Submit to this Journal Review for this Journal Propose a Special Issue

Article Menu

Share Help Cite Discuss in SciProfiles

Open AccessArticle

Peer-Review Record

A Molecular Force Field-Based Optimal Deployment Algorithm for UAV Swarm Coverage Maximization in Mobile Wireless Sensor Network

Processes 2020, 8(3), 369; https://doi.org/10.3390/pr8030369

by Xi Wang

, Guan-zheng Tan^*, Fan-Lei Lu, Jian Zhao and Yu-si Dai

Reviewer 1: Anonymous

Reviewer 2: Anonymous

Reviewer 3: Anonymous

Processes 2020, 8(3), 369; https://doi.org/10.3390/pr8030369

Submission received: 13 February 2020 / Revised: 15 March 2020 / Accepted: 16 March 2020 / Published: 22 March 2020

(This article belongs to the Special Issue Active Flow Control Processes with Machine Learning and the Internet of Things)

Round 1

Reviewer 1 Report

In this manuscript, the authors treat optimization of UAV positions for a mobile wireless sensor network. The scheme proposed here seems to be promising, showing some signs in the simulation results, but, in the reviewer’s opinion, the manuscript does not include sufficient evidence for validity of the proposed scheme. Also, the description plot through the manuscript should be enhanced by revising sequences of descriptions. The summary of the comments from the reviewer is listed below.

(1) In Introduction (section 1), there is no description saying what is the purpose of this manuscript; only the background of this study is described. The part in section 3 from Lines from 185 to 220 is suitable for insertion at the end of section 1.

(2) The reviewer requests the authors to revise Subsections 4.2 and 4.3. The manuscript includes only small parts of the simulation results after applying the algorisms proposed here. Most powerful evidences will be specific evolutions of spatial positions with coverage enhancement in Figure 9. Could you show specific situations, data, and spatial positions etc. at several iteration steps (for instance, iteration #1, iteration #5, iteration #13, iteration #29, and iteration #49) for each Test?

(3) On basics of paper descriptions

(a) Subjective expressions should be removed from scientific papers. For instance, the reviewer finds the following words in the manuscript, and they should be removed from your future revised manuscript: Line 9: "very important" Line 11: "great"

(b)Figure and table captions should include sufficient information about the corresponding figures and tables. The following captions should be revised: Figure 6, Figure 7, Figure 8, Table 1, and Table 2.

(c) In conclusion, “future work” (lines 450-452) may not be included. At the end of section 3, the author can mention some of them.

Author Response

List of Responses

Dear Editors and Reviewers,

Thank you for your letter and for the reviewers’ comments concerning our manuscript entitled "A molecular force field-based optimal deployment algorithm for UAV swarm coverage maximization in mobile wireless sensor network" (ID: processes-731765). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have studied comments carefully and have made a correction which we hope meet with approval. Revised portion are marked in red in the paper. The main corrections in the paper and the response to the reviewer’s comments are as following. As the number of figures has been changed, the figure number in the response are based on the revised version.

Responds to the reviewer’s comments:

Reviewer #1:

Comment 1#: In Introduction (section 1), there is no description saying what is the purpose of this manuscript; only the background of this study is described. The part in section 3 from Lines from 185 to 220 is suitable for insertion at the end of section 1.

Response: Based on the reviewer's suggestion, the introduction has been rewritten.

Introduction

A mobile wireless sensor network (MWSN) is a wireless network formed by a large number of mobile sensor nodes deployed in a designated area. Over recent decades, MWSNs have evolved rapidly and many new applications have emerged, including target search and detection, disaster rescue, environmental monitoring, indoor positioning, and so on. However, for most situations, the random deployment of mobile sensors cannot guarantee the required coverage ratio and may cause overlapping coverage or coverage holes. So, how to deploy the mobile sensors is a fundamental problem in MWSN [[1]], as it greatly influences the performance of the coverage of the network. Usually, it is difficult to manually deploy the MWSN in special environments, such as unknown, hostile, or disaster areas [[2]]. To solve this problem, it is possible to use a multi-rotor unmanned aerial vehicle (UAV) swarm to carry the sensors and build the network autonomously. The reason for choosing multi-rotor UAVs (abbreviated as UAVs below) is that they have some key characteristics, such as high flexibility, high speed, airborne hovering ability, and being unrestricted by terrain or obstacles. A typical application is in a military action or disaster situation, where the existing communication facilities have been destroyed. The UAVs can carry the communication sensors by hovering in the air, automatically building an MWSN to provide communication services. Therefore, designing a deployment algorithm to deploy the UAVs and cooperatively form an MWSN with maximum coverage ratio is a key issue in our study.

