Design of coverage algorithm for mobile sensor networks based on virtual molecular force

Journal Pre-proof Design of coverage algorithm for mobile sensor networks based on virtual molecular force Song Liu, Runlan Zhang, Yongheng Shi

PII: DOI: Reference:

S0140-3664(19)31187-9 https://doi.org/10.1016/j.comcom.2019.11.001 COMCOM 6003

To appear in:

Computer Communications

Received date : 15 September 2019 Revised date : 15 October 2019 Accepted date : 1 November 2019 Please cite this article as: S. Liu, R. Zhang and Y. Shi, Design of coverage algorithm for mobile sensor networks based on virtual molecular force, Computer Communications (2019), doi: https://doi.org/10.1016/j.comcom.2019.11.001. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.

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Design of Coverage Algorithm for Mobile Sensor Networks Based on Virtual Molecular Force Song Liu1, a, Runlan Zhang2, b, Yongheng Shi2, c 1

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Key Laboratory of Information & Computing Science, Guizhou Normal University 550003, Guiyang, China 2 Information technology College, Guizhou Vocational Technology Institute 550023, Guiyang, China Email：[email protected], [email protected], [email protected] *Corresponding Author: [email protected]

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Abstract

General virtual force algorithm, when the density of sensor nodes is large in the monitoring area, there are some shortcomings, such as uneven distribution of nodes, more overlap of coverage area and so on. In view of these shortcomings, based on the basic idea of air molecular

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theory, a virtual molecular force model of mobile sensor networks is established, and the virtual molecular force algorithm for node deployment and mobile coverage of mobile sensor networks is given. The virtual molecular force algorithm assumes that there is interaction

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between nodes in mobile sensor networks, and the resultant force of these forces constitutes the resultant force network of sensor nodes in the monitoring area, which drives the sensor nodes to move to the corresponding location to repair the monitoring blind area, so as to maximize the coverage of the network. In order to verify the feasibility and effectiveness of the virtual molecular force algorithm, the virtual molecular force algorithm for mobile sensor network node deployment and mobile coverage is simulated and analyzed by using MATLAB simulation tool. The simulation results show that the virtual molecular force algorithm can make the sensor nodes repair the monitoring blind area efficiently and quickly, and maximize the monitoring coverage area of the sensor network. In terms of repairing monitoring blind areas and improving network coverage, the virtual molecular force algorithm is superior to

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other network coverage algorithms such as general virtual force algorithm. Keywords: mobile sensor network; network coverage; monitoring blind area; algorithm design; simulation

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1. Introduction Mobile sensor networks are composed of several mobile sensor nodes. In addition to monitoring the surrounding areas of sensor nodes and collecting and transmitting environmental data information around sensor nodes, it can also dynamically monitor fixed or

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moving targets through the movement of sensor nodes, and repair the monitoring blind areas in network monitoring areas, so as to cover the monitoring areas continuously and equally [1]. The characteristics of mobile sensor network dynamic coverage of monitoring targets can be

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applied in environmental monitoring, intelligent city, intelligent transportation, national defense and military fields [2].

Due to the limited sensing range of sensor nodes and other reasons, there will always be

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some areas which cannot be covered by sensor nodes in the monitoring area of mobile sensor networks, that is, there will inevitably be some monitoring blind areas. For example, in the initial deployment of mobile sensor networks, due to environmental or other random reasons, sensor nodes are unevenly distributed in the monitoring area, and there is a monitoring blind

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area in the initial deployment. For example, due to various reasons, sensor nodes are invalid or damaged, which makes the original monitored area without sensor nodes coverage, there are new monitoring blind areas. The existence of monitoring blind area will make the data collected by sensor network incomplete, and lead to the decline of monitoring quality and even monitoring failure of network [3].

