## 3 Control System Design
### LKA Control System Design  
For the LKA control system, the desired target steering angle is determined based on the inputs of the vehicle's current position and the lateral deviation at the lookahead position. These inputs are obtained from the lane detection sensor. The lane detection sensor detects the position of the vehicle relative to the lane lines. Based on this information, the system calculates the lateral deviation of the vehicle from the center of the lane at the lookahead position. The current position status of the vehicle is also taken into account to determine the desired target steering angle, considering two key variables, namely yaw angle and the difference in distance from the lookahead point to the left and right lane lines. Figure 6 illustrates a simplified diagram of the system model. In Figure 6(1), AC and BD are a pair of parallel lane detection lines separated by 4 m. The sensor's center position is assumed to be at the centroid O, and OV represents the vehicle's longitudinal central axis. CD can be approximated as a tangent line to the right lane arc intercepted by AC and BD. Line OE passes through centroid O and is parallel to CD, so the yaw angle \(\alpha\)', i.e., the angle between OV and OE, can be obtained. The sensor provides coordinates for points O, V, C, and D in the vehicle's coordinate system. Through geometric relationships and coordinate calculations, the value of \(\alpha\) can be calculated.  
In Figure 6(2), \(L_{1}\) and \(L_{2}\) represent the distances from the intersection point of the vehicle's central axis with the lane detection line CD to the left and right detection points B and D, respectively. The difference between \(L_{1}\) and \(L_{2}\) determines the angle \(\beta^{\prime}\) that needs  
Figure 5: AEB control logic.  
Figure 6: Simplified diagram.  
to be adjusted for the vehicle's center of mass to reach the lookahead point on the lane centerline. The specific calculation process is shown in Equation (6).  
\[\beta^{\prime}=\left[\frac{L_{2}}{L_{1}+L_{2}}-0.5\right] \tag{6}\]  
The ultimate desired target steering angle \(\theta\) is determined by both \(\alpha^{\prime}\) and \(\beta^{\prime}\), and the calculation process is shown in Equation (7), where \(k_{1}\) and \(k_{2}\) are proportional parameters required for converting to the steering wheel angle.  
\[\theta=k_{1}\alpha^{\prime}+k_{2}\beta^{\prime} \tag{7}\]  
Furthermore, regarding the triggering conditions of the LKA system (independent control), whether the vehicle is deviating from the lane depends on the distance from the vehicle's body edge on the deviation side to the lane edge on the same side. The distance serves as the criterion to ascertain if there is a tendency for the vehicle to deviate from the lane and is used as the triggering condition for the LKA system. The lane deviation scenario in curves is illustrated as Figure 7, where A and B represent the two nearest points on the deviation side, respectively. \(L^{\prime}\) is the distance between points A and B, and it is the critical value for judging lane deviation tendency. In addition, a certain safety redundancy \(d\) is considered; for example, 0.4 m selected in this study. When \(L^{\prime}\leq d\), it is assumed that the deviation caused by the emergency braking in curves would make the vehicle deviate from the original lane. In this case, the LKA system is triggered, adjusting the steering wheel angle to keep the vehicle's position as close as possible to the lane centerline. Conversely, when \(L^{\prime}>d\), it is assumed that the deviation caused by the emergency braking will not make the vehicle deviate from the original lane. In this situation, the LKA system remains inactive.