## 4 Simulation and Analysis
### Curvature Radius \(R=60\ m\)  
The simulation results for a vehicle running at 60 km/h on a curved road with a radius of 60 m are depicted in Figure 8. Figure 8a-d show the trajectory, distance from the center of mass to the lane centerline, steering wheel angle, and vehicle speed, respectively. Figure 8e-h display the relative distance, lateral acceleration, longitudinal acceleration, and yaw rate, respectively. Figure 9 provides a schematic representation of the simulation results for different systems in this scenario.  
It is evident that all three control systems activate emergency braking at \(t=5.6\) s. The braking deceleration is increased in stages to effectively avoid a collision with the vehicle in front. By approximately \(t=8.1\) s, the distances between the host vehicle and the obstacle vehicle are 1.05 m, 1.11 m, and 1.15 m for Systems 0, 0, and 0 respectively. Furthermore, in System 0, the lateral offset of the vehicle's center of mass gradually increases during emergency braking on the curved road. Eventually, at rest, the lateral offset reaches up to 1.72 m, causing the vehicle to deviate from its original lane. In System 0, when the vehicle engages in emergency braking, the lateral offset of the center of mass also increases gradually. However, at \(t=6.2\) s, the system detects a tendency for the vehicle to deviate from its current lane and triggers the LKA system to make an urgent steering action. This prevents the vehicle from deviating from its original lane. At rest, the lateral displacement of the center of mass is only 0.29 m, keeping the vehicle close to the lane centerline. However, due to the emergency steering action, the vehicle's yaw rate experiences significant changes, resulting in reduced lateral stability. In contrast, in System 0, the LKA system is immediately triggered as the vehicle deviates laterally during emergency braking. The steering wheel is adjusted accordingly. At rest, the lateral offset of the center of mass is only 0.21 m. As the LKA system is activated earlier, the steering wheel adjustment is smaller than that of System 0, resulting in smoother changes in yaw rate and better lateral stability.  
Furthermore, simulation tests are conducted with an initial vehicle speed of 50 km/h. Table 3 presents the simulation results for two different vehicle speeds in the scenario with a 60 m radius curve. It can be observed that under both initial vehicle speeds of 50 km/h and 60 km/h, collision avoidance is achieved when the three different collision avoidance systems are triggered in the 60 m radius-curve scenario. In System 0, there is a significant lateral offset of the center of mass during the emergency braking process. However, with the participation of the LKA system, the lateral offsets in Systems 0 and 0 are noticeably reduced.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Vehicle mass (kg) & 1406 \\ Center-of-gravity (C.G.) height (m) & 0.480 \\ Distance from the front axle to the rear axle (m) & 2.700 \\ Tire radius (m) & 0.225 \\ Track width (m) & 1.505 \\ Vehicle length (m) & 4.430 \\ Vehicle width (m) & 1.860 \\ Vehicle height (m) & 1.310 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Main parameters of the ego vehicle.  
Figure 8: _Cont._