In the research of coverage control of mobile sensor networks, many achievements have been made, and many algorithms for node deployment and mobile coverage have been proposed [4][5]. Among them, the representative mature algorithms include the best relay node placement algorithm [6], distributed deployment algorithm [7], centralized coverage algorithm

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[8], gradient-based coverage optimization strategy [9], distributed sensor coordination algorithm [10], virtual force algorithm [11]. As well as the recently studied algorithms: density function algorithm [12], distributed fireworks algorithm [13], bipartite graph optimal matching algorithm [14], improved ant lion algorithm [15], and so on. These algorithms have their own characteristics, and each has its own specific application environment and conditions. Considering the application scenarios with high density and obstacles of sensor nodes, this paper mainly studies the virtual force algorithm. 2

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Virtual Force Algorithms (VFA) regards sensor nodes as some kind of "charged particles" and sets a "zero gravity" node spacing. When the sensor node spacing is less than this zerogravity distance, the node gravity is repulsive. When the distance between sensor nodes is larger than the zero gravitational distance, the attraction of sensor nodes is suction [16]. Virtual force algorithm has a wide range of adaptability, especially in the scene of sparse node density

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in the monitoring area. Therefore, virtual force algorithm has always been one of the most concerned coverage algorithms. In recent years, the research on virtual force algorithm is still

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in the ascendant. For example, the research of virtual force algorithm for comprehensive coverage energy consumption and coverage efficiency [17] [19] [20], and the research of improving and improving the coverage efficiency of virtual force algorithm [18] [21].

The general virtual force algorithm can cover the monitoring area uniformly when the

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number of sensor nodes is small. However, when the number of nodes is large, the peripheral nodes of the monitoring area will push the nodes of the monitoring area center, resulting in uneven distribution of sensor nodes in the monitoring area. The density of the nodes in the

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center of the monitoring area is relatively large, and the coverage area of the nodes has a large overlap. The peripheral nodes of the monitoring area are sparse and there are many blind areas [22].

This paper will focus on the shortcomings of the general virtual force algorithm.，based on the basic idea of air molecule theory, this paper establishes a virtual molecular force model (VMFM) for mobile sensor networks. A virtual molecular force algorithm (VMFA) for node deployment and mobile coverage in mobile sensor networks is proposed. The virtual molecular force algorithm assumes that there exists an interaction force similar to that of air molecules between nodes of mobile sensor networks. By calculating the resultant force between sensor

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nodes, the resultant force network of sensor nodes in the monitoring area is constructed, and the monitoring blind area in the monitoring area is found, which drives the nodes to move to the corresponding location to repair the blind area and maximizes the coverage of the network. In order to verify the feasibility and effectiveness, we will use MATLAB simulation tools to simulate and analyze the proposed virtual molecular force algorithm.

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2. Virtual Molecular Force Model (VMFM) According to the theory of air molecule, there are interacting molecular forces among air molecules. Air molecule force is expressed by gravitation or repulsion at the same time, and its

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value is related to the distance between air molecule. When the distance between molecules is a certain value, the force of attraction and repulsion is equal, and the force of interaction

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between molecules is zero; when the distance between molecules is less than a certain value, the force of attraction and repulsion increases, but the force of repulsion increases faster, and the force of interaction between molecules is repulsion; when the distance between molecules is greater than a certain value, the force of attraction and repulsion decreases, but the force of repulsion decreases faster, and the force of interaction between molecules is gravitation. When

and can be neglected.

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the distance between molecules is larger, the interaction force between molecules is very small

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If the sensor node is regarded as an air molecule, the sensor node distributed in a certain range can be regarded as a certain volume of air. When there are enough sensor nodes, the interaction force between them will drive the sensor nodes to cover the whole monitoring area. When the sensor nodes are limited, the gravity between the nodes will aggregate the sensor nodes into a certain range. When the distance between sensor nodes is small, the repulsion force between nodes will ensure that the sensor nodes will not collide too close. Based on this assumption, we will build the following virtual molecular force model for mobile sensor networks based on air molecule theory.

There are 𝑛 sensor nodes distributed in a monitoring area. Under the action of virtual

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molecular force, the sensor nodes reach their equilibrium positions through mobile adjustment, which constitutes the network coverage map shown in Figure.1. At this time, the coverage area of sensor nodes is the largest and the monitoring blind area is the smallest.

