## 3 Required Data Rate in V2V for Safe Overtaking
### Vehicle Movement  
In this section, a condition for safe overtaking is discussed from the viewpoint of vehicle movement. In [22], it was said that preventable accidents that can be predicted  
Figure 2: Illustration of the ego vehicle equipped with a 3D LiDAR sensor trying to execute overtaking. The yellow region is the sensing region of the ego vehicle’s LiDAR sensor. rationally must not be caused in the ODD (Operational Design Domain) of automated vehicles. From this rule, collision with the oncoming vehicle that can be predicted by automotive sensors should be prevented in the assumed overtaking scenario. To achieve this goal from the viewpoint of vehicle movement, we focused on overtaking movement and braking. The braking movement was considered for an emergency case where the ego vehicle and the oncoming vehicle have to brake during the overtaking. This movement ensures no collision after the braking of both vehicles. The overtaking movement was considered for safe overtaking. This movement ensures no collision with the blocking and oncoming vehicles during the overtaking. The following paragraphs explain the details. To ensure no collision in an emergency case, we defined the required braking distance. Braking types are classified into the emergency type and comfortable type. When a driver notices an unexpected object on a road, emergency braking occurs with a deceleration of more than 4.5 m/s\({}^{2}\). Usually, almost all drivers brake with a deceleration of more than 3.4 m/s\({}^{2}\). This deceleration enables a driver to keep the vehicle in a lane without losing control when braking on a wet roadway. Furthermore, 3.4 m/s\({}^{2}\) is regarded as being a comfortable rate of deceleration. Comfortable braking is desirable to provide comfortable driving in automated vehicles. The comfortable braking distance is given as follows[23; 24]. \[d_{0}=0.039\cdot\frac{V^{2}}{3.4} \tag{1}\]  
where \(V\) is the velocity (km/h) of a vehicle and \(d_{0}\) is the braking distance (m). Considering the reaction time of drivers, the minimum brake reaction times can be 0.64 s for alerted drivers and 1.64 s for an unexpected event [23]. In automated vehicles, electronic control units can perform control in milliseconds. Therefore, the brake reaction time was regarded as negligible. Since both the ego vehicle and the oncoming vehicle have to avoid the collision in this scenario, the required braking distance became \(2d_{0}\). To ensure overtaking movement, firstly, we defined a driving path for overtaking. The driving path is shown in Figure 3 as a black arrow. This driving path was designed to avoid the collision with the blocking vehicle so that the ego vehicle had to turn two times. For example, if we wanted to describe this driving path very simply, it could be described by four quadrants. However, this curve design did not consider vehicle dynamics. Figure 3: The driving path of overtaking and the two types of curves for approximation. \[x(t) = \int_{0}^{t}\cos\frac{A\theta^{2}}{2}d\theta \tag{2}\] \[y(t) = \int_{0}^{t}\sin\frac{A\theta^{2}}{2}d\theta\]  
The clothoid described as Equation (2) is one of the curves that considers the vehicle dynamics, where \(A\) is the clothoid parameter. The clothoid is defined as a trajectory that meets \(RL=A^{2}\), where \(R\) is the radius of curvature and \(L\) is the length of the curve. Curvature \(\kappa\) of the clothoid can be calculated as \(\kappa=At\). Curvature and vehicle dynamics relate in terms of vehicle handling. In general, when a vehicle enters a curve, a driver has to turn the steering wheel along the curve. If we make the driving path with four quadrants, a vehicle entering this driving path has to turn the steering wheel quickly. This quick turning is caused by a curvature gap between a straight line and a quadrant. On the other hand, if we use a part of the clothoid from \(t=0\), as shown in Figure 3, the driver does not have to turn the steering wheel quickly, and since \(\kappa\) increases linearly from \(\kappa=0\), it is enough to turn at a constant velocity.