# Coordinated Multi-UAV Reconnaissance Scheme for Multiple Targets
## 3 Problem Model
### Model Establishment  
Based on the analysis of the dynamic task allocation problem in multi-UAV cooperative reconnaissance, this paper makes the following reasonable assumptions to simplify the model:  
1. Each UAV must achieve a minimum reconnaissance revenue before leaving the task area and moving on to the next target location;
2. Each task area can only be reconnoitered once by a single UAV;
3. The flight path of a UAV is barrier-free, and there are no collisions between UAVs; that is, when UAVs travel from the current position to the next location, they just fly along a straight line between two points, and the Euclidean distance between two points is the path length of this flight;
4. When a new task emerges, its location, area, value coefficient, and other relevant information can be obtained. In general, the reconnaissance of task areas by UAVs is constrained by their cruising time and the reconnaissance resources they carry. It is often challenging to ensure complete information reconnaissance for each task area. Therefore, the information certainty metric is considered to measure the reconnaissance revenue of a UAV in the task area in a specific time [52]. The formula is listed as follows:  
\[I(t)=I_{0}+I_{1}(1-e^{-\beta t}), \tag{1}\]  
where \(I\) is the information certainty, \(I\in[0,1]\); \(I_{0}\) is the known information of the UAV in the task area before the start of reconnaissance. In this paper, we assume that \(I_{0}=0\); \(I_{1}\) refers the information uncertainty part of the UAV in the task area, which satisfies \(I_{0}+I_{1}=1\)[52]; \(\beta\) denotes the ability index of the reconnaissance load carried by the UAV for reconnaissance of the task area. In this paper, the performance of the UAV reconnaissance payload is known. The reconnaissance capability of the UAV for each task area can be expressed by the known flight speed and scanning width. Therefore, the reconnaissance capability index \(\beta_{ij}\) of the UAV\({}_{i}\) in the task area \(j\) is defined as follows:  
\[\beta_{ij}=\frac{w_{i}\cdot v_{i}}{S_{j}}, \tag{2}\]  
where \(S_{j}\) is the size of the task area; \(w_{i}\) is the effective scanning width of the UAV for the task area; and \(v_{i}\) is the flight speed of the UAV. It can be seen from assumption 3 that the Euclidean distance between \(a\) and \(b\) is the path length of the UAV flying from a to b. Assuming that the coordinates of a are \((x_{a},y_{a})\)  
Figure 2: Multi-UAV cooperative reconnaissance dynamic task allocation. and the coordinates of b are \((x_{b},y_{b})\), the distance between the two places is calculated as follows:  
\[d(a,b)=\sqrt{(x_{a}-x_{b})^{2}+(y_{a}-y_{b})^{2}}. \tag{3}\]  
The reconnaissance sequence \(q_{i}\) stores the task areas that need to be reconnoitered by UAV\({}_{i}\) in a specific reconnaissance sequence. For a given reconnaissance sequence \(q_{i}\), the distance of UAV\({}_{i}\) consists of three parts: the path length from the base to the first reconnaissance target, the cumulative path length from the first reconnaissance target to the last reconnaissance target following the reconnaissance sequence, and the path length from the last reconnaissance target back to the base. The formula for calculating the total distance of a single UAV is as follows:  
\[D_{i}=d(b_{i},a_{q_{i,1}})+d(a_{q_{i,|q_{i}|}},b_{i})+\sum_{k=1}^{|q_{i}|-1}d( a_{q_{i,k}},a_{q_{i,k+1}}), \tag{4}\]  
where \(a_{j}\) represents task area \(j\); \(b_{i}\) represents the base of UAV\({}_{i}\); \(d()\) is the function used to calculate the distance between two places; \(q_{i,k}\) represents the \(k\)-th reconnaissance task area of UAV\({}_{i}\); and \(|q_{i}|\) is the length of the reconnaissance sequence \(q_{i}\), which denotes the number of task areas to be reconnoitered by UAV\({}_{i}\).