## 3 Hierarchical Path-Planning
All experiments were performed on an Intel Core i7-9700K (eight cores of 3.6 GHz) with 32 GB of memory in the same benchmark environment; several rooms were connected by corridors, as in the real world. The SIRRT* was compared with the IRRT* to verify that the SIRRT* is more efficient in constructing the proposed navigable graph structure that needs multiple intra-regional planning runs among junction nodes. The stability of the SIRRT* in terms of computational time and the final costs is shown in Table 1. The start and goal positions are given in Figure 6a. The IRRT* and SIRRT* performed 1000, 2000, and 3000 informed sampling optimizations after obtaining an initial solution. For each optimization number, one-hundred experiments were performed. In the SIRRT*, the initial solution is deterministically computed by skeletonization employing the Harris corner detector; random sampling is not in play. However, the IRRT* algorithm uses RRT* sampling to achieve an initial solution throughout the entire environment. The total number of IRRT* iterations is the sum of the RRT* samplings required until an initial solution is obtained and the number of informed samplings required for optimization. As the IRRT* performs the RRT* sampling to obtain an initial solution, the computational time is negatively affected. If initial solution computation is slow, the number of RRT* samplings increases, as does the computational time. The mean IRRT* computational times were 8.01, 8.74, and 7.46 s. However, the differences were not significant; the SDs were very large (5.86, 6.59, and 7.39 s). Thus, the IRRT* performed very differently during each trial, although the start and goal positions were the same. By contrast, the SIRRT* computational times were faster and more stable (means 0.51, 0.83, and 1.19 s) than those of the IRRT*. The SDs were relatively small at 0.08, 0.11, and 0.12 s. The SIRRT* generated initial solutions faster than did the IRRT*, and the total computational time for the final solution was lower and more robust than that of the IRRT*. The final costs of the SIRRT* were relatively larger than those of the IRRT*. However, the IRRT* SDs were larger than those of the SIRRT*. Sampling-based \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & \multicolumn{6}{c}{**\# of Iterations for Optimization**} \\ \cline{3-8}  & & \multicolumn{2}{c}{**1000**} & \multicolumn{2}{c}{**2000**} & \multicolumn{2}{c}{**3000**} \\ \cline{3-8}  & & **IRRT*** & **SIRRT*** & **IRRT*** & **SIRRT*** & **IRRT*** & **SIRRT*** \\ \hline \multirow{4}{*}{Computational time (s)} & Mean & 8.01 & 0.51 & 8.74 & 0.83 & 7.46 & 1.19 \\ \cline{2-8}  & Std. & 5.86 & 0.08 & 6.59 & 0.11 & 7.39 & 0.12 \\ \cline{2-8}  & Min. & 1.02 & 0.37 & 1.45 & 0.59 & 1.23 & 0.93 \\ \cline{2-8}  & Max. & 32.08 & 0.72 & 40.08 & 1.14 & 49.04 & 1.44 \\ \hline \multirow{4}{*}{Final cost (pixels)} & Mean & 1441.27 & 1555.33 & 1451.28 & 1535.60 & 1442.94 & 1516.71 \\ \cline{2-8}  & Std. & 61.90 & 16.53 & 64.49 & 21.65 & 54.54 & 20.52 \\ \cline{2-8}  & Min. & 1389.36 & 1506.31 & 1388.81 & 1475.96 & 1390.23 & 1465.13 \\ \cline{2-8}  & Max. & 1680.39 & 1583.75 & 1676.32 & 1577.36 & 1630.01 & 1563.89 \\ \hline \multirow{4}{*}{\# of total iterations} & Mean & 7611.26 & & 7469.60 & & 7106.37 & \\ \cline{2-8}  & Std. & 2684.09 & & 2353.94 & & 2895.54 & \\ \cline{1-1} \cline{2-8}  & Min. & 3758.00 & & 3610.00 & & 3669.00 & \\ \cline{1-1} \cline{2-8}  & Max. & 16,027.00 & & 15,124.00 & & 20,554.00 & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: A comparison of the IRRT* and the SIRRT*. algorithms such as the RRT variants are more likely to achieve an optimal solution as the number of samples increases. The larger number of the total IRRT* iterations reduced the mean final cost, but at the expense of large SDs. Constructing the navigable graph structure requires conducting the local planning algorithm multiple times to obtain the intra-regional paths among junction nodes.