Recently, many studies on co-operative work in UAV swarms have been carried out by scholars, as the performance given by a single UAV is limited. For example, in [[3]], a UAV swarm is used to build a queuing network. In [[4]], to find the optimal position of each UAV in areas with large obstacles, a method using the PSO algorithm was proposed. In [[5]], to maximize the detection area formed by a swarm of UAVs, a combination of an Ant Colony-based algorithm and chaotic dynamics (CACOC) was proposed. In [[6]], a UAV swarm was used for target tracking. In [[7]], optimal deployment and movement schemes for a UAV swarm were studied.

At present, many intelligent algorithms have been used to solve the MWSN coverage problem [[8]], such as those presented in [[9]][[10]], in which, based on the multi-objective genetic algorithm (MOGA), the coverage area was maximized and the movement distance was optimized. In [[11]] and [[12]], in order to increase the coverage ratio and save energy consumption, the multi-objective evolutionary algorithm (MOEA) and the multi-objective immune algorithm (MOIA) were proposed, respectively. Moreover, in [[13]], a coverage model considering the maximum coverage ratio and minimum redundancy were given and an optimization strategy based on the quantum-inspired cultural algorithm was proposed. In [[14]], EDA-I and EDA-II were proposed to achieve a high sensing coverage ratio in the monitored field. In [[15]], a virtual force-based deployment algorithm—the Virtual Force Algorithm (VFA)—was proposed, which was then improved in [[16]][[17]][[18]]. The Voronoi diagram is a famous computational geometric structure [[19]], which has been widely used for sensor deployment problems [[20]][[21]][[22]][[23]][[24]][[25]]. Guiling Wang et al. [[26]] designed and evaluated distributed self-deployment protocols for mobile sensors based on the Voronoi diagram; three algorithms (VECtor, VORonoi, and Minimax) have been proposed to optimize this problem. In [[27]][[28]], the centroid (geometric center) was introduced to improve the original Voronoi deployment algorithm. Combining particle swarm optimization (PSO) and the Voronoi diagram, the PSO_Voronoi and WSNPSOcon algorithms have been proposed in [[29]][[30]]. In [[31]] and [[32]], the proposed movement strategies were based on the distances of each sensor and the points inside its Voronoi polygon from the edges or vertices of the polygon. In [[33]], based on a rigorous mathematical analysis, a Delaunay-based co-ordinate-free mechanism (DECM) was proposed for full coverage. In [[34]], a distributed greedy algorithm was proposed by Sung and Yang, which can improve the effective field coverage of directional sensor networks. In order to save energy and extend the lifetime, the authors proposed the Centralized Immune-Voronoi deployment Algorithm (CIVA) [[35]] to maximize coverage. In [[36]], a gradient-based non-linear optimization approach was applied to find a target point for each sensor, following which the local coverage increases as much as possible when the sensor moves to this point. Mahboubi et al. proposed a set of distributed deployment algorithms based on the distances of each sensor and the points inside its co-ordinate Voronoi polygon from the edges or vertices of the polygon [[37]][[38]]. In [[39]], the authors modeled the sensor deployment problem as a constrained source coding problem and designed Lloyd-like algorithms to provide a trade-off between sensing coverage and energy consumption.

In this study, we found the VFA-based algorithm to be suitable for solving the coverage problem in our application scenario, as it is simple and efficient, and does not require a centralized computing mechanism during implementation as long as the UAVs can perform distributed computing in the same connected MWSN. However, there are still some shortcomings in traditional VFA-based algorithms:

(1) In the traditional VFA-based algorithm, the magnitude of the virtual force is only inversely proportional to the distance between the UAVs. However, we found that the distance and the virtual force should not be in a linear relationship. The closer the distance between each pair of UAVs, the greater the impact will be. Thus, we should give a higher weight to the closer UAVs, such that the interference of some of the farther UAVs can be filtered out.