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b

R

2 3R

a

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3R 3R

3/2 R

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Y

Figure.1 Diagram of position relationship of sensor nodes If the sensor radius is 𝑅, the distance between adjacent nodes is √3𝑅, the distance between sub-adjacent nodes is 3𝑅 or 2√3𝑅, and the interaction force between nodes is zero when the

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sensor nodes in the monitoring area are in the position shown in Figure.1. At this time, the perceptual area of the node forms a stable hexagonal structure, the relative position between the nodes is stable, and will not be deformed by the traction of excessive force between the

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nodes. The coverage area is the largest. In the monitoring area, the distance between nodes is 𝑑, and the interaction force 𝐅⃗ between nodes can be calculated according to formula (1). 𝑑 𝑎 −(√3𝑅) 𝑑𝑎

0,

𝑎

⃗⃗⃗ 𝑫

𝒂𝒃 ⋅ ‖𝑫 , ⃗⃗⃗ ‖ 𝑎𝑏

3𝑅−𝑑

𝑒 √3𝑅−𝑑 ⋅ 𝑠𝑖𝑛 (3−

√3)𝑅

𝐅⃗ =

0,

𝜋∙

𝑑−3𝑅

𝑒 √3𝑅−𝑑 ⋅ 𝑠𝑖𝑛 (2

√3−3)𝑅

0, {

𝑒 √3𝑅−𝑑 ⋅

⃗⃗⃗𝑎𝑏 𝑫 , ⃗⃗𝑎𝑏 ‖ ‖𝐷 ⃗⃗⃗ 𝑫

𝒂𝒃 𝜋 ⋅ ‖𝑫 , ⃗⃗⃗ ‖ 𝑎𝑏

⃗⃗⃗𝒂𝒃 𝑫 , ⃗⃗⃗𝑎𝑏 ‖ ‖𝑫

𝑑 < √3𝑅 𝑑 = √3𝑅 √3𝑅 < 𝑑 < 3𝑅 𝑑 = 3𝑅

(1)

3𝑅 < 𝑑 < 2√3𝑅 𝑑 = 2√3𝑅 𝑑 > 2√3𝑅

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⃗⃗𝑎𝑏 denotes the distance In the formula, α (α ≥ 1) is the gravitational coefficient; 𝐷 ⃗⃗𝑎𝑏 , the direction of vector from node a to node b, the direction of suction is the same as 𝐷 ⃗⃗ 𝐷

⃗⃗𝑎𝑏 , and 𝑎𝑏 is the unit vector. Figure.2 is an image representation repulsion is opposite to 𝐷 ⃗⃗ ‖ ‖𝐷 𝑎𝑏

of the piecewise function of formula (1).

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3

3R 2 Distance between nodes ( d )

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0

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Interaction force between nodes (scalar)

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Figure.2 Interaction force model between sensor nodes When the distance between sensor nodes 𝑑 < √3𝑅, in order to reduce the overlap of sensing area and affect coverage efficiency, the interaction force between nodes is repulsive

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force, which is inversely proportional to the α power of distance 𝑑. When the nodes are closer to each other, the repulsion force between nodes will increase sharply to avoid collision because the distance between nodes is too small.

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When the distance between sensor nodes is √3𝑅 < 𝑑 < 2√3𝑅, there are perception holes between sensor nodes. Therefore, the interaction force F between nodes should be suction to drive the nodes closer to each other. With the increase and decrease of node spacing, the attraction between nodes increases and decreases, so that the node spacing is stable at √3𝑅 , 3𝑅 , or 2√3𝑅 , etc.

When the distance between sensor nodes is greater than 2√3𝑅, the gravity between nodes decreases rapidly to ensure that the peripheral nodes in the monitoring area do not exert pressure on the intermediate nodes, thus maintaining the uniformity of node distribution in the

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monitoring area.

In practical applications, mobile sensor networks are usually deployed in a given area. The mobility of sensor nodes needs to be limited within the boundaries of the network monitoring area, as shown in Figure 1. In addition, there may be obstacles that need to be avoided in the network monitoring area, such as rocks, buildings, gullies and so on. When sensor nodes move, they need to keep a certain distance from these obstacles [23].

