## 4 Simulation Results
Time consumption of the simulation calculation is an effective indicator used to reflect the real-time performance of the proposed algorithm. As Figure 20 shows, in case 1 and case 2 in which the ego vehicle is not required to decelerate, the calculation time cost generally stays around 8 ms except for some fluctuations. Although some simulation calculations in case 2 are relatively time-consuming, they are no bigger than 100 ms. In addition, long time-consuming calculations mainly occur between the 7 th and 10 th seconds of the simulation in case 2. During this time period, the ego vehicle is parked and waiting for the oncoming vehicle to pass first (referring to Figure 18). Thus these long time-consuming calculations will not affect the safety of obstacle avoidance and the real-time decision making when the ego vehicle is running. Figure 12:0 The time history of the time-to-collision between ego vehicle and the oncoming vehicle (Case 1: Collision avoidance at uniform speed; Case 2: Collision avoidance by acceleration; Case 3: Collision avoidance by deceleration). Figure 12:1 Speed comparison under different cases (Case 1: Collision avoidance at uniform speed; Case 2: Collision avoidance by acceleration; Case 3: Collision avoidance by deceleration). Table 2 shows changes in related parameters while the ego vehicle is running. The data in the table proves that the ego vehicle can avoid obstacles stably and safely within the speed and acceleration limits and further confirms the reliability of the proposed algorithm. Figure 21 shows the real trajectories of the ego vehicle in three cases. And the minimum distance between ego vehicle and obstacle are 0.52 m (in case 1), 0.24 m (in case 2) and 0.5 m (in case 3), which verify the effectiveness of the proposed algorithm as the functions of obstacle avoidance and lane keeping in the urban traffic condition. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **A** & \\ \hline
**Symbol** & **Range** & **Unit** \\ \hline Longitudinal speed & 10.8–11.8 & m/s \\ Steering wheel angle & \(-\)3.1–3.2 & \({}^{\circ}\)(degree) \\ Longitudinal acceleration & \(-\)1.2–2.2 & m/s\({}^{2}\) \\ Lateral acceleration & \(-\)2.4–2.5 & m/s\({}^{2}\) \\ \hline \hline  & **B** & \\ \hline
**Symbol** & **Range** & **Unit** \\ \hline Longitudinal speed & 11–15.2 & m/s \\ Steering wheel angle & \(-\)2.3–2.8 & \({}^{\circ}\)(degree) \\ Longitudinal acceleration & \(-\)1.9–3.1 & m/s\({}^{2}\) \\ Lateral acceleration & \(-\)2.5–3.3 & m/s\({}^{2}\) \\ \hline \hline  & **C** & \\ \hline
**Symbol** & **Range** & **Unit** \\ \hline Longitudinal speed & 0–11 & m/s \\ Steering wheel angle & \(-\)8.3–4.8 & \({}^{\circ}\)(degree) \\ Longitudinal acceleration & \(-\)2.1–3.3 & m/s\({}^{2}\) \\ Lateral acceleration & \(-\)4.1–3.1 & m/s\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Related parameters while the ego vehicle is running. **A. ** Parameters in case1; **B. ** Parameters in case2; **C.** Parameters in case3. Figure 20: Time consuming of simulation calculation under different cases (Case 1: Collision avoidance at uniform speed; Case 2: Collision avoidance by acceleration; Case 3: Collision avoidance by deceleration). In addition, a comparison simulation is also established to prove the superiority of TL-MPC system. In order to promise real-time performance, reference [31] give a method of linear MPC based on a triple integrator chain. The original method which cannot adjust the speed after overtaking the obstacles is modified to adapt to this research. Figure 22 shows the comparison in case 1 (collision avoidance at uniform speed). Even in this case under which there is no relative high requirement of speed control for the ego vehicle, the compared method cannot easily converge due to lack of model accuracy. At the same time, it also has great fluctuations in controlling the steering wheel angle. The same problem, that it is difficult to converge, can also be found in the results of reference [18].