(2) The final coverage result is affected by the initialization result in a single test as, for most traditional VFA-based deployment algorithms, the initialization is random; the only requirement is that the UAVs must be deployed in the working area. In this case, the UAVs in some areas may be significantly denser or sparser than those in other areas due to the randomness. If the random initialization is applied to the convex polygon coverage, it may cause slower convergence or even become stuck in a local optimum. Only by repeating the experiments (re-initializing for each experiment) to obtain the optimal deployment scheme, can the robustness of the traditional VFA-based algorithms be embodied.

(3) Most traditional VFA-based algorithms can only be used to cover a rectangular area; some even do not have a boundary to constrain the position of the UAVs, but just maximize the coverage area of the UAVs.

In this paper, to overcome the shortcomings of the traditional VFA-based deployment algorithms, a deployment algorithm for a UAV swarm is proposed, which can maximize the ground coverage of an MWSN formed by the UAVs in a designated area. Its main feature is the introduction of the molecular force field to make the force model more accurate. We also designed two initialization methods, which can make the initial distribution of the nodes more uniform, such that the probability of falling into a local optimum and the computational complexity are reduced, while the convergence rate is improved. In addition, convex polygon boundary constraints are added.

Comment 2#: The reviewer requests the authors to revise Subsections 4.2 and 4.3. The manuscript includes only small parts of the simulation results after applying the algorisms proposed here. Most powerful evidences will be specific evolutions of spatial positions with coverage enhancement in Figure 9. Could you show specific situations, data, and spatial positions etc. at several iteration steps (for instance, iteration #1, iteration #5, iteration #13, iteration #29, and iteration #49) for each Test?

Response: More experimental data similar to Figure 9 have been added to section 4.

Section 4.1

The optimal deployment scheme of Test 3 (method 2) is shown in Figure 11, where the “*” symbols represent the initial positions of the UAVs, the “+” symbols represent the optimal positions of the UAVs, and the circles represent the covered area when the UAVs are at their optimal positions. We can observe that, for most UAVs, the distance between each pair of UAVs was near the ideal value (). The distribution of UAVs was close to the ideal deployment scheme, and the boundaries and vertices were basically covered.

(a) (b)

Figure 11: The optimal deployment scheme obtained by the proposed deployment algorithm, where method 2 (Test 3) was used to initialize the positions of the UAVs: (a) represents the position of the UAVs in iteration #1; (b) represents the position of the UAVs at iteration #17; (c) represents the position of the UAVs at iteration #34; and (d) represents the position of the UAVs at iteration #50.

Section 4.2

The relationship between the coverage ratio and the number of iterations of the proposed algorithm is shown in Figure 12, which corresponds to the above Tests (1–6). The two curves in the figures represent the results of the two rounds of the experiments where Cr 1 and Cr 2 were obtained, respectively.

(a) (b)

(e) (f)

Figure 12 The relationship between the coverage ratio and the number of iterations of the proposed algorithm in the six tests. Figures (a)–(f) represent Tests 1–6, respectively.

Section 4.3

From Table 2 and Figure 12 in section 4.2, we can observe that our proposed algorithm obviously surpassed the other three deployment algorithms in terms of coverage ratio, especially in a high-density environment, when the number of the UAVs approached or exceeded the ideal value. As for Test 1, because the number of used UAVs was too small, the coverage ratio was not improved by the proposed deployment algorithm; however, relying only on the initialization methods, an acceptable deployment scheme can also be obtained, whose coverage ratio is about the same as the other three algorithms. For Tests 2–6, with the help of the proposed molecular force field-based deployment algorithm, the coverage ratio increased after initialization. Comparing Cr 1 with Cr 2, it seems that Cr 1 converged faster, but it was selected after 20 rounds of experiments. Meanwhile, only one round was needed to obtain Cr 2, thus reducing the required computation.

Comment 3#: Subjective expressions should be removed from scientific papers. For instance, the reviewer finds the following words in the manuscript, and they should be removed from your future revised manuscript: Line 9: "very important" Line 11: "great"

Response: All the subjective expressions have been revised in our manuscript.

Comment 4#: Figure and table captions should include sufficient information about the corresponding figures and tables. The following captions should be revised: Figure 6, Figure 7, Figure 8, Table 1, and Table 2.

Response: The captions of the figures and tables have been checked and revised carefully.

