# Disaster Region Coverage Using Drones: Maximum Area Coverage and Minimum Resource Utilisation

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Problem Statement

^{4}). Hence, the optimum issue is non-deterministic and exponential. An NP-hard problem is one which cannot be solved by the model. These problems are at least as hard as the NP-complete problems and they do not have to be decision problems.

#### 2.1. Device Coverage

$\theta :$ | $angleofview$ |

$R:$ | depth of field |

$i:$ | $DeviceID$ |

${x}_{i},{y}_{i}:$ | $Device{i}^{\prime}sposition$ |

${d}_{i}:$ | $directionvectordefininginitialposition$ |

${\phi}_{i}:$ | $Theanglebetweenthevector{d}_{i}andx-axis$ |

$j:$ | $objectID$ |

${x}_{i},{y}_{i}:$ | $Object{j}^{\prime}spositions.$ |

${v}_{j}:$ | $Objectvectorfromdeviceitoobjectj.$ |

${\beta}_{ij}:\text{}$ | $theanglebetweenthedeviceviewingdirection$ ${V}_{ij}$ and direction vector ${d}_{i}$_{.} |

#### 2.2. Area Coverage

#### 2.3. Image Footprint Based on Ground Sample Distance (GSD)

## 3. Drone Optimisation

**PSO Pseudocode**(Algorithm 1)

Algorithm 1 |

$1:\mathbf{For}i=\mathrm{i}(Nto\mathrm{N}=\mathrm{number\; of\; particles})$ |

$2:\mathrm{Initialise}P\left[i\right]$$$ |

$3:\mathrm{Initialise}V\left[i\right]$$$ |

$4:\mathrm{Initialise}\mathrm{swarm}$ |

5: End for |

6: Repeat until stop criteria is satisfied |

7: For i = 1 to M (M = max iterations) |

8: For j = 1 to N |

$9:\mathrm{Evaluate}P\left[j\right]$ |

$10:\mathrm{if}\mathrm{new}\mathrm{population}\mathrm{is}\mathrm{better}\mathrm{than}{P}_{best}$$\left[j\right]=P\left[j\right]$ |

$11:{g}_{best}$$=\mathrm{Best}\mathrm{particle}\mathrm{position}\mathrm{in}P\left[j\right]$ |

$12:V\left(j+1\right)=wV\left(j\right)+c1\ast random1\ast \left(P{p}_{best}-P\left(j\right)\right)+c2\ast random1\ast \left(P{g}_{best}-P\left(j\right)\right)$ |

$13:\mathbf{if}V(j+1)\mathrm{is}\mathrm{not}\mathrm{within}({\mathrm{velocity}}_{\mathrm{min}},{\mathrm{velocity}}_{\mathrm{max}})$ |

14: then update velocity to be within (velocity_{min}, velocity_{max}) |

$15:P\left(j+1\right)=P\left(j\right)+V\left(j+1\right)$ |

$16:\mathbf{if}P\left(j+1\right)\mathrm{is}\mathrm{not}\mathrm{within}(\mathrm{upper}\mathrm{bound},\mathrm{lower}\mathrm{bound})$ |

17: then update position to be within (upper bound, lower bound) |

18: End for |

19: End for |

**GA Pseudocode**(Algorithm 2)

Algorithm 2: GA(n, χ, µ) |

Initialise generation 0: |

k:= 0; |

Pk:= a population of n randomly-generated individuals; |

Evaluate Pk: |

Compute fitness(i) for each i ∈ Pk; |

do { |

Create generation |

k + 1: |

1. Copy: |

Select (1 − χ) × n members of Pk and insert into Pk+1; |

2. Crossover: |

Select χ × n members of Pk; pair them up; produce offspring; insert the offspring into Pk+1; |

