1. Introduction

Wireless sensor networks (WSNs) have been widely used in many applications such as environmental monitoring, military mission, smart agriculture, structural monitoring, and intelligent transportation [1–4]. Typically, there are a large number of sensor nodes and a data sink or base station in one WSNs, and thus, it is able to collect sensory data from its surrounding physical environments. As we all know, due to size and cost restrictions of sensor nodes, traditional wireless sensor networks are energy-limited and application-specific [5]. Hence, these two characteristics pose new challenges in terms of data collecting and energy supply. Sensor nodes in traditional WSNs are mainly powered by energy-limited batteries, so the lifetime of sensor networks is very limited. Generally speaking, sensor nodes are expected to operate over years with limited power supply. Thus, the energy consumption becomes the foremost design constraint.

To prolong the lifetime of WSNs, extensive studies have been conducted in past years, which can be divided into two categories. One way is to reduce energy consumption as much as possible from all aspects. Much research effort has been dedicated to resolving energy conservation problem of WSNs such as energy-efficient communication protocols [6]. However, in classic wireless multi-hop transmission manner, in addition to transmitting their own sensory data, sensor nodes have to transmit relay data resulting in additional energy consumption. This situation is especially worse for those sensor nodes close to sink node, which is called “hotspot” problem [7]. As Figure 1, sensor nodes within “hotspot” region are prone to transmit or relay more data, so these nodes will consume more energy than others. In other words, sensor nodes near sink node have to transfer much more network flow, and therefore, they will deplete their energy much earlier [8]. This is an inherent defect of the traditional fixed-sink data acquisition manner. Fortunately, it will reduce energy consumption of sensor nodes with mobile data collecting method by utilizing mobility characteristic of mobile sinks. Usually, mobile vehicles with relatively more energy are usually taken as mobile data collectors. In this way, sensor nodes only need to transmit their own sensory data to mobile sinks with smaller transmission distances when mobile sinks get close to them.

For the second category, the stored energy of sensor nodes needs to be replenished, and most of recent researches focus on energy replenishment fundamental problem. Wireless energy transfer is a new technology that can be used to recharge sensor nodes’ batteries in wireless manner [9–11]. To prolong the lifetime of WSNs, a variety of wireless charging techniques have been proposed to provide additional energy supply for WSNs. With recent advances in radio energy harvesting techniques, it is possible to recharge sensor nodes in a relative long distance (>10 m away). Since the long-distance charging provides much weaker harvesting power, mobile charging method with short distance is often used to achieve high charging efficiency. In general, there are two different sensor charging categories [11]. One is to enable sensors to harvest energy from their surrounding environments. The main drawback of this method is that the energy harvesting rates are extremely unstable due to time-varying environments. The other is to employ mobile charging vehicles to travel to the vicinity of sensors and recharge them using wireless energy transfer method. Thus, sensor nodes can be charged via wireless energy transfer technology with highly stable charging rates [12]. Consequently, the energy replenishing problem can be transformed into a new problem of finding an optimized charging path. Hence, recent research resorts to the optimal or suboptimal recharging trajectory so as to improve charging effect.

To solve energy problem, some researches jointly apply the emerging techniques of wireless power transfer and intelligent mobile vehicles to develop a new paradigm of rechargeable wireless sensor networks. As far as we know, there are few researches that consider mobile data collecting and wireless energy supply comprehensively. Moreover, the mobility of charging and data collectors brings new issues. In this paper, we study the interesting problem of co-locating one wireless charger and mobile sink on the same mobile platform, which is named as wireless charging vehicle (WCV) in this paper. The WCV travels along a preplanned path inside the region of interest (RoI) in wireless sensor networks. For example, as shown in Figure 2, six sensor nodes will be charged by one charging robot and three charging robots, respectively. Each charging robot or WCV starts from base station to charge sensor nodes and returns to base station after completing its charging task. The optimal goal is to minimize energy consumption of multiple WCVs and improve energy efficiency of wireless sensor networks. Extensive simulation results verify that the proposed method has a more efficient performance in terms of path length and energy consumption; thus, it is very suitable for mobile data collection in rechargeable WSNs.

