# Overlap Avoidance of Mobility Models for Multi-UAVs Reconnaissance
## 3 Proposed Model
### Overlap Avoidance for Random Waypoint Mobility Model
#### 3.2.2 Proposed Overlap Avoidance Scheme for Random Waypoint  
We enhance the performance of Random Waypoint model by preventing duplicated reconnaissance of each UAV in the scanning area. In Random Waypoint model, since a UAV chooses a waypoint randomly as a destination, some UAVs may generate a waypoint near the waypoint of another UAV. If UAVs move to similar destinations at the same time, coverage loss occurs because these UAVs reconnoiter the same area duplicately.  
In order to avoid overlapped searches, we apply the trajectory-prediction scheme. Figure 2b is an example of predicting the trajectory for \(N\) time steps. The black points present destinations and the dotted line means predicted trajectory. As shown in Figure 2b, a UAV manages two destinations, the current and the next ones, because the predicting trajectory for \(N\) time steps can be passed over the current destination.  
UAVs broadcast their trajectory information periodically to neighboring nodes in order to predict overlapped area among UAVs. UAVs detect all overlaps which occur in the predicted trajectory and they turn to avoid them. Thus, each UAV can decide whether it belongs to a group of UAVs with overlapped area. For example, Figure 3a shows that three UAVs have two overlapped areas. We regard UAVs with overlaps in the predicted trajectory as one group and then change the direction of UAVs belonging to that group.  
Figure 3: Examples of overlap avoidance: (**a**) Overlap detection; (**b**) generating guidance lines among three UAVs; and (**c**) generating a guidance line between two UAVs.  
Figure 2: Examples of Random Waypoint model: (**a**) Random Waypoint model in mobile ad-hoc networks (MANET); and (**b**) Random Waypoint model in flying ad-hoc networks (FANET).  
We generate guidance lines for changing directions of UAVs which share the overlapped area. First, we calculate the central point of overlapped UAVs, denoted by \(p_{c}~{}=~{}(x_{c},y_{c})\), as follows:  
\[x_{c}~{}=~{}\frac{1}{n}\sum_{u_{i}\in U_{o}}x_{i} \tag{1}\]  
\[y_{c}~{}=~{}\frac{1}{n}\sum_{u_{i}\in U_{o}}y_{i} \tag{2}\]  
where \(U_{o}\) is a set of UAVs in an overlapped area and \(n\) is the number of UAVs in \(U_{o}\).  
Once the center point is calculated, the guidance line is generated to determine the direction to which the UAV moves. The guidance line is defined by the intermediate line between two virtual lines which head to the central point from the UAV and its right-side UAV. For instance, Figure 3b,c show the examples of generating guidance lines when the number of UAVs are three and two, respectively. Thus, assuming that UAVs in the overlapped area are sorted in the counter-clockwise order, the guidance line of UAV \(u_{i}\) is defined by:  
\[y_{i}~{}=~{}\frac{\theta_{i}+\theta_{i+1}}{2}(x_{i}-c_{x})+c_{y} \tag{3}\]  
where \(\theta_{i}\) is the degree from the \(u_{i}\) toward central point and \(\theta_{n+1}~{}=~{}\theta_{1}\).  
Each UAV creates a new waypoint on its guidance line and moves to that waypoint as shown in Figure 3b. When the UAV generates a waypoint, the next destination is also generated for trajectory prediction.