# A Hybrid Battery Charging Approach for Drone-Aided Border Surveillance Scheduling

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## Abstract

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## 1. Introduction

- To extend the capability of drones using the proposed hybrid approach: By implementing the proposed hybrid approach, we can lengthen the flight duration per charge from the initial launching point.
- To cope with the uncertainty in the DWCS and reduce the landing time of drones on the SWCS: The proposed hybrid approach can complement the major drawback of each wireless charging system.
- To propose a mathematical model to determine optimal locations of the wireless charging systems so as to minimize the total cost of the hybrid system. Furthermore, the proposed model provides optimal drone flight paths including the time to land on the SWCS.

## 2. Problem Description

## 3. Mathematical Formulation Model

## 4. Numerical Experiments

#### 4.1. A Case Study

#### 4.2. Numerical Results

#### 4.3. Analysis on One-Time Surveillance Flight

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

Indices | |

I | Set of waypoints ($i,j,u\in I$), |

K | Set of drones (i.e., $k\in K$), |

R | Set of ground control centers (depot) ($r\in R$), |

S | $I\cup R.$ |

Parameters | |

m | The number of flights for a mission per given period, |

M | A sufficiently large number, |

${B}_{k}$ | Maximum flight duration (battery capacity) of drone k, |

${P}_{k}$ | Operation cost of drone k, |

$D{P}_{ij}$ | Possibility of DWCS installation between waypoints i and j, |

$D{O}_{ij}$ | Operation cost of DWCS between waypoints i and j, |

$D{I}_{ij}$ | Installation cost of DWCS between waypoints i and j, |

$S{P}_{i}$ | Possibility of SWCS installation at waypoint i, |

$S{O}_{i}$ | Operation cost of SWCS at waypoint i, |

$S{I}_{i}$ | Installation cost of SWCS at waypoint i, |

$F{T}_{ij}$ | Flight time for flight segment ($i\to j$), |

$DC{E}_{ijk}$ | Charging efficiency when drone k flies over DWCS installed between waypoints i and j, |

$SC{E}_{ik}$ | Charging efficiency when drone k lands on SWCS installed at waypoint i, |

$F{D}_{ij}$ | The number of possible flights between waypoints i and j. |

Decision Variables: Our aim is to determine where to install the DWCS and the SWCS are installed, | |

and which drones should be assigned for surveillance flights while minimizing the overall cost of | |

the hybrid system. Accordingly, we define decision variables as: | |

${x}_{ijk}$ | 1 if drone k flies from waypoint i to waypoint j (i.e., segment ($i\to j$)); 0 otherwise, |

${h}_{ij}$ | 1 if DWCS are installed between waypoints i and j; 0 otherwise, |

${f}_{i}$ | 1 if SWCS are installed at waypoint i; 0 otherwise, |

${g}_{k}$ | 1 if drone k is utilized to fly; 0 otherwise, |

${l}_{ik}$ | 1 if drone k lands on SWCS installed at waypoint i to charge its battery; 0 otherwise, |

${n}_{i}$ | The number of drones landing at waypoint i for charging (landing on SWCS), |

$r{f}_{ik}$ | Remaining flight duration when drone k arrives at waypoint i, |

$l{t}_{ik}$ | Landing time of drone k at waypoint i to charge the drone battery, |

