# DroneTank: Planning UAVs’ Flights and Sensors’ Data Transmission under Energy Constraints

^{*}

^{†}

^{‡}

## Abstract

**:**

## 1. Introduction

- First, we formally define the joint UAV flight planning and sensor transmission scheduling (UfpSts) problem. Using three key observations, we decouple the joint problem into two subproblems: UAV flight planning (UAV-FP) and sensor transmission scheduling (SEN-TS).
- Then, for the UAV-FP problem that determines the flight path and speed, we reduce it to determine the number of turns and turning locations. We then propose a dynamic programming approach to produce an optimal solution.
- Next, with the flight plans given, the SEN-TS problem determines for each sensor the time slot assignment and power control. We introduce a novel technique named water-tank to compute for a sensor its transmission power in given time slots. We then design a dynamic programming algorithm that uses water-tank as a subroutine to optimally solve the SEN-TS problem.
- Finally, in our simulations, the separately computed flight plan and transmission schedule are compared with the optimal solution for the original joint problem. The simulation results show that our proposed algorithms produce a near-optimal solution.

## 2. Related Work

## 3. Formulating the Problem

**Remark**

**1.**

**Definition**

**1.**

## 4. Problem Decoupling and Subproblems

**Observations 1**(Fly closer). According to the Shannon-Hartley Theorem of the AWGN channel, when a UAV flies closer to a sensor, the sensor transmits data to the UAV with greater energy efficiency.

**Observations 2**(Fly slower). The slower the UAV flies, the more time for sensors to deliver data, and hence, more data are collected. However, flying close to every sensor and flying slow costs energy, and the UAV has a limited energy budget for the data-collection trip. When conflict occurs, our third observation can guide the trade-off.

**Observations 3**(More energy, more important). If a sensor has a larger energy budget, it can deliver more data to the UAV; so, the energy budget is the most important aspect of flight planning.

#### 4.1. Planning UAV Flights

**Definition**

**2.**

#### 4.2. Scheduling Sensor Transmission

**Definition**

**3.**

- (a)
- $({\beta}_{i},{e}_{i}]$ is a subset of available slot sets $({b}_{i},{e}_{i}]$.
- (b)
- Assignments, $({b}_{i},{e}_{i}],1\le i\le n$, are mutually disjoint. Without loss of generality, we assume$$0\le {\beta}_{1}\le {\epsilon}_{1}\le {\beta}_{2}\le {\epsilon}_{2}\le \dots {\beta}_{n}\le {\epsilon}_{n}\le m.$$

**Definition**

**4.**

**Definition**

**5.**

## 5. Optimally Solving the UAV-FP Problem

Algorithm 1: UAV-FP-SVR |

## 6. Optimally Solving the SEN-TS Problem

#### 6.1. The Single-Sensor SEN-TS-1 Problem

**Lemma**

**1.**

**Proof**

**of**

**Lemma**

**1.**

#### 6.2. The Water-Tank Technique

**Theorem**

**1.**

**Proof**

**of**

**Theorem**

**1.**

Algorithm 2:WaterLevel |

Algorithm 3:WaterTank |

Input: $E,(b,e],floor,ceiling$Output: ${\sum}_{j=b+1}^{e}log(1+\frac{{p}_{j}}{{d}_{j}^{\alpha}})$ and ${p}_{j}$1 Sort tanks by their floor heights;2 Let $floor(j)={d}_{j}^{\alpha},ceiling(j)=floor(j)+{p}^{max}$, for $j\in (b,e]$;3 $u=$ WATERLEVEL($E,(b,e),floor,ceiling)$;4 Compute ${p}_{j}$ by Equation (31), for $j\in (b,e]$;5 return ${\sum}_{j=b+1}^{e}log(1+\frac{{p}_{j}}{{d}_{j}^{\alpha}})$ and ${p}_{j}$ |

**Observation 4**. From Figure 3’s water tank model, or Equation (31), we observe that the tank with smaller ${d}_{j}$ has a larger value ${p}_{j}$ in the optimal solution, meaning that it is more productive and energy efficient for the mobile sink to collect data in those slots when it is closer to the sensor.

