sensors Article
Multi-Robot Cyber Physical System for Sensing Environmental Variables of Transmission Line Fei Fan 1, * , Gongping Wu 1, *, Man Wang 1 , Qi Cao 2 and Song Yang 2 1 2
*
School of Power and Mechanical Engineering, Wuhan University, Wuhan 430072, China;
[email protected] State Grid Jilin Electric Power Co., Ltd., Baishan Power Company, Baishan 134300, China;
[email protected] (Q.C.);
[email protected] (S.Y.) Correspondence:
[email protected] (F.F.);
[email protected] (G.W.); Tel.: +86-134-7682-8338 (F.F.); +86-133-9710-9579 (G.W.)
Received: 11 August 2018; Accepted: 15 September 2018; Published: 18 September 2018
Abstract: The normal operation of a power grid largely depends on the effective monitoring and maintenance of transmission lines, which is a process that has many challenges. The traditional method of the manual or remote inspection of transmission lines is time-consuming, laborious, and inefficient. To address this problem, a novel method has been proposed for the Multi-Robot Cyber Physical System (MRCPS) of a power grid based on inspection robots, a wireless sensor network (WSN), and multi-agent theory to achieve a low-cost, efficient, fault-tolerant, and remote monitoring of power grids. For the sake of an effective monitoring system for smart grids, the very research is conducted focusing on designing a methodology that will realize the efficient, fault-tolerant, and financial balance of a multi-robot team for monitoring transmission lines. Multiple testing scenarios are performed, in which various aspects are explored so as to determine the optimal parameters balancing team performance and financial cost. Furthermore, multi-robot team communication and navigation control in smart grid environments are introduced. Keywords: multi-robot; multi-agent; cyber physical system; team/coalition formation; WSN; inspection robot; transmission lines monitoring; smart grid
1. Introduction The normal supply of electricity is one of the basic requirements of modern society. With the rapid development of the economy, the power grid is expanding rapidly toward the target of a smart power grid. The safe operation and efficient monitoring of transmission lines are facing many challenges [1]. Overhead high-voltage transmission lines are usually distributed in the wild and exposed to bad environments. Such transmission lines suffer from corrosion and lowered safety levels, and may even be damaged [2]. The changing climate will also cause serious damage to the transmission lines, such as conductor galloping and icing, which will jeopardize the supply of electricity [3]. Therefore, it is very important to monitor the transmission lines efficiently. The normal operation of a power grid largely depends on the effective monitoring and maintenance of transmission lines. The traditional method of manual inspection is time-consuming, laborious, and inefficient [4]. With the rapid development of sensors, robots, and a WSN, more requirements are set for the intelligence of a power grid monitoring system, which bears the advantages described below. Firstly, the intelligent system can run continuously, which is a necessary measure for the fault detection and monitoring of transmission lines; secondly, the system can reduce labor costs; thirdly, the intelligent system can provide high-quality monitoring information. Currently, some challenges of smart grid monitoring need to be addressed. One of the challenges is to work under harsh conditions, posing greater requirements for sensors, computers, and robots [5,6]. Sensors 2018, 18, 3146; doi:10.3390/s18093146
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The other challenge is about the continuous operation of the monitoring system without any interruption or failure. These challenges can be dealt with by designing flexible fault-tolerant cyber physical systems with additional components, such as a wireless sensor network (WSN) and multi-robot system. For monitoring the transmission lines in a remote place, a large-scale sensors network may be required. Therefore, a mobile sensing system may be an appropriate solution [7,8]. In this article, a heterogeneous multi-robot system is applied to a sensing smart grid. The Multi-Robot Cyber Physical System (MRCPS) contains a variety of inspection robots and portable inspection devices to provide a flexible and diversified method of inspection. MRCPS can monitor the conditions of transmission lines, such as power line breakage and galloping, as well as the environmental conditions, such as vegetation occlusion and snow cover. In carrying out task planning and assignments, heterogeneous robots’ abilities were also considered. Based on graph theory, a task-based weighted synergy graph was established to describe the system structure. The robot team is formed based on simulated annealing algorithm. Some incidental challenges, such as the communication and navigation control of a multi-robot system, are also considered. All of the systems are verified by simulation and on-site experiments. In summary, a heterogeneous robot team is proposed to monitor the state of transmission lines for cyber physical system applications. The main innovations are as follows: 1.
2.
3.
Robot technology, WSN technology, and multi-agent theory are integrated to propose a Multi-Robot Cyber Physical System (MRCPS) for the monitoring of overhead transmission lines. MRCPS enhanced the fault tolerance, and reduced the failures and emergencies. By using a smaller number of mobile nodes in comparison with traditional WSN systems, MRCPS achieves a good balance between monitoring performance and deployment costs. A model of a multi-robot task-based weighted synergy graph was established to better understand the interactive relationship between the performance of robots, robots’ social relations, and the capability of the team. In addition, various test scenarios were explored to verify the validity of the system and the preset parameters. A multi-robot team formation strategy is introduced to ensure the optimal structure for a robot team. Additionally, many efforts are made to solve problems regarding the multi-robot team communication and navigation control in a smart grid environment.
