## 4 Path-Planning Method Considering Passenger Tolerance Characteristics
### Proposal of a Path-Planning Method  
The proposal is based on the path-planning method proposed in the previous study [12]. The existing method [12] consists of three path planners: the global path planner, the middle path planner, and the local path planner. As Figure 11 shows, the middle path planner outputs intermediate target paths by utilizing the global path to the destination the global path planner provides. This planner considers future interactions with pedestrians based on the positional information of the PMV and the recognized pedestrians, along with map data. Subsequently, the local path planner considers the intermediate target paths generated by the middle path planner to produce the final control values for the PMV, namely, the target speed \(v\) and steering angle \(\delta\). The middle path planner plays a role in proactively preventing pedestrians within a mid-range distance of up to 10 m from the vehicle from entering the PS. The local path planner, on the other hand, is responsible for avoiding closer pedestrians within a range of 5 m. Therefore, in the proposed method, the local path planner is improved to suppress avoidance behavior for tolerable pedestrians, while the functions of the middle path planner and global path planner remain unchanged. In [12], the local path planner outputs a combination of \(v\) and \(\delta\), maximizing the evaluation function in Equation (3). \(L_{goal}\) denotes the distance to approach the intermediate target path within an evaluation time step \(T_{local}\), \(L_{inv}\) denotes the PS invasion ratio of the surrounding pedestrians, and \(\beta_{goal}\) and \(\beta_{inv}\) denote the weighting constants of \(L_{goal}\) and \(L_{inv}\), respectively. \(L_{inv}\) is expressed by Equation (4), incorporating the PS invasion ratios \(l_{wall}(t)\) from static obstacles, such as walls, and \(I_{ped}(t)\) from surrounding pedestrians, acting as a penalty item that decreases as the PS invasion ratio increases. Additionally, in [12], the PS of a passenger is constant, and Equation (5) is used to calculate the sum of the PS invasion ratio for each pedestrian, where \(I_{j}(t)\) and \(l_{k}(t)\) represent the PS invasion ratios of pedestrians \(j\) and \(k\), respectively. This study proposes an improved path-planning method by refining this local path planner. \[G(v,\delta)=\beta_{goal}\;L_{goal}+\beta_{inv}L_{inv} \tag{3}\]  
\[L_{inv}=-\int_{0}^{T_{local}}(I_{wall}(t)+I_{ped}(t))dt \tag{4}\]  
\[I_{ped}(t)=\sum_{j\in\{k|I_{k}(t)>0\}}I_{j}(t) \tag{5}\]  
In the proposed method, the evaluation of the PS invasion ratio is reduced for the pedestrians for whom the passenger can tolerate, compared to other pedestrians. This function is achieved by decreasing the penalty in \(L_{inv}\), thereby suppressing the PMV's avoidance behavior. The PS size of the passenger is changed for pedestrians for whom the passenger can tolerate to reduce the PS invasion ratio evaluation. Specifically, the size of the PS in the forward direction is reduced based on the behavioral history of the target pedestrian to make the PS invasion ratio smaller than it is. Based on the analysis results, the size of the PS in the forward direction is calculated using the minimum curvature  
Figure 11: Paths generated by 3-layer path planners. radius \(R_{min}\) of the predicted pedestrian's trajectory among the range where the pedestrian is 6.0-7.0 m ahead of the PMV, as shown in Equation (6). Here, \(\gamma_{R}\) is a constant satisfying Equation (7), and a threshold of 0.5 is set for the rate of PS size reduction to prevent collisions between the PMV and the pedestrians caused by an excessively small PS. As depicted in Figure 12, the larger the \(R\), the shorter \(l_{f}\prime\), thereby reducing the PS invasion ratio, as expressed in Equation (8).