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Directional WPT Charging for Routing-Asymmetric WRSNs with a Mobile Charger

Zhenguo Gao, Qi Zhang, Qingyu Gao, Yunlong Zhao, Hsiao-Chun Wu

TL;DR

The paper tackles energy-constrained routing-asymmetric wireless rechargeable sensor networks (RA-WRSNs) by formulating the Asymmetric DMC Charge Scheduling (ADMCCS) problem. It proposes a four-step framework and the RA-DMCS algorithm to minimize total energy loss while satisfying node energy demands, using a minimum-size charging position set (KCPG), a minimum functional direction set (cMFRDS), a linear program solved by CPlex for transmission times, and a routing tour computed by LKH. The problem is shown to be NP-hard via reduction to ATSP, and extensive simulations and a test-bed demonstrate that RA-DMCS outperforms symmetric or non-optimized baselines. The work also integrates state-of-the-art TSP/ATSP methods to address the asymmetric routing and energy transfer challenges, enabling practical deployment in RA-WRSNs.

Abstract

Mobile Charge Scheduling for wirelessly charging nodes in Wireless Rechargeable Sensor Networks (WRSNs) is a promising but still evolving research area. Existing research mostly assumes a symmetric environment, where the routing costs in opposite directions between two locations are considered identical. However, various factors such as terrain restrictions and wind or water flows may invalidate the routing-symmetric assumption in practical environments, thereby significantly limiting the performance of these solutions in routing-asymmetric WRSNs (RA-WRSNs). To address the routing-asymmetric challenges in mobile charge scheduling for WRSNs, this paper systematically investigates the underlying Asymmetric Directional Mobile Charger (DMC) Charge Scheduling (ADMCCS) problem, aiming to minimize energy loss while satisfying the charging demands of the network nodes. The DMC model is assumed because its results can be easily applied to the specialized case of an Omnidirectional Mobile Charger (OMC). To solve the ADMCCS problem, we propose a four-step framework. First, a minimum-size efficient charging position set is selected using our designed K-means-based Charging Position Generation (KCPG) algorithm, addressing the challenge of the unlimited charging position selection space. Next, minimum-size functional-equivalent direction sets at these positions are determined using an optimal algorithm, tackling the challenge of infinite charging directions. Subsequently, the optimal energy transmission time lengths for all directions at the positions are obtained by formulating and solving a Nonlinear Program (NLP) problem. Finally, the Lin-Kernighan Heuristic (LKH) algorithm for the Asymmetric Traveling Salesman Problem is adapted to obtain a highly probable optimal loop tour, addressing the routing-asymmetric challenge.

Directional WPT Charging for Routing-Asymmetric WRSNs with a Mobile Charger

TL;DR

The paper tackles energy-constrained routing-asymmetric wireless rechargeable sensor networks (RA-WRSNs) by formulating the Asymmetric DMC Charge Scheduling (ADMCCS) problem. It proposes a four-step framework and the RA-DMCS algorithm to minimize total energy loss while satisfying node energy demands, using a minimum-size charging position set (KCPG), a minimum functional direction set (cMFRDS), a linear program solved by CPlex for transmission times, and a routing tour computed by LKH. The problem is shown to be NP-hard via reduction to ATSP, and extensive simulations and a test-bed demonstrate that RA-DMCS outperforms symmetric or non-optimized baselines. The work also integrates state-of-the-art TSP/ATSP methods to address the asymmetric routing and energy transfer challenges, enabling practical deployment in RA-WRSNs.

Abstract

Mobile Charge Scheduling for wirelessly charging nodes in Wireless Rechargeable Sensor Networks (WRSNs) is a promising but still evolving research area. Existing research mostly assumes a symmetric environment, where the routing costs in opposite directions between two locations are considered identical. However, various factors such as terrain restrictions and wind or water flows may invalidate the routing-symmetric assumption in practical environments, thereby significantly limiting the performance of these solutions in routing-asymmetric WRSNs (RA-WRSNs). To address the routing-asymmetric challenges in mobile charge scheduling for WRSNs, this paper systematically investigates the underlying Asymmetric Directional Mobile Charger (DMC) Charge Scheduling (ADMCCS) problem, aiming to minimize energy loss while satisfying the charging demands of the network nodes. The DMC model is assumed because its results can be easily applied to the specialized case of an Omnidirectional Mobile Charger (OMC). To solve the ADMCCS problem, we propose a four-step framework. First, a minimum-size efficient charging position set is selected using our designed K-means-based Charging Position Generation (KCPG) algorithm, addressing the challenge of the unlimited charging position selection space. Next, minimum-size functional-equivalent direction sets at these positions are determined using an optimal algorithm, tackling the challenge of infinite charging directions. Subsequently, the optimal energy transmission time lengths for all directions at the positions are obtained by formulating and solving a Nonlinear Program (NLP) problem. Finally, the Lin-Kernighan Heuristic (LKH) algorithm for the Asymmetric Traveling Salesman Problem is adapted to obtain a highly probable optimal loop tour, addressing the routing-asymmetric challenge.
Paper Structure (29 sections, 4 theorems, 15 equations, 7 figures, 5 tables, 2 algorithms)

This paper contains 29 sections, 4 theorems, 15 equations, 7 figures, 5 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Charging with Stationary Chargers
  4. Charging with Mobile Chargers
  5. Mobile Charging in Asymmetric Environments
  6. Preliminary Models
  7. System Model
  8. Asymmetric Routing Model
  9. Energy Consumption Model of the DMC
  10. WPT Energy Transfer Model
  11. Directional Energy Transfer Coefficient Model
  12. The ADMCCS Problem
  13. Structure of Charging Schedule List
  14. The ADMCCS Problem
  15. Solve the ADMCCS Problem
  16. ...and 14 more sections

Key Result

Theorem 1

The ADMCCS problem is NP-hard.

Figures (7)

  • Figure 1: Outline of the RA-DMCS algorithm for the ADMCCS problem
  • Figure 2: An example RA-WRSN
  • Figure 3: Coverage sector of a DMC
  • Figure 4: Charging tours determined by the algorithms
  • Figure 5: Effects of the number of nodes
  • ...and 2 more figures

Theorems & Definitions (8)

  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Theorem 3
  • proof
  • Theorem 4
  • proof