# Dynamic UAV Inspection Boosted by Vehicle Collaboration Under Harsh Conditions in the IoT Realm
## 3 Problem Formulation
### Initial Static Task Model
#### 3.1.1 Vehicle Route Planning Model  
In the multi-UAV-vehicle cooperative data acquisition problem, the vehicle, upon receiving commands from the center console, sequentially transports \(m\) UAVs to the moorings near the target mission point according to a planned driving route. After the vehicle arrives at a particular docking anchor point, the UAVs disperse and take off to their respective mission points for data collection. In order to record the traveling route of the vehicle and determine the delivery and arrival points of the UAVs, we introduce the concept of anchor points. As shown in Figure 2, in the target region \(\Omega\) (\(\Omega\
eq\emptyset\)), based on the clustering and partitioning results, after the discretization process, one candidate anchor point is set at every certain distance. In order to improve the efficiency of the system, the route of the vehicle needs to be minimized as much as possible. Therefore, it is necessary to select certain suitable points from these candidate anchor points as stopping anchor points, where the vehicle will wait for the UAV to perform the data collection task, such that the set of vehicle route nodes is \(A_{c}=\left\{a_{k_{1}},a_{k_{2}},\ldots,a_{k_{n}}\right\}(A_{c}\subseteq A)\), where \(a_{k_{i}}\in A\) (\(i=1,2,\ldots,n\)). Once the stopping anchor points are determined, the vehicle's route planning problem involves determining the route from the starting point, traversing each route node in the set \(A_{c}\), and, finally, returning to the starting point. We use the symbol \(r_{0}\) to indicate that there is exactly one vehicle travel route. The vehicle travel route \(r_{0}\) consists of the starting point \(A_{\text{start}}\) and the selected stop anchor points (all the points in the set \(A_{c}\)), denoted \(r_{0}=\left\{A_{\text{start}},a_{k_{1}},a_{k_{2}},\ldots,a_{k_{n}},A_{\text{start }}\right\}\). That is, the vehicle starts from the starting point \(A_{\text{start}}\); passes through the stop anchors \(a_{k_{1}}\), \(a_{k_{2}}\), and so on in a sequential manner; and finally returns to the starting point \(A_{\text{start}}\). Let any two stop anchors \(a_{k_{i}}\) and \(a_{k_{j}}\) be separated by a distance \(d_{a_{k_{j}},a_{k_{j}}}\); then, the time it takes for the vehicle to travel from anchor point \(a_{k_{i}}\) to \(a_{k_{j}}\) can be denoted as \(t^{c}_{a_{k_{j}},a_{k_{j}}}\). The time \(t^{c}_{a_{k_{j}},a_{k_{j}}}\) can be represented as follows:  
\[t^{c}_{a_{k_{j}},a_{k_{j}}}=\frac{d_{a_{k_{j}},a_{k_{j}}}}{v_{c}} \tag{1}\]  
In addition, a variable \(x(a_{i},r_{0})\) is introduced to indicate whether the candidate anchor point \(a_{i}\) is selected as a stopping anchor point and included in the path \(r_{0}\). If yes, then \(x(a_{i},r_{0})=1\); otherwise, \(x(a_{i},r_{0})=0\). Meanwhile, a binary auxiliary decision variable \(p_{r_{0}}(a_{i},a_{j})\) is used to indicate whether the stopping anchor point \(a_{i}\) in the path \(r_{0}\) is adjacent to the anchor point \(a_{j}\) and whether the anchor point \(a_{i}\) appears before \(a_{j}\). If so, then