## 3 Hierarchical Path-Planning
As shown in Figure 6a, the start region and the goal region have two junction nodes. The hierarchical path-planning includes the inter-regional graph-search and four intra-regional path-plannings using the SIRRT*. Therefore, the computational time of the hierarchical planning is higher than that of the SIRRT*. The sampling areas of the hierarchical planning's intra-regional planning are restricted as the small parts of the entire environment. In contrast, the sampling area of the SIRRT* is the whole environment. The hierarchical planning can achieve the lower cost solution using only a lower number of optimization iterations. ## 5 Conclusions

A hierarchical path-planning method using a navigable graph structure of the environment evaluated via the SIRRT* was proposed in this paper. Conventional global path-planning algorithms find \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & \multicolumn{6}{c}{\# of Iterations for Optimization} \\ \cline{3-10}  & & **50** & **100** & **200** & **500** & **1000** & **2000** & **3000** \\ \hline \multirow{4}{*}{Computational time (s)} & Mean & 0.28 & 0.36 & 0.56 & 1.49 & 3.93 & 11.20 & 21.94 \\ \cline{2-10}  & Std. & 0.02 & 0.02 & 0.03 & 0.06 & 0.07 & 0.14 & 0.28 \\ \cline{2-10}  & Min. & 0.25 & 0.32 & 0.52 & 1.40 & 3.83 & 11.06 & 21.51 \\ \cline{2-10}  & Max. & 0.32 & 0.40 & 0.63 & 1.63 & 4.07 & 11.57 & 21.51 \\ \hline \multirow{4}{*}{Final cost (pixels)} & Mean & 1420.60 & 1420.00 & 1420.00 & 1420.00 & 1420.00 & 1420.00 & 1420.00 \\ \cline{2-10}  & Std. & 2.18 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 \\ \cline{2-10}  & Min. & 1420.00 & 1420.00 & 1420.00 & 1420.00 & 1420.00 & 1420.00 & 1420.00 \\ \cline{2-10}  & Max. & 1431.00 & 1420.00 & 1420.00 & 1420.00 & 1420.00 & 1420.00 & 1420.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Hierarchical path-planning using the pre-built map; 3000 iterations. Figure 7: A comparison of the IRRT*, the SIRRT*, and the hierarchical path-planning using SIRRT* (H-SIRRT*): (**a**) Computational time. (**b**) Final cost. optimal paths by processing entire single-layer environments. In the proposed approach, paths are identified on the intrinsic hierarchical structure; inter- and intra-regional searches are performed. The navigable, environmental graph structure using local map segments and safe junction nodes is defined in the hierarchical path-planning. The inter-regional paths from start regions to goal regions are revealed when navigable graph structures are explored using the Dijkstra graph-search algorithm; the intra-regional paths are computed using the SIRRT*. The hierarchical approach assured stable and efficient performance. The SIRRT* was compared with the IRRT*; the SIRRT* was optimal for the proposed hierarchical path-planning because the SDs of the computational times were lower than those of the IRRT*. Experimentally, hierarchical path-planning using the SIRRT* (over various iterations) afforded efficient, final path convergences (from the start to the end) using few iterations. The proposed method will aid stable and efficient path-planning in large environments. The proposed method assumes a general global planning situation when a robot finds a global path from the start to the goal before it starts to navigate. Although we can use local planners in dynamic environments, global planners also need to cope with dynamic situations in real time. The hierarchical approach can efficiently handle such dynamic situations because it can re-plan the path by performing the intra-regional planning in the changed area and connecting the new intra-regional path with the inter-regional path. Detecting dynamic obstacles and integrating them into the navigation framework in highly dynamic environments need to be investigated in the future. In addition, applying the proposed approach to non-grid-based maps can be valuable for a wide range of practical applications. This research was supported by a project of the Korean government (No. 10073166). The author declares no conflict of interest.