# A Novel Maneuver-Based Driving Envelope Generation Approach for Driving Safety Assessment
## 5 Experiments  
(1). The Longitudinal Distance Error of the Evasive Motion Model  
The evasive motion mentioned in Section 2.2 is decomposed into lateral motion and longitudinal motion. To obtain the applicable scope of the evasive motion model, the longitudinal distance errors at different constant speeds have been calculated. We set \(H\) as 3.5 m, and \(t_{lat}\) as 5 s. The maximum lateral velocity can be obtained, which is about 1.4 m/s, so the velocity should be higher than 1.4 m/s. As shown in Figure 18a, when the vehicle moves at a constant speed, the longitudinal distance error decreases as the velocity increase. When velocity equals 2 m/s, the distance error is about 1 m. As shown in Figure 18b, the minimum speed is set 2 m/s, when the vehicle moves at a constant longitudinal acceleration, the distance errors at different initial longitudinal speeds and accelerations are calculated. When the longitudinal speed is higher than 2 m/s, the longitudinal distance errors are lower than 1 m, and the longitudinal distance error decreases as the speed increases. Figure 17: The different cases of calculating \(t_{arrive}\). (**a**) The vehicle faces the direction of the target lateral position. (**b**) The vehicle faces the opposite direction of the target lateral position. (**c**) The vehicle is preparing for a left side evasive maneuver. (**d**) The vehicle is preparing for a right side evasive maneuver. (2). The Safe Longitudinal Position at Different State  
Given the allowed maximum lateral acceleration, the longitudinal safe position is influenced by the and the vehicle state. Taking the scenario of avoiding collision with a slow front vehicle \(L_{0}\) as an example, as shown in Figure 19. The speed of the host vehicle is 20 m/s, the speed of the front vehicle is 15 m/s, the longitudinal distance between them is 30 m.  
The safe distance for vehicle \(L_{0}\) is denoted as \(D_{L0,s}\). The maximum safe longitudinal position of the host vehicle \(s_{max}=s_{L0}-D_{L0,s}\). The longitudinal safe distance \(D_{L0,s}\) at the different lateral positions can be calculated according to Section 2.3, and the safe position at each different lateral positions can be obtained. As is shown in Figure 19, the red bounding box represents the host vehicle, the green bounding box represents the vehicle \(L_{0}\). The red solid line represents the safe positions at the different lateral positions with the minimum safe distance proposed in Section 2.3, the maximum acceleration of the evasive model in Equation (2) is set as 0.9 m/s\({}^{2}\). The proposed method can reflect the influence of the lateral motion on the safety distance. The closer the vehicle is to the right lane marking, the farther the safe distance is required  
Figure 19: The safe positions for avoiding collision with the front vehicle. (**a**) \(\varphi(t_{0})=0\). (**b**) \(\varphi(t_{0})>0\). (**c**) \(\varphi(t_{0})<0\). Figure 18: The longitudinal distance errors of the evasive motion model. (**a**) The distance errors at different constant speeds. (**b**) The distance errors at different accelerations. for the evasive maneuver. The vertical black dashed line represents the safe positions determined by TTC, the TTC threshold is set as 4 s. The TTC is obtained by dividing the relative distance by the relative speed. As shown in the figure, the TTC method cannot reflect the influence of the lateral motion. The green solid line represents the safe positions determined by the constant lateral acceleration motion model in [6], the constant lateral acceleration is set as 0.9 m/s\({}^{2}\). The shape of the green solid line is similar to the proposed method in this paper. However, the method in [6] is only used to calculate the safe distance to the front obstacles, the rear dynamic obstacles are not considered. In this paper, the distance to the rear dynamic obstacles can also be calculated. (3). The Driving Envelope in Double-Lane Traffic Scenario  
Taking the scenario of avoiding collision with a slow front vehicle \(L_{0}\) as an example.