${\mu}_{i}$ | The order of sequence of visiting waypoint i in a flight path. |

## References

- Kim, S.J.; Lim, G.J.; Cho, J.; Côté, M.J. Drone-Aided Healthcare Services for Patients with Chronic Diseases in Rural Areas. J. Intell. Robot. Syst.
**2017**, 88, 163–180. [Google Scholar] [CrossRef] - Kim, S.J.; Lim, G.J. Drone-Aided Border Surveillance with an Electrification Line Battery Charging System. J. Intell. Robot. Syst.
**2018**, 92, 657–670. [Google Scholar] [CrossRef] - Lim, G.J.; Kim, S.; Cho, J.; Gong, Y.; Khodaei, A. Multi-UAV Pre-Positioning and Routing for Power Network Damage Assessment. IEEE Trans. Smart Grid
**2018**, 9, 3643–3651. [Google Scholar] [CrossRef] - Larson, M.D.; Simic Milas, A.; Vincent, R.K.; Evans, J.E. Multi-depth suspended sediment estimation using high-resolution remote-sensing UAV in Maumee River, Ohio. Int. J. Remote Sens.
**2018**, 39, 5472–5489. [Google Scholar] [CrossRef] - Kim, S.J.; Lim, G.J.; Cho, J. Drone flight scheduling under uncertainty on battery duration and air temperature. Comput. Ind. Eng.
**2018**, 117, 291–302. [Google Scholar] [CrossRef] - Kim, S.J.; Ahmadian, N.; Lim, G.J.; Torabbeigi, M. A Rescheduling Method of Drone Flights under Insufficient Remaining Battery Duration. In Proceedings of the 2018 International Conference on Unmanned Aircraft Systems (ICUAS), Dallas, TX, USA, 12–15 June 2018; pp. 468–472. [Google Scholar] [CrossRef]
- Lyon, D. Surveillance Studies: An Overview; Polity: Chicago, IL, USA, 2007. [Google Scholar]
- Williams, A.; Yakimenko, O. Persistent mobile aerial surveillance platform using intelligent battery health management and drone swapping. In Proceedings of the 2018 4th International Conference on Control, Automation and Robotics (ICCAR), Auckland, New Zealand, 20–23 April 2018; pp. 237–246. [Google Scholar]
- Lee, D.; Zhou, J.; Lin, W.T. Autonomous battery swapping system for quadcopter. In Proceedings of the 2015 International Conference on IEEE, Unmanned Aircraft Systems (ICUAS), Denver, CO, USA, 9–12 June 2015; pp. 118–124. [Google Scholar]
- Humavox. Drone Charging Stations: What’s the Best Way to Charge Your Drone? Available online: http://www.humavox.com/blog/drone-charging-stations-whats-the-best-way-to-charge-your-drone/ (accessed on 17 September 2018).
- Campi, T.; Cruciani, S.; Feliziani, M. Wireless Power Transfer Technology Applied to an Autonomous Electric UAV with a Small Secondary Coil. Energies
**2018**, 11, 352. [Google Scholar] [CrossRef] - Wang, C.; Ma, Z. Design of wireless power transfer device for UAV. In Proceedings of the 2016 IEEE International Conference on IEEE, Mechatronics and Automation (ICMA), Harbin, China, 7–10 August 2016; pp. 2449–2454. [Google Scholar]
- Junaid, A.B.; Lee, Y.; Kim, Y. Design and implementation of autonomous wireless charging station for rotary-wing UAVs. Aerosp. Sci. Technol.
**2016**, 54, 253–266. [Google Scholar] [CrossRef] - Global Energy Transmission. In-Flight Wireless Charging–Outdoor Demonstration. Available online: http://getcorp.com/in-flight-wireless-charging-outdoor-demonstration/ (accessed on 17 September 2018).
- Gilchrist, A.; Wu, H.; Sealy, K. Novel system for wireless in-motion EV charging and disabled vehicle removal. In Proceedings of the 2012 IEEE International IEEE, Electric Vehicle Conference (IEVC), Greenville, SC, USA, 4–8 March 2012; pp. 1–4. [Google Scholar]
- Lu, M.; Bagheri, M.; James, A.P.; Phung, T. Wireless Charging Techniques for UAVs: A Review, Reconceptualization, and Extension. IEEE Access
**2018**. [Google Scholar] [CrossRef] - Wang, J.; Hu, M.; Cai, C.; Lin, Z.; Li, L.; Fang, Z. Optimization design of wireless charging system for autonomous robots based on magnetic resonance coupling. AIP Adv.
**2018**, 8, 055004. [Google Scholar] [CrossRef] - Park, B.; Park, J.; Shin, Y.; Park, C.; Ahn, S.; Han, I.S.; Jeong, J.; Lee, K.S. Wireless Charging System Using Soft Magnetic Composite for Unmanned Aerial Vehicle. Int. J. Commun.
**2017**, 2, 59–62. [Google Scholar] - Miller, C.E.; Tucker, A.W.; Zemlin, R.A. Integer programming formulation of traveling salesman problems. J. ACM (JACM)
**1960**, 7, 326–329. [Google Scholar] [CrossRef] - Öncan, T.; Altınel, İ.K.; Laporte, G. A comparative analysis of several asymmetric traveling salesman problem formulations. Comput. Oper. Res.
**2009**, 36, 637–654. [Google Scholar] [CrossRef] - GAMS. General Algebraic Modeling System (GAMS) Release 25.1.1. Available online: http://www.gams.com (accessed on 17 September 2018).
- The Optimization Firm. BARON 18.5.8. Available online: https://minlp.com (accessed on 17 September 2018).
- Google, Map Data. 2018. Available online: https://www.google.com/maps (accessed on 17 September 2018).

