## 5 Results
### Case Study  
The simulation scenario for the case study is described in Figure 11. The LTAP-OD scenario has been used for the evaluation of the proposed and base algorithms. The SMPC without an uncertainty estimator is denoted as a base algorithm in this chapter. In the conventional LTAP-OD scenario, the subject vehicle tries to turn left while oncoming targets are going straight. In this study, LTAP-OD has been modified to swap the driving route of the ego and target vehicles. In other words, the target vehicle turns left while the ego vehicle attempts to pass straight through the intersection. The values of initial \(d_{DTLego}\) of 80 m, initial \(d_{DTLtarget}\) of 60 m, the initial velocity of 45 km/h, and the maximum velocity of 50 km/h have been used as an initial condition. The difference in the initial condition of \(d_{DTl}\) was intended to make the target vehicle enter the intersection first, which creates the situation where the ego vehicle will yield. Under the same initial condition, the simulation has been performed three times for each algorithm with different levels of sensor noise. In each of the three simulation runs, the measurement noise of the environment sensor and perception algorithm has been assumed to be a normal distribution. The standard deviation of the sensor noise has been set to 0.5-times, 1 time, and 2 times the reference value from the quantitative analysis of the previous study [25]. Figure 11: LTAP-OD scenario for case study. The simulation results of the proposed and base algorithms have been summarized in Figures 12 and 13, respectively. A history of the variables has been represented with respect to the \(d_{DTI}\) to prevent the misinterpretation caused by a different driving time. As shown in Figures 12 and 13, the behavior changes of the ego vehicle occurred at \(d_{DTI}\) = 30 m, where the target vehicle was detected by the sensor model for the first time. The driving mode of all simulations was transitioned to yield mode after target detection. As a result of the simulation, it can be confirmed that the \(TTC_{conf}\) and \(C_{conf}\) were maintained above the \(TTC_{conf,min}\) and \(C_{conf,min}\) in all simulation cases. However, the difference in behavior shown in the simulation results was significant. From the simulation results of the proposed algorithm shown in Figure 12, it can be confirmed that the response to the perception and prediction uncertainty has been effectively made. The magnitude of the deceleration command is proportional to the sensor noise level because the probability distribution of the chance constraint is adapted to the uncertainty estimate from the recursive covariance estimator. Specifically, the amount of the deceleration is increased to respond to large uncertainty of the \(\sigma_{sensor}\) = 2 \(\sigma_{ini}\) case. Then, in a situation where the influence of uncertainty is reduced due to the decrease in \(C_{conf}\), the acceleration command is generated earlier than the \(\sigma_{sensor}\) = \(\sigma_{ini}\) case because the safety margin is already secured. In the case of \(\sigma_{sensor}\) = 0.5 \(\sigma_{ini}\), the SMPC can trust the prediction results more than other cases, because the prediction algorithm estimates the small uncertainty. Therefore, the risk caused by approaching targets can be managed at a point close to the conflict point region. The braking command is generated at a later moment than the other two cases. As the proposed algorithm can actively respond to the uncertainty of the sensor, the trajectories of \(TTC_{conf}\) vs. \(C_{conf}\) show a similar shape while complying with the constraints for \(TTC_{conf}\) and \(C_{conf}\). Figure 12: Simulation results of the proposed algorithm. (**a**) History of longitudinal acceleration; (**b**) history of longitudinal velocity; (**c**) history of \(TTC_{conf}\) (**d**) trajectory of \(TTC_{conf}\) and \(C_{conf}\).