*4.1. Scenarios and Honeycomb-Map Generation*

Figures 11 and 12 show the movements made by the UAVs in the simulations of Scenarios 1 and 2, respectively. Figures 13 and 14 present the exploration order of each UAV with the respective hexagon-definition algorithm to be explored, FIFO and Euclidean distance. The blue line correspond to UAV 1, the red is UAV 2, and the green is UAV 3 (when the simulation had three UAVs).

The yellow circle identifies the highest-traffic hexagon. Hexagon traffic means how many times a UAV went through the hexagon. Table 1 shows the max traffic number in the simulations. Considering the *ids* of Table 1, and relating them in Figures 11 and 12, these most accessed hexagons were located in places characterized as doors or passageways.

In the simulations, the movements of each UAV were recorded. Displacement means that a UAV moved from a hexagon to an adjacent one. Table 2 shows the displacement number and average per UAV in each simulation in Scenario 1. Table 3 shows the same for Scenario 2. Table 4 bring the exploration time. Tables 5 and 6 details data from both exploration order and displacement.


**Table 2.** Displacement number—Scenario 1.


(**a**) Scenario 1 - 2 UAVs—First-In–First-Out (FIFO). (**b**) Scenario 1. Two UAVs–Euclidean distance (ED).

**Figure 11.** Displacement—Scenario 1.



(**a**) Scenario 2-2. UAV–FIFO. (**b**) Scenario 2-2. UAV–Euclidean distance.

(**c**) Scenario 2-3. UAV–FIFO. (**d**) Scenario 2-3. UAV–Euclidean distance.

**Figure 12.** Displacement—Scenario 2.

(**a**) Scenario 1-2. UAV–FIFO. (**b**) Scenario 1-2. UAV–Euclidean distance.

**Figure 13.** *Cont.*

(**c**) Scenario 1-3. UAV–FIFO. (**d**) Scenario 1-3. UAV–Euclidean distance.

(**a**) Scenario 2-2. UAV–FIFO. (**b**) Scenario 2-2. UAV–Euclidean distance.

**Figure 14.** Exploration order—Scenario 2.



**Table 5.** Exploration order.


#### **Table 6.** Displacement order.



**Table 6.** *Cont.*

#### *4.2. Cube View and Temperature Caption*

In addition to performing the mapping honeycomb in a hexagonal shape, further information can be generated for rescue teams. With the RGB-D sensor, a cube view can be generated. Figure 15 shows the Scenario 1 cube projection (Figure 8a), while Figure 16 shows the honeycomb map.

A cutout of 41 and 44 hexagons from the generated map of Figure 16, and the location of these hexagons in the simulator, are shown in Figure 17. In Section 3.1.7, the TransformRGB-D Algorithm 1 shows how RGB-D points are converted into 3D cubes.

In Figure 16, red lines (continuous or dashed) indicate the temperature reading above a reference value. Then, a fire-spot photo was recorded. Figure 18 shows the caption of hexagon 14 in Scenario 1.

**Figure 15.** Three-dimensional cube view.

**Figure 16.** Honeycomb-map simulation—Scenario 1, three UAVs, Euclidean distance algorithm.

(**a**) Three-dimensional cube view—hexagons 41 and 44.

(**b**) V-REP scenario 1—hexagons 41 and 44. **Figure 17.** Clipping of hexagons 41 and 44 of Figure 16.

**Figure 18.** Fire-spot—hexagon 14 of Scenario 1.

#### **5. Discussion**

Topological mapping reduces information processing compared to metric mappings. The graph structure allows the execution of generic algorithms, such as the Dijkstra algorithm, used in trajectory planning. The data presented in Section 4 show the behavioral differences in the simulations considering number of UAVs, and algorithms in the definition of places to be explored, besides environment characteristics. By comparing the simulations, we verified that traffic in the hexagons was reduced when there was an algorithm change (FIFO for Euclidean Distance), as can be seen in Table 1. When comparing the change in UAV number, there was a slight increase in the maximum traffic value and exploration time, as can be seen in Table 4. When Scenario 2 is analyzed, the variation in the number of UAVs from two to three, in both FIFO and Euclidean Distance algorithms, reduces the exploration time. Already in Scenario 1 the opposite occurs. This happens due to the characteristics of the scenarios, where Scenario 2 has wide passages and more space for maneuvers, while Scenario 1 is composed of rooms and narrow doors, which influences the processing to avoid collisions in this points that were bottlenecks on the map. To decrease these values, an algorithm that considers not only Euclidean distance, but also the arrangement of UAVs and hexagons as a whole, should be evaluated.

On UAV displacement in the simulated scenario, Tables 2 and 3 exhibited a strong reduction in UAV movement when increasing the number of UAVs and changing the algorithm of choosing hexagons to explore. For Scenario 1, the change in the number of UAVs in the FIFO algorithm showed 31.63% reduction in average displacement per UAV. For the Euclidean distance algorithm, the reduction was 21.21%. By changing the simulation with two UAVs to three, and the FIFO algorithm for the Euclidean distance algorithm, reducing displacement in the scenario reached 42.52%; the same analysis for Scenario 2 showed a displacement decrease of 37.7%. This saves both energy and exploration time .

#### **6. Conclusions**

This work presented an environment mapping method inspired by how bees build their hives. Since only one bee constructs and occupies the space of a honeycomb, a topological map was constructed so that UAVs involved in the mapping process behaved similarly to bees. The definition of which honeycomb the UAV should map depends on a metric. The performed simulations considered two metrics to define which honeycomb should be mapped, FIFO and Euclidean Distance. In addition, simulations were performed by changing the number of UAVs. This demonstrated that setting the exploration order has direct impact on the number of offsets and a UAV in the environment, considering its position on the map. This can result in saving both energy and exploration time. Generating RGB-D and thermal-reading information enables rescuers to be prepared for obstacles and dropped objects, but also life-threatening elements such as high temperatures.

#### *Future Work*

Improvements in the definition of the spaces to be explored can be made, with metrics that consider not only distance from the initial hexagon (Euclidean distance), but also UAV location and environmental characteristics. In addition, in identifying points that may endanger the life of the rescue team, the use of gas or other toxic-element sensors may be applied. There is still the challenge of gathering this information and processing it with the use of game theory and machine learning. So far, each UAV works independently; however, it is not identified when a failure occurs with another one. A way of detecting failures and generating contingency plans needs to be implemented in future work. In this work, the representation of the hexagons is made in a projection of the *x* and *y* axes. In future work, the *z* axis will be added, so that this representation has several layers.

**Author Contributions:** R.d.R. developed the software and contributed to methodology, investigation, data curation, formal analysis, resourses, validation and writing (original draft). M.A.W. contributed to resourses, project administration, supervision, validation and writing (review and editing). T.B., J.L.L. and A.I.P.N.P. contributed to conceptualization, resourses and supervision. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Federal University of Technology (UTFPR), Federal Institute of Education, Science and Technology (IFPR) and Polytechnic of Bragança (IPB).

**Acknowledgments:** We would like to thank UTFPR and IFPR for their support in providing the equipment to run the simulations.

**Conflicts of Interest:** The authors declare no conflict of interest.