3. Mutate: |

Select µ × n members of Pk+1; invert a randomly-selected bit in each; |

Evaluate Pk+1: |

Compute fitness(i) for each i ∈ Pk; |

Increment: |

k:= k + 1; |

} |

while the fitness of the fittest individual in Pk is not high enough; |

return the fittest individual from Pk; |

#### 3.1. Utilization of Resources for Optimal Outcome by Parameter Tuning

^{2}. Initial results were computed to assess the number of drones required to generate the best area coverage. According to the initial analysis and the above results, optimal results are achieved when using 12 drones (Table 3b). The total number of drones used in the experiment was 12, each having the technology and ability to fly at the maximum altitude of 121.97 m, which is approximately 400 ft. $FoVx$ and $FoVy$ are the horizontal and vertical fields of view, respectively.

#### Comparison with GA Results

#### 3.2. Factors Affecting the Energy Consumption in Drones

#### 3.2.1. The Weather Effect

#### 3.2.2. Speed of Drones and Payload

- hovering,
- vertical flight: change of altitude by vehicle, landing or take-off
- horizontal flight: level flight or vehicle cruising

## 4. Power Utilization Models for Drones

#### 4.1. Power Consumption in Horizontal Movement

#### 4.2. Maximum Flying Speed

#### 4.3. Power Consumption during High Speeds

#### 4.4. Factors Affecting Drone Energy Consumption

#### 4.5. Minimum Energy Consumption Model

**Initial Power Constants**

## 5. Conclusions

- i
- Reaching the target with optimal battery consumption
- ii
- Assigning and maintaining the position of particles to cover the maximum area.
- iii
- Optimal usage of a minimum number of drones.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

Iteration | Inertia Coefficient | $\mathbf{Objective}\mathbf{Function}\mathbf{Value}\left(\mathbf{k}{\mathbf{m}}^{2}\right)$ | $\mathit{g}$$\mathbf{Best}\mathbf{Position}\left(\mathit{x},\mathit{y}\right)$ |
---|---|---|---|

1 | 0.9 | 98.25242778509373 | [−5.88992833 7.59274691] |

2 | 0.875 | 166.1080146338387 | [−7.56059946 10.] |

3 | 0.85 | 172.72538867068536 | [−7.86179693 10.] |

4 | 0.825 | 173.57247234463873 | [−7.90035293 10.] |

5 | 0.8 | 173.648669201639 | [−7.90382112 10.] |

6 | 0.775 | 173.65343241781065 | [−7.90403793 10.] |

7 | 0.75 | 173.65364285853295 | [−7.9040475 10.] |

8 | 0.725 | 173.65364297446501 | [−7.90404751 10.] |

9 | 0.7 | 173.65364297446501 | [−7.90404751 10.] |

10 | 0.675 | 173.65364297595357 | [−7.90404751 10.] |

11 | 0.65 | 173.65364297596602 | [−7.90404751 10.] |

12 | 0.625 | 173.65364297596608 | [−7.90404751 10.] |

13 | 0.6 | 173.65364297596608 | [−7.90404751 10.] |

14 | 0.575 | 173.65364297596608 | [−7.90404751 10.] |

15 | 0.55 | 173.65364297596608 | [−7.90404751 10.] |

16 | 0.525 | 173.65364297596608 | [−7.90404751 10.] |

Iteration | Inertia Coefficient | $\mathbf{Objective}\mathbf{Function}\mathbf{Value}\left(\mathbf{k}{\mathbf{m}}^{2}\right)$ | ${\mathit{g}}_{\mathit{b}\mathit{e}\mathit{s}\mathit{t}}\mathbf{Position}(\mathbf{x},\mathbf{y})$ |
---|---|---|---|