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Journal Pre-proof The distance between the sensor node and the boundary or obstacle is 𝑑𝐵 , and the normal repulsion force of the boundary or obstacle in the monitoring area is ⃗F𝐵 . ⃗F𝐵 can be calculated according to formula (2).

⃗F⃗𝐵 = {

𝛼

⋅ ⃗B⃗,

0,

𝑑𝐵 ≤

√3𝑅 2

𝑑𝐵 >

√3𝑅 2

(2)

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√3𝑅

( 2 ) −𝑑𝐵 𝛼 𝑑𝐵 𝛼

⃗⃗ is the unit normal vector of the boundary or obstacle in the monitoring In the formula, 𝐵

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area, and α(α ≥ 1) is the gravitational coefficient.

When the distance between the sensor node and the boundary or obstacle of the monitoring area 𝑑𝐵 > √3 , 2

the normal repulsion ⃗F⃗𝐵 has no effect on the sensor node. When the

⃗⃗𝐵 pushes the sensor node away from the boundary or the normal repulsion F

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distance 𝑑𝐵 ≤

√3 𝑅, 2

obstacle of the monitoring area. Normal repulsion force ⃗F⃗𝐵 is inversely proportional to distance 𝑑𝐵 . When 𝑑𝐵 approaches zero, 𝐹⃗𝐵 tends to infinite to ensure that sensor nodes do not move to

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regional boundaries or close to obstacles.

When mobile sensor networks deploy nodes and mobile coverage, sensor nodes will be subject to the force of other nodes in the monitoring area. When the sensor node moves to the boundary of the monitoring area or near the obstacle, the sensor node will also be subjected to the normal repulsion of the boundary of the area or the obstacle. The resultant force of these forces will determine the moving direction of sensor nodes. Let 𝐹⃗𝑖𝑗 be the force acting on node 𝑖 by node 𝑗, and its value can be calculated according to formula (1). 𝐹⃗𝑖𝐵𝑗 denotes the normal repulsion of boundary 𝐵𝑗 to node 𝑖, and its value can be calculated by formula (2). The resultant

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force 𝐹⃗𝑖 of sensor node 𝑖 can be calculated according to formula (3). ⃗ 𝐹⃗𝑖 = ∑𝑛𝑗=1,𝑗≠𝑖 𝐹⃗𝑖𝑗 + ∑𝑚 𝑗=1 𝐹𝑖𝐵𝑗

(3)

In the formula, n denotes the number of sensor nodes in the monitoring area, and m denotes the number of repulsions suffered by node 𝑖 , which come from the boundary of the monitoring area and the obstacles in the monitoring area.

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3. Virtual Molecular Force Algorithms (VMFA) According to the virtual molecular force model of mobile sensor networks, we will propose the following node deployment and mobile coverage algorithms for mobile sensor networks.

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In mobile sensor networks, the movement direction of sensor node is determined by the direction of resultant forces [24]. At 𝑡 time, the velocity of sensor node is 𝑣. After a period of time ∆𝑡 moves, the distance of sensor node moving along the direction of resultant force is 𝑣 ∙

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∆𝑡. At the time 𝑡 + ∆𝑡, the nodes in the monitoring area will redefine the magnitude and direction of the resultant force according to the new position relationship, and then move along the resultant force direction until the resultant force of each node in the network is close to 0.

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Let the resultant force of node 𝑖, 𝑖 ∈ {1,2, ⋯ , 𝑛} in the initial state be 𝐹⃗𝑖𝑜 , and the position vector of node 𝑖 relative to the origin of coordinate is 𝑅⃗⃗𝑖𝑜 . After the first movement, the position vector of node 𝑖 : ⃗