The structure of this paper is as follows. Section 2 summarizes the latest research status. Section 3 describes the components of MRCPS and the communication and navigation methods of the robot team in the smart grid environment in detail. Section 4 discusses the developed methods and algorithm. In Section 5, the field experiments for validating the composition and algorithms of the MRCPS are described. The corresponding discussions and conclusions are provided in the last two sections, respectively. 2. State of the Art Since the state of the technology of smart grid monitoring is extensive [9], only the main contributions have been selected and organized into two parts. Firstly, the main detection target parameters and monitoring methods of transmission lines are introduced, because they are in relation to the design of the sensing system. Again, the research progress of the transmission line robot is reviewed, which provides a useful reference for the development of multi-robot team. 2.1. Transmission Line Monitoring The smart grid is a complex cyber physical system with strong electric field and magnetic field and changeable climatic conditions [10,11]. This system is a highly complex nonlinear coupling control system that is greatly affected by external disturbances.
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The applications of smart grid monitoring can be found in numerous publications [12–17]. The algorithms of such systems involve a control method of traditional proportional integral derivative (PID), fuzzy control, adaptive control, H∞, etc. These control algorithms were proposed based on the environment in which the transmission lines work. The shape parameters, environmental parameters, energy parameters, and spatial parameters of transmission lines were obtained through the monitoring system. Intelligent, non-contact technology, and remote sensing are the trends of smart grids [18], due to the requirements for reducing accidents and improving the automatic diagnosis of power grids. Therefore, this paper focuses on reviewing the intelligent non-contact detection methods to obtain the parameters of transmission lines. These detection methods can be divided into sensing based on camera, infrared device, and laser radar, by which different parameters can be obtained as shown in Table 1. Table 1. Characteristic parameters obtained by different detection methods. LiDAR: Light Detection and Ranging. Parameter Class
Inspection Target
Phenomenon
Sensing Methods
Line
Untwisted or broken strand Foreign body coverage
Visible light imaging sensing Visible light imaging sensing
On-line device
Color variation Aging, corrosion
Visible light imaging sensing Visible light imaging sensing
Line
Covering foreign bodies Galloping
Visible light imaging sensing Visible light imaging sensing
On-line device
Color variation
Visible light imaging sensing
vegetation
Distance change
visible light imaging/LiDAR
climate
Meteorological change
Other sensing
Shape
Environment
Line
Value anomaly
infrared imaging sensing
On-line device
Value anomaly
infrared imaging sensing
Line
Galloping Sag change
visible light imaging sensing visible light imaging/LiDAR
Energy
Space On-line device
Displacement
visible light imaging/LiDAR
vegetation
Distance change
visible light imaging/LiDAR
2.1.1. Characteristic Parameters of Transmission Lines (1)
Shape parameters
Overhead transmission lines and on-line devices are key to the operation of a transmission grid. The shape parameters of transmission lines and devices are the most intuitive physical parameters [2,7,18]. The aging, corrosion, and breaking of transmission lines and devices can be directly reflected by the shape parameters. Obtaining the shape parameters is the key target of the inspection of transmission lines. The common shape parameters are as follows.
• • • (2)
The integrity of the line, such as untwisted and broken strand, foreign body coverage, etc. Aging, corrosion, breaking, and even loss of on-line devices represented by insulators, clamp, chain suspension, vibration damper, and spacer. The lines and devices are sometimes covered by dirt, and they show color variation caused by lightning strike. Environment parameters
Transmission lines are usually in the wild. The safe operation of a power grid is closely related to environmental changes [19]. The environment parameters of transmission lines include two categories: natural environmental impacts and non-natural impacts.
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•
(3)
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The natural environment, including climate change and vegetation growth, poses a great challenge to the transmission grid. Common climatic effects involve rain, snow, strong wind, and lightning strike. In spring, vegetation growth will threaten power supply safety and cause fires. Coverage by foreign bodies, such as plastic bags, kites, or civilian unmanned aerial vehicles (UAVs) are the non-natural influencing factors. Energy parameters
Transmission lines generate strong electromagnetic fields and large heat while transmitting electric energy. Monitoring the electromagnetic field or temperature changes of a transmission grid is beneficial to the prediction and positioning of transmission line faults [20]. (4)
Space parameters
The space parameters of transmission lines are mainly related to the spatial changes of transmission lines in a dynamic environment as follows.
• • • •
The galloping and sag of the transmission line. The displacement and deformation of an on-line device. The structural deformation of the power tower. Changes in the natural environment such as vegetation growth.
2.1.2. Non-Contact Sensing Methods (1)
Based on visible light imaging
The most important method for the automatic inspection of transmission lines is machine vision monitoring based on visible light [21,22]. The method uses optical sensors to capture the images of transmission lines, on-line devices, and the environment. A variety of parameters of the power grid can be obtained through this method. These parameters include the shape parameters, environment parameters, and space parameters of transmission lines. (2)
Based on infrared imaging
Although most of the monitoring parameters can be obtained by visible light imaging, the energy distribution of the grid cannot be obtained [22]. The detection method based on infrared imaging can effectively overcome this shortcoming. Through the thermodynamic equation, Joule law, and Kirchhoff’s law, the operation data of the power grid can be obtained. (3)
Based on Light Detection and Ranging (LiDAR)
This method can acquire the spatial parameters of transmission lines [23]. In addition, the acquired Light Detection and Ranging (LiDAR) data can be used to achieve the modeling of the transmission network and environmental space [24–26]. (4)
Other methods In addition to the above monitoring methods, other methods include:
• •
The monitoring of energy parameters such as the magnetic field and electric field of transmission lines. The monitoring of space parameters based on ultrasonic technology.
2.2. Robots for Inspecting Transmission Lines Most of the existing transmission lines’ monitoring systems are based on wireless sensor network (WSN) technology [27]. In these applications, cameras, infrared imagers, and LiDAR sensors are installed on power towers or other devices in order to measure and detect the objective parameters.
