Sensor Network with Unmanned Aerial Vehicle-enabled Wireless Power Transfer: Optimal Clustering and Trajectory Designing

In this work, we investigate the application of an unmanned aerial vehicle (UAV)-enabled wireless power transfer (WPT) system in large-scale wireless sensor networks (WSNs). The specific research described in this paper can be divided into three parts. Firstly, it is well known that the energy consumption of WSNs and the limited-capacity battery of nodes lead to the limited lifetime of WSNs. To improve the lifetime of the WSNs, the UAV’s optimal position and the optimal clustering scheme are determined using an improved differential evolution (DE) algorithm in multicluster scenarios. The corresponding energy consumption is determined by comparing different clustering schemes. Meanwhile, the shortest time for the UAV to charge nodes is determined by utilizing the proposed DE algorithm to search for the optimal charging location. Since the UAV usually acts as both a base station and an energy transmitter, the algorithm requires joint optimization of the clustering scheme and the UAV’s charging location. Secondly, as the scale of WSNs increases, some areas will be in the “dead” state within the WSNs, which will greatly affect the performance. On the basis of the above studies, an improved local permutation algorithm is applied to plan an optimal path subject to the dormancy rate constraint in all regions. With the algorithm, the UAV needs to “rescue” the target region and charge regions along the path as much as possible. Finally, numerical results show that the optimized UAV trajectory can significantly improve the energy transmission efficiency, and the proposed optimal path planning improves the lifetime of WSNs.


Introduction
Wireless power transfer (WPT) is widely considered a key technology in our time. (1) What makes this technology particularly attractive is the nonrequirement of line of sight (LOS) and its sensitivity to the neighboring environment. There are many principles of WPT, such as magnetic resonance, magnetic coupling, and capacitive coupling. (2)(3)(4) Owing to the maturity of magnetic resonance coupling, it has been quickly applied to the commercial market. (5) In recent years, renewable sensor networks (RSNs) with WPT have been regarded as the next generation of wireless sensor networks (WSNs). (6,7) Through periodic WPT, WSNs can have 3 schemes and optimal positions for the UAV becomes an issue. For simplification, every node can be considered a cluster head regardless of the residual energy of the nodes and the cluster head rotation. Through a differential evolution (DE) algorithm, the optimal position for the UAV to charge nodes can be obtained. Motion planning (24) and a cooperative multiagent search with resource constraints (25) have also been considered.
In this study, large-scale WSNs are segmented into several regions, as mentioned above. To charge sensors in one region, the UAV only needs to visit the optimal position of the region. (26) On the basis of the conventional energy charging model, a method of optimizing the traveling path is proposed. This optimization problem is constrained by the dormancy rate in all the regions and the requirement of the shortest path. By employing the local permutation algorithm, an optimal path for the UAV is efficiently determined. According to our numerical results, this solution enables us to address the charging problem in WSNs.
This paper is organized as follows. In Sect. 2, the mathematical model in this study is described. In Sect. 3, we present two formulations of two optimization problems, and the optimal solutions for the two problems are developed in Subsects. 3.1 and 3.2. In Sect. 4, numerical results are presented to demonstrate the validity of the solutions. In Sect. 5, we conclude this paper.

Mathematical Modeling
In this section, the energy charging behavior and energy consumption model of sensors are described in detail.

Energy charging behavior
The wireless channel between the UAV and each ER is normally LOS-dependent, as described in Refs. 24 and 27. The UAV hovers at position (x(t), y(t), H) and broadcasts wireless energy to charge the sensors. I denotes the set of all nodes. Each sensor i g ∈ I is at a fixed location on the ground, denoted by (x(t), y(t)). The channel power gains from the UAV to the sensor i g (i g ∈ I) are modeled as where β 0 denotes the channel power gained at a reference distance d 0 of 1 m. The power harvested by the sensor at time t is thus given by where P is a constant transmitted power of the UAV and η denotes the energy conversion efficiency of the rectifier at each sensor.

Energy consumption of sensors
The model for the radio sensor energy dissipation is described in this subsection. When transmitting an l-bit message at distance d, the energy consumption can be given by When receiving a message, the energy consumption of the radio can be expressed as where ε fs and ε mp are both energy factors, and E elec , E DA , and d 0 are the electronics energy, the energy consumption for data fusion, and a distance threshold, (28) respectively. There are many factors, such as modulation, coding, filtering, and spreading of signals, included in the electronics energy E elec . E DA indicates the unit fusion energy consumption. The energy parameters are set as E elec = 100 nJ/bit, ε fs = 10 pJ/bit/m 2 , and ε fs = 0.0013 pJ/bit/m 4 . (29,30)