Our main contributions are the following:

Statement of Contributions: (1) This paper investigates mobile sensory data collecting and long-distance wireless energy recharging concurrent strategy for sensor nodes, which is mapped to traditional Close-Enough Traveling Salesman Problem (CETSP); (2) this paper uses SOM (self-organizing feature map) based unsupervised learning algorithm to solve CETSP. To the best of our knowledge, this is the first report to design compatible considering both data collecting and energy charging mobile path for wireless sensor networks. The rest of this paper is organized as follows. Section 2 gives some related works on wireless energy transfer and mobile data collecting in wireless sensor networks. Section 3 presents the problem statement with rechargeable sensor networks. In Section 4, data collecting and energy charging oriented mobile path design algorithm based on SOM unsupervised learning and Bezier curve is presented in details. Simulation results are shown in Section 5 to verify our proposed algorithm, followed by the conclusions in Section 6.

2. Related Works and Preliminaries

Energy efficiency problem has been a fundamental constraint and challenge faced by many applications of WSNs. Due to the harshness of environments, unattended operability of WSNs for long time is desirable. Energy management mechanisms and routing protocols in traditional WSNs are no longer suitable for rechargeable WSNs, and new solutions must be proposed. To mitigate the limited energy problem in wireless sensor networks, some researchers have proposed different efficient approaches. Since it is not efficient to install densely located fixed sinks, expensive multi-hop transmission can be avoided using mobile sink mode. The traditional energy consumption in the sink information retrieval can be reduced by the factor of hop number. Consequently, the movement strategy of sink node is very crucial to the WSNs performance.

A recent breakthrough in the wireless power transfer technique based on strongly coupled magnetic resonances has drawn plenty of attentions [13, 14]. Wireless energy transfer (WET) is a new technology that can be used to charge the batteries of sensor nodes without wires. Although wireless, WET does require a charging station to be brought within reasonable range of a sensor node so that good energy transfer efficiency can be achieved [15]. Cheng et al. [16] survey the latest research on charging programming in rechargeable wireless sensor networks from different dimensions. Guo et al. [17] propose the VBMERS (mobile energy replenishment strategy with virtual backbone) algorithm to solve the fast energy expenditure problem of backbone nodes. Banoth et al. [18] propose a deep reinforcement learning-based mobile charger scheduling strategy called dynamic partial mobile charger scheduling using deep-Q-networks (DPMCS). It is generally accepted that, wireless power charging is a very promising technique to prolong the lifetime of WSNs. On the other hand, it has been well recognized that data collection with mobile robots has significant advantages over static one. Therefore, it is logical to consider these two methods together.

3. Preliminaries and Problem Statement

In this section, we first introduce the network model and propose a novel simultaneous energy charging and data collecting model, and we then define the problems. Since ultra-fast charging batteries will be commercialized in the new future and will be widely used in wireless sensor networks, therefore, wireless charging takes far more time than wireless data transmission. As a result, we ignore the time spent by mobile chargers per charging round in the following sections.

Existing studies of sensor nodes’ energy replenishment via wireless charging vehicles assumed that either just one or multiple mobile charging vehicles are deployed. Our investigation focuses on sparsely deployed networks; the WCV operates on a rechargeable battery and has much higher computation and communication capabilities. Individual sensor nodes are immobile and store a number of packets for transmission to the WCV. We also assume that WCVs are aware of position of sensor nodes and number of packets on every node. This can be achieved by a traditional sensor node registration procedure.

For clarity, the principle topology of recharging wireless sensor networks is described in Figure 3. As depicted in Figure 3, there are n sensor nodes (S_i, i = 1, 2, ⋯, n) with coordinates s_i = (x_i, y_i) ∈ ℝ² and m mobile charging vehicles (MR_j, j = 1, 2, ⋯, m) deployed randomly in the rectangle area. Sensor nodes can monitor and collect parameters of the surroundings and then transmit sensory data via wireless communication within maximal range. It is assumed that sensor nodes can replenish energy with long-distance wireless power transfer technology. Mobile WCVs have the ability of collecting data from sensor nodes while moving along the preset trajectory; moreover, they can provide power supply capability to such sensor nodes within maximal range of wireless power transfer. Additionally, it is assumed that battery-stored energy of mobile WCVs is enough to support the complete traversal of a scheduled trajectory and replenish all sensor nodes. With the development of new technology, long-distance wireless charging technology has become more and more mature. In this paper, we assume that the mobile WCVs have sufficient amount of energy to support its travel, data collection, and energy transfer to sensor nodes before they return to the service station.