Figure 6, Figure 7, and Figure 8 have been combined into Figure 8:

(a) Test 1 (b) Test 2 (c) Test 3

Figure 8: The initial position of UAVs obtained by three initialization methods: (a) is the result of random initialization; (b) and (c) are the results of the proposed initialization methods 1 and 2, respectively. The black “*” points represent the positions of the UAVs in the working area. The lines represent the dividing lines and boundaries.

Table 1: The simulation results of the best and avg coverage ratio of Tests 1–3.

Test	P (%)
Test	Initial	Best	Avg
1	76.51	97.15	94.47
2	84.78	97.81	96.67
3	88.82	97.16	-

Table 2: Comparison of the coverage ratio of the four deployment algorithms in six tests.

Test	Size	n (used)	n (ideal)	Coverage ratio (%)
Test	Size	n (used)	n (ideal)	PSO_Voronoi	WSNPSOcon	CIVA	Cr 1	Cr 2
1	50×50	10	21	58.36	57.96	60.24	56.97	59.83
2	50×50	20	21	94.23	93.34	93.55	95.17	94.75
3	50×50	30	21	98.80	98.64	97.37	100.00	100.00
4	100×100	60	86	77.62	73.56	78.59	83.48	81.74
5	100×100	80	86	88.13	81.66	88.94	97.66	96.68
6	100×100	100	86	92.70	84.90	92.47	99.87	99.91

Comment 5#: In conclusion, “future work” (lines 450-452) may not be included. At the end of section 3, the author can mention some of them.

Response: The future work part has been moved to the end of section 3.1.

However, the proposed strategy still has a shortcoming: the round function is used, so the number of the UAVs must be corrected after initialization. We will resolve this issue in future research.

References

[1]. Senouci, M. R.; Mellouk, A.; Asnoune, K.; Bouhidel, F. Y. Movement-Assisted Sensor Deployment Algorithms: A Survey and Taxonomy. IEEE Commun. Surv. Tutorials 2015, 17, 2493–2510, doi:10.1109/COMST.2015.2407954..

[2]. Mohamed, S. M.; Hamza, H. S.; Saroit, I. A. Coverage in mobile wireless sensor networks (M-WSN): A survey. Computer Communications, 2017, 110: 133-150.

[3]. Kirichek, R.; Paramonov, A.; Koucheryavy, A. Swarm of public unmanned aerial vehicles as a queuing network. In Communications in Computer and Information Science; 2016; Vol. 601, pp. 111–120.

[4]. Spanogianopoulos, S.; Zhang, Q.; Spurgeon, S. Fast Formation of Swarm of UAVs in Congested Urban Environment. IFAC-PapersOnLine 2017, 50, 8031–8036, doi:10.1016/j.ifacol.2017.08.1228.

[5]. Rosalie, M.; Dentier, J. E.; Danoy, G.; Bouvry, P.; Kannan, S.; Olivares-Mendez, M. A.; Voos, H. Area exploration with a swarm of UAVs combining deterministic chaotic ant colony mobility with position MPC. In 2017 International Conference on Unmanned Aircraft Systems, ICUAS 2017; 2017; pp. 1392–1397.

[6]. Brust, M. R.; Zurad, M.; Hentges, L.; Gomes, L.; Danoy, G.; Bouvry, P. Target tracking optimization of UAV swarms based on dual-pheromone clustering. In 2017 3rd IEEE International Conference on Cybernetics, CYBCONF 2017 - Proceedings; 2017.

[7]. Koyuncu E, Khodabakhsh R, Surya N, et al. Deployment and trajectory optimization for UAVs: A quantization theory approach//Wireless Communications and Networking Conference (WCNC), 2018 IEEE. IEEE, 2018: 1-6.

[8]. Zou, Y.; Chakrabarty, K. Sensor Deployment and Target Localization Based on Virtual Forces. Twenty-Second Annu. Jt. Conf. IEEE Comput. Commun. 2003, 2, 1293–1303, doi:10.1109/INFCOM.2003.1208965.

[9]. Qu, Y.; Georgakopoulos, S. V Relocation of wireless sensor network nodes using a genetic algorithm. In Wireless and Microwave Technology Conference (WAMICON), 2011 IEEE 12th Annual; IEEE, 2011; pp. 1–5.

[10]. Jia, J.; Chen, J.; Chang, G.; Wen, Y.; Song, J. Multi-objective optimization for coverage control in wireless sensor network with adjustable sensing radius. Comput. Math. with Appl. 2009, 57, 1767–1775, doi:10.1016/j.camwa.2008.10.037.