#### 6.3. Optimally Solving the General SEN-TS Problem

Algorithm 4: SEN-TS-SVR |

## 7. Evaluations

#### 7.1. Brute Force Searching for the Optimal Solution

Algorithm 5:BruteForceSearchForOptimal |

#### 7.2. Simulation Settings

#### 7.3. Simulation Results

## 8. Conclusions and Future Work

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Li, Z.; Liu, Y.; Hayward, R.; Zhang, J.; Cai, J. Knowledge-based Power Line Detection for UAV Surveillance and Inspection Systems. In Proceedings of the 23rd International Conference Image and Vision Computing New Zealand (IVCNZ), Christchurch, New Zealand, 26–28 November 2008; pp. 1–6. [Google Scholar]
- Mohammed, F.; Idries, A.; Mohamed, N.; Al-Jaroodi, J.; Jawhar, I. UAVs for Smart Cities: Opportunities and Challenges. In Proceedings of the 2014 International Conference on Unmanned Aircraft Systems (ICUAS), Orlando, FL, USA, 27–30 May 2014; pp. 267–273. [Google Scholar]
- Candiago, S.; Remondino, F.; de Giglio, M.; Dubbini, M.; Gattelli, M. Evaluating Multispectral Images and Vegetation Indices for Precision Farming Applications from UAV Images. Remote Sens.
**2015**, 7, 4026–4047. [Google Scholar] [CrossRef] [Green Version] - Lin, X.; Yajnanarayana, V.; Muruganathan, S.; Gao, S.; Asplund, H.; Maattanen, H.; Bergstrom, M.; Euler, S.; Wang, Y. The Sky Is Not the Limit: LTE for Unmanned Aerial Vehicles. IEEE Commun. Mag.
**2018**, 56, 204–210. [Google Scholar] [CrossRef] [Green Version] - Abdulla, A.E.A.A.; Fadlullah, Z.M.; Nishiyama, H.; Kato, N.; Ono, F.; Miura, R. An Optimal Data Collection Technique for Improved Utility in UAS-aided Networks. In Proceedings of the IEEE INFOCOM 2014—IEEE Conference on Computer Communications, Toronto, ON, Canada, 27 April–2 May 2014; pp. 736–744. [Google Scholar]
- Zhan, C.; Zeng, Y.; Zhang, R. Energy-efficient Data Collection in UAV Enabled Wireless Sensor Network. IEEE Wirel. Commun. Lett.
**2018**, 7, 328–331. [Google Scholar] [CrossRef] - Gong, J.; Chang, T.; Shen, C.; Chen, X. Flight Time Minimization of UAV for Data Collection over Wireless Sensor Networks. IEEE J. Sel. Areas Commun.
**2018**. [Google Scholar] [CrossRef] - Zeng, Y.; Zhang, R.; Lim, T.J. Throughput Maximization for UAV-enabled Mobile Relaying Systems. IEEE Trans. Commun.
**2016**, 64, 4983–4996. [Google Scholar] [CrossRef] - Zeng, Y.; Zhang, R. Energy-efficient UAV Communication with Trajectory Optimization. IEEE Trans. Wirel. Commun.
**2017**, 16, 3747–3760. [Google Scholar] [CrossRef] - Wu, Q.; Zeng, Y.; Zhang, R. Joint Trajectory and Communication Design for Multi-UAV Enabled Wireless Networks. IEEE Trans. Wirel. Commun.
**2018**, 17, 2109–2121. [Google Scholar] [CrossRef] [Green Version] - Yang, D.; Wu, Q.; Zeng, Y.; Zhang, R. Energy Tradeoff in Ground-to-UAV Communication via Trajectory Design. IEEE Trans. Veh. Technol.
**2018**, 67, 6721–6726. [Google Scholar] - Ozel, O.; Tutuncuoglu, K.; Yang, J.; Ulukus, S.; Yener, A. Resource Management for Fading Wireless Channels with Energy Harvesting Nodes. In Proceedings of the 2011 Proceedings IEEE INFOCOM, Shanghai, China, 10–15 April 2011; pp. 456–460. [Google Scholar]
- Ozel, O.; Tutuncuoglu, K.; Yang, J.; Ulukus, S.; Yener, A. Transmission with Energy Harvesting Nodes in Fading Wireless Channels: Optimal Policies. IEEE J. Sel. Areas Commun.
**2011**, 29, 1732–1743. [Google Scholar] [CrossRef] [Green Version] - Antepli, M.A.; Uysal-Biyikoglu, E.; Erkal, H. Optimal Packet Scheduling on an Energy Harvesting Broadcast Link. IEEE J. Sel. Areas Commun.
**2011**, 29, 1721–1731. [Google Scholar] [CrossRef] [Green Version] - Ozel, O.; Yang, J.; Ulukus, S. Optimal Broadcast Scheduling for an Energy Harvesting Rechargeable Transmitter with a Finite Capacity Battery. IEEE Trans. Wirel. Commun.
**2012**, 11, 2193–2203. [Google Scholar] [CrossRef] [Green Version] - Ahmad, Z.; Ullah, F.; Tran, C.; Lee, S. Efficient Energy Flight Path Planning Algorithm Using 3-D Visibility Roadmap for Small Unmanned Aerial Vehicle. Int. J. Aerosp. Eng.
**2017**, 2017, 2849745. [Google Scholar] [CrossRef] - Modares, J.; Ghanei, F.; Mastronarde, N.; Dantu, K. UB-ANC Planner: Energy Efficient Coverage Path Planning with Multiple Drones. In Proceedings of the 2017 IEEE International Conference on Robotics and Automation (ICRA), Singapore, 29 May–3 June 2017; pp. 6182–6189. [Google Scholar]
- Ren, X.; Liang, W.; Xu, W. Data Collection Maximization in Renewable Sensor Networks via Time-Slot Scheduling. IEEE Trans. Comput.
