Trajectory optimization of laser-charged UAV to minimize the average age of information for wireless rechargeable sensor network☆,☆☆
Introduction
Wireless Sensor Networks (WSNs) have wide applications in human production and life. In some applications with high real-time requirement, such as earthquake, hurricane and other natural disaster relief activities, fast collection and analysis of environment information obtained from the network deployed monitoring area play a key role in the safety of people's lives and property. Therefore, the real-time performance of sensory data in WSNs has been a hot research topic, such as [2][3]. Recently, many researchers use the metric of Age of Information (AoI) to characterize the real-time of sensory data [4][5]. The AoI depicts the time difference between the time of data arriving destination and the time of data collection beginning for any sensor [6]. Currently, mobile vehicles or UAVs are widely used as data collectors to gather data from WSNs [7] [8].
Due to the battery capacity of sensors, the energy they carry can not enough to support data transmission from sensors to data collectors. With the development of the wireless energy transfer technologies, such as frequency signals [9], the sensors can be charged through equipping rechargeable lithium-ion battery and an energy harvesting module [10]. Then the received energy of sensors can be used for data transmission. The networks that are composed of rechargeable sensors are called Wireless Rechargeable Sensor Networks (WRSNs). Compared with the other energy saving strategies, such as scheduling [11] and load balancing techniques [12], energy supplement can better solve the energy shortfall problem. Therefore, WRSNs are more attractive than traditional WSNs for long-term surveillance applications. Currently, mobile vehicles or UAVs are also widely applied as mobile Radio Frequency (RF) signal energy source to replenish energy for sensors in WRSNs [13].
However, due to the complexity of terrain and environment of monitoring areas, mobile vehicles that are used for data collection or charging of sensors can not go back to the source quickly and efficiently. Compared with the mobile vehicles, Unmanned Aerial Vehicle (UAVs) with high maneuverability, good speed and flexibility can guarantee appropriate charging positions by getting around obstacles and provide wireless connectivity for sensors without infrastructure coverage when the network is damaged by natural disasters. Nevertheless, since UAVs are powered by batteries, they may suffer from lacking of energy during performing data collection and wireless energy transfer tasks in the network. To solve the energy limitation problem of UAVs, researchers have put forward the energy supplement scheme where the Laser Beam Directors (LBDs) are used to supply energy for UAVs by emitting laser beams [14].
Inspired by the novel wireless energy transfer technologies, e.g. frequency signal and laser beams, joint the benefit of UAV as mobile station and charger, in this paper, we study the average Age of Information Optimization (AoIO) problem in laser charged UAV-assisted WRSNs. The objective of the problem aims at designing an optimal flight plan of UAV by optimizing its flight path and hovering points for data gathering, energy transfer and energy receiving to minimize the average AoI of data collected from sensors such that all data of the network are transported to the base station and the remaining energy of any sensor exceeds a certain threshold. The contribution of paper is shown as below.
(1) We propose a new laser-charged UAV-assisted WRSN architecture, where the UAV is not only used as mobile collector for gathering data from sensors but also used as mobile charger to refuel sensors, and it also can be replenished energy by laser beams transmitted by LBDs. In the architecture, we identify the average Age of Information Optimization (AoIO) problem, which aims at finding an optimal flight plan of UAV to minimize the average AoI of all data collected from network. Then we prove that the AoIO problem is NP-hard.
(2) We first study a sub-problem of the AoIO problem, which is called Total Flight Time Minimizing of UAV (TFTM). Its objective is to design an optimal charging solution of UAV to minimize the total flight time of UAV based on the given order of sensors visited by UAV. Then we prove that the TFTM problem is NP-hard by transforming its special case to the Minimum Weighted Set Cover (MWSC) problem. Afterwards, we propose a heuristic problem to solve the TFTM problem.
(3) Based on the TFTM problem, we propose an approximation algorithm to solve the AoIO problem. Then we conduct extensive simulations to illustrate the effectiveness of the proposed algorithm.
The rest of the paper is organized as follows. In Section 2, we briefly introduce the literature related with the investigated problem. In Section 3, we introduce the model and definitions for the investigated problems. In Section 4, we propose a heuristic algorithm to solve TFTM problem. In Section 5, we propose an approximation algorithm to solve the AoIO problem. In Section 6, we present the simulation results to verify the validity of the proposed algorithm. In Section 7, the paper is concluded.
Section snippets
Related works
In this section, we briefly review the literature related with the investigated problem in following three types: charging for WSN with UAV, data collection with laser-charged UAV, AoI optimization with UAV.
Network model
In this paper, we consider a new laser-charged UAV assisted WRSN architecture which consists of n ground wireless rechargeable sensors, a UAV equipped with half-duplex hybrid access point, m ground LBDs, and a base station , as shown in Fig. 1. In the architecture, sensors are randomly deployed in a monitoring area to detect environment. Let represent the set of n sensors, in which each stores energy and units of data. The UAV carries E energy and flies at a
Algorithm for the TFTM problem
In this section, we propose a heuristic algorithm to solve the TFTM problem, which is called TFTMA. The algorithm aims at finding an optimal charging solution for UAV such that the time consumption of UAV is minimized.
Before describing the algorithm, we introduce some parameters used in the algorithm. For any , we use parameters and to denote the time instant of UAV arriving and leaving , respectively. Then we
Algorithm for the AoIO problem
In this section, we propose an approximation algorithm to solve the AoIO problem, which is called AoIOA. The algorithm aims at finding an optimal flight plan of UAV such that the average AoI of the network is minimized. The algorithm consists of the following three phases.
In the first phase, we compute the order of sensors visited by UAV and the hovering points set . We first use the 1.5-approximation algorithm for the TSP problem to compute the flight path
Performance evaluation
In this section, we give the performance analysis of the AoIOA algorithm through a large number of experiments using MATLAB and Java programming. In the simulations, sensors and LBDs are deployed in the 4000 m ⁎ 4000 m square area and each result is the average of 100 runs. The basic simulation parameters are listed in Table 1.
In the following, we first evaluate the change of the total time cost T of UAV obtained by AoIOA algorithm. Then we compare the lower bound of the total time consumption
Conclusion
In this paper, we investigate the average Age of Information Optimization (AoIO) problem in a new laser-charged UAV assisted wireless rechargeable sensor network (WRSN). The objective of the problem is to minimize the average AoI of data collected from sensors such that all data of the network are transported to the base station and the remaining energy of any sensor exceeds a certain threshold. Then we prove that the AoIO problem is NP-hard. To solve the AoIO problem, we first study the Total
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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Cited by (2)
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This article belongs to Section A: Algorithms, automata, complexity and games, Edited by Paul Spirakis.
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A preliminary version [1] of this paper appeared in International Conference on Algorithmic Aspects in Information and Management (AAIM 2022). This work was supported in part by the National Natural Science Foundation of China under Grant (62202054, 62002022, 32071775), also supported by the Fundamental Research Funds for the Central Universities under grants (2021ZY88).