# Study on the Improvement of a Collision Avoidance System for Curves
## 4 Simulation Scenarios and Results
### Simulation Results  
A curve with a constant curvature and a reversed curve were simulated to examine the performance of the curvilinear coordinate-based AEB system. The simulation results of the conventional AEB system and the proposed AEB system were compared for curves.  
Figure 9 compares the performances of the AEB systems on a curve with constant curvature. As the conventional AEB system always assumed a constant curvature, it was expected that both the AEB systems would exhibit similar performances.  
As the host vehicle initially moved at an even velocity and was slowed down by TTC, it initially exhibited a uniform motion, followed by a uniformly accelerated motion. Accordingly, the relative distance between the two vehicles decreased at a constant rate, and the gradient showed a gradual changed only during deceleration. In Figure 9a, as previously expected, the conventional AEB system and the proposed AEB system exhibited a constant decrease in velocity, and the gradient had a gradual change when the TTC flag operated at partial and full braking. In addition, the proposed AEB system and conventional AEB system had similar relative distances, with initial relative distances of 64.3 m and 64.7 m, respectively, and ultimate relative distances of 1.8 m and 1.7 m, respectively. The relative velocities and times for TTC and TTC flag indicated that the AEB systems oper  
Figure 8: Simulation scenario: (a) curve with constant curvature; (b) reversed curve.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Unit** & **Value** \\ \hline Velocity of host vehicle & km/h & 60 \\ Velocity of target vehicle & km/h & 0 \\ Minimum plane curve radius & m & 140 \\ Minimum plane arc length & m & 70 \\ Curve road form & - & Curve with constant curvature \\  & & Reversed curve \\ \hline \hline \end{tabular}
\end{table}
Table 3: Simulation parameters.  
Finally, comparing the results of the four parameters, both AEB systems yielded similar performances on a constant curvature.  
Figure 10 presents the analysis results of the performances of the AEB systems in a reversed curve, where Figure 10a is relative distance, Figure 10b is relative velocity, Figure 10c is TTC, and Figure 10d is TTC flag.  
Figure 10: Simulation results of the AEB systems on a curve with a constant curvature: (**a**) relative distance; (**b**) relative velocity; (**c**) TTC; (**d**) TTC flag.  
Figure 9: Simulation results of the AEB systems on a curve with a constant curvature: (**a**) relative distance; (**b**) relative velocity; (**c**) TTC; (**d**) TTC flag.  
The proposed AEB system and the conventional AEB system had initial relative distances of 99.9 m and 91.9 m, respectively, and ultimate relative distances of 1.12 m and 0.02 m, respectively. Since each vehicle had the same initial position, the initial relative distance needed to be similarly estimated. However, the difference between the initial relative distances of the two AEB systems is about 10 m.  
The proposed AEB system on the curve road is the same as the AEB system on straight roads through the transformation of the curvature coordinate system. Therefore, in the proposed AEB system, the relative distance decreases slowly and constantly, whereas in the existing AEB system, there is a section in which the phase distance changes rapidly. This indicates that the proposed AEB system accurately derived the relative distance irrespective of the alignment of the curve road, and performed appropriate braking accordingly. On the other hand, when the relative distance increased sharply at the point where the road changed direction (4.8s), the relative distance affected the operating timing of the partial braking and full braking in the existing AEB system. Therefore, because the final relative distance is too close, the existing AEB system does not seem to be able to avoid the collision in Scenario 2.