𝐹 𝑅⃗⃗𝑖1 = 𝑅⃗⃗𝑖0 + Δ𝑅⃗⃗𝑖𝑜 = 𝑅⃗⃗𝑖𝑜 + 𝑣 ∙ 𝛥𝑡 ⋅ ‖𝐹𝑖𝑜 ‖ ,

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𝑖𝑜

After 𝑘(𝑘 ≥ 1) times of movement, the position vector of node 𝑖: 𝑅⃗⃗𝑖𝑘 = 𝑅⃗⃗𝑖(𝑘−1) + 𝛥𝑅⃗⃗𝑖(𝑘−1) = 𝑅⃗⃗𝑖0 + Δ𝑅⃗⃗𝑖𝑜 + Δ𝑅⃗⃗𝑖1 +, ⋯ , +Δ𝑅⃗⃗𝑖(𝑘−1) , i ∈ {1,2, ⋯ , 𝑛}

(4)

If the endpoints of the vector 𝑅⃗⃗𝑖0 , 𝑅⃗⃗𝑖1 , 𝑅⃗⃗𝑖2 , ⋯ , 𝑅⃗⃗𝑖𝑘 are connected by a curve, the trajectory of the node can be obtained, as shown in Figure.3. Y

Ri1

Ri2

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Ri0

O

Rin

X

Figure.3 Schematic diagram of sensor node trajectory When the resultant force of each node in the monitoring area is small, it can be determined that each node has moved to the appropriate location, then the node movement can be 8

Journal Pre-proof terminated, and the deployment of sensor nodes or mobile coverage work is finished [25]. For any node 𝑖, 𝑖 ∈ {1,2, ⋯ , 𝑛}，according to formula (3), in the monitoring area, the combined force is 𝐹⃗𝑖𝑘 after 𝑘(≥ 1) rounds of movement. When the maximum resultant force (absolute value) of the nodes in the monitoring area is less than or equal to a given small positive number τ, that is, when max[‖𝐹⃗1𝑘 ‖, ‖𝐹⃗2𝑘 ‖, ⋯ , ‖𝐹⃗𝑛𝑘 ‖] ≤ τ, all the nodes in the monitoring area are

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very close to the appropriate location and the mobile deployment of the nodes can be completed.

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Accordingly, we present the following node deployment or mobile coverage algorithms for mobile sensor networks.

(1) 𝑘 = 0, determine the initial position vector of 𝑛 nodes: 𝑅⃗⃗10 , 𝑅⃗⃗20 , ⋯ , 𝑅⃗⃗𝑛0 ; (2) According to the location of each node, the distance between nodes is

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calculated: (𝑘)

𝑑𝑖𝑗 = 𝑅⃗⃗𝑖𝑘 − 𝑅⃗⃗𝑗𝑘 , 𝑖, 𝑗 ∈ {1,2, ⋯ , 𝑛}, 𝑖 ≠ 𝑗; and the distance from each node (𝑘)

to the boundary or obstacle of the monitoring area: 𝑑𝑖𝐵𝑗 , 𝑖 ∈ {1,2, ⋯ , 𝑛}, 𝑗 ∈

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{1,2, ⋯ , 𝑚};

(3) Computing the resultant forces of 𝑛 nodes according to formula (3): 𝐹⃗1𝑘 , 𝐹⃗2𝑘 , ⋯ , 𝐹⃗𝑛𝑘 ;

(4) If max[‖𝐹⃗1𝑘 ‖, ‖𝐹⃗2𝑘 ‖, ⋯ , ‖𝐹⃗𝑛𝑘 ‖] ≤ τ, the node stops moving, and turn (7); Otherwise, turn (5);

(5) Computing the moving distance vector of 𝑛 nodes: 𝐹⃗

[‖𝐹1𝑘‖ 1𝑘

𝐹⃗2𝑘 ‖𝐹2𝑘 ‖

…

𝐹⃗𝑛𝑘 ] ‖𝐹𝑛𝑘 ‖

∙ 𝑣 ⋅ 𝛥𝑡;

(6) 𝑘 = 𝑘 + 1, Computing the new position vectors of 𝑛 nodes by formula (4): 𝑅⃗⃗1𝑘 , 𝑅⃗⃗2𝑘 , ⋯ , 𝑅⃗⃗𝑛𝑘 ；turn (2).

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(7) The node deployment or mobile coverage finished, output results.