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WSNs has the characteristics of being fault-tolerant, flexible, modular, and having low power consumption. On the one hand, the architecture of WSNs are not fixed, so they can be regrouped and expanded. Therefore, the whole network will still be workable, even with structural faults. On the other hand, the embedded technology development, WSNs with low power consumption, have been widely applied, which makes the WSN more clean and environmentally friendly. However, the network structure and efficiency of a WSN depend heavily on the investment cost. Due to the fixed installation of WSN communication nodes and sensors, a large number of nodes need to be deployed in order to improve the coverage area and system fault tolerance. A traditional WSNs’ monitoring system for a smart grid needs high investment and maintenance costs, and this solution may be prohibitive. The robot for a transmission line has been developed gradually and has made important progresses and advantages in its application to the smart grid in recent years. Due to the mobility of robots, they can be used as mobile nodes to carry all kinds of sensors to measure dynamically anywhere in a smart grid, which may help reduce the cost of the WSN. They can be used not only for the dynamic monitoring of transmission lines and the environment, but also for power grid maintenance tasks, such as on-line device replacement and cleaning. In Table 2 of this paper, recent major robots for transmission line monitoring and maintenance are summarized and compared, considering their applications and scenarios. In addition, robots for transmission line maintenance and operation are also used in some applications. However, when regarding power smart grids, the application of a cyber physical system based on a multi-robot team can be considered as a new contribution of this paper. Table 2. Robots for transmission lines. References
Institutions
Application
Scenario
[3,9,10,23]
Hydro-Québec (Canada)
Monitoring, Maintenance (Deicing )
Overhead transmission line
[14,15]
HiBot (Japan)
Monitoring
Overhead transmission line, Power tunnel
[11–13,20,24–27]
Wuhan university (China)
Monitoring, Maintenance (Deicing, Replacement)
Overhead transmission line
[19,21]
Chinese Academy of Sciences (CAS, China)
Monitoring
Overhead transmission line
[6,16]
Shanghai university (China)
Monitoring
Overhead transmission line
[4]
Electric Power Research Institute (EPRI USA)
Monitoring
Overhead transmission line
[17,22]
Eletrobras-Cepel (Brazil)
Monitoring
Overhead transmission line
[5,8]
University of KwaZulu-Natal (South Africa)
Monitoring
Overhead transmission line
3. System Description 3.1. Overhead Transmission Line and Robot Inspection Overhead transmission lines are exposed to a harsh environment, such as acid rain corrosion and wind-induced vibration, which limit the service lives of lines. Therefore, the importance of the continuous inspection and maintenance of the power grid is definite. For example, China’s power grid has more than 300,000 km transmission lines with a voltage of 220 kV or above, which need regular inspection and maintenance. The common on-line devices of transmission lines are shown in Figure 1, including insulators, clamp, chain suspension, vibration damper, spacers, amendments, etc. [2]. Conventional inspection methods for transmission lines mainly rely on manual means for troubleshooting. Inspectors use telescopes, cameras, portable infrared detectors, and small UAVs to
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inspect power lines in sectional modes. This method requires a lot of manpower, material resources, and time. Generally, it takes weeks or even months to complete the inspection of long-distance Sensors 2018, 18, x FOR PEER REVIEW 6 of 29 transmission lines in remote areas by this method. Sensors 2018, 18, x FOR PEER REVIEW 6 of 29
(a)(a)
(b) (b)
(c) (c)
Figure 1. Several common on-linedevices. devices. (a) (a) Insulators; Spacers; (c) (c) Vibration damper. Figure 1. common on-line (b) Spacers; damper. Figure 1. Several Several common on-line devices. (a) Insulators; Insulators;(b) (b) Spacers; (c) Vibration Vibration damper.
As the economy is increasing, transmission lines continuetotoexpand, expand,and andin in the meantime, meantime, the As increasing, transmission lines continue the cost Asthe theeconomy economyisis increasing, transmission lines continue to expand, andthe in the meantime, the cost of traditional manual inspection is dramatically growing. Therefore, the use of robots has of traditional manual inspection is dramatically growing. Therefore, the use of robots has become cost become of traditional manual inspection is dramatically growing. Therefore, the use of robots has a considerable alternative, aiming to improve the automation level of power grid abecome considerable alternative,alternative, aiming to improve to theimprove automation of power grid of monitoringgrid so a considerable the level automation monitoring so as to save manpower, aiming cost, and improve the quality of inspection.level By using power robots, as to save manpower, cost,manpower, and improve the quality of inspection. By using robots, carry a monitoring so asatopan–tilt–zoom save and improve the quality inspection. Bywhich using robots, which carry (PTZ)cost, camera, infrared detector, laserofscanning radar, and other pan–tilt–zoom (PTZ) camera, infrared detector, laser scanning radar, and other equipment, can be which carry a pan–tilt–zoom infrared detector, laser robot scanning radar, and other equipment, can be applied (PTZ) in an camera, easier way. A typical inspection for the overhead applied in an easier way. A typical inspection robot for the overhead transmission lines that have been transmission lines that have been developed is shown in Figure 2. equipment, can be applied in an easier way. A typical inspection robot for the overhead developed is shown in Figure 2. developed is shown in Figure 2. transmission lines that have been
(a)
(b)
Figure 2. A typical inspection robot for overhead high-voltage transmission lines. (a) (a) (b) Automatic inspection by LiDAR method. (b) Obstacle-crossing capacity;
Figure 2. A typical for high-voltage overhead high-voltage transmission lines. to (a) Figure A typical inspection robot forrobot overhead transmission lines. (a) Obstacle-crossing A 2.transmission lineinspection inspection robot usually uses two modes (manual and automatic) Obstacle-crossing capacity; (b) Automatic inspection LiDARmainly method. capacity; (b) Automatic inspection by LiDAR method. conduct transmission lines inspection. The manual by method relies on the experience and