In order to illustrate design detailed methodology of proposed algorithm, we summarize the simplified notation in Table 1 for the reader’s convenience.

The detailed energy charging model and wireless energy charging model will be described as follows.

4. Data Collecting and Energy Charging Oriented Path Design for Mobile WCVs

4.2. SOM-Based Heuristic Solution Algorithm

The SOM for CETSP follows the standard Kohonen’s SOM [32] with few modifications due to the solution of routing problems. It can be considered as a two-layered neural network as Figure 4, where the input layer serves for presenting the sensing sites (input signals) towards which the network is adapted using the unsupervised learning. The output layer is organized as an array of neurons, which defines a sequence of visits to the targets, and the neurons’ weights directly represent point locations in the input space. The neurons can be connected into a ring because of the array structure of output layer and thus represent a closed path in the input space.

The SOM-based unsupervised learning is performed with an iterative procedure in which all the targets are presented to the network. The best matching neuron is selected in the winner selection procedure, and then the winner neuron is adapted towards the presented input together with neighboring neurons to the winner neuron with decreasing power of the adaptation defined by the neighboring function. The SOM based CETSP is a set of nodes S₁, ⋯, S_n organized in a one-dimensional structure that is called an iterative ring of nodes. Therefore, the total iteration process of SOM-based CETSP is comprised of three main parts: (1) winner selection, (2) winner adaptation, and (3) results output.

In the winner selection process, the closed point $$ of the iterative ring of the current sensor $$ with the expected waypoint location $$ at which $$ can be covered is determined. The ring of nodes $$ can be considered as a sequence of straight line segments defined by two consecutive node locations v_i and v_i+1. The closest point $$ of the ring to $$ is determined as the closest point of the segments (v_i, v_i+1), i.e.,

$$ (5)

subject to

$$ (6)

Having the point $$, a new winner node v^∗ is created and inserted between the respective v_i nodes.

The winner adaptation is a movement of the winner node (together with its neighboring nodes) towards its waypoint $$. The neighboring function used in SOM adaptation is defined for the active neuron in a similar way as in a regular SOM for TSP [33].

$$ (7)

where M is the current number of nodes in the ring $$, σ is the learning gain, and d is the distance of the adapted node to the new winner node in the number of nodes in the ring $$. Each node in the r × M neighborhood of the winner node v is adapted towards new winner node v^∗, and r is the neighborhood region factor.

As described in [34], the new location v will be updated according to

$$ (8)

where f(σ, d) is the above neighboring function and $$ is the waypoint location associated with the newly added winner node v^∗.

Since all winner nodes in the ring have associated waypoints, a feasible solution can be constructed by traversing the ring and connecting the waypoints.

4.3. Bezier Curve-Based Trajectory Design

As we know, Bezier curves [35] can be easily connected into a smooth path from multiple segments. In this section, we use Bezier interpolation method for mobile data collection. A general Bezier curve of the wth degree can be parametrized by

$$ (9)

where P_t denote the control points and B_w,t(u) is the Bezier polygon of the wth degree which prescribes weights for the control points.

$$ (10)

The utilized cubic Bezier curve can be expressed as

$$ (11)

where P₀ and P₃ denote end points, P₁ and P₂ denote control point, u ∈ [0, 1]. It is noted that the first-order derivative of cubic Bezier curve is continuous [33].

In order to make curves smooth and trajectory closed, the four control points of each cubic Bezier curve are selected following such definition in [36], which is shown as Figure 5.

