## 5 Results
### Monte Carlo Simulation  
Monte Carlo simulation has been conducted to evaluate the proposed algorithm in various situations. The test scenario has been generated by randomly selecting the sensor noise level, initial position, initial velocity, maximum velocity, and the driving route of the target vehicles. Five target vehicles have been used when configuring the test scenarios. Sets of the sensor noise, initial position, initial velocity, and maximum velocity are generated by using a normal distribution as follows:  
\[ \begin{array}{l}\sigma_{sensor}=N(0.3\,\mathrm{m},\,0.05\,\mathrm{m})\\ d_{DT,ini}=N(100\,\,\mathrm{m},\,20\,\mathrm{m})\\ v_{ini}=N(40\,\,\mathrm{km}/\mathrm{h},\,\,10\,\mathrm{km}/\mathrm{h})\\ v_{\mathrm{max}}=N(50\,\,\mathrm{km}/\mathrm{h},\,\,5\,\mathrm{km}/\mathrm{h}) \end{array}  \tag{24}\]  
The example case of the Monte Carlo simulation scenario is shown in Figure 14.  
Figure 13: Simulation results of the base algorithm. (**a**) History of longitudinal acceleration; (**b**) history of longitudinal velocity; (**c**) history of \(TTC_{conf}\); (**d**) trajectory of \(TTC_{conf}\) and \(C_{conf}\). A total of 100 simulations were performed for both algorithms. The distributions of the simulation result on the \(TTC_{\mathit{conf}}\) vs. \(C_{\mathit{conf}}\) plane are depicted in Figure 15. As the two vehicles approach the intersection, the \(TTC_{\mathit{conf}}\) and \(C_{\mathit{conf}}\) decrease, and trajectories are headed to the origin of the \(TTC_{\mathit{conf}}\) vs. \(C_{\mathit{conf}}\) plane. Then, the motion planner applied braking inputs to manage the risks caused by approaching targets and prevent the reduction of \(TTC_{\mathit{conf}}\). After the target vehicle passing through the intersection, \(TTC_{\mathit{conf}}\) and \(C_{\mathit{conf}}\) increase to the right top of the \(TTC_{\mathit{conf}}\) vs. \(C_{\mathit{conf}}\) plane. From this point of view, it can be seen that the proposed algorithm maintains its control performance robustly against changes in sensor uncertainty from the distribution toward the top right side of the \(TTC_{\mathit{conf}}\) vs. \(C_{\mathit{conf}}\) plane. On the other hand, the results of the base algorithm show that few trajectories are heading to the top right. This shows that the base algorithm does not have the ability to respond to changes in sensor uncertainty. In particular, since the risk was not properly assessed, the braking input was increased only after \(TTC_{\mathit{conf},min}\) and \(C_{\mathit{conf},min}\) were exceeded. In other words, the results of the proposed algorithm were maintained above the safety constraints \(TTC_{\mathit{conf},min}\) and \(C_{\mathit{conf},min}\). However, the base algorithm cannot guarantee the safety constraints, even though more deceleration was used. In order to analyze the ride comfort of both algorithms, the histogram of the acceleration usage is illustrated in Figure 16. The acceleration usage of the proposed algorithm was concentrated near 0 m/s2 and most of it is in the range of \(-\)3 to 1 m/s2, which is the typical range of human drivers. However, the histogram of the base algorithm is evenly distributed  
From the perspective of computational time, the proposed SMPC-based motion planner was able to determine the desired acceleration within 30 ms even though the algorithm was implemented in MATLAB/Simulink environments. When implemented on an autonomous vehicle, a velocity controller calculates the throttle and brake inputs with much faster sampling to track the target acceleration determined by the proposed algorithm. In addition, since the speed of the vehicle is not fast in the uncontrolled intersection driving situation, the error caused by the calculation time of 30 ms is not significant. Furthermore, since the 30 ms is shorter than the typical LiDAR or camera sensor processing time, a sampling time of 30 ms is fast enough to determine the target motion based on environmental information.