1 | 0.55 | 161.46087064166917 | [9.89232861 −7.42906912] |

2 | 0.55 | 161.4815220862256 | [9.89142012 −7.43070174] |

3 | 0.55 | 161.48153790723256 | [9.89141942 −7.43070299] |

4 | 0.55 | 161.48153791935488 | [9.89141942 −7.43070299] |

5 | 0.55 | 161.48153791936414 | [9.89141942 −7.43070299] |

6 | 0.55 | 161.48153791936414 | [9.89141942 −7.43070299] |

7 | 0.55 | 161.48153791936414 | [9.89141942 −7.43070299] |

8 | 0.55 | 161.48153791936414 | [9.89141942 −7.43070299] |

9 | 0.55 | 161.48153791936414 | [9.89141942 −7.43070299] |

Iteration | $\mathbf{Objective}\mathbf{Function}\mathbf{Value}\left(\mathbf{k}{\mathbf{m}}^{2}\right)$ |
---|---|

1 | 102.31 |

2 | 102.31 |

3 | 102.31 |

4 | 102.31 |

5 | 102.72 |

6 | 102.72 |

7 | 105.09 |

8 | 105.09 |

9 | 105.09 |

10 | 110.69 |

11 | 112.86 |

12 | 112.86 |

13 | 112.86 |

14 | 112.86 |

15 | 113.55 |

16 | 113.55 |

17 | 117.61 |

18 | 117.61 |

19 | 118.73 |

20 | 120.53 |

## References

- Sitek, P.; Wikarek, J. Capacitated vehicle routing problem with pick-up and alternative delivery (CVRPPAD): Model and implementation using hybrid approach. Ann. Oper. Res.
**2019**, 273, 257–277. [Google Scholar] [CrossRef] [Green Version] - Sitek, P. A Hybrid Approach to the Two-Echelon Capacitated Vehicle Routing Problem (2E-CVRP). In Advances in Intelligent Systems and Computing; Springer Science and Business Media LLC: Turin, Italy, 2014; Volume 267, pp. 251–263. [Google Scholar]
- Nielsen, I.E.; Dang, Q.-V.; Bocewicz, G.; Banaszak, Z. A methodology for implementation of mobile robot in adaptive manufacturing environments. J. Intell. Manuf.
**2015**, 28, 1171–1188. [Google Scholar] [CrossRef] - Yakıcı, E. Solving location and routing problem for UAVs. Comput. Ind. Eng.
**2016**, 102, 294–301. [Google Scholar] [CrossRef] - Bolton, G.E.; Katok, E. Learning by doing in the newsvendor problem: A laboratory investigation of the role of experience and feedback. Manuf. Serv. Oper. Manag.
**2008**, 10, 519–538. [Google Scholar] [CrossRef] [Green Version] - Avellar, G.S.C.; Pereira, G.A.S.; Pimenta, L.C.D.A.; Iscold, P. Multi-UAV routing for area coverage and remote sensing with minimum time. Sensors
**2015**, 15, 27783–27803. [Google Scholar] [CrossRef] [Green Version] - Khosiawan, Y.; Nielsen, I. A system of UAV application in indoor environment. Prod. Manuf. Res.
**2016**, 4, 2–22. [Google Scholar] [CrossRef] [Green Version] - Montemerlo, M.; Becker, J.; Bhat, S.; Dahlkamp, H.; Dolgov, D.; Ettinger, S.; Haehnel, D.; Hilden, T.; Hoffmann, G.; Huhnke, B.; et al. Junior: The stanford entry in the urban challenge. In The DARPA Urban Challenge; Springer: Berlin/Heidelberg, Germany, 2009; Volume 56, pp. 91–123. [Google Scholar] [CrossRef] [Green Version]
- Khosiawan, Y.; Park, Y.; Moon, I.; Nilakantan, J.M.; Nielsen, I. Task scheduling system for UAV operations in indoor environment. Neural Comput. Appl.
