# A New Mobility Model for Multi-UAVs Reconnaissance Based on Partitioned Zone
## 3 Proposed Model
### Random Destination with Pheromone Zone Mobility Model
#### 3.2.1 Selecting Border Zone  
In the proposed method, the area to be scouted is divided into \(N\) zones. Each UAV stochastically selects and moves to the next zone which has been visited less than other zones nearby. As we assume the whole area to be a rectangular shape, the area is divided into \(N\)(=\(M_{1}\times M_{2}\)) zones. An operator configures the size of a zone according to the rotation radius of a UAV. If the distance to the destination in the next zone from the current position is shorter than the rotation diameter, the UAV may not reach the destination by keeping circuitous flight around the point. To prevent the possible circuitous flight, we decide the minimum size of a zone to be greater than the rotation diameter. For example, when the size of the simulation area is 10 km \(\times\) 10 km and the maximum rotation diameter of the UAV is 1 km, the maximum number of zones which can be divided is 100 (=10 \(\times\) 10).  
The zones are classified into _border zones_ which are located in the boundary area of the scanning region, and _intermediate zones_ for other zones inside. For example, the scanning area in Figure 4 is divided into 16 zones from \(z_{1}\) to \(z_{15}\). In Figure 4a, intermediate zones include \(z_{5}\), \(z_{6}\), \(z_{9}\), and \(z_{10}\), while the other zones belong to border zones.  
A UAV selects the next destination border zone in the other sides from the current boundary. If the current zone is located in \(z_{1}\) or \(z_{2}\), as shown in Figure 4a, the possible destination border zones are the eight shaded zones. On the other hand, if the current zone is located in the edge of the scanning area such as \(z_{0}\), the candidates of destination border zone are \(z_{7}\), \(z_{11}\), \(z_{13}\), \(z_{14}\), and \(z_{15}\), as shown in Figure 4b. As \(z_{0}\) belongs to both the western border zone and the southern border zone, those border zones are excluded when a UAV decides a destination border zone.  
When the destination border zone is decided, we consider the number visited in each zone so that a higher probability is assigned to the zone with lower number of visits. Let us denote \(N_{z}\) as the number of visited waypoints in a zone. For a given set of border zones, \(B\), the probability of selecting a border zone \(z\) is defined by:  
\[P_{z}=\left\{\begin{array}{cl}\dfrac{N_{total}-N_{z}}{(|B|-1)\times N_{total }}&\text{if }N_{total}\
eq 0\\ \dfrac{1}{|B|}&\text{if }N_{total}=0\end{array}\right. \tag{1}\]  
where \(N_{total}\) is the total number of waypoints in all zones in \(B\).  
Let us consider Figure 5 as an example, where the current zone is \(z_{2}\) and the six dots indicate the waypoints previously visited. The set of candidate zones, B, becomes \(\{z_{4}\), \(z_{7}\), \(z_{8}\), \(z_{11}\), \(z_{12}\), \(z_{13}\), \(z_{14}\), \(z_{15}\}\). The total number of waypoints visited in \(B\) is 6. Table 2 shows the probabilities of eight candidate border zones according to Equation (1). The probability of selecting \(z_{4}\) is the lowest because it has the highest number of visited waypoints. On the contrary, zones with no visited waypoints, such as \(z_{7}\), \(z_{12}\), and \(z_{13}\), have higher probabilities than others.  
\begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline \multicolumn{8}{c}{**The Probability of Selecting Zone**} \\ \hline
**Zone** & \(z_{4}\) & \(z_{7}\) & \(z_{8}\) & \(z_{11}\) & \(z_{12}\) & \(z_{13}\) & \(z_{14}\) & \(z_{15}\) \\
**Probability** & \(\dfrac{3}{42}\) & \(\dfrac{6}{42}\) & \(\dfrac{5}{42}\) & \(\dfrac{5}{42}\) & \(\dfrac{6}{42}\) & \(\dfrac{6}{42}\) & \(\dfrac{5}{42}\) & \(\dfrac{6}{42}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: The probabilities of selecting border zones in Figure 5.  
Figure 4: The examples of selecting candidates for destination border zone (shading squares are candidates for destination border zone): (**a**) the candidate border zones of \(z_{1}\) and \(z_{2}\); and (**b**) the candidate border zones of \(z_{0}\).