[11]. Jin, L.; Jia, J.; Sun, D. Node Distribution Optimization in Mobile Sensor Network Based on Multi-Objective Differential Evolution Algorithm. 2010 Fourth Int. Conf. Genet. Evol. Comput. 2010, 51–54, doi:10.1109/ICGEC.2010.21.

[12]. Abo-Zahhad, M.; Ahmed, S. M.; Sabor, N.; Sasaki, S. Coverage maximization in mobile Wireless Sensor Networks utilizing immune node deployment algorithm. In Canadian Conference on Electrical and Computer Engineering; 2014.

[13]. Guo, Y. N.; Liu, D.; Liu, Y.; Chen, M. The coverage optimization for wireless sensor networks based on quantum-inspired cultural algorithm. In Lecture Notes in Electrical Engineering; Springer, 2013; Vol. 254 LNEE, pp. 87–96.

[14]. Lin T Y, Santoso H A, Wu K R, et al. Enhanced deployment algorithms for heterogeneous directional mobile sensors in a bounded monitoring area. IEEE Transactions on Mobile Computing, 2017, 16(3): 744-758.

[15]. Zou, Y.; Chakrabarty, K. Sensor Deployment and Target Localization in Distributed Sensor Networks. ACM Trans. Embed. Comput. Syst. {(TECS)} 2004, 3, 61–91.

[16]. Loscrí, V.; Natalizio, E.; Mitton, N. Performance evaluation of novel distributed coverage techniques for swarms of flying robots. In IEEE Wireless Communications and Networking Conference, WCNC; 2014; pp. 3278–3283.

[17]. Sallam G, Baroudi U, Al-Shaboti M. Multi-Robot Deployment Using a Virtual Force Approach: Challenges and Guidelines. Electronics, 2016, 5(3): 34.

[18]. Wang X, Tan G, Liu X, et al. A Molecular Force-Based Deployment Algorithm for Flight Coverage Maximization of Multi-Rotor UAV. Journal of Intelligent & Robotic Systems, 2018: 1-16.

[19]. F. Aurenhammer , R. Klein , D.-T. Lee , R. Klein , Voronoi Diagrams and Delaunay Triangulations, World Scientific, 2013 .

[20]. Han, Y. H.; Kim, Y. H.; Kim, W.; Jeong, Y. S. An energy-efficient self-deployment with the centroid-directed virtual force in mobile sensor networks. Simulation 2012, 88, 1152–1165, doi:10.1177/0037549711411314.

[21]. Pavone, M.; Arsie, A.; Frazzoli, E.; Bullo, F. Distributed algorithms for environment partitioning in mobile robotic networks. IEEE Trans. Automat. Contr. 2011, 56, 1834–1848, doi:10.1109/TAC.2011.2112410.

[22]. Qu, Y. Wireless Sensor Network Deployment, 2013. FLORIDA International University,2013.

[23]. Qiu C, Shen H. A delaunay-based coordinate-free mechanism for full coverage in wireless sensor networks. IEEE Transactions on Parallel and Distributed Systems, 2014, 25(4): 828-839.

[24]. Sung T W, Yang C S. Voronoi-based coverage improvement approach for wireless directional sensor networks. Journal of Network and Computer Applications, 2014, 39: 202-213.

[25]. Bartolini N, Bongiovanni G, La Porta T, et al. Voronoi-based deployment of mobile sensors in the face of adversaries//Communications (ICC), 2014 IEEE International Conference on. IEEE, 2014: 532-537.

[26]. Wang, G.; Cao, G.; Porta, T. La Movement-assisted sensor deployment. In Proceedings - IEEE INFOCOM; 2004; Vol. 4, pp. 2469–2479

[27]. Lee, H. J.; Kim, Y. H.; Han, Y. H.; Park, C. Y. Centroid-based movement assisted sensor deployment schemes in wireless sensor networks. In IEEE Vehicular Technology Conference; 2009.

[28]. Fang, W.; Song, X.; Wu, X.; Sun, J.; Hu, M. Novel efficient deployment schemes for sensor coverage in mobile wireless sensor networks. Inf. Fusion 2018, 41, 25–36, doi:10.1016/j.inffus.2017.08.001.