**2018**, 31, 5431–5459. [Google Scholar] [CrossRef] [Green Version] - Zhang, M.; Su, C.; Liu, Y.; Hu, M.; Zhu, Y. Unmanned aerial vehicle route planning in the presence of a threat environment based on a virtual globe platform. ISPRS Int. J. Geo Inf.
**2016**, 5, 184. [Google Scholar] [CrossRef] [Green Version] - Xiang, J.; Liu, Y.; Luo, Z. Flight safety measurements of UAVs in congested airspace. Chin. J. Aeronaut.
**2016**, 29, 1355–1366. [Google Scholar] [CrossRef] [Green Version] - Khosiawan, Y.; Khalfay, A.; Nielsen, I.E. Scheduling unmanned aerial vehicle and automated guided vehicle operations in an indoor manufacturing environment using differential evolution-fused particle swarm optimization. Int. J. Adv. Robot. Syst.
**2018**, 15, 172988141775414. [Google Scholar] [CrossRef] - Krishnanand, K.; Ghose, D. Glowworm swarm based optimization algorithm for multimodal functions with collective robotics applications. Multiagent Grid Syst.
**2006**, 2, 209–222. [Google Scholar] [CrossRef] [Green Version] - Kashef, S.; Nezamabadi-Pour, H. An advanced ACO algorithm for feature subset selection. Neurocomputing
**2015**, 147, 271–279. [Google Scholar] [CrossRef] - Zargham, M.; Ribeiro, A.; Ozdaglar, A.; Jadbabaie, A. Accelerated dual descent for network flow optimization. IEEE Trans. Autom. Control
**2013**, 59, 905–920. [Google Scholar] [CrossRef] - Mirjalili, S. Genetic algorithm. In Evolutionary Algorithms and Neural Networks; Springer: Berlin/Heidelberg, Germany, 2019; pp. 43–55. [Google Scholar]
- Meng, Z.; Pan, J.-S.; Xu, H. QUasi-Affine TRansformation Evolutionary (QUATRE) algorithm: A cooperative swarm based algorithm for global optimization. Knowl. Based Syst.
**2016**, 109, 104–121. [Google Scholar] [CrossRef] - Frazzoli, E.; Bullo, F. Decentralized algorithms for vehicle routing in a stochastic time-varying environment. In Proceedings of the 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601), Nassau, Bahamas, 14–17 December 2004; Volume 4, pp. 3357–3363. [Google Scholar]
- Sundar, K.; Venkatachalam, S.; Rathinam, S. Analysis of mixed-integer linear programming formulations for a fuel-constrained multiple vehicle routing problem. Unmanned Syst.
**2017**, 5, 197–207. [Google Scholar] [CrossRef] - Shi, W.; Li, J.; Xu, W.; Zhou, H.; Zhang, N.; Zhang, S.; Shen, X. Multiple drone-cell deployment analyses and optimization in drone assisted radio access networks. IEEE Access
**2018**, 6, 12518–12529. [Google Scholar] [CrossRef] - He, X.; Yu, W.; Xu, H.; Lin, J.; Yang, X.; Lu, C.; Fu, X. Towards 3D deployment of UAV base stations in uneven terrain. In Proceedings of the 2018 27th International Conference on Computer Communication and Networks (ICCCN), Hangzhou, China, 30 July–2 August 2018; pp. 1–9. [Google Scholar]
- Feng, Y.; Zhang, R.-Q.; Jia, G. Vehicle routing problems with fuel consumption and stochastic travel speeds. Math. Probl. Eng.
