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

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## 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

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**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 | $\ge 0$ |

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**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