4. Simulation Analysis

In order to verify the feasibility and validity of the proposed Virtual Molecular Force Algorithm, we use MATLAB simulation tool to simulate and analyse it [26]. There are 30 sensor nodes in the network, which are distributed in the monitoring area of 25m × 25m, and

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Journal Pre-proof the sensing radius of sensor nodes is 3m. The simulation analysis of Virtual Molecular Force The simulation results of VMFA and VFA are compared and analysed as follows.

4.1 Simulation of Mobile Coverage without Obstacles Figure.4 and Figure.5 show the mobile coverage process of sensor nodes in the simulation area

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using VMFA algorithm and VFA algorithm respectively. As shown in Figure.4 and Figure.5, in the initial state, sensor nodes are randomly distributed in the centre of the monitoring area. The distance between nodes is small, and the interaction force is repulsive. The closer the node

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is, the faster the repulsion force is, and the faster the node diffuses outward.

The mobile coverage process of sensor nodes can be divided into two stages. The repulsion force plays a major role in the first stage, and the nodes diffuse and move around. The second

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stage is the interaction of repulsion and suction, in which the repulsion force includes the repulsion force produced by the node approaching the monitoring boundary. In this stage, the repulsion and suction force work together to adjust the position of the node.

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As shown in Figure 4, mobile coverage using VMFA algorithm, in the first stage, under the action of virtual molecular force, sensor nodes deploy rapidly in the monitoring area, and the nodes are relatively uniform, and as close as possible to the boundary, so as to cover the entire monitoring area. In the second stage, the resultant forces of interaction between nodes play a role to gradually adjust the position of nodes and ensure the coverage area as large as possible.

As shown in Figure.5, mobile deployment using general VFA algorithm, under the action of virtual repulsion, sensor nodes also move rapidly from the centre of the monitoring area to around. However, because of the single interaction force between nodes set by VFA algorithm, when the node density is large, the nodes near the monitoring area boundary are pushed to the

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central nodes by the repulsion force and boundary repulsion force, which results in the dense distribution of nodes in the monitoring area centre, while the nodes near the monitoring area boundary are sparse and unevenly distributed. In the second stage, the adjustment range of node position is small, and the reasonable position cannot be reached, and the monitoring blind area is large.

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Figure.4 Node trajectory diagram of VMFA algorithm

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Figure.5 Node trajectory diagram of VFA algorithm

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Figure.6 and Figure.7 show the change of coverage area of sensor nodes in the mobile deployment process in the monitoring area when using VMFA and VFA algorithms, respectively. From the initial state to the end of mobile coverage is divided into 8 phases. The mobile coverage status of sensor nodes in the monitoring area corresponds to 8 coverage status

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maps. The grey part of the coverage state map represents the area that all nodes in the monitoring area can cover, and the white part represents the area that is not covered.

Mobile coverage using VMFA algorithm, as shown in Figure.6, 8 phases of coverage state map, respectively, 6-1, 6-2, … ,6-8. In the initial phase of mobile coverage (6-1, 6-2), the nodes are concentrated in the monitoring area center, the coverage area is small, and the monitoring blind area is large. In the node deployment phase (6-3, … ,6-6). With the node moving, the coverage area of the node gradually increases and the blind area gradually decreases. In the final phase (6-7, 6-8), except for the small blind areas on the boundary, all other areas can be

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completely covered without blind areas.

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6-1

6-5

6-7

6-4

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6-6

6-3

Figure.6 Mobile coverage phase maps of VMFA algorithms

Mobile coverage using VFA algorithm, as shown in Figure.7, 8 phases of coverage area

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map, respectively, 7-1, 7-2, …, 7-8. In the initial phase of mobile coverage (7-1, 7-2), similar to VMFA algorithm, nodes are concentrated in the monitoring area center, the coverage area of nodes is small, and the monitoring blind area is large. In the node deployment phase (7-3,

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…, 7-6), with the node moving, the blind area is also reduced slightly, but the coverage effect is lower than VMFA algorithm. In the final phase (7-7, 7-8), there are still many blind areas that cannot be covered, and there are large-scale blind areas in the monitoring area boundary. 7-1