**2017**, 2017, 1–16. [Google Scholar] [CrossRef] - Kinney, G.W.; Hill, R.R.; Moore, J.T. Devising a quick-running heuristic for an unmanned aerial vehicle (UAV) routing system. J. Oper. Res. Soc.
**2005**, 56, 776–786. [Google Scholar] [CrossRef] - Santos, R.M.; Orozco, J.; Ochoa, S.F.; Meseguer, R.; Mosse, D. Providing real-time message delivery on opportunistic networks. IEEE Access
**2018**, 6, 40696–40712. [Google Scholar] [CrossRef] - Tang, B.; Fang, Q.; Zhu, Z.; Ma, W. Effective 2D route planning of UAV based on improved ant colony algorithm. Xibei Gongye Daxue Xuebao. J. Northwest. Polytech. Univ.
**2013**, 31, 683–688. [Google Scholar] - Vickers, N.J. Animal Communication: When I’m Calling You, Will You Answer Too? Curr. Biol.
**2017**, 27, R713–R715. [Google Scholar] [CrossRef] [PubMed] - Alyassi, R.; Khonji, M.; Chau, S.C.-K.; Elbassioni, K.; Tseng, C.-M.; Karapetyan, A. Autonomous recharging and flight mission planning for battery-operated autonomous drones. arXiv
**2017**, arXiv:1703.10049. [Google Scholar] - Dorling, K.; Heinrichs, J.; Messier, G.G.; Magierowski, S. Vehicle routing problems for drone delivery. IEEE Trans. Syst. Man Cybern. Syst.
**2017**, 47, 70–85. [Google Scholar] [CrossRef] [Green Version] - Guerriero, F.; Surace, R.; Loscrí, V.; Natalizio, E. A multi-objective approach for unmanned aerial vehicle routing problem with soft time windows constraints. Appl. Math. Model.
**2014**, 38, 839–852. [Google Scholar] [CrossRef] - Habib, D.; Jamal, H.; Khan, S.A. Employing multiple unmanned aerial vehicles for Co-operative path planning. Int. J. Adv. Robot. Syst.
**2013**, 10, 235. [Google Scholar] [CrossRef] - Wu, J.; Zhang, D.; Pei, D. Autonomous route planning for UAV when threats are uncertain. In Proceedings of the 2014 IEEE Chinese Guidance, Navigation and Control Conference, Yantai, China, 8–10 August 2014; pp. 19–22. [Google Scholar]
- Micheletto, M.; Petrucci, V.; Santos, R.; Orozco, J.; Mosse, D.; Ochoa, S.F.; Meseguer, R. Flying real-time network to coordinate disaster relief activities in urban areas. Sensors
**2018**, 18, 1662. [Google Scholar] [CrossRef] [Green Version] - Zhang, J.; Jia, L.; Niu, S.; Zhang, F.; Tong, L.; Zhou, X. A space-time network-based modeling framework for dynamic unmanned aerial vehicle routing in traffic incident monitoring applications. Sensors
**2015**, 15, 13874–13898. [Google Scholar] [CrossRef] [Green Version] - Abu-Mostafa, Y.S. Neural networks and learning. In Conference Series-Institute of Physics; IOP Publishing Ltd.: Bristol, England, 1992; Volume 127, p. 7. [Google Scholar]
- Joo, H.; Hwang, H.-Y. Surrogate aerodynamic model for initial sizing of solar high-altitude long-endurance UAV. J. Aerosp. Eng.
**2017**, 30, 04017064. [Google Scholar] [CrossRef] - Hasanova, N. A Comparative study of particle swarm optimization and genetic algorithm. Qubahan Acad. J.
**2020**, 1, 33–45. [Google Scholar] [CrossRef] - Thibbotuwawa, A.; Nielsen, P.; Zbigniew, B.; Bocewicz, G. Energy Consumption in Unmanned Aerial Vehicles: A Review of Energy Consumption Models and Their Relation to the UAV Routing. In Advances in Intelligent Systems and Computing; Springer: Berlin/Heidelberg, Germany, 2018; Volume 853, pp. 173–184. [Google Scholar]
- Pedley, T.J. The simple science of flight: From insects to jumbo jets.henk tennekes. Q. Rev. Biol.