[29]. Aziz, N. A. B. A.; Mohemmed, A. W.; Alias, M. Y. A wireless sensor network coverage optimization algorithm based on particle swarm optimization and Voronoi diagram. In 2009 International Conference on Networking, Sensing and Control; 2009; pp. 602–607.

[30]. Azlina, N.; Aziz, A. Wireless Sensor Networks Coverage-Energy Algorithms Based on Particle Swarm Optimization. Emirates J. Eng. Res. 2013, 18, 41–52.

[31]. Mahboubi, H.; Vaezi, M.; Labeau, F. Mobile Sensors Deployment Subject to Location Estimation Error. IEEE Trans. Veh. Technol. 2017, 66, 668–678, doi:10.1109/TVT.2016.2537403.

[32]. Bartolini, N.; Bongiovanni, G.; Porta, T. La; Silvestri, S.; Vincenti, F. Voronoi-based deployment of mobile sensors in the face of adversaries. In 2014 IEEE International Conference on Communications, ICC 2014; 2014; pp. 532–537.

[33]. Qiu, C.; Shen, H. A delaunay-based coordinate-free mechanism for full coverage in wireless sensor networks. IEEE Trans. Parallel Distrib. Syst. 2014, 25, 828–839, doi:10.1109/TPDS.2013.134.

[34]. Sung, T. W.; Yang, C. S. Voronoi-based coverage improvement approach for wireless directional sensor networks. J. Netw. Comput. Appl. 2014, 39, 202–213, doi:10.1016/j.jnca.2013.07.003.

[35]. Abo-Zahhad, M.; Sabor, N.; Sasaki, S.; Ahmed, S. M. A centralized immune-Voronoi deployment algorithm for coverage maximization and energy conservation in mobile wireless sensor networks. Inf. Fusion 2016, 30, 36–51, doi:10.1016/j.inffus.2015.11.005.

[36]. Habibi, J.; Mahboubi, H.; Aghdam, A. G. A gradient-based coverage optimization strategy for mobile sensor networks. IEEE Trans. Control Netw. Syst. 2017, 4, 477–488, doi:10.1109/TCNS.2016.2515370.

[37]. Mahboubi H, Moezzi K, Aghdam A G, et al. Distributed deployment algorithms for improved coverage in a network of wireless mobile sensors. IEEE Transactions on Industrial Informatics, 2014, 10(1): 163-174.

[38]. Mahboubi H, Vaezi M, Labeau F. Mobile Sensors Deployment Subject to Location Estimation Error. IEEE Trans. Vehicular Technology, 2017, 66(1): 668-678.

[39]. Guo J, Jafarkhani H. Movement-efficient sensor deployment in wireless sensor networks//2018 IEEE International Conference on Communications (ICC). IEEE, 2018: 1-6.

Author Response File: Author Response.docx

Reviewer 2 Report

Please carefully revise the level of English.

Line 89 onwards: please clarify what you mean by convex polygon. After having read the whole paper it seems it is the generic area to be covered, this should be clarified on page 3.

Apparently the optimal positioning of the UAVs is calculated online, please clarify (lines 103-122).

Please fully describe the steps used to get equations 2-3.

Line 141, is "positive infinity" actually correct?

Line 153 "... method needs to divide a triangle into equal areas" what is the reason for that?

I understand that R is fixed in this paper. But how should a designer determibe it, e.g. based on what?

Figure 1. It seems that the UAV are placed in the centre of each circle. But after the optimisation, Figure 11 shows "*" which I suppose are the UAVs. Please can you clarify this.

Author Response

List of Responses

Dear Editors and Reviewers,

Responds to the reviewer’s comments:

Reviewer #2:

Comment 1#: Please carefully revise the level of English.

Response: We have improved the level of English, and this manuscript has been polished by MDPI.

Comment 2#: Line 89 onwards: please clarify what you mean by convex polygon. After having read the whole paper it seems it is the generic area to be covered, this should be clarified on page 3.

Response: A convex polygon is defined as a polygon with all its interior angles less than 180°, this means that all the vertices of the polygon will point outwards, away from the interior of the shape, we have clarified the meaning of the convex polygon in the revised manuscript.

Definition 6. The working area is a convex polygon with M sides and area S. A convex polygon is defined as a polygon with all interior angles less than 180°; this means that all vertices of the polygon will point outwards, away from the interior of the shape. Its vertex coordinates are set as [(xv₁, yv₁), (xv₂, yv₂), …, (xv_M, yv_M)], which are sorted clockwise. The position information of the UAVs, which are defined as [(xu₁, yu₁), (xu₂, yu₂), …, (xu_n, yu_n)], can be exchanged through the MWSN.