ability of operators to remote control the robot, so as to realize the remote monitoring of
A line inspection usually uses two (manual andautomatic automatic) to conduct Atransmission transmission line inspection robot usually usesmodes twooperations. modes (manual and mode automatic) to transmission lines. This method isrobot mainly applied to emergency The is a transmission inspection. The manual mainly relies on the experience and ability of conduct transmission lines inspection. Themethod manual method mainly relies oninformation, the experience method oflines robot identification and analysis based on existing transmission line and and operators remote control thespecific robot, so as realize the remote monitoring ofaccording transmission automatic operation process. robotso divides inspection to thelines. ability oftooperators tothrough remote control thetoThe robot, as totherealize the area remote monitoring of span between the two powertois towers, and it operations. completes the automatic inspection ofautomatic This method islines. mainly applied emergency The automatic mode adifferent methodspan of robot transmission This method mainly applied to emergency operations. Theis mode is a sections autonomously. identification and analysis basedand on existing line information, andline automatic operation method of robot identification analysistransmission based on existing transmission information, and The steps of the implementing automatic inspection method are as follows. through specific process. The robot divides the inspection area according to the span between the two automatic operation through specific process. The robot divides the inspection area according to the Step 1: Set up a Task Database (TD) for the inspection mission, including the distance of power towers, and completes the automatic different spaninspection sections autonomously. span between the ittwo power towers, and it inspection completes of the automatic of different span inspection, the number of segments, the number and type of devices, the power tower type of each The autonomously. steps of the implementing automatic inspection method are as follows. sections segment, etc. Step 1: Set2:up a Task (TD) for the inspection mission, including theDetection distanceSequence of inspection, The Step steps of the implementing automatic inspection methodthe are as follows. When the Database robot autonomously detects the K segment, K segment the number of segments, the number and type of devices, the power tower type of each segment, Step 1: Set up a Task Database (TD) for the inspection mission, including the distanceetc. of (DS) is sequentially obtained. Step 2: When the robot autonomously detects the K segment, the K segment Detection Sequence inspection, the3: number of segments, number and type of devices,stop the at power tower typeand of each Step When approaching thethe target, the robot will decelerate, the checkpoint, (DS) is sequentially obtained. adjust the PTZ camera to capture the image. segment, etc. Step 3:2:When approaching theside target, the robot the will stop the checkpoint, and adjust When the on robot detects Kdecelerate, segment, K at segment Detection Sequence StepFor the target the autonomously same of the ground line, the externalthe camera is used to capture the the PTZ camera to capture the image. (DS) is sequentially obtained. image. 3: the When approaching theside target, robotline, will stopisat thetocheckpoint, StepFor target on the opposite of thethe ground thedecelerate, internal camera used capture the and • For the target on the same side of the ground line, the external camera is used to capture the image. adjust theimage. PTZ camera to capture the image.
For the target on the same side of the ground line, the external camera is used to capture the image. For the target on the opposite side of the ground line, the internal camera is used to capture the image.
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7 of 29 For the target on the opposite side of the ground line, the internal camera is used to capture the image. Step 4: Store the captured image in the Inspection Database (ID) corresponding to the target parameter. Step 4: Store the captured image in the Inspection Database (ID) corresponding to the target parameter. Step Step5:5:The Thedata dataofofthe theInspection InspectionDatabase Database(ID) (ID)and andTask TaskDatabase Database(TD) (TD)are arecompared comparedand and analyzed to assess the operation status of transmission lines. analyzed to assess the operation status of transmission lines. The Sequence (DS) (DS)can can generated based onstructure the structure of the Task The Detection Detection Sequence bebe generated based on the model model of the Task Database Database (TD). As shown in Figure 3, the DS is generated by first using segment numbers to search (TD). As shown in Figure 3, the DS is generated by first using segment numbers to search the TD to get the to get the motion parameters inspection on the current it theTD motion parameters and inspectionand information oninformation the current segment; then, itsegment; assigns athen, unique assigns unique number to eachtotarget accordingAtotypical their locations. generation of ais numbera to each target according their locations. generationAoftypical a Detection Sequence Detection Sequence is presented in Table 3 for the scene shown in Figure 3. presented in Table 3 for the scene shown in Figure 3.
•
Table Table3.3.Detection Detectionsequences sequencesofofwaiting-inspection waiting-inspectiontargets. targets. Point Detection Sequence Number Detection Sequence LineLine Number Inspection Inspection Point ① A-phase A 1
A-phase A ② Ground wire B B 2 Ground wire ③ C-phase C C 3 C-phase 4 B-phase ④ B-phase D D 5 A-phase ⑤ A-phase E E 6
C-phase E ⑥ C-phase E
Coordinate Coordinate XA, ZA XA , ZA ZBB X XBB,, Z XCC, ZCC X ZDD XDD,, Z XEE,, Z ZEE X XE , ZF XE, ZF
Class Class Shape
Shape Shape Shape Environment Environment Space Space Shape Shape Environment
Environment
Ground wire
XA
Y A ZB
A-phase B-phase C-phase
ZA ZD ZE ZC ZF
XB
Ground wire (walking path)
XC
B C
2
XD
XE
D
X
E
1 4 3
6
5
Z
Vegetation
Figure 3. Steps of implementing automatic inspection by inspection robot. Figure 3. Steps of implementing automatic inspection by inspection robot.