**1998**, 73, 343. [Google Scholar] [CrossRef] - National Academies of Sciences and Medicine, E. Commercial Aircraft Propulsion and Energy Systems Research. In Commercial Aircraft Propulsion and Energy Systems Research: Reducing Global Carbon Emissions; National Academies Press: Washington, DC, USA, 2016. [Google Scholar] [CrossRef]
- Farokhi, S. Future Propulsion Systems and Energy Sources in Sustainable Aviation. In Future Propulsion Systems and Energy Sources in Sustainable Aviation; John Wiley & Sons, Ltd.: Hoboken, NJ, USA, 2019. [Google Scholar] [CrossRef]
- Greitzer, E.M. 16. Unified: Thermodynamics and Propulsion Prof. ZS Spakovszky (2008). 2017. Available online: https://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/notes.html (accessed on 1 January 2022).
- Pagliaroli, T.; Camussi, R.; Candeloro, P.; Giannini, O.; Bella, G.; Panciroli, R. Aeroacoustic study of small scale rotors for mini drone propulsion: Serrated trailing edge effect. In Proceedings of the 2018 AIAA/CEAS Aeroacoustics Conference, Atlanta, GA, USA, 25–29 June 2018; American Institute of Aeronautics and Astronautics: Atlanta, GA, USA, 2018; p. 3449. [Google Scholar]
- Kroon, R. Mechanics and thermodynamics of propulsion. J. Frankl. Inst.
**1965**, 280, 454–455. [Google Scholar] [CrossRef] - Thibbotuwawa, A.; Nielsen, P.; Bocewicz, G.; Banaszak, Z. UAVs Fleet Mission planning subject to weather fore-cast and energy consumption constraints. In Conference on Automation; Springer: Cham, Switzerland, 2019; pp. 104–114. [Google Scholar]
- Nigam, N.; Bieniawski, S.; Kroo, I.; Vian, J. Control of Multiple UAVs for persistent surveillance: Algorithm and flight test results. IEEE Trans. Control Syst. Technol.
**2011**, 20, 1236–1251. [Google Scholar] [CrossRef] - Kunz, P.J. Aerodynamics and Design for Ultra-Low Reynolds Number Flight (Issue June); Stanford University: Stanford, CA, USA, 2003. [Google Scholar]
- Thibbotuwawa, A.; Nielsen, P.; Zbigniew, B.; Bocewicz, G. Factors affecting energy consumption of unmanned aerial vehicles: An analysis of how energy consumption changes in relation to UAV routing. In Proceedings of the International Conference on Information Systems Architecture and Technology, Wrocław, Poland, 15–17 September 2018; Springer: Cham, Switzerland; pp. 228–238. [Google Scholar]
- Sugimoto, A. The effectiveness of feedback on Japanese language presentation. Int. J. Hum. Cult. Stud.
**2019**, 2019, 38–42. [Google Scholar] [CrossRef] - Aloyce, O. Cost-Benefit Analysis of Wind Turbines Installation and Use in Dodoma Municipality; The University of Dodoma: Dodoma, Tanzania, 2016. [Google Scholar]
- Thibbotuwawa, A.; Bocewicz, G.; Nielsen, P.; Zbigniew, B. Planning deliveries with UAV routing under weather forecast and energy consumption constraints. IFAC-PapersOnLine
**2019**, 52, 820–825. [Google Scholar] [CrossRef] - Thibbotuwawa, A.; Bocewicz, G.; Nielsen, P.; Banaszak, Z. UAV Mission planning subject to weather forecast constraints. In Advances in Intelligent Systems and Computing; Springer: Berlin/Heidelberg, Germany, 2019; Volume 1004, pp. 65–76. [Google Scholar]