7-6

7-3

7-7

7-4

7-8

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7-5

7-2

Figure.7 Mobile coverage phase maps of VFA algorithms

Figure.8 shows the coverage comparison curve of mobile deployment process of sensor nodes using VMFA algorithm and VFA algorithm. As shown in Figure.8, the coverage of VMFA and VFA is almost the same before the 10th move. Between 10 and 15 times, the 12

Journal Pre-proof coverage of VFA algorithm is slightly higher than that of VMFA algorithm. After 15 moves, the coverage of VFA algorithm is about 89.6%. However, the VMFA algorithm has entered the second stage, fine-tuning the location of nodes, so that the coverage area of nodes is close to the theoretical coverage area, basically eliminating the monitoring blind area, and finally the coverage rate is stable at about 97.3%. X: 25 Y: 0.9729

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0.8

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0.6

0.4 0.2

VMFA VFA

0.0 0

5

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Percentage of Area Covered ( 100 % )

1.0

10 15 20 Number of Nodes Movements (Rounds)

25

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Figure.8 Comparisons of mobile coverage rates

4.2 Simulation of Mobile Coverage with Obstacles When there are obstacles in the monitoring area, using VMFA algorithm for node deployment or mobile coverage is also significantly better than VFA algorithm in terms of obstacle avoidance performance and coverage efficiency. Under the same conditions as the simulation environment and parameters set in the previous section, there is a rectangular obstacle of 6m×9m in the monitoring area.

As shown in Figure.9 and Figure.10, when using VMFA algorithm in the same monitoring

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area and the same obstacle, the obstacle avoidance trajectory of nodes is smooth and the coverage effect is good. When using VFA algorithm, the obstacle avoidance trajectory of nodes is tortuous, the path of movement is long, and the coverage effect is not good. In addition, due to the long and tortuous obstacle avoidance route, the node energy consumption of VFA algorithm will increase, thus reducing the effective monitoring time of nodes.

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Figure.10 Node obstacle avoidance trajectory of VFA

Figure.9 Node obstacle avoidance trajectory of VMFA

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Figure.11 and Figure.12 represent the changes of the coverage area of sensor nodes in the process of obstacle avoidance movement in the monitoring area when using VMFA and VFA algorithms, respectively.

11-1

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The obstacle-avoiding mobile coverage using VMFA algorithm is shown in Figure.11. In the initial phase (11-1, 11-2), the nodes are concentrated in the monitoring area centre, and the coverage area is limited to the central part of the monitoring area. The coverage area is small, and the monitoring blind area is large. In the node deployment phase (11-3, … ,11-6), the coverage area of nodes gradually increased, and the nodes entered obstacle avoidance adjustment movement. In the final phase (11-7, 11-8), in addition to several blind areas on the boundary, there are no blind areas in the monitoring area, and the surrounding areas of obstacles are basically covered. 112

113

114

116

117

118

Figure.11 Phase maps of obstacle avoidance mobile coverage by VMFA

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Journal Pre-proof Obstacle-avoiding mobile coverage using VFA algorithm is shown in Figure.12. In the initial phase (12-1, 12-2), the coverage of VMFA algorithm is similar. Nodes are concentrated in the monitoring area center, the coverage area of nodes is small, and the monitoring blind area is large. In the node deployment phase (12-3, … ,12-6), the monitoring blind area is also reduced slightly, but the effect is lower than VMFA algorithm. In the final phase (12-7, 12-8),

area around the obstacle. 12-2

12-3

12-5

12-6

12-7

12-4

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there are a lot of blind areas on the boundary of the monitoring area, and there is a large blind

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Figure.12 Phase maps of obstacle avoidance mobile coverage by VFA Figure.13 shows the coverage comparison curve of mobile deployment process of sensor node obstacle avoidance using VMFA algorithm and VFA algorithm. As shown in Figure.13, the VMFA algorithm is superior to the VFA algorithm in eliminating blind areas in the case of obstacles. After the second move, the coverage of VMFA algorithm is always greater than that of VFA algorithm. After 36 moves, the node coverage of VMFA algorithm is stable at

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96.7%, while VFA algorithm stops at 91.8%.