Problem Formulation and Statement
As shown in Fig. 2, the WSN is divided into several regions labeled (1), (2), (3), and so on. The node identified by the triangle is the cluster head in the region, and the other nodes are ordinary nodes. I represents the set of nodes. G = {g| g = 1, 2, 3, ..., G'} denotes the set of regions. I g = {i g | i g = 1 g , 2 g , 3 g , ...,} shows the node set of the gth region.
Below is the relationship between the set of nodes and the regions. The total number of clustering schemes is M = N 1 × N 2 × ... × N g × ... × N G' , and N g represents the number of clusters in the gth region. It is assumed that sensors generate or gather l-bit data before being charged. e i = E TX (l, d i,i j ) is the energy consumption of node i. e i j = E TX (l, d i j ,B ) is the energy consumption of cluster head i j . To achieve this optimization goal, the following tasks must be accomplished. From the mathematical modeling that we discussed in Sect. 2, one performance objective is to minimize τ, which is the time required for the UAV to charge the sensors. Considering the above scenario, the optimization problem can be formulated as follows: .
Here, y min ≤ y ≤ y max and x min ≤ x ≤ x max indicate the WSN range in which the UAV charges nodes. In this study, the nodes are fully charged to E max . As shown in Fig. 3, some nodes may experience saturation before all the nodes are fully charged. Therefore, the longest time Let x * and y * denote the coordinates of an optimal UAV location that maximizes the minimum of the function The improved DE algorithm is applied to solve the optimization problem. From the above scenarios, there exists an optimal and practical strategy for the UAV to charge sensors. An optimal path plan can be proposed for the UAV to charge sensors. It is meaningful to shorten the total time τ taken for the UAV to charge the sensor network. Prolonging the lifetime of the network is also an important target. In large-scale WSNs, a high dormancy rate greatly affects the performance. Therefore, it is necessary for the UAV to have an optimal path plan.
For example, Fig. 3 shows the dormancy rate level of the region. When the UAV flies to the target region, it should "rescue" the target region as soon as possible, i.e., ensure that all nodes have sufficient power by charging as necessary. If not, the target region will be close to the "paralyzed" state, which will affect the performance of the whole WSN. In Subsect. 3.2.2, T need represents the longest time for which the UAV flies to "rescue" the target region as soon as possible.
In practical applications, the UAV is required to do more things besides saving the target region. Within the allowable time, the UAV is required to rescue as many regions as possible.
The problem can be formulated as follows. , 2 : max In the above, ρ is the average dormancy rate.

DE algorithm for cluster head election and optimal UAV position
The WSN is composed of numerous tiny nodes that have limited battery power. Through sensing or controlling the physical parameters, the nodes can interact with their environment. These nodes collect data and carry out data fusion. As shown in Fig. 4, the sensors transmit their information to the cluster head through a single hop. Firstly, the cluster head integrates the received information into data packets. Then, the information is transmitted to the mobile base station UAV through a single hop.
Clustering plays an important role in improving the network scalability and lifetime. The nodes transmit their data to their cluster heads. There are a number of clustering algorithms, such as LEACH, particle swarm optimization, genetic algorithms, and DE. In this study, we propose a clustering algorithm based on the DE algorithm. In particular, this algorithm can determine the optimal position for the UAV, which is the mobile base station and the energy provider. Different schemes of cluster head selection correspond to different charging times and different optimal positions for the UAV. As shown in Fig. 5, nodes C, D, E, and F are selected  as cluster heads by the DE algorithm. Regions labeled (1), (2), and (3) correspond to the 1st region, the 2nd region, and the 3rd region, respectively. The UAV hovers at the optimal position where it spends the shortest time to charge nodes.

Detailed explanation of improved optimization algorithm
The pseudocode for the improved DE algorithm proposed in this study is shown as Algorithm 1.
In this algorithm, m is the mth clustering scheme and M is the total number of schemes. i denotes one node in the region. In the mth scheme, x y represents the optimal position at which the UAV should hover under the optimal scheme m opt , which is (x * , y * ) in Sect. 3. i j denotes the cluster head. The key principles of this algorithm can be represented by the flowchart shown in Fig. 6.

Path planning for the UAV
In practical applications, it is meaningful to shorten the total time needed for the UAV to charge sensors. Prolonging the lifetime of the WSN is also an important target. However, it is very difficult to find the shortest time necessary for the UAV to charge nodes, just as P2 shows. For simplification, the optimal position (x opt , y opt ) for the UAV to charge nodes in a region is regarded as path point o here. o′ is a point in the neighborhood of o. As shown in . o c q c ∈ ). In this study, a local permutation algorithm and its improved algorithm are used to plan the path and prolong the lifetime of the network. A recursive algorithm is applied to find the shortest path, and an iterative method is used for optimization. The basic principles of the algorithms are described as follows. Firstly, choose the target points T in the flight range through perceptual behavior, and plan an initial shortest path from S, which can be shown as the result sequence σ. Secondly, during each step of the iteration, choose the path point o with  Fig. 8, A 2 can be replaced by A 1 or A 3 , which both belong to the set A.c = {A 1 , A 3 }. Fourthly, test all the possible points in set o.c that satisfy t < t need or others.
To explain the algorithm, the local permutation algorithm and its improved algorithm to solve P2 are shown in detail below.