Comment 3#: Apparently the optimal positioning of the UAVs is calculated online, please clarify (lines 103-122).

Response: Yes, the optimal position of the UAVs is calculated online, in this process, each UAV needs to obtain the location information of other UAVs through this MWSN. We have clarified it in the revised manuscript.

Definition 8. The working area information will be sent by the base. After the UAVs receive the working area information, a UAV can independently calculate its optimal position, based on the positions of other UAVs obtained through the MWSN and its sequence number. This process is calculated on-line and will be adjusted in real-time, according to situation changes. For example, if the working area changes or some UAVs malfunction, the UAVs can still obtain the required information through the MWSN and update the deployment scheme independently.

Comment 4#: Please fully describe the steps used to get equations 2-3.

Response: The description of the steps used to get equations 2-3 has been added to the revised manuscript. And Figure 3 has been modified to help understand.

At this time, the definition of S_s is the inscribed hexagon area in the coverage area of a sensor (i.e., the overlapping area has been removed), as shown in Equation 2 and Figure 3. Therefore, to calculate the average effective coverage area (S_r) of each UAV requires compensation for the wasted area; based on many experiments, the ratio of the compensation was set to 90%. Finally, S_r can be obtained by Equation 3:

,	(2)
.	(3)

Figure 3: The ideal deployment scheme when using equal circles to cover. where the center distance of each two circles is , and the definition of S_s is shown.

Comment 5#: Line 141, is "positive infinity" actually correct?

Response: Yes, it is correct. The function ceil is from the MATLAB.

The MATLAB function ceil indicates rounding upward (i.e., toward positive infinity):

Comment 6#: Line 153 "... method needs to divide a triangle into equal areas" what is the reason for that?

Response: The reason for divide a triangle into equal areas is: If the area of these divided areas are equal and only one UAV is deployed in each area, the position of each UAV is restricted to these areas, so that the distribution of UAVs in this triangle is more uniform, and the UAVs will not be distributed too densely or sparsely in some areas of this triangle. as shown in the figure below.

Comment 7#: I understand that R is fixed in this paper. But how should a designer determine it, e.g. based on what?

Response: First The designer needs to know the communication range (R_c) between the sensor and the user of the sensor he used. Then the flight altitude of UAVs is determined based on the R_c, the selection range of the flight altitude is [0, R_c]. Finally, the value of R can be determined by R_c and the flight altitude of the UAVs. as shown in Figure 2. Due to the different Rc of the various sensors, the corresponding flight altitude is also different. In order to simplify the calculation, the value of R will be directly assigned.

Figure 2 The schematic of the communication coverage area of a UAV on the ground.

Definition 2. When a UAV hovers in the air with a communication sensor, the communication range between the communication sensor and the users is denoted as R_c. The interior of the sphere with the UAV as the center and R_c as the radius will be considered the communication space. In this case, the hover altitude (h) should be lower than R_c, such that there will be an intersecting circular plane between this sphere and the ground, which is defined as the communication coverage area of the sensor on the ground, the radius of which is denoted by R. The communication sensor can provide communication services to users in this coverage area on the ground. It forms a right-angled triangle with the known R_c (hypotenuse) and hover altitude h (cathetus) and, thus, the value of R can be obtained by the Pythagorean theorem, as shown in Figure 2.

Comment 8#: Figure 1. It seems that the UAV are placed in the centre of each circle. But after the optimisation, Figure 11 shows "*" which I suppose are the UAVs. Please can you clarify this.

Response: Yes, the UAVs are placed in the center of each circle. For Figure 11, the “*” represent the initial positions, the “+” represent the optimal positions, and the circles represent the covered area when the UAVs at the optimal positions. The descriptions of it have been revised in the manuscript.

(a) (b)

Author Response File: Author Response.docx

Reviewer 3 Report

The submitted manuscript studies the problem of coverage maximization for UAV-enabled mobile wireless sensor networks. The introduction is not well written and suffers from lack of motivation. After going through the related work, it is still not clear for me why this work is important and what novelty it brings to the community. Furthermore, the assumptions and formulations used are too simplistic and important aspect of the problem is missing. To be more specific, the authors have not mentioned anything about the communication aspect of the problem. With considerations in mind, I am afraid that the submitted manuscript may not be suitable for publication. However, the authors are encouraged to resubmit after thoroughly revising their paper, resolving all the existing issues (please below for a detailed list of comments).