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Figure.13 Comparisons of obstacle avoidance mobile coverage rates

5. Conclusion

Due to the limited sensing range of sensor nodes, there will always be some monitoring blind

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areas in the monitoring area of mobile sensor networks. The existence of monitoring blind area will make the data collected by mobile sensor network incomplete, resulting in the decline of monitoring quality and even monitoring failure. Mobile sensor networks can dynamically cover fixed or mobile monitoring targets through the movement of sensor nodes, repair the monitoring blind areas in the network monitoring area, and continuously balance the monitoring coverage of the monitoring area.

In the research of coverage control of mobile sensor networks, many achievements have been made, and many algorithms for node deployment and mobile coverage have been proposed. Considering the application scenarios with high density and obstacles of sensor

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nodes, this paper mainly focuses on virtual force algorithm.

General Virtual Force algorithm can repair the monitoring blind area to a certain extent when there are fewer nodes, but when there are more nodes, there will be uneven distribution of nodes, and the coverage will decrease. To overcome these shortcomings, a virtual molecular force model (VMFM) for mobile sensor networks is proposed based on the basic idea of air molecular theory. VMFM assumes that there exists a force similar to that of air molecules 16

Journal Pre-proof between nodes of mobile sensor networks. When there are enough sensor nodes, the interaction force between them will drive the sensor nodes to cover the whole monitoring area. When the sensor nodes are limited, the gravity between the nodes will aggregate the sensor nodes into a certain range. When the distance between sensor nodes is small, the repulsion force between nodes will ensure that the sensor nodes will not collide too close. Based on this model, we set the distance between adjacent and sub-adjacent "zero gravity" nodes and the corresponding

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mobile coverage in mobile sensor networks is presented.

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interaction force. A virtual molecular force algorithm (VMFA) for node deployment and

In order to verify the feasibility and validity of virtual molecular force algorithm for mobile sensor network node deployment and mobile coverage, we use MATLAB simulation tool to simulate and analyse it. The simulation results show that the VMFA algorithm focuses on the uniform distribution of sensor nodes in the monitoring area, and reasonably sets the

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"zero gravity" distance between adjacent and sub-adjacent sensor nodes, as well as the corresponding interaction force. The resultant force of the interaction force between sensor nodes is formed in the resultant force network in the monitoring area, which drives the sensor

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nodes to move to the corresponding location to repair the monitoring blind area. It can effectively avoid the situation that the nodes around the monitoring area push the nodes in the centre of the monitoring area, and ensure the uniformity of sensor nodes in the monitoring area. The coverage area overlap is small and the coverage area is maximized. In addition, Virtual molecular force algorithm has good obstacle avoidance performance and can repair the monitoring blind area around the obstacle. In terms of repairing monitoring blind areas and improving network coverage, VMFA algorithm is superior to other network coverage algorithms such as general VFA algorithm.

Acknowledgements

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This paper is a result of the Project “Research on wireless sensor network system based on environment and safety monitoring” (QianKeHe-J [2013] 2204), which is supported by the Natural Science Foundation of Department of Science and Technology of Guizhou Province.

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Song Liu, Dr., Associate Professor of Key Laboratory of Information and Computing Science of Guizhou Normal University. His research interests include computer network technology, computer graphics and parallel computing. Several research results have been published in international journals, such as "Routing Design and Simulation Analysis of Body Area Network Group Cooperative Communication", etc. Email: [email protected] Runlan Zhang, Master's Degree in Information Technology College of Guizhou Vocational Technology Institute. Her research interests include computer network technology. Published research papers include "Energy Balanced WSN Monitoring Blind Area Repair Strategy and Routing Design”, etc. Email: [email protected]

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Authors

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wireless sensor networks [J]. Minicomputer system, 2018,39(10): 2222-2225.

Yongheng Shi, Master of Engineering, Teacher of Information Technology College of Guizhou Vocational Technology Institute. His research interests include computer network technology. Published research papers include "Research on Mountain slide WSN monitoring system for Karst area", etc. Email: [email protected]

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There was no conflict of interest in the submission of the manuscript, and the author agreed to publish it. I declare that the work described is an original study that has not been published before and is not considered elsewhere, in whole or in part.

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