InInorder ordertotoachieve achievelong-distance long-distanceinspection inspectionand andmaintenance, maintenance,robots robotshave havetotorecognize recognizevarious various structures structuresand andcross crossobstacles obstacles[8]. [8].Robots Robotsusually usuallyneed needtotoidentify identifyand andcross crosstwo twotypical typicalobstacles. obstacles. One Oneisisthe themost mostcommon commonvibration vibrationdamper damperand andclamp-on clamp-onlines. lines.The Theother otherone oneisisthe thepower powertower. tower. Figure shows the theimages imagesof of robots passing through different from the which the Figure 44 shows robots passing through different powerpower towers,towers, from which difficulty difficulty of developing mobile robots across them is demonstrated. of developing mobile robots across them is demonstrated.
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(a)
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(b)
Figure 4. The images of robot crossingdifferent different towers. Tangent tower ; (b) Tension support tower.tower. Figure 4. The images of robot crossing towers.(a)(a) Tangent tower; (b) Tension support
3.2. Multi-Robot Cyber Physical System(MRCPS) (MRCPS) 3.2. Multi-Robot Cyber Physical System As mentioned above, a Multi-RobotCyber Cyber Physical Physical System forfor transmission lineslines is As mentioned above, a Multi-Robot System(MRCPS) (MRCPS) transmission is developed and tested. The use of robot teams to replace single robots or traditional WSN systems developed and tested. The use of robot teams to replace single robots or traditional WSN systems may may provide the following benefits: provide the following benefits:
1.
2.
3.
4.
5.
1.
Quality: A robot team works better than a single robot. In the same task, the robots in the team
Quality: A robot with teameach works better thaninteraction a single robot. In the same task,based the robots in the can cooperate other for data and integration. Again, on team teamdetection can cooperate with we each interaction integration. information, canother makefor up data for the shortage ofand single test data. Again, based on team 2. Efficiency: A robot we teamcan is make more efficient than a single of robot. Under the same conditions, a detection information, up for the shortage single test data. robot team can call on more resources to complete a task. For example, team can Efficiency: A robot team is more efficient than a single robot. Under thea multi-robot same conditions, a robot increase coverage space while reducing the operating time. team can call on more resources to complete a task. For example, a multi-robot team can increase 3. Flexibility: A robot team is more flexible than a single robot or WSN sensor system, as it can adapt coverage space while reducing the operating time. to different scenarios by changing the organization structure and task assignment of the team. Flexibility: A robot team is more flexible than a single robot or WSN sensor system, as it can 4. Cost: A robot team is more cost-effective than a single robot or traditional WSN monitoring adapt to different scenarios by efficiency changingofthe organization structure and task system. On the one hand, the a single robot is low, and it needs muchassignment time and of the team. human assistance (for example, at least two weeks are required to complete the inspection of a transmission line). cost-effective A robot team can work autonomously, the working time, Cost:100-km A robot team is more than a single robot orreducing traditional WSN monitoring and saving the labor cost. On the other hand, a multi-robot system can use a small number of and system. On the one hand, the efficiency of a single robot is low, and it needs much time mobile nodes instead of a large-scale WSN system that deploys a large number of sensors. human assistance (for example, at least two weeks are required to complete the inspection of a 5. Fault tolerance: A robot team can reduce the frequency of failures. If one robot in the team fails, 100-km transmission line). A robot team can work autonomously, reducing the working time, other robots can take over its responsibilities. and saving the labor cost. On the other hand, a multi-robot system can use a small number of In the following we will introduce the robot team members, and mobile nodes insteadsections, of a large-scale WSN system that deploys a large sensing numbersystems, of sensors. communication and navigation control algorithms. Fault tolerance: A robot team can reduce the frequency of failures. If one robot in the team fails, other robots can take over its responsibilities. 3.2.1. Robots in the Multi-Robot Team
In the following sections, wetypes willofintroduce thebeen robot team members, In previous work, different robots have developed and used tosensing inspect systems, and and communication and navigation control algorithms. maintain transmission lines [11–13,20,24–27]. The robots are categorized in accordance to their ability of obstacle avoidance.
3.2.1. Robots the Team The in first is Multi-Robot the Portable Inspection Robot (PIR), which can cross the on-line device, but cannot go through the power tower. The next one is Traversing Inspection Robot (TIR), which has the
In previous work, different types of robots have been developed and used to inspect and maintain ability to cross all kinds of on-line devices and some power towers (auxiliary crawling device transmission lines [11–13,20,24–27]. The robots are categorized in accordance to their ability of should be installed on tower structure). The last one is the Climbing Inspection Robot (CIR), which obstacle avoidance. imitates the behavior of animals climbing on the line, and can cross most of obstacles, including The firstdevices is the Portable Inspection (PIR), can cross the UAVs on-lineinto device, but cannot on-line and power towers. InRobot addition, thewhich integration of small the robot team go through theinspection power tower. The next one Traversing Inspection Robotof(TIR), which the ability for the of transmission linesiswas also studied. The proposal this paper is has to apply a team these kinds of robots. The robots aretowers shown (auxiliary in Figure 5,crawling and their device main features to cross allcomposed kinds ofofon-line devices and some power should be are described detail as follows. installed on towerinstructure). The last one is the Climbing Inspection Robot (CIR), which imitates the behavior of animals climbing on the line, and can cross most of obstacles, including on-line devices and power towers. In addition, the integration of small UAVs into the robot team for the inspection of transmission lines was also studied. The proposal of this paper is to apply a team composed of
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these kinds of robots. The robots are shown in Figure 5, and their main features are described in detail as follows. Sensors 2018, 18, x FOR PEER REVIEW 9 of 29
(b)
(b)
(a) (a)
(c) (c)
(d) (d)
Figure 5. The candidaterobots robots for a multi-robot (a) Portable Inspection Robot (PIR); (b)(PIR); Figure 5. The The candidate multi-robotteam. team. Portable Inspection Robot Figure 5. candidate robots forfora amulti-robot team. (a) (a) Portable Inspection Robot (PIR); (b) Traversing Inspection Robot I (TIR I); (c) Traversing Inspection Robot II (TIR II); (d) Climbing (b) Traversing Inspection Robot I (TIR I); (c) Traversing Inspection Robot II (TIR II); (d) Climbing Traversing Inspection Robot I (TIR I); (c) Traversing Inspection Robot II (TIR II); (d) Climbing Inspection Robot (CIR). Inspection Robot Inspection Robot (CIR). (CIR).