- The introduction is not well structured and there are some flaws. It seems that the introduction in its current form is more suitable to be titled “Related Work” rather than the “Introduction”, where a clear definition of the problem under study, objectives, motivation, and contribution(s) is needed. I suggest that the authors give it another try and write a thorough and insightful introduction section from scratch. Nevertheless, the authors have done a good job compiling the related work on the topic.

- Before presenting the problem formulation, the reader expects to see the system model, which is missing part in the submitted manuscript.

- The authors have used simplistic models. Given the fact the paper focuses on mobile wireless sensor networks (MWSN), the communication model is not clear.

- Can the authors explain what Fig. 5 illustrates?

- Some figure captions are not representative, e.g., Fig. 9.

- The authors are encouraged to revise their manuscript for many writing issues and grammatical mistakes.

Author Response

List of Responses

Dear Editors and Reviewers,

Responds to the reviewer’s comments:

Reviewer #3:

Comment 1#: The introduction is not well structured and there are some flaws. It seems that the introduction in its current form is more suitable to be titled “Related Work” rather than the “Introduction”, where a clear definition of the problem under study, objectives, motivation, and contribution(s) is needed. I suggest that the authors give it another try and write a thorough and insightful introduction section from scratch. Nevertheless, the authors have done a good job compiling the related work on the topic.

Response: Based on the reviewer's suggestion, the introduction has been rewritten.

Introduction

Comment 2#: Before presenting the problem formulation, the reader expects to see the system model, which is missing part in the submitted manuscript.

Response: The system has been added at the beginning of the section 2.

In this paper, we consider the communication coverage problem of the MWSN in the environment of a three-dimensional space, when the existing communications facilities are destroyed by the war or natural disaster. Our goal is to use lots of communication sensors to form the MWSN and covering a working area on the ground, meanwhile provide the communication services for the ground users, the communication sensors are carried by the hovering multi-rotor UAVs. What the proposed deployment algorithm needs to solve is how to optimally deploy these UAVs to maximize the coverage ratio of this working area. As shown in Figure 1.

Figure 1. The system model of the communication coverage problem of the MWSN. The black points represent the UAVs, and their communication coverage areas on the ground are the circles.

Comment 3#: The authors have used simplistic models. Given the fact the paper focuses on mobile wireless sensor networks (MWSN), the communication model is not clear.

Response: The describes of the communication model have been added to the section 2. And the models we used are the common models, which are widely used in the related works.

The coverage sensor model used in our study is the binary model, also known as the Boolean disk coverage sensor model, which is the most widely used sensor coverage model [9][11][29]. The communication model of the MWSN is defined as follows:

Definition 1. Each sensor can communicate with other sensors through single or multiple hops in the same connected MWSN.

Definition 3. To guarantee network connectivity, the communication range between the sensors is set by at least 2R_c.

Definition 4. All sensors in the MWSN are treated as nodes. There is no obstacle in the working area and collision avoidance is not considered.

Comment 4#: Can the authors explain what Fig. 5 illustrates?

Response: This figure is used to show the number of the convex polygons with each difference value between n_a and n-1 according to the experiment result in this section. The description of it has been revised in the manuscript.

The number of convex polygons with each difference value are shown in Figure 7. We can see that, in the 1000 convex polygons, there were 574 convex polygons whose difference value between n_a and n - 1 was zero and, for most convex polygons, the difference value was either -1, 0, or 1. The typical difference value between n_a and n - 1 was quite small, and all of them fell in the range [-2, 2].

Figure 7: The number of the convex polygons with each difference value.

Comment 5#: Some figure captions are not representative, e.g., Fig. 9.

Response: The captions of the figures and tables have been checked and revised carefully.

For example:

(a) (b)

Figure 9: For ease of observation, two figures are used to show the comparison of the three experiments in the relationship between coverage ratio and the number of iterations. The comparison between Tests 1 and 3 is shown in (a), and the comparison between Tests 2 and 3 is shown in (b).

Comment 6#: The authors are encouraged to revise their manuscript for many writing issues and grammatical mistakes.