## 5 Validation of Proposed Method
### Discussion on the Proposed Method  
Results showed that the proposed method has the potential to demonstrate efficient autonomous mobility without increasing passenger discomfort compared to the existing method in crowded scenarios with a pedestrian density of \(0.15/\mathrm{m}^{2}\) or higher. This result is likely due to the increased occurrence of scenes where the passenger can tolerate invasion as the pedestrian density rises, providing more opportunities for the PMV to suppress avoidance behavior. Particularly, comparing the paths generated by each method in a trial with 50 pedestrians (pedestrian density \(0.21/\mathrm{m}^{2}\)) revealed a significant difference in the chosen directions, as shown in Figure 19. In this scene, pedestrians A and B approached the PMV. Pedestrian A, walking along the wall, moved more linearly than pedestrian B, who was walking near the pathway center, as depicted in Figure 19a. The autonomous PMV with the existing method steers toward the direction of pedestrian B to reduce the number of PS invasions. By contrast, the autonomous PMV with the proposed method tolerated the approach of pedestrian A and suppressed the avoidance behavior. Consequently, 1 s later, as depicted in Figure 19b, the autonomous PMV with the existing method moved toward the pathway center, obstructing the pedestrian flow, and leading to a substantial increase in the PS invasion ratio and travel time compared to the proposed method. The existing method makes avoidance actions for all approaching pedestrians, leading to results where the PMV heads toward the pathway center to reach the destination and gets sandwiched by numerous pedestrians on both sides. On the other hand, the proposed method suppresses avoidance behavior to the approach of pedestrians moving in a straight line, particularly for those who are moving in a straight path in a streamlined pedestrian flow. In contrast to the existing method, the proposed method steers toward pedestrians moving in a straight line, especially those walking along the wall, aiming to maintain a straight trajectory without opposing the pedestrian flow, as shown in the lower figure of Figure 19a. This behavior is assumed to have contributed an efficient autonomous navigation in high pedestrian density environments. Figure 19: Comparison of PMV behavior between the existing and proposed methods in two scenes 1 s apart. As the introduction mentions, safety is also a crucial requirement for an autonomous PMV. The collision count between the PMV and pedestrians per simulation trial was compared between the existing and proposed methods. As illustrated in Figure 20, the proposed method showed less collision count than the existing method in environments of higher pedestrian density. This difference is attributed to the fact that the proposed method exhibits fewer abrupt changes in behavior to the pedestrian flow. By following a trajectory closer to the wall, the proposed method can decrease the number of instances pedestrians invade the PMV's path. Thus, it is suggested that the proposed method can also contribute to the improvement as well as the achievement of efficient autonomous navigation in crowded environments with high pedestrian density. However, in low pedestrian conditions, such as with 20 pedestrians (pedestrian density 0.08/m\({}^{2}\)), the proposed method may result in a longer avoidance duration (Figure 15), a higher PS invasion ratio (Figure 17), and an increased travel time (Figure 18) compared to the existing method. In addition, as shown in Figure 20, under the condition of 10 pedestrians (pedestrian density 0.04/m\({}^{2}\)), the proposed method may result in a higher likelihood of collisions. Concerning the causes of these negative effects of the proposed method, the proposed method tolerates pedestrians approaching, even in situations with a sufficient margin around the PMV to freely perform avoidance behavior, and it could not initiate avoidance, such as turning in advance, as in the existing method.