# Strategy and Evaluation of Vehicle Collision Avoidance Control via Hardware-in-the-Loop Platform
## 3 Proposed System
Let  
\[N_{t}=2l_{f}C_{f}\left(\delta_{f}+\frac{l_{f}}{V_{x}}\gamma-\beta\right)-2l_{r }C_{r}\left(\frac{l_{r}}{V_{x}}\gamma+\beta\right) \tag{6}\]  
\[N_{in}=(N_{t}+N_{d})+N_{z}=N_{td}+N_{z} \tag{7}\]  
\[N_{td}=N_{t}+N_{d} \tag{8}\]  
Figure 2: Distance from the front to rear. This paper proposed a solution to deal with two-dimensional CAS. Note that when the rear vehicle overtakes the front one by steering to avoid two-dimensional collisions, \(r_{f}\) and \(r_{r}\) are the safe radius of the front and rear cars, and \(r_{\min}\) is the minimum radius of the rear steering. When the distance between vehicles is \(0.5\,r_{\min}\), the system will automatically steer the steering wheel to avoid the collision by \(30^{\circ}\) or \(45^{\circ}\), provided that the adjacent lane is clear. The steering schematic is shown in \[{v_{r}}^{2}={v_{r0}}^{2}+2a_{r}s \tag{1}\]0 Generally, the minimum steering radius follows the formula of geometric relationships. \[{v_{r}}^{2}={v_{r0}}^{2}+2a_{r}s \tag{1}\]1  
Herein lies the equation \(L=l_{f}+l_{r};l_{a}\) is the distance from the front bumper to the front wheels. The yaw moment can be controlled by the ESC. Stable steering of the vehicle produces the order of the yaw rate as  
\[{v_{r}}^{2}={v_{r0}}^{2}+2a_{r}s \tag{1}\]2  
Here, \(k\) is the adjustable gain and \(\frac{1}{1+\tau s}\) is the low-pass filter. In this scheme, the yaw moment control should be guaranteed. Consequently, the ESC should be activated all the time. Otherwise, the vehicle may fall into an unstable scenario when performing an overtaking. \begin{table}
\begin{tabular}{c c c c} \hline
**Strategy Map** & \(\mathbf{s^{\prime}<20\text{ m}}\) & \(\mathbf{20\leq s^{\prime}<40\text{ m}}\) & \(\mathbf{40\leq s^{\prime}<60\text{ m}}\) \\ \hline \(v_{r}<30\text{ km}/\text{h}\) & 60\% Braking & 50\% Braking & 40\% Braking \\ \(30\leq v_{r}<60\text{ km}/\text{h}\) & 80\% Braking & 70\% Braking & 60\% Braking \\ \(v_{r}\geq 60\text{ km}/\text{h}\) & 100\% Braking & 90\% Braking & 80\% Braking \\ \hline \end{tabular}
\end{table} 
Table 1: Braking conditions for one-dimensional CAS (collision avoidance system). Figure 4: Motion model of vehicle. Figure 3: Schematic of the vehicle changing lanes to avoid collision. In this paper, the two-dimensional CAS is called the dynamic collision avoidance control (DCAC). It combines all the mentioned technologies in a dynamic situation. Figure 6 shows the flowchart of the presented system. As can be seen in this figure, the presented system covers the functions of ACC and AEB. Additionally, the DCAC can achieve collision avoidance in a dynamic way. Thus, it appears to be an overtaking scenario; the rear vehicle should change its lane once or twice. Evaluations in the following section will be carried out to verify the proposed algorithm. Note that it has the potential to be employed on the Intelligent Transportation Systems (ITSs). For a wheeled vehicle with tires, our proposed approach, namely the DCAC, can be applied to trucks, buses, and even linked vehicles, such as railway trains. The proposed approach can be a foundation for modern autonomous vehicles. It endows the autonomous vehicles with nimble and reliable reactions on motion and safety regarding collision avoidance. Consequently, for further investigations at the next stage, the proposed approach can be applied to a full-scale autonomous vehicle for ground tests. Figure 5: Steering basis of vehicle. Figure 6: Flowchart of the proposed approach.