Furthermore, the approximate length of cubic Bezier curve can be calculated as follows [37]:

$$ (12)

5. Simulation Results

To evaluate the performance of the proposed method, we conduct a series of simulations with MATLAB software, by generating a series of random deployments of mobile WCVs and sensor nodes. In our simulation, there are n sensor nodes distributed in a rectangle region of L × W unit² randomly, with different communication distance and recharging radius R. At present, the practical wireless power supply distance is several meters, not more than 10 meters. Nevertheless, the wireless data transmission range is much larger than 10 meters. Hence, for the sake of unification, we set both to the same value. Moreover, there are m mobile WCVs with wireless power supply capability used to collect sensory data from different sensor nodes. Therefore, battery energy of sensor nodes can be replenished when mobile WCVs approaching, i.e., the distance between certain WCV and sensor node is smaller than R. The MATLAB 2016b simulator is used as the simulation platform, and simulation trajectories under different network topology are exhibited. The simulations are repeated with 100 × n rounds, and the average value is derived to reflect the results. Some important parameters are listed in the following Table 2. The selection basis of main parameters is based on the existing literature integrating mobile data acquisition and wireless charging energy supply. In this section, simulation results are provided to demonstrate the performance of the proposed algorithm over existing algorithms. Figures 6–9 depict four derived trajectories of our simulation scenario when n = 40/100, m = 2, and R = 2/5. The iterative processes of our SOM-based solution method with n = 40, m = 2, and R = 5; n = 100, m = 2, and R = 5; and n = 140, m = 4, and R = 5 are shown in Figures 10–12, respectively. The average lengths of designed trajectory are shown in Table 3, which show that the total length of WCV will increase when the number of sensor nodes increase. Moreover, the total length of designed trajectories will decrease when the number of WCVs increase.

Furthermore, we test the performance changes with different parameters in SOM-based unsupervised learning method. There are four key parameters: learning gain σ, gain decreasing rate α, learning rate μ, and neighbor node factor r. In our simulations, using the same networks topology as n = 100, m = 4, and R = 5, we change these four important parameters to get final results as Figure 13. It is worth noting that when single parameter changes, other parameters are set according to the default settings in Table 2. Figure 13 verifies that our proposed algorithm satisfies the convergence property which is proven in [38]. Moreover, the comparison results provide a basis for selecting the optimal parameters in the following simulations.

Finally, we evaluate energy efficiency of the proposed algorithm. In our simulation, it is supposed that each WCV will stop at each site and replenish 0.1% energy, i.e., 1 mJ to its adjacent sensor node. In each round, each WCV will move to the next point, and each sensor node will transmit Bi cached data to mobile WCVs. For simplicity, the charging time and efficiency are considered to be fixed with a relatively small region. As we know, residual energy level is an important metric to address this problem, and it can prolong the life cycle of WSNs. Residual energy level denotes the ratio between average residual energy between initial energy after finishing 100 times WCVs’ cruising cycle. The derived energy efficiency results are illustrated in Figure 14; it is obvious that the residual energy level using multiple WCVs is able to maintain a relatively higher level than just using mobile sinks.

Furthermore, the proposed algorithm outperforms previous approaches for the CETSP in terms of the solution quality and required computational time. As a result, compared to traditional long-distance transmission manner, the proposed path planning method can improve the lifetime of wireless sensor networks from residual energy level.

6. Conclusions

This paper investigates optimal and suboptimal trajectory design model of mobile data collection and wireless energy supplement for rechargeable wireless sensor networks. At first, we model the optimal path design problem as a kind of CETSP problem. Then, SOM-based unsupervised learning algorithm is used to solve CETSP with one or more mobile WCVs as data collectors and wireless power suppliers. Simulation results demonstrate that the proposed algorithm can reduce the length of path trajectories and extend the network energy efficiency. The herein presented learning procedure is a conceptually simple algorithm which outperforms previous mobile path design approaches for the TSP in terms of the solution quality and required computational time. In our future works, path design with obstacle avoidance will be considered in the process of mobile data collection and wireless energy recharging.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Authors’ Contributions

M.Z. and W.C. proposed the main idea and generated the simulation results and drafted the manuscript. They also responded to the reviewers’ comments. These authors contributed equally to this work.