Portable Inspection Robot (PIR). The PIR is light in weight and easy to transport, but it does
Portable Inspection Robot (PIR). The PIR is light in weight and easy to transport, but it does not Portable (PIR). Thetowers. PIR isItlight in weightused and to easy to transport, but it not have Inspection the capabilityRobot of trans-power is commonly inspect the operation of does have the capability of trans-power towers. It is commonly used to inspect the operation of transmission not have the capability of devices trans-power towers. It issegment commonly used two to inspect the operation transmission lines and on a long-distance (between power towers). It is of lines especially and devices on a long-distance segment (between two power towers). It is especially convenient convenient for the inspection of transmission lines in(between rivers andtwo lakes. Compared with It is transmission lines and devices on a long-distance segment power towers). for the inspection transmission lines in rivers and lakes. Compared with other robots,Ititcan has the other robots, itof has the the characteristics especially convenient for inspectionofofminiaturization, transmission light, lines economy, in rivers and andenergy-saving. lakes. Compared with characteristics of miniaturization, light, economy, and energy-saving. It can carry out long-term out itlong-term inspection or emergency inspection for special section lines. with a weightIt can othercarry robots, has the characteristics of miniaturization, light, economy, and PIR energy-saving. of 15 kg and an average motionfor speed of 2–3 km/hlines. can carry a 5 kga weight sensor, such inspection or emergency inspection special section PIR with of 15 as kgvisible and anlight average carry out long-term inspection or emergency inspection for special section lines. PIR with a weight sensing equipment, infrared etc.such as visible light sensing equipment, infrared motion speed of 2–3 km/h can sensing carry aequipment, 5 kg sensor, of 15 kg and an average motion speed of 2 3 km/h can carry a 5 kg sensor, such as visible light Traversing etc. Inspection Robot (TIR). The mechanical structure of the TIR is shown in Figure 6. sensing equipment, sensing equipment, infrared sensingon equipment, etc. The TIR has two arms suspended the The ground wire, withstructure each arm consisting walking in joint, a Traversing Inspection Robot (TIR). mechanical of the TIRofisa shown Figure 6. Traversing Inspection Robot (TIR). The mechanical structure of theforce. TIR is shown in Figure 6. pressing joint, and a rotating joint. The walking joint provides the driving The pressing joint The TIR has two arms suspended on the ground wire, with each arm consisting of a walking joint, The TIR hasthe two arms on theangles ground wire, with The eachrobot arm can consisting of a walking joint, a allows robot to suspended adapt to different of inclination. use its arms to move on a pressing joint, and a rotating joint. The walking joint provides the driving force. The pressing joint pressing and acan rotating joint. release The walking joint provides the driving force. The pressing line. joint, The arms alternatively the pressing wheel to cross the obstacles. The TIR has a joint allows the robot tothan adapt to different angles of ainclination. The robotdevices. can use itsaverage arms toinspection move on line. weight of less 50 kg, is able to carry of inspection allows the robot to adapt toand different angles ofvariety inclination. The robot canThe use its arms to move on The arms can alternatively release the pressing wheel to cross the obstacles. The TIR has weight speed is 2.5 km/h. The self-developed TIR has been applied to China’s state grid. line. The arms can alternatively release the pressing wheel to cross the obstacles. TheaTIR has of a less than 50 kg, and is able to carry a variety of inspection devices. The average inspection speed is weight of less than 50 kg, and is able to carry a variety of inspection devices. The average inspection Walking roller 2.5 km/h. self-developed TIR has TIR beenhas applied to China’s Walking roller speed is 2.5The km/h. The self-developed been applied to state grid. s state grid. Walking joint
Walking roller Ground wire (Walking path) Walking joint
Ground wire joint Pressing (Walking path) Revolute joint
Walking rollerroller Pressing
Moving joint
Pressing joint Pressing roller
Body
Pressing joint Pressing joint Revolute joint
Moving joint
(a)
Body
(b)
Figure 6. The mechanical structure of the Traversing Inspection Robot (TIR). (a) The diagram of the working principle of TIR;(a) (b) The obstacle crossing behavior of Traversing Inspection (b) Robot II (TIR II).
Climbing Inspectionstructure Robot of (CIR). As shownInspection in FigureRobot 7, the(TIR). CIR (a) hasThe a more complex Figure 6. The mechanical the Traversing diagram of the mechanical structure than Compared the TIR, the CIR has an additional working principle of TIR; (b)the TheTIR. obstacle crossingwith behavior of Traversing Inspection Robot IIpitching (TIR II).