**Figure 8.**Contour plot representation of the objective function value in a specified boundary within the defined upper and lower bounds.

**Figure 11.**Particles convergence at the ${g}_{best}$ position within the upper and lower bound in 3D representation.

Algorithms | GSO | ACO | PSO | GA |
---|---|---|---|---|

Year | 2005 | 1992 | 1995 | 1975 |

Author | K.N. Krishnanand and Debasish Ghose | Marco Dorigo | James Kennedy & Russell Eberhart | John Holland |

Optimisation | Meta Heuristic Optimisation | Metaheuristic Optimisation | Stochastic Optimisation | Discrete Optimisation |

Purpose | Finding the local finest solution | Finding the shortest path | Reaching target with minimal duration | Locating the best among the rest. |

Advantages | Ability to solve multi-model optimisation and nonlinear problems. | Rapid selection of good solutions, applicable in a dynamic environment, resolve travelling salesman problems effectively. | Applicable for scientific and engineering research. There is no mutation calculation and overlapping. Search is based on the speed of particles. | Efficiently investigate and solve large combinatorial problems. It is faster than “brute force” exhaustive searches. |

Disadvantages | Weakness in locating global optimal solutions, low calculation accuracy, lower speed to converge. | The local optimum issue, lower convergence speed, and stagnation. | Local optimum and low convergence speed. | Computationally expensive, time-consuming and different in design objective function. |

Genetic Algorithm | PSO | |
---|---|---|

Influence of population size on solution time | Exponential | Linear |

Accuracy | Requires a large number of variables and constraints to produce an optimal solution | Always produces optimal results |

Number of iterations | Requires more iterations | Requires fewer iterations |

Require ranking of solutions | Yes | No |

Additional techniques required | Additional techniques required to reach an optimal solution | None |

Continuity of search space | Low | High |

Ability to reach a good solution without local search | Low | High |

Influence of best solution on population | Medium | Most |

Average fitness cannot become worse | False | False |

Parameters | Symbol | Value | Units |
---|---|---|---|

Maximum Elevation of the drones | ${h}_{max}$ | 121.97 | $\mathrm{m}$ |

Elevation of the drones in the solution | $h$ | 120 | $\mathrm{m}$ |

Total number of drones | $n$ | 12 | - |

Drone field of view of X | $Fo{V}_{x}$ | 83.97 | $\mathrm{deg}$ |

Drone field of view of Y | $Fo{V}_{y}$ | 61.93 | $\mathrm{deg}$ |

Area Coverage | $A$ | 146.04 | ${\mathrm{km}}^{2}$ |

Number of Drones | Area Coverage (km^{2}) |
---|---|

4 | 57.52 |

6 | 69.63 |

8 | 59.00 |

10 | 112.79 |

12 | 146.04 |

Parameters | Symbol | Value |
---|---|---|

Population size | num_of_particles | 12 |

Maximum numbers of iterations | $ma{x}_{Iter}$ | 100 |

Inertia weight maximum | ${w}_{max}$ | 0.9 |

Inertia weight minimum | ${w}_{min}$ | 0.4 |

Inertia constant weight | $w$ | 0.55 |

Cognitive weight | ${c}_{1}$ | 1 |

Social weight | ${c}_{2}$ | 2 |

Number of trials | - | 20 |

Upper bound | $ub$ | 10 |

Lower bound | $lb$ | −10 |

Minimum velocity | ${v}_{min}$ | $-4\mathrm{m}/\mathrm{s}$ |

Maximum velocity | ${v}_{max}$ | $20\mathrm{m}/\mathrm{s}$ |

Height (m) | $\mathbf{Area}\mathbf{Coverage}\left(\mathbf{k}{\mathbf{m}}^{2}\right)$ |
---|---|

5 | 0.38142738731860704 |

20 | 6.102838197097713 |

40 | 20.430856111522864 |

60 | 38.22438299912847 |

80 | 78.38570877418226 |

100 | 119.63576552278626 |

120 | 182.6190839211001 |

Parameters | Symbol | Value | Units |
---|---|---|---|

Total weight of the drone (weight of the device + weight of camera) ** No payload weight considered as the drone is not expected to deliver any relief ** → Assumption | $W$ | 17.06 | $\mathrm{kg}$ |

The density of the air | $D$ | 0.7 | $\mathrm{kg}/{\mathrm{m}}^{3}$ |

Total number of drones | $n$ | 12 | - |

Projected frontal area | $A$ | 0.827 | ${\mathrm{m}}^{2}$ |

Aerodynamic drag coefficient of drone | ${\mathrm{drag}}_{\mathrm{coefficient}}$ | 0.004 | - |

