## 4 Simulation Results
If there is a risk of collision when the ego vehicle keeps speed unchanged during the CA process, and this risk can be avoided if ego vehicle accelerates to allowable maximum speed, then the ego vehicle will be required to accelerate. Although deceleration and waiting for oncoming vehicle passing the parked vehicle is another option for ego vehicle, considering the time cost and convenience, acceleration is an optimal solution with the promise of safety. In case 3, the calculated \(PET\) is smaller than \(PET_{safe}\), so the ego vehicle will then be required to decelerate. The acceleration, the steering wheel angle and vehicle longitudinal speed under case 3 are shown as Figure 16.  
Figure 16: (**a**) Longitudinal and lateral acceleration, (**b**) Steer wheel angle and (**c**) longitudinal speed of ego vehicle in case 3 (ego car needs to decelerate for a safe overtaking). Figure 15: Collision avoidance process of ego vehicle under case 2. (**a**) Relative positions between vehicles at t = 1 s; (**b**) Relative positions between vehicles at t = 3.4 s; (**c**) Relative positions between vehicles at t = 6.6 s; (**d**) Relative positions between vehicles at t = 20 s.  
Figure 17 shows the CA process of ego vehicle under case 3. When the calculation shows that this is not a safe time under uniform speed or acceleration for avoiding both parked vehicle and oncoming vehicle in the same time, the ego vehicle will be required to decelerate to wait for the oncoming vehicle passing the parked vehicle firstly, as shown in Figure 17c. After the oncoming vehicle has passed, the ego vehicle then restarts and continues the CA process. Figures 12a,c, 14a,c and 16a,c show the acceleration and velocity of the vehicle during the whole obstacle avoidance process, respectively. Based on different \(PET\), the vehicle will be required to choose corresponding behavior, which is shown by figures of acceleration and velocity. As shown in Figures 12b, 14b and 16b, due to the low-speed urban condition, the vehicle front wheel steering angle under the three cases is small. When the ego vehicle begins to turn, the steering wheel angle also fluctuates lightly, and the maximum value of the steering wheel is about \(8^{\circ}\). The comparison of the longitudinal speed under three cases is shown in Figure 18.  
From Figure 18, the comparison of speed under three different cases, in case 1, the velocity still maintains at about 11m/s despite fluctuations, which meets the requirement of keeping the speed as reference when the situation permits. In case 2, in order to reduce the time waste on the premise of ensuring safety, the vehicle chooses to accelerate to avoid obstacles, and its speed and acceleration are all within the preset boundaries. After passing obstacles, the vehicle decelerates to the reference speed. In case 3, the vehicle cannot avoid obstacles safely even if it accelerates to the maximum allowable speed. Therefore, in this case, the ego vehicle decelerates until the oncoming vehicle has already passed, then it restarts and avoids the parked vehicle. The final speeds of ego vehicle in three cases will be controlled to return to the reference speed after obstacle avoidance. Figure 17: Collision avoidance process of ego vehicle under case 3. (**a**) Relative positions between vehicles at t = 1 s; (**b**) Relative positions between vehicles at t = 8.7s; (**c**) Relative positions between vehicles at t = 13.2 s; (**d**) Relative positions between vehicles at t = 20 s.  
At the same time, the time history of TTC between the ego vehicle and the oncoming vehicle is also established, as Figure 19 shows. These two cars go towards each other, so finally the TTC will be zero. Smaller initial TTC will bring higher safety risk during the CA process. If the ego vehicle can safely avoid collision by acceleration, then deceleration is not necessary. This is to ensure the rapid passing of the ego vehicle to prevent congestion and save passengers' time.