**Figure 1.**Air gap in dynamic wireless charging systems (DWCS). (

**a**) E-line systems for drones [2]; (

**b**) E-lane systems for electric vehicles (EVs).

**Figure 3.**Vertical and horizontal distances between a drone and a dynamic wireless charging system (DWCS).

**Figure 4.**Case study: part of the U.S.- Mexico border in Arizona, U.S. [23].

**Figure 5.**Optimal flight paths under different charging efficiency of DWCS. (

**a**) DCE: Uniform (0.0, 0.5); (

**b**) DCE: Uniform (0.1, 0.5); (

**c**) DCE: Uniform (0.2, 0.5); (

**d**) DCE: Uniform (0.3, 0.5); (

**e**) DCE: Uniform (0.4, 0.5); (

**f**) DCE: Constant 0.5.

Parameter | Value | Unit | |
---|---|---|---|

Drone | Flight duration (B) | Type I = 30 | minute |

Type II = 25 | minute | ||

Operation cost (P) | Type I = 30 | U.S. Dollar ($) | |

Type II = 25 | U.S. Dollar ($) | ||

DWCS | Installation cost ($DI$) | 250 | U.S. Dollar ($) per 0.25 km |

Operation cost ($DO$) | 0.25 | U.S. Dollar ($) per flight | |

Charging efficiency ($DCE$) | Uniform (0.0–0.4, 0.5) | minutes/ 0.25 km | |

SWCS | Installation cost ($SI$) | 1000 | U.S. Dollar ($) per ea |

Operation cost ($SO$) | 1 | U.S. Dollar ($) / minute ($lt$) | |

Charging efficiency ($SCE$) | 0.5 | minutes / minute ($lt$) | |

Capacity to accommodate drones (${n}_{i}$) | 1 | ea | |

No. of border patrol mission per given period (m) | 300 |

DCE | Hybrid Charging System | Number of Required Drones | Actual Flight Time | |||||
---|---|---|---|---|---|---|---|---|

DWCS | SWCS | Total Cost | ||||||

Installation | Length | Installation | $\mathit{l}\mathit{t}$ | |||||

Uniform (0.0, 0.5) | None | 0 km | $n12$ | 58 min | $ 27,400 | Type I: 1 | 59 min | |

Uniform (0.1, 0.5) | None | 0 km | $n9$ | 58 min | $ 27,400 | Type I: 1 | 59 min | |

Uniform (0.2, 0.5) | None | 0 km | $n10$ | 58 min | $ 27,400 | Type I: 1 | 59 min | |

Uniform (0.3, 0.5) | $n15$–$n17$ | 1.25 km | $n7$ | 22 min | $ 27,225 | Type I: 2 | 32–41 min | |

& $n21$–$n24$ | ||||||||

Uniform (0.4, 0.5) | $n15$–$n18$ | 1.25 km | $n6$ | 22 min | $ 27,225 | Type I: 2 | 32–41 min | |

& $n20$–$n22$ | ||||||||

Constant 0.5 min | $n15$–$n19$ | 1.00 km | $n1$ | 22 min | $ 26,900 | Type I: 2 | 32–41 min |

DCE | Spent Time (min) | ||
---|---|---|---|

Flight | Charging (Landed on the SWCS) | Total | |

Uniform (0.0, 0.5) | 59 | 58 | 117 |

Uniform (0.1, 0.5) | 59 | 58 | 117 |

Uniform (0.2, 0.5) | 59 | 58 | 117 |

Uniform (0.3, 0.5) | 32–41 | 22 | 32–63 |

Uniform (0.4, 0.5) | 32–41 | 22 | 32–63 |

Constant 0.5 min | 32–41 | 22 | 32–63 |

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**MDPI and ACS Style**

Kim, S.J.; Lim, G.J.
A Hybrid Battery Charging Approach for Drone-Aided Border Surveillance Scheduling. *Drones* **2018**, *2*, 38.
https://doi.org/10.3390/drones2040038

**AMA Style**

Kim SJ, Lim GJ.
A Hybrid Battery Charging Approach for Drone-Aided Border Surveillance Scheduling. *Drones*. 2018; 2(4):38.
https://doi.org/10.3390/drones2040038

**Chicago/Turabian Style**

Kim, Seon Jin, and Gino J. Lim.
2018. "A Hybrid Battery Charging Approach for Drone-Aided Border Surveillance Scheduling" *Drones* 2, no. 4: 38.
https://doi.org/10.3390/drones2040038