# Overlap Avoidance of Mobility Models for Multi-UAVs Reconnaissance
## 3 Proposed Model
### Overlap Avoidance for Random Markov Process Mobility Model
#### 3.3.2 Proposed Overlap Avoidance Scheme for Random Markov Process  
In Random Waypoint model, UAVs are able to predict trajectories because they have their own destinations. In Random Markov Process model, on the other hand, UAVs cannot predict their trajectories because the model does not have a destination but decides next direction. Instead, we define  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**Next Action Probability**} \\ \cline{2-4}
**Current Action** & **Turn Left** & **Straight Ahead** & **Turn Right** \\ \hline Turn left & 70\% & 30\% & 0\% \\ Straight ahead & 10\% & 80\% & 10\% \\ Turn right & 0\% & 30\% & 70\% \\ \hline \hline \end{tabular}
\end{table}
Table 2: UAV action table.  
the protected zone as the area within a certain distance (e.g., twice of camera scanning distance) and detect overlaps in case that other UAVs are located in the protected zone. Figure 4a shows the example of detecting the overlap between two UAVs.  
If the protected zones are duplicated, we generate guidance vectors to lead UAVs to change directions. The proposed model assigns more probability to the direction of the guidance vector in order to avoid overlapped reconnaissance. In case of two overlapped UAVs, the guidance vectors are simply two repulsive vectors from the central point to each UAV, as shown in Figure 4a.  
However, when a UAV is overlapped with more than two UAVs, we need a mechanism to obtain the guidance vector. Let us define \(v_{ij}\) as the repulsive vector of UAV \(u_{i}\) due to \(u_{j}\). The direction of \(v_{ij}\) is from the central point of \(u_{i}\) and \(u_{j}\) to the \(u_{i}\). The size or magnitude of \(v_{ij}\) is given in proportion to the overlapped area. Then, the guidance vector of a UAV is defined by the summation of its all repulsive vectors. For example, the UAV \(u_{2}\) in Figure 4b is overlapped with \(u_{1}\) and \(u_{3}\). The guidance vector \(v_{2}\) is obtained by adding two repulsive vectors \(v_{21}\) and \(v_{23}\).  
When the guidance vector is obtained, we give a higher probability to the direction of the guidance vector in order to avoid overlap area. For example in Figure 4a, UAV \(u_{1}\) is guided to turn left, while \(u_{2}\) is led to turn right. In case of \(u_{4}\) in Figure 4b, it is guided to turn left since the UAV is much overlapped with UAV \(u_{3}\).  
Figure 4: Examples of generating guidance vectors: (**a**) Two UAVs; and (**b**) three UAVs.  
Thus, we need a new decision probability table different from Table 2, in order to avoid the overlap area depending on the direction of the guidance vector. If the guidance vector heads to the left side of the current direction, the next action probability follows the second row of Table 3. For example, when a UAV is currently turning right, its next probability of flying straight is 100% because the UAV cannot turn left immediately. If the current direction is flying straight, the probability for turning left is 70% and that of flying straight is 30%. Lastly, when a UAV turns left, we give 90% probability of turning left. Similarly, if the guidance vector is in the right side, the next action probability follows the third row of Table 2 so as to guide the UAV to the right direction.  
Once a UAV has no more overlapped area, we maintain the UAV to fly straight for a while. This reduces the possible hovering due to overlap avoidance. Let us note that we use five time steps of straight head in our simulations. After a certain period of keeping straight, the UAV again follows Table 2 as usual.