(b)
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Inspection Robot (CIR). As shown in Figure 7, the CIR has a more complex mechanical SensorsClimbing 2018, 18, x FOR PEER REVIEW 10 of 29 structure than the TIR. Compared with the TIR, the CIR has an additional pitching mechanism and a clamping mechanism mounted to the robot’s each arm, the robot also perform interleaving mechanism and a clamping mechanism mounted to theand robot’s eachcan arm, and the robot can also behaviorsinterleaving by the two arms. The robot animals’ behavior whenclimbing crossing obstacles. perform behaviors by theimitates two arms. The climbing robot imitates animals’ behavior The following areThe repeated when the robot is crossing an obstacle: arm grasping line, when crossing actions obstacles. following actions are repeated when the robotsingle is crossing an obstacle: then crossing arm. The is aboutarm. 60 kg, and it caniscarry a variety of devices, withaan average single arm grasping line,weight then crossing The weight about 60 kg, and it can carry variety of speed ofwith 1.8 km hour.speed of 1.8 km per hour. devices, an per average Walking roller
Walking joint Clamping joint
Ground wire (Walking path)
Pressing joint Pressing roller
Pressing joint Revolute joint
Pitching joint
Pitching joint Body Moving joint
(a)
(b)
Figure Figure 7. 7. The The mechanical mechanical structure structure of of the the Climbing Climbing Inspection Inspection Robot Robot (CIR). (CIR). (a) (a) The The diagram diagram of of the the working thethe CIR; (b)(b) TheThe obstacle-crossing behavior of theof Climbing Inspection Robot (CIR). workingprinciple principleofof CIR; obstacle-crossing behavior the Climbing Inspection Robot (CIR).
A small UAV is also used as a member of the robot team to increase the flexibility of the A small UAV alsoparameters used as a member of the robot team to UAV increase flexibility of the overall system. Theiskey of the inspection robots and arethe shown in Table 4. overall system. The key parameters of the inspection robots and UAV are shown in Table 4. Table 4. Key parameters of inspection robots and unmanned aerial vehicles (UAV). PTZ: pan–tilt–zoom. Table 4. Key parameters of inspection robots and unmanned aerial vehicles (UAV). PTZ: pan–tilt–zoom. Robot Robot Specifications Dimensions (mm) Specifications Weight (mm) Dimensions Speed Weight Autonomy Speed Charge Autonomy Load capacity Charge Equipment Cameras Load capacity Equipment Sensors Cameras Sensors
other
other
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PIR PIR
TIR TIR
CIR CIR
UAV (DJ-Innovations, UAVDJI (DJ-Innovations, Phantom 4) DJI Phantom 4)
510 × 270 × 156 510 ×15.2 270kg × 156 0.65 m/s 15.2 kg 3h 0.65 m/s 2.5 h h 53 kg 2.5 h
910 × 420 × 816 910 ×44.8 420 kg × 816 0.72 m/s 44.8 kg 8.5 h 0.72 m/s 6h 8.5 h 20 kg 6h
950 × 420 × 1100 kg1100 950 × 56.6 420 × 0.52 m/s 56.6 kg 7.8 h 0.52 m/s 6h 7.8 25 h kg 6h
289.5 × 289.5 × 196 289.5 ×1.38 289.5kg× 196 20 m/s 1.38 kg 28 min 20 m/s 1h 28 min / 1h
PTZ5 camera kg Temperature, humidity, inclination PTZ camera Temperature, humidity, inclination Infrared camera
Infrared camera
PTZ ×202kg cameras PTZ 25 × 2kg cameras Temperature, Temperature, humidity, inclination humidity, inclination PTZ × 2 cameras PTZ × 2 cameras Infrared camera, Temperature, humidity, Temperature, humidity, Laser radar, Infrared camera, inclination inclination Inertial Measurement Laser radar, Infrared camera, Laser Unit/Global IMU/GPS radar, Inertial Positioning System Measurement Infrared camera, Laser (IMU/GPS) Unit/Global radar, IMU/GPS Positioning System (IMU/GPS)
Down/ camera / Down camera /
/
/
In the previous chapters, the smart grid sensing methods in different literatures have been 3.2.2. Sensors discussed. The power grid characteristic parameters and non-contact sensing methods are also In the previous chapters, the smart grid sensing methods in different literatures have been discussed. summarized. The power characteristic parameters non-contact methods are also summarized. In thisgrid work, a Multi-Robot Cyber and Physical Systemsensing (MRCPS) is designed to measure the In this work, a Multi-Robot Cyber Physical System (MRCPS) is designed to measure the variation variation in the parameters of the transmission line. In different tasks, different sensors can be in the parameters line. to In obtain different different canfor be selected according selected accordingoftothe thetransmission actual situation thetasks, desired data. sensors Especially small UAVs with limited load capacity and battery capacity, it usually carries only small cameras for short-time inspection tasks. The robot team chooses the PZT camera (ER580) as the main measuring instrument for the visible light sensing method. In addition, special custom measuring instruments are adopted as
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to the actual situation to obtain the desired data. Especially for small UAVs with limited load capacity and battery capacity, it usually carries only small cameras for short-time inspection tasks. The robot team chooses the PZT camera (ER580) as the main measuring instrument for the visible light sensing method. In addition, special custom measuring instruments are adopted as well for infrared camera and LiDAR devices. In other measurements, II/DAS-20 measures the tilt angle of the robot so as to calculate the wind direction and wind speed, and the DS18B20 measures the temperature of the robot and environment. All of these sensors can be selectively installed on the Inspection Robot to fit its intended use, especially for infrared camera and LiDAR sensors, which can be installed at both ends of the robot (TIR, CIR) in different applications. 3.2.3. Communication and Navigation Methods In a previous study [27], we proposed a Robot Delay-Tolerant Sensor Network (RDTSN) for a multi-robot system used in the inspection of transmission grids. Several inspection robots and communication nodes deployed along the transmission line formed an intermittently-connected mobile wireless sensor network. The communication nodes include static nodes (SNs) and wireless central nodes (WCNs). The WCNs are connected to an Optical Fiber Composite Overhead Ground Wire (OPGW). The main feature of RDTSN is that all of the nodes in the network do not need to maintain real-time communication. Data interaction occurs when a mobile robot approaches other nodes. When the static network is interrupted, the network data is eventually carried by the robot to the nearest WCNs. In addition, the robot will choose a multi-hop transmission path according to the signal strength and transitivity of the nodes in the network. In addition, a multi-robot navigation and movement method was proposed, namely the Bidirectional Multi-robot Inspection (BMI) [27]. In a multi-robot system, the motion model based on formation control will be more advantageous in terms of reliability and efficiency. Therefore, the BMI model combines the vehicle traffic (two-way traffic rule) and formation control strategy. In the initial state, the members of the robot team are evenly distributed on two ground wires. In the process of motion, each robot will maintain an equidistant formation to maximize the efficiency of inspection. In addition, robots on two ground lines can only move in different directions. This allows the entire robot team to cycle clockwise or counterclockwise along the power line. The high-voltage ground wire is regarded as the path-constraint S, the power tower is considered the constraint point P, and the robot is a mobile node. (1) (2)
The coordinates at the unit center are the average of the multiple robots in a short time. Robots perform uniform distribution in inspection tasks.