**2015**, 64, 1870–1883. [Google Scholar] [CrossRef] - Zhao, M.; Yang, Y. Optimization-based Distributed Algorithms for Mobile Data Gathering in Wireless Sensor Networks. IEEE Trans. Mob. Comput.
**2012**, 11, 1464–1477. [Google Scholar] [CrossRef] - Shi, Y.; Hou, Y.T. Theoretical Results on Base Station Movement Problem for Sensor Network. In Proceedings of the IEEE INFOCOM 2008—The 27th Conference on Computer Communications, Phoenix, AZ, USA, 13–18 April 2008; pp. 376–384. [Google Scholar]
- Shi, Y.; Hou, Y.T. Some Fundamental Results on Base Station Movement Problem for Wireless Sensor Networks. IEEE/ACM Trans. Netw.
**2012**, 20, 1054–1067. [Google Scholar] [CrossRef] - Yun, Y.; Xia, Y. Maximizing the Lifetime of Wireless Sensor Networks with Mobile Sink in Delay-tolerant Applications. IEEE Trans. Mob. Comput.
**2010**, 9, 1308–1318. [Google Scholar] - Chakrabarti, A.; Sabharwal, A.; Aazhang, B. Communication Power Optimization in a Sensor Network with a Path-constrained Mobile Observer. ACM Trans. Sens. Netw.
**2006**, 2, 297–324. [Google Scholar] [CrossRef] - Ma, M.; Yang, Y. SenCar: An Energy-efficient Data Gathering Mechanism for Large-scale Multihop Sensor Networks. IEEE Trans. Parallel Dist. Syst.
**2007**, 18, 1476–1488. [Google Scholar] [CrossRef] - Song, L.; Hatzinakos, D. Architecture of Wireless Sensor Networks with Mobile Sinks: Sparsely Deployed Sensors. IEEE Trans. Veh. Technol.
**2007**, 56, 1826–1836. [Google Scholar] [CrossRef] - Zhao, M.; Li, J.; Yang, Y. A Framework of Joint Mobile Energy Replenishment and Data Gathering in Wireless Rechargeable Sensor Networks. IEEE Trans. Mob. Comput.
**2014**, 13, 2689–2705. [Google Scholar] [CrossRef] - Wang, W.; Srinivasan, V.; Chua, K.-C. Extending the Lifetime of Wireless Sensor Networks Through Mobile Relays. IEEE/ACM Trans. Netw.
**2008**, 16, 1108–1120. [Google Scholar] [CrossRef] - Xing, G.; Li, M.; Wang, T.; Jia, W.; Huang, J. Efficient Rendezvous Algorithms for Mobility-enabled Wireless Sensor Networks. IEEE Trans. Mob. Comput.
**2012**, 11, 47–60. [Google Scholar] [CrossRef] - Tse, D.; Viswanath, P. Fundamentals of Wireless Communication; Cambridge University Press: Cambridge, UK, 2005. [Google Scholar]
- Yang, J.; Ulukus, S. Transmission Completion Time Minimization in an Energy Harvesting System. In Proceedings of the 2010 44th Annual Conference on Information Sciences and Systems (CISS), Princeton, NJ, USA, 17–19 March 2010; pp. 1–6. [Google Scholar]
- Yang, J.; Ulukus, S. Optimal Packet Scheduling in an Energy Harvesting Communication System. IEEE Trans. Commun.
**2012**, 60, 220–230. [Google Scholar] [CrossRef] [Green Version] - Shan, F.; Luo, J.; Wu, W.; Li, M.; Shen, X. Discrete Rate Scheduling for Packets with Individual Deadlines in Energy Harvesting Systems. IEEE J. Sel. Areas Commun.
**2015**, 33. [Google Scholar] [CrossRef] - Tutuncuoglu, K.; Yener, A. Short-term Throughput Maximization for Battery Limited Energy Harvesting Nodes. In Proceedings of the 2011 IEEE International Conference on Communications (ICC), Kyoto, Japan, 5–9 June 2011; pp. 1–5. [Google Scholar]
- Tutuncuoglu, K.; Yener, A. Optimum Transmission Policies for Battery Limited Energy Harvesting Nodes. IEEE Trans. Wirel. Commun.
**2012**, 11, 1180–1189. [Google Scholar] [CrossRef] [Green Version] - MAVProxy. Available online: http://ardupilot.github.io/MAVProxy (accessed on 18 September 2017).
- Boyd, S.; Vandenberghe, L. Convex Optimization; Cambridge University Press: Cambridge, UK, 2004. [Google Scholar]

