## 5 Validation of Proposed Method
### Evaluation Results
#### 5.3.2 Personal Space Invasion Ratio  
The PS invasion ratio was compared between the two methods in two pedestrian categories: tolerable and intolerable pedestrians. To investigate the difference in the invasion ratios between tolerable and intolerable pedestrians with each method, the relative metric \(I_{relative}\) calculated using Equation (12) with PS invasion ratios of tolerable and intolerable pedestrians was evaluated.  
\[I_{relative}=I_{tolerable}-I_{intolerable} \tag{12}\]  
\(I_{tolerable}\) and \(I_{intolerable}\) denote the time-averaged PS invasion ratios of tolerable and intolerable pedestrians, respectively. As shown in Figure 16, the invasion ratio of tolerable pedestrians is generally smaller than that of intolerable pedestrians, and the difference increases as pedestrian density grows. This is because intolerable pedestrians have a smaller \(h\) and approach the PMV more closely, and as pedestrian density increases, more pedestrians invade the PS.  
For the perspective of examining whether the proposed method satisfies the required function set in Section 4.1, in the condition with 20 pedestrians (pedestrian density 0.08/m\({}^{2}\)), \(I_{relative}\) was significantly smaller for the proposed method compared to the existing method (_p_ < 0.05). On the other hand, in higher pedestrian density conditions, specifically in the condition with 40 pedestrians (pedestrian density 0.17/m\({}^{2}\)) and with 50 pedestrians (pedestrian density 0.21/m\({}^{2}\)), the relative metric was significantly larger for the proposed method compared to the existing method (_p_ < 0.05). This trend of the increasing metric, especially in higher pedestrian density conditions, suggests the PS invasion ratio tends to increase more for tolerable pedestrians than for intolerable pedestrians in autonomous navigation with the proposed method. Accordingly, the proposed method can suppress avoidance for tolerable pedestrians more likely than intolerable pedestrians in high pedestrian density environments.  
The time-averaged PS invasion ratio of intolerable pedestrians \(I_{intolerable}\) was also evaluated to estimate passenger discomfort during autonomous navigation of the existing  
Figure 16: Comparison of the relative metric regarding the PS invasion ratios of tolerable and intolerable pedestrians.  
and proposed methods. As shown in Figure 17, the proposed method demonstrated smaller values than the existing method, particularly in high pedestrian density scenarios. In the condition with 40 pedestrians (pedestrian density 0.17/m\({}^{2}\)), the PS invasion ratio was 0.015 for the existing method and 0.014 for the proposed method. Furthermore, in the condition with 50 pedestrians (pedestrian density 0.21/m\({}^{2}\)), the ratio was 0.026 for the existing method and 0.024 for the proposed method. The PS invasion ratio of the proposed method was significantly smaller than that of the existing method (\(p<0.05\)). Based on the positive correlation between the PS invasion ratio of surrounding pedestrians and passenger discomfort [12], this result suggests that the discomfort caused by intolerable pedestrians can be reduced. Therefore, it can be considered that the proposed method does not increase passenger discomfort.