The power needed to overcome the drag | ${\mathrm{P}}_{\mathrm{drag}}$ | - | $Watt$ |

The power needed to lift | ${\mathrm{P}}_{\mathrm{lift}}$ | - | $Watt$ |

Width of drone | $b$ | 0.5 | $\mathrm{m}$ |

Total power consumed (Power needed to overcome the drag + Power required to lift the drone) | ${P}_{total}$ | - | $Watt$ |

$\mathbf{Velocity}(\mathbf{m}/\mathbf{s})$ | $\mathbf{Power}\mathbf{Consumed}\left(\mathit{W}\right)$ | $\mathbf{Drag}\mathbf{Power}\left(\mathit{W}\right)$ | $\mathbf{Lift}\mathbf{Power}\left(\mathit{W}\right)$ |
---|---|---|---|

−4 | −4990.208047542857 | −0.07409919999999999 | −415.7765714285714 |

−3 | −6652.800270057143 | −0.03126059999999999 | −554.368761904762 |

−2 | −9978.748863085713 | −0.009262399999999999 | −831.5531428571428 |

−1 | −199,57.28932217143 | −0.0011577999999999998 | −1663.1062857142856 |

0 | 0.0 | 0.00 | 0 |

1 | 19,957.28932217143 | 0.0011577999999999998 | 1663.1062857142856 |

2 | 9978.748863085713 | 0.009262399999999999 | 831.5531428571428 |

3 | 6652.800270057143 | 0.03126059999999999 | 554.368761904762 |

4 | 4990.208047542857 | 0.07409919999999999 | 415.7765714285714 |

5 | 3993.191785714285 | 0.144725 | 332.62125714285713 |

6 | 3329.213589028572 | 0.25008479999999994 | 277.184380952381 |

7 | 2855.8048517387756 | 0.39712539999999996 | 237.58661224489796 |

8 | 2501.7729517714283 | 0.5927935999999999 | 207.8882857142857 |

9 | 2227.6034820190475 | 0.8440361999999999 | 184.7895873015873 |

10 | 2009.6211428571428 | 1.1578 | 166.31062857142857 |

11 | 1832.7901478337662 | 1.5410317999999998 | 151.1914805194805 |

12 | 1687.114426514286 | 2.0006783999999995 | 138.5921904761905 |

13 | 1565.6992721670326 | 2.5436865999999996 | 127.93125274725274 |

14 | 1463.6437118693877 | 3.1770031999999997 | 118.79330612244898 |

15 | 1377.3759285714284 | 3.9075749999999996 | 110.87375238095237 |

16 | 1304.2378998857143 | 4.742348799999999 | 103.94414285714285 |

17 | 1242.2166349512604 | 5.6882714 | 97.82978151260504 |

18 | 1189.7649990095238 | 6.752289599999999 | 92.39479365079364 |

19 | 1145.6791196932331 | 7.941350199999999 | 87.53190977443609 |

20 | 1109.0125714285714 | 9.2624 | 83.15531428571428 |

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## Share and Cite

**MDPI and ACS Style**

Munawar, H.S.; Hammad, A.W.A.; Waller, S.T.
Disaster Region Coverage Using Drones: Maximum Area Coverage and Minimum Resource Utilisation. *Drones* **2022**, *6*, 96.
https://doi.org/10.3390/drones6040096

**AMA Style**

Munawar HS, Hammad AWA, Waller ST.
Disaster Region Coverage Using Drones: Maximum Area Coverage and Minimum Resource Utilisation. *Drones*. 2022; 6(4):96.
https://doi.org/10.3390/drones6040096

**Chicago/Turabian Style**

Munawar, Hafiz Suliman, Ahmed W.A. Hammad, and S. Travis Waller.
2022. "Disaster Region Coverage Using Drones: Maximum Area Coverage and Minimum Resource Utilisation" *Drones* 6, no. 4: 96.
https://doi.org/10.3390/drones6040096