**Figure 1.**Illustration of a drone flies along a coastline to collect data from deployed sensors. By mainstream open-source or commercial flight controllers, a flight path consists of a sequence of way-points that the drone visits and makes turn at, so they are also called turning points (red solid points). More turning points means more energy consumption of the drone since more flight time and distance to cover, however, it also means closer the drone can fly to sensors to collect data. Fewer turning points consumes less drone energy, but cost sensors to use higher power to transmit data due to the longer distance. The best trade-off with limited drone and sensors energy must be found.

**Figure 2.**An example of the SEN-TS-1 problem, where the available slots are $(0,7]$. Each circle represents the flight position in each time slot and dashed lines show the distance between this position and sensor s. The goal is to determine the optimal transmission power p in each slot, such that the data transmitted by s (collected by sink S) is maximized with the battery’s limited energy E.

**Figure 3.**Illustration of the water-tank technique. Given a distance set $\{{d}_{j}\}$, identical tanks are put at different heights: tank j at height ${d}_{j}^{\alpha}$. Each tank has a unit-area base and a capacity of ${p}^{max}$. The amount of E water is injected into these tanks, and the amount of water in tank j is the solution for ${p}_{j}$.

**Figure 4.**The performance comparisons measured by the total amount of data collected. The default setting parameters are: network size is 20 (number of sensors), the average sensor energy budget is 250 mJ, the UAV energy budget is 300 units, the UAV speed is 7 m/s, the transmission range is 15 m, and the energy cost for each turn is 20 unit UAV energy. (

**a**) Impact of network size, varying from 11 to 29, with step of 3. (

**b**) Impact of average sensor energy budget, varying from 100 mJ to 400 mJ with step of 50 mJ. (

**c**) Impact of UAV energy budget, varying from 260 to 380 with step of 20 units of UAV energy. (

**d**) Impact of UAV speed, varying from 7 m/s to 19 m/s, with step 2 m/s. (

**e**) Impact of wireless transmission range, varying from 9 m to 21 m, with step 2 m. (

**f**) Impact of turn energy cost, varying from 17 to 23, with step 1 unit.

**Table 1.**Possible Combinations of Value Ranges among Lagrangian Multipliers. (

**a**) ${\lambda}_{j}$ and ${p}_{j}$; (

**b**) ${\omega}_{j}$ and ${p}_{j}$; (

**c**) ${p}_{j}$, ${\lambda}_{j}$ and ${\omega}_{j}$.

(a) | (b) | (c) | |||||

Case | ${\lambda}_{j}$ | ${p}_{j}$ | ${\omega}_{j}$ | ${p}_{j}$ | ${p}_{j}$ | ${\lambda}_{j}$ | ${\omega}_{j}$ |

1 | 0 | >0 | >0 | ${p}^{max}$ | =0 | $\ge 0$ | 0 |

2 | >0 | 0 | 0 | $[0,{p}^{max})$ | $\in (0,{p}^{max})$ | 0 | 0 |

3 | 0 | 0 | 0 | ${p}^{max}$ | =${p}^{max}$ | 0 | $\ge 0$ |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Xiong, R.; Shan, F.
DroneTank: Planning UAVs’ Flights and Sensors’ Data Transmission under Energy Constraints. *Sensors* **2018**, *18*, 2913.
https://doi.org/10.3390/s18092913

**AMA Style**

Xiong R, Shan F.
DroneTank: Planning UAVs’ Flights and Sensors’ Data Transmission under Energy Constraints. *Sensors*. 2018; 18(9):2913.
https://doi.org/10.3390/s18092913

**Chicago/Turabian Style**

Xiong, Runqun, and Feng Shan.
2018. "DroneTank: Planning UAVs’ Flights and Sensors’ Data Transmission under Energy Constraints" *Sensors* 18, no. 9: 2913.
https://doi.org/10.3390/s18092913