch of the driving path of the host vehicle and turned left. This modification of the LTAP scenario increased the risk \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(dt\) & \(N\) & \(a_{\min}\) & \(a_{\max}\) & \(a_{jerk,\max}\) \\ \hline
0.1 s & 30 & \(-5\) m/s\({}^{2}\) & \(1\) m/s\({}^{2}\) & \(2\) m/s\({}^{3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters for target state decision for approach motion. with the target vehicle by making the target vehicle appear from the blind spot. The initial conditions and parameters for the case study were set as follows:  
\[ \begin{array}{l}p_{ini,HOST}=80\;\mathrm{m}\\ p_{ini,TAR}=\;60\;\mathrm{m}\\ v_{ini}=30\;\mathrm{km}/\mathrm{h}\\ v_{\mathrm{max}}=50\;\mathrm{km}/\mathrm{h}\\ \end{array}  \tag{10}\]  
The simulation results are summarized as histories of \(v\), \(a\), \(C\), and _TTC_ with respect to _dDTI_ as shown in Figure 7. Histories of \(C\) and _TTC_ only appeared when the target vehicle was detected by the host vehicle. Since the _dDTI_ decreased during the simulation, the _x_-axis of each graph was flipped to improve the graph interpretation. Since the initial condition was configured so that the target vehicle entered the intersection first, the host vehicle should decelerate to avoid collision and yield to the target vehicle. Therefore, the braking motion appeared in the results of both algorithms. The host vehicle, which is controlled by the base algorithm, accelerated to maximum velocity until detecting the target vehicle at about _dDTI_ = 25 m, as shown in Figure 7a,b. At this moment, the velocity of the host vehicle, 44 km/h, was too fast to react to the target vehicle coming from the blind spot. As shown in Figure 7c,d, \(C\) and _TTC_ were already reduced to the risky level, 46 m and 3.9 s, when the approaching target was first detected. This means that the host vehicle should apply maximum braking to avoid or mitigate a collision with the approaching target, as shown in Figure 7b. Even though maximum braking was used, the host vehicle could not stop at the stop line and stopped at _dDTI_ = \(-\)3 m. The simulation results from the base algorithm, which did not utilize the proactive motion planner, creating a highly dangerous situation for the driver and the other traffic participants. Meanwhile, the simulation results from the proposed proactive motion planner showed a more human-like behavior than the base algorithm.