# Study on the Improvement of a Collision Avoidance System for Curves
## 3 AEB System Model  
Figure 3 shows the overall configuration of the proposed AEB system based on the curvilinear coordinate system. This system consists of two main parts. The first part conveys data from velocity sensors and GPS sensors, which are installed in each vehicle, through V2V communication. The second part derives a relative distance between the host and target vehicles by converting the data of these vehicles to the curvilinear coordinate system and calculating TTC using the relative distance. Thus, a collision risk is calculated by reflecting the geometric road information. \begin{table}
\begin{tabular}{l} \hline
**def bisect(func, a, b):** \\ \hline
\begin{tabular}{l} 'Find root of continuous function where f(a) and f(b) have opposite signs' \\  assert not samesign(func(a), func(b)) \\  for i in range(54): \\  midpoint = (a + b) / 2.0 \\  if samesign(func(a), func(midpoint)): \\  a = midpoint \\  else: \\  b = midpoint \\  return midpoint \\ \end{tabular} \\ \hline \end{tabular}
\end{table} 
Table 1: Pseudo code of the bisection method. The communication unit measures the velocity and acceleration of the host vehicle through in-vehicle sensors and the absolute position and azimuth angle of the host vehicle through the differential global positioning system (DGPS). In addition, the data of the target vehicle, including the absolute position, velocity, and acceleration, are obtained through V2V communication. Figure 4 is a flow diagram of the risk determination algorithm for the proposed AEB system. The AEB system automatically engages the braking system based on a collision risk, which is calculated from the relative velocity and relative distance. The velocity and position data of the target vehicle are used to derive the relative velocity and distance [4]. As the risk of a head-on collision needs to be considered for the operation of the AEB system, TTC was used as the risk indicator. Furthermore, V2V communication-based data was used to calculate TTC. Meanwhile, if the information of the target vehicle is obtained through V2V communication, the challenges related to limited sensing range and blind spots peculiar to sensors, including camera, RADAR, and LiDAR, can be solved. The brake engagement time is determined by comparing TTC, which is the collision risk with the target vehicle, and \(TTC_{min}\), which is the minimum brake engagement time for avoiding a collision. Figure 4: Flow diagram of risk judgment for the proposed AEB system. Figure 3: Configuration of the proposed system. Note: AEB = autonomous emergency braking; TTC = time-to-collision; V2V = vehicle-to-vehicle. In other words, as expressed in Equation (7), the brake application time is considered to be the period when TTC becomes lower than \(TTC_{min}\). At this time, the braking system is applied in the host vehicle. \[\text{TTC}<TTC_{min} \tag{7}\]  
The parameters of TTC and \(TTC_{min}\) for determining brake engagement time can be obtained using Equations (8) and (9). As the host vehicle is considered to be moving at a uniform speed until it is stopped by the braking system, the collision risk can be defined by using the formula of a uniformly accelerated motion [16]. The minimum collision distance according to deceleration can be calculated using Equation (10). In Equation (9), \(TTC_{min}\) can be calculated using the velocity obtained from the minimum collision distance and V2V communication [17]. \[\text{TTC}=\frac{S_{rel}}{V_{rel}}[\text{s}] \tag{8}\]  
\[TTC_{min}\] (9  
The performance of the proposed AEB system was analyzed using the Mercedes Benz's PRE-SAFE. It is a system intended to bridge the gap between primary safety, which aims to prevent a car from being involved in an accident, and secondary safety, which is the protection provided during a collision. At speeds above 30 km/h, PRE-SAFE monitors the dynamic state of the vehicle (speed, rotation, etc.) and the driver's inputs to steering, accelerator and brake, to determine whether or not emergency action is being taken.