• •
The whole transmission line is divided into two heterogeneity regions. The robots are evenly distributed on different ground lines in the two regions.
(3)
L The distance between any two robots on each ground line satisfies d ∈ ( n− 1 − a,
(4)
On each path, the moving node can only move in one direction. It moves in the opposite direction on the S to S’. At point P, it takes the time of Tpause ∈ (Tmin , Tmax ) to remain stationary or complete an obstacle-climbing process.
(5)
L n−1 ),
n > 1.
In the BMI model, d denotes the distance between the two robots on each ground line; L denotes the length of each ground line; n denotes the number of robots; and a denotes the accuracy of formation. All of the robots need to configure their GPS or network-based localization algorithm. The robots can inspect all of the transmission lines around it, including two ground lines. Therefore, the uniform distribution of the robots can achieve the best inspection efficiency.
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4. Methods and Algorithms In the previous section, we introduced the inspection process of a single robot in a real-world environment. However, the MRCPS is a multi-robot system. The process of determining the composition and structure of a multi-robot team is directly related to the monitoring capabilities Sensors 2018, 18, x FOR PEER REVIEW 12 of 29 of the MRCPS. In this section, we study the problem of robot team formation, i.e., the generation of an efficientincooperative multi-robot team through robotic we capabilities and atheir social relationships. addition, order to make the MRCPS more economical, tried to find multi-robot team with a In addition, in order to make the MRCPS more economical, we tried to find a multi-robot team with a smaller team size and more efficient work. smaller team size and more efficient work. With references to the literature [28–31], the method of graph theory to model the multi-robot references to thethe literature [28–31], the method graph theorystudied. to modelInthe multi-robot team teamWith is introduced, and formation of robot team isofthen deeply practical tasks, the is introduced, and the formation of robot team is then deeply studied. In practical tasks, the overall overall performance of the multi-robot team is not the simple adding of each robot’s working performance team notsocial the simple adding of each robot’s working performance. It is performance.ofItthe is multi-robot often affected by isthe relationships between robots, such as communication often affected by the and social relationships between robots, suchperformance as communication protocols, protocols, software hardware compatibility, and their in tasks. How tosoftware form an and hardware compatibility, and their performance in tasks. How to form an efficient robot team efficient robot team based on task allocation is a hot topic in the field of multi-agent/robot andbased cyber on task allocation is a hotand topic inalso the field of multi-agent/robot and cyber physical system [32–34], physical system [32–34], it is the focus of this paper. and it is also the focus of this paper.
4.1. Robot Performances 4.1. Robot Performances Heterogeneous robots have different abilities, which affect their performance in tasks. One Heterogeneous robots have different abilities, which affect their performance in tasks. One way to way to depict the ability of heterogeneous robots is to assign a value Ci to each robot Ri, where Ci depict the ability of heterogeneous robots is to assign a value Ci to each robot Ri , where Ci corresponds corresponds to the average ability of robot Ri in tasks. In this work, we measure the ability of a to the average ability of robot Ri in tasks. In this work, we measure the ability of a robot according to its robot according to its contribution to overall team performance in a task, rather than in a binary contribution to overall team performance in a task, rather than in a binary manner (capable/incapable). manner (capable/incapable). This method, as shown in Figure 8a, will affect the ability of robots in This method, as shown in Figure 8a, will affect the ability of robots in different missions. different missions.
LiDAR
PZT Camera Infrared Camera
Figure 8. 8. The The main main sensors sensors and and installation installation of of the the inspection inspection robot. robot. Figure
Although Although the the model model represents represents the the average average ability ability of of all all of of the the robots robots in in tasks, tasks, itit cannot cannot achieve achieve the comprehensive evaluation under dynamic task scenarios. Since robots are working the comprehensive evaluation under dynamic task scenarios. Since robots are workingin inaadynamic dynamic environment, environment, their their performance performance may vary vary greatly greatly according according to to specific specific scenarios. scenarios. Since Since the the robot’s robot’s ability is in un-modal distribution, its deviation may vary in different tasks. Therefore, we ability is in un-modal distribution, its deviation