Local permutation algorithm
The index process of the local permutation algorithm is given in detail in Fig. 8. Firstly, the shortest path 2 2 S A B T → → → is found from S to T, and the average dormancy rate along this  path is ρ. ρ 0 (ρ 0 < 1) is the target dormancy rate, which can be set in accordance with the actual situation. The numbers next to the arrows stand for distances between points. If the paths do not meet, they will be updated. Assuming that the dormancy rate at point A 2 is the lowest along the path, it will be replaced by another point whose dormancy rate is higher. As Fig. 8 shows, A 2 can be replaced by A 1 or A 3 to construct a new path. Finally, a new path is updated with A 2 replaced by A 1 because the distance change is smaller than the change in A 3 .
path, and the current average dormancy rate is ρ.
The pseudocode of the local permutation algorithm is given as Algorithm 2.

Improved local permutation algorithm
To plan a more suitable path for P2, the improved local permutation algorithm is introduced here. Unlike the local permutation algorithm, there is no requirement of 0 ρ ρ < in the improved local permutation algorithm. The numbers next to the arrows stand for distances d l between points. V represents the speed of the UAV between path points o. The basic principle of the improved local permutation algorithm is as follows.
Firstly, find the shortest path (the initial path) The average dormancy rate along this path is ρ . Secondly, find the point (such as A 2 shown in Fig.   9) that has the lowest dormancy rate along the initial path. Thirdly, find the point with a higher dormancy rate around A 2 ; there are two points (A 1 and A 3 ) that can replace A 2 . The path constructed with A 2 replaced by A 1 is longer than that constructed with A 2 replaced by A 3 . Through k iterations, the path is gradually updated. Therefore, the new path → is updated from the initial path, and the current average dormancy rate is new ρ . Finally, the time must be checked to determine whether it meets the following requirement shown as P2. 1 1 Here, T need is the maximum time taken for the UAV to arrive at the target point T, and the UAV can spend more time hovering at path points if t path < T need . As shown in Fig. 9, the black line ( represents the final path updated from the initial path (the red line; The diagram of the algorithm is shown in Fig. 9, and the pseudocode for the algorithm is given as Algorithm 3.

Simulation and Analysis
In this section, some numerical results are presented to demonstrate how to obtain the optimal scheme for the UAV and WSNs. The optimal path plan for the UAV to perform energy transfer is proposed.

Simulation settings
The following experiments are conducted under the MATLAB environment. Sensor nodes are assumed to be deployed over a 1000 × 1000 m 2 square area. The base station is at (500, 500) (in m). The WCV's home service station is assumed to be at the origin. The speed of the WCV is V = 5 m/s. Let E max = 10.8 kJ and E min = 540 J.

Results of P1 and P2
For simplification, one result in P1 is shown for a small network. As shown in Fig. 10(a), the position represented by the small red circle is the shortest time required for the UAV to charge nodes. At the same time, the scheme in Fig. 10(a) is the best among all the possible schemes for clustering. Figure 10(b) shows the graph of the object function value, showing its iterative convergence.
In Subsect. 3.2.2, the optimal path is found by the improved local permutation algorithm. In Fig. 7, path planning is based on optimal positions for the UAV in several regions, as described in Subsect. 3.1. Figure 11 shows the path plan obtained through the local permutation algorithm discussed in Sect. 3. However, the path plan in Subsect. 3.2.1 needs to meet the target dormancy rate ρ 0 . Because the target dormancy rate ρ 0 is a constant, the optimization of the dormancy rate cannot be considered in this path plan.
Below are some simulations of the improved permutation algorithm described in Subsect. 3.2.2. As shown in Fig. 12(a), if T need = 9, there is one optimal path for P2. When T need = 11, the corresponding path plan is also shown in Fig. 12(a). There are no optimal paths that meet t path = 9 < T need = 11 or have a lower dormancy rate ρ .
When T need = 19, the corresponding path plan is shown in Fig. 12(b). The UAV flies to the charge target region along the path where the UAV can rescue more regions in the shortest time. The time of the flight along this path is t path = 17, which meets the following requirement in P2.
For the ease of understanding, dormancy rates are compared among possible paths when T need is set to 11 or 19. From Fig. 13(a), the average dormancy rate with t path = 9 is smaller than that with t path = 10 when T need is set to 11 or 19. Clearly, the path with t path = 9 is better than other possible paths. Similarily, the path with t path = 10 has a higher average dormancy rate than the others, which means that the UAV can spend more time hovering at path points to rescue them (charge them) before the UAV arrives at the target point S. The higher average dormancy rate of the path means that these path points need to be rescued more than the others.

Conclusions
In this study, a UAV-enabled WPT system was applied in a large-scale WSN. First, an improved DE algorithm was developed by jointly optimizing the clustering schemes and the positions for the UAV to charge nodes. Second, with the improved local permutation algorithm, the optimal path plan for the UAV to visit the regions and charge nodes successively was determined. Finally, using the numerical results, we demonstrated a UAV-enabled WPT system while addressing the lifetime problem for large-scale WSNs.