# A Novel Maneuver-Based Driving Envelope Generation Approach for Driving Safety Assessment
## 5 Experiments
The speed of the host vehicle is 20 m/s, the speed of the front vehicle is 15 m/s, the distance between them is 23 m. The boundary trajectories of the driving envelope for avoiding collision with the slow front vehicle is shown in Figure 20.  
The red rectangle represents the host vehicle, the green rectangle represents the vehicle \(L_{0}\). The dashed red line \(\tau_{posi}\) denotes the safe position obtained according to the safe distance derived in Section 2.3, the solid red line \(\tau_{outside}\) denotes the boundary trajectory to arrive at the outermost lateral safe position, the solid blue line \(\tau_{interside}\) denotes the boundary trajectory to arrive at the innermost lateral safe position. The line \(\tau_{interside}\) starts from the corresponding point on line \(\tau_{posi}\). From Figure 20, we can see that the driving envelope considers not only the safe distance to obstacles, but also the input of the driver. The driving can reflect the safety margin in the future. In a dynamic traffic scenario with four traffic participants \(F_{d}\), \(L_{d}\), \(F_{0}\) and \(L_{0}\), the driving envelope for a lane-change maneuver and a lane-change abortion maneuver is obtained as shown in Figure 21. The red bounding box represents the host vehicle, the green bounding boxes represent the traffic participants \(F_{d}\), \(L_{d}\), \(F_{0}\) and \(L_{0}\). The maximum lateral acceleration is set as 0.9 m/s\({}^{2}\) for evasive maneuver. When all vehicles are driving at 15 m/s, the driving envelope of continuing lane-change is shown in Figure 21a, the driving envelope of lane-change abortion maneuver is shown in Figure 21b. When the speed of vehicle \(L_{d}\) is 5 m/s and other vehicles drive at 15 m/s, the safe distance constraint of lane change  
Figure 20: The boundary trajectories for avoiding collision with a slow front vehicle. (**a**) The boundary trajectories of lane-change maneuver, \(\varphi(t_{0})=0\). (**b**) The boundary trajectories of lane-change maneuver, \(\varphi(t_{0})<0\). cannot be satisfied. Therefore, the driving envelope of continuing lane-change maneuver cannot be obtained. The safe distance constraint of lane-change abortion is satisfied, it's safe to cancel lane-change, and the driving envelope of lane-change abortion is shown in Figure 21c. The simulation is carried out in C++ using Intel I7-3520 CPU. In the traffic scenario shown in Figure 21, the CPU runs at 2.9 GHz, the average total time used to calculate the safe distance and generate the driving envelope for each driving maneuver is about 1 ms. The drivable area in [24] is represented as connected collision free convex sets. Owing to the consumption of computational resource, the computation time is 75 ms for time horizon 3 s on a 2.6 GHz Core, which is not enough for lane change in dynamic traffic flow. For the driving envelope generation method in [43], lots of points are generated, and the safety regions are computed using a Hamilton-Jacobi approach. When there are 70 longitudinal sampling points and 8 lateral sampling points, the calculation time is 34 ms. The above methods are very time-consuming. In order to use the methods in real-time applications, the time horizon has to be reduced. In the experiment scenarios, the average total time for driving envelope generation is about 1 ms. The boundary paths of the reachable-set are generated to reflect the influence of the driver's input and the steering limitation. The algorithm complexity of generating the boundary paths of the reachable-set is \(O(n)\). In order to restrict the driving envelope within the road boundary, the evasive path to avoid collision with the road boundary, and the boundary paths of reachable-set are connected, as shown in Figure 12. The algorithm complexity for this path generation part is \(O(n)\). The connection point is determined by searching the points on the two paths. The algorithm complexity for determining the connection point is \(O(nlog_{2}n)\). The safe distances for collision avoidance with obstacles are calculated.