# A Low Overhead Mapping Scheme for Exploration and Representation in the Unknown Area
## 3 Experiments
### The Coverage Performance Rmap  
The performance of the applied case of the Rmap for coverage was measured. This study implemented the Rmap algorithm to the robot as in Figure 8d. The Rmap was integrated with the DP-SLAM algorithm for mapping. Additionally, other coverage algorithms, such as the sector-based and random coverage algorithms were implemented for comparison. The sector-based coverage algorithm is an algorithm that corrects for poor sensing by dividing the space into sectors and improving the localization on a sector [22]. The random coverage algorithm visits the area randomly as the words. It is simple to implement and it is a widely used an algorithm for many cleaning robots. The experiments were conducted in the actual environment of Figure 8c. That is a blueprint of some house and the inside area of the red line is the actual target area that has an area of approximately 8 m \(\times\) 13 m.  
Figure 10a shows the grid map output from the DP-SLAM. The grid map also shows some outer information of the area through the open doors. It represents the area with 26,732 cells. Figure 10b-e show the process of map building of the Rmap by the number of the _VNode_. As the number of _VNode_ increases, the quality of the map also increases. With only 80 _VNodes_, the map shows a very similar quality to the map with the grid map of the previous section. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Results** & **(a)** & **(b)** & **(c)** & **(d)** \\ \hline The number of rectangles (\(n\)) & 19 & 50 & 113 & 522 \\ The size of the minimum rectangle (m\({}^{2}\)) & 1.015 & 0.25 & 0.05 & 0.01 \\ The number of _ACP_ & 23 & 78 & 136 & 477 \\ Similarity compared to the grid map (\%) & 92 & 95 & 97 & 99 \\ Elapse Time (sec) performed in 2 Ghz CPU & 0.875 & 1.063 & 1.375 & 3.281 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The numerical results of the memory efficiency experiment. Figure 9: The memory efficiency experiment results of the Rmap in a simulated Figure 8a environment. The n is the number of rectangles used for the map representation. (**a**) \(n=19\), (**b**) \(n=50\), (**c**) \(n=133\), (**d**) \(n=522\). The graph of Figure 11 shows the coverage performance of the Rmap compared with the other algorithms. The covered area was calculated by comparing the total area and the area visited by the robot in the real environment. For eighty minutes, the Rmap visited almost 95% of the whole area, the sector-based algorithm visited 48%, and the random coverage algorithm visited only 36%. From analyzing the experiment results, the rate of overlapped visits for the area was only 2% for the Rmap algorithm. On the other hand, the rate for sector-based algorithm was 21%, and the random coverage algorithm was 62%. The Rmap algorithm showed the best performance for coverage. In addition, the performance of the Rmap was evaluated in another extreme case of an environment using the simulator, as shown in Figure 12a. The Rmap, proposed in this paper, built a map using the number of rectangles. Therefore, this approach can have a disadvantage for the rounded environment. Therefore, to prove the robustness of the Rmap scheme, this study added an extreme case of an environment which had many rounded curves inside in it. The environment has an area of 4 m \(\times\) 4 m.  
Figure 11: The results of coverage performance according to the path planning method are as follows: The Y axis is the ratio of the coverage area, the X axis is the time (min). The redline is the Rmap scheme, the green line is the sector based algorithm, the blue line is the random algorithm. Figure 10: The coverage process using Rmap scheme in Figure 8c. (**a**) is the grid map of the coverage area; (**b**–**e**) shows the process of Rmap generated by increasing the number of nodes. The Rmap scheme shows a quick increase of the covered area to 80% in contrast to other algorithms, as shown in Figure 12b.