# Hybrid Path Planning for Efficient Data Collection in UAV-Aided WSNs for Emergency Applications
## 3 Formulation
### Problem Formulation  
We consider a UAV scenario as a mobile data collector to gather information from a set of \(N\) sensors, denoted as \(\{s_{n},1\leq n\leq N\}\). The position of the sensor \(S_{n}\) is expressed as \(p_{n}\in R^{2\times 1}\). Clustering sensor nodes is crucial to lessen the network delay and avoid collision during the data collection period. Therefore, sensor nodes are clustered using the unequal clustering algorithm, as discussed in [43; 44]. At first, sensor nodes share their head status (i.e., node identifier, residual energy, and location coordinates) to all the sensor nodes within their range. The node with the highest energy is chosen as CH for that region. If any node is selected as CH, no other CH will be selected within its competition range. After a CH is nominated, sensor nodes send a join request to the CH. Then, the CH selects its cluster members based on distance and the number of cluster members it can accommodate. CHs are accountable for gathering data from their cluster members before UAV arrives. At every round, after UAV-to-CH communication, the remaining energy of CH is compared with the minimum energy required to be CH. If the remaining energy of a CH is lower than the minimum required energy, the CH selection process is restarted.  
Each sensor senses the surrounding environment and transfers information bits to the CH; subsequently, the CH aggregates and uploads data to the UAV using a hybrid medium access control (MAC), as discussed in [44]. CHs use line-of-sight (LOS) communication to transfer data to UAV. Intelligent computing methods can be considered to minimize the computation time as well as the energy of power-constrained devices. Different cost-optimization strategies are discussed in [45] to minimize power-constrained devices' computation time and energy. We will consider one of the efficient computing techniques in our upcoming project. The UAV flies at a certain height, \(H\), and velocity, \(v\), from the start point (\(X_{s}\), \(Y_{s}\), \(Z_{s}\)) to the endpoint (\(X_{e}\), \(Y_{e}\), \(Z_{e}\)). We assume that \(||X_{s}-X_{e}||\leq v_{max}\times T\), such that there exists at least one feasible trajectory from \(P_{start}\) to \(P_{end}\) within \(T\) even when the velocity is at the maximum. The UAV's starting and final positions are assumed to be predetermined, with horizontal coordinates denoted as \(X_{s},\ X_{e}\in R^{2\times 1}\), respectively. The UAV's trajectory projected on the ground is denoted as \(X_{(t)}\in R^{2\times 1},\ 0\leq t\leq T\). \(T\) is partitioned into m time slots for convenience, i.e., \(T=m\delta t\), where \(\delta t\) denotes the elemental slot length for the ground sensors to approximate the UAV's location.  
We assume that the sleep and wake-up mechanism is employed, and one CH, at most, wakes up to communicate with the UAV at each time slot. We denote the wake-up schedule variable as \(x_{n}[m]\), where \(x_{n}[m]=1\) if \(CH_{n}\) wakes up at time slot \(m\), and \(x_{n}\left[m\right]=0\) otherwise. Hence, we have \(\sum\limits_{m=1}^{N}xn[m]\leq 1,\ \forall m\). If \(x_{n}[m]=1\), subsequently, \(s_{n}\) transmits data with transmission energy \(E_{trans}\). During no transmission, the UAV flies at the maximum speed \(v_{max}\) to minimize the total flight time. The UAV receives data when it is flying or hovering [46]. Both the cases considered for data collection are shown in Figure 2 and modeled as follows.