# Social and Robust Navigation for Indoor Robots Based on Object Semantic Grid and Topological Map
## 6 Experimental Results
### Segmented Global Path Planning Results
#### 6.3.3 Global Path Planning Efficiency  
Tables 6 and 7 shows the global path planning results for robots of different sizes in home and office environments. Considering that A* and Dijkstra were successfully implemented and tested as the path planning algorithms for mobile robots, we employed A* and Dijkstra to compare with our proposed segmented global path planning algorithm. Multiple conclusions can be extracted from these results:  
* Compared with A* and Dijkstra, the segmented global path planning algorithm greatly reduced the number of traversed cells for the three robot sizes and two environments, reaching a decrease of up to 76.29% (e.g., see 0.18 m radius in the office scene) and 94.54% (e.g., see 0.23 m radius in the office scene). * The reason why the proposed method improves the navigation efficiency is that the correct heuristic direction pointing to ANPs is generated by segmented global path planning. However, the heuristic \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Radius (m)** & **NA** & **A*** & **DJ** & **CA (\%)** & **CD (\%)** \\ \hline \multirow{3}{*}{Home} & 0.18 & 9161 & 13,125 & 64,782 & 30.20 & 85.86 \\  & 0.23 & 7865 & 10,188 & 55,557 & 22.80 & 85.84 \\  & 0.28 & 9122 & 12,456 & 44,865 & 26.77 & 79.67 \\ \hline \multirow{3}{*}{Office} & 0.18 & 36,404 & 153,531 & 631,475 & 76.29 & 94.24 \\  & 0.23 & 37,527 & 142,595 & 686,758 & 73.68 & 94.54 \\ \hline \multicolumn{2}{l}{Average} & - & 100,079 & 331,895 & 1,483,437 & 69.85 & 93.25 \\ \hline \hline \end{tabular}  
NA: numbers when using segmented global path planning. A*: numbers when using A*. DJ: numbers when using Dijkstra. CA: increase of segmented global path planning compared to A*. CD: increase of segmented global path planning compared to Dijkstra.  
\end{table} 
Table 6: Results of traversed cells numbers. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Radius (m)** & **NA** & **A*** & **DJ** & **CA (\%)** & **CD (\%)** \\ \hline \multirow{3}{*}{Home} & 0.18 & 1469 & 1402 & 1408 & \(-\)4.78 & \(-\)4.33 \\  & 0.23 & 1348 & 1281 & 1283 & \(-\)5.23 & \(-\)5.07 \\  & 0.28 & 1472 & 1419 & 1437 & \(-\)3.73 & \(-\)2.43 \\ \hline \multirow{3}{*}{Office} & 0.18 & 7608 & 7136 & 7138 & \(-\)6.61 & \(-\)6.58 \\  & 0.23 & 7602 & 7084 & 7086 & \(-\)7.31 & \(-\)7.28 \\ \hline \multicolumn{2}{l}{Average} & - & 19,499 & 18,322 & 18,352 & \(-\)6.42 & \(-\)6.25 \\ \hline \hline \end{tabular}  
NA: length when using segmented global path planning. A*: length when using A*. DJ: length when using Dijkstra. CA: increase of segmented global path planning compared to A*. CD: increase of segmented global path planning compared to Dijkstra.  
\end{table} 
Table 7: Results of path length. direction of A\({}^{*}\) method and segmented global path planning both are correct and similar for the simple and no branching path. In these scenarios, the improvements of segmented global path planning compared to A*, are not obvious or even negative. For example, there were three paths in the home environment: bed in master room to sink, bed in master room to fridge, fridge to sink, whose results of traversed cells of A* are shown in Figure 11. It can be seen that the heuristic search direction of A* was approximate to the optimal search direction. Specifically, our method forced the robot navigation path to pass through the ANPs, leading to a slightly or negative improvement compared with A*. * The increase of navigation efficiency by our method is more significant in the scene with large areas and complex plane structure. Comparing the two scenes' experimental data, the reduction of traversed cell numbers was larger in the office scene (up to 30.20% and 85.86% in the home scenario, while 73.68% and 94.54% in the office scenario). There were two doors, and the arrangement of things was more disorderly and scattered in the Lab. So, it was more likely for A* to provide wrong heuristic search directions, resulting in inefficiency cell traversal and large computational time.