# Dynamic UAV Inspection Boosted by Vehicle Collaboration Under Harsh Conditions in the IoT Realm
## 3 Problem Formulation
### Initial Static Task Model  
We abstract the entire process of multiple UAVs collaborating with vehicles for data acquisition into a UAV and vehicle route planning and synchronized scheduling problem based on the 2E-VRP (Two-Echelon Vehicle Routing Problem). Within this framework, the initial solution focuses on the vehicle route planning problem, specifically determining how to transport the UAVs to the vicinity of the task nodes. Once the UAVs are transported, they independently execute their respective data acquisition tasks in parallel after departing from the vehicle, forming their own local flight routes. The entire process is illustrated schematically in Figure 1.  
To facilitate the depth of the research, we made the following assumptions regarding UAVs and vehicles:  
1. The speed of the UAV was denoted as \(v_{uav}\) and the speed of the vehicle was denoted as \(v_{c}\). 2. The UAV landed on the vehicle for a negligible amount of time to replace the battery and it was considered to be 100% charged after the battery replacement. 3. The time spent by the UAVs for data collection (photography) at each task point was negligible. Figure 1: Illustration of the multi-UAV and vehicle coordinated data collection problem. 4. The communication radius of the UAV was denoted as \(R_{c}\). To enable real-time communication between the UAV and the vehicle for transmitting collected data and receiving tasks, it was ensured that the distance between the UAV and the vehicle always remained less than \(R_{c}\). 5. The maximum distance that a UAV could cover in a single flight was denoted as \(d_{max}\). 6. Within the target area, the vehicle could travel more than 500 km on a full tank of gas. Therefore, in the problem scenario studied in this paper, the vehicle was assumed to have no range or communication limitations. It was also assumed that the vehicle maintained constant communication with the central console. 7. The communication latency between the UAV and the vehicle and the vehicle and the central console, as well as the data processing latency, were all considered negligible. In the multi-UAV-vehicle collaborative data acquisition system, regardless of speed fluctuations, the initial static optimized solution is computed by the central console based on the received static task before the mission begins. This solution is generated using an initial greedy solution construction algorithm followed by optimization with the Hybrid Genetic Algorithm (HGA) [43] to provide optimal route planning and task assignments for the multi-UAVs and the vehicle. Next, we will specifically explore the initial static task model. In the target region \(\Omega\) (\(\Omega\
eq\emptyset\)), scattered tasks need to be performed for data collection. Let the set of all initial task points be \(P_{0}=\{p_{1},p_{2},\ldots,p_{n}\}\), where \(p_{i}\in\Omega\) and \(i=1,\ldots,n\). All initial task information is known. For each task point \(p_{i}\) (\(i=1,\ldots,n\)), its position in two-dimensional Cartesian coordinates is denoted as \(p_{i}=(x_{p_{i}},y_{p_{i}})\). If there is a line segment connecting two tasks, the set of line segments is denoted as \(E=\{(p_{i},p_{j})\mid p_{i},p_{j}\in P,i\
eq j\}\). The distance between tasks \(p_{i}\) and \(p_{j}\) is represented as \(d_{p,p_{j}}\). If the task satisfies real constraints of the urban network, the data from the road network should be read to calculate the distance between points based on actual road conditions. Let the set of UAVs be \(U=\{u_{1},u_{2},\ldots,u_{k}\}\). It is important to note that each point in the set \(P\) will be visited by a UAV exactly once and only once. Therefore, all data collection task points in the initial set must be assigned to these UAVs. This is similar to the Bin Packing Problem (BPP), but it also requires considering factors such as the locations of the task points and the battery capacity of the UAVs for the allocation. Multiple unmanned vehicles start from the initial point \(A_{\text{start}}\), perform all tasks, and then return to the initial point.