## 2 Risk Prediction under Occluded Vision for Proactive Braking Control Design
### Quantification of Hazardous Speed Region for Right Turn  
Depending on the scenario in which the vehicle darts out, the system executes one of the following two patterns of action. (a) Collision avoidance by mild and moderate deceleration. (b) The ego vehicle passes in front of the darting-out object. This paper defines the maximum velocity satisfying the condition (a) as the safe velocity \(V_{safe}\) and the minimum velocity satisfying the condition (b) as the escapable velocity \(V_{esc}\), as shown in Figure 3. The safe velocity \(V_{safe}\) is calculated based on the method proposed by [PERSON] et al. [24]. Figure 3: Driving according to hazardous speed criteria \(V_{safe}\) and \(V_{esc}\). (**a**) Deceleration in case of condition; (**b**) turning right in case of condition. Figure 2: Schematic overview of proposed proactive braking system for intersection right turn. In this research, there is an on-board sensor installed on the right-front edge of the ego vehicle. The on-board sensor is assumed to be a LIDAR, which provides information on the object's position and speed after detection. When the on-board sensor detects an occluding vehicle, the system predicts the conflict area by calculating the predicted trajectories of the darting-out object and the ego vehicle. First, a Triclothoidal curve is used to predict the trajectory of the ego vehicle's rear-axle center point during a right turn (vehicle-fixed coordinates (x, y) and the relative yaw angle from the current ego vehicle yaw angle at each coordinate), as shown in Figure 4. Based on the predicted trajectory of the center point of the rear axle and the size of the vehicle, the trajectory of the entire vehicle is predicted. Next, in order to predict the risk before the darting out actually occurs, a virtual darting-out object is assumed to dart out from the blind area. The virtual darting-out object is defined as traveling straight in the center of the oncoming lane at a constant speed. The conflict area is calculated by finding the area where the predicted trajectory of the entire ego vehicle overlaps with the defined trajectory of the virtual darting-out object. The stop position when the ego vehicle avoids a collision is defined as the position where the on-board sensor can see through the blind driving corridor at the same time that there is a margin of distance to the conflict area. Equation (1) expresses the safe velocity \(V_{safe}\) at which the vehicle can smoothly decelerate when darting out occurs and stop in front of the predicted conflict area where the sensor can see through the blind driving corridor. \[V_{safe}(t)=a_{b}T_{d}+\sqrt{\left(a_{b}T_{d}\right)^{2}-2a_{b}D_{stop}(t)} \tag{1}\]  
where \(T_{d}\) is the system activation delay time and \(a_{b}\) is the acceleration for mild deceleration. In addition, as shown in Figure 5, \(D_{stop}\) is the distance on the predicted trajectory from the ego-vehicle current position to the stop position. The safe speed \(V_{safe}\) is the speed criterion for stopping by decelerating at \(a_{b}\). Therefore, if the vehicle speed is so high that the vehicle cannot stop even if it continues to decelerate with acceleration \(a_{b}\) when entering an intersection, AEBS will be activated to take over the braking maneuver in order to avoid a collision. Figure 4: Predicted trajectory of ego vehicle and defined trajectory of virtual darting-out object. In the oncoming corridor, the time \(T_{vir}\) from when the on-board sensor recognizes the darting out until the object reaches the conflict area is as follows:  
\[T_{vir}(t)=\frac{D_{vir}(t)}{V_{vir}} \tag{2}\]  
where \(D_{vir}\) is the distance from the darting-out point to the conflict area and \(V_{vir}\) is the assumed virtual velocity of the darting-out object. Equation (4), derived from Equation (3), is the minimum velocity \(V_{esc}\) at which the vehicle can escape the conflict area before contact with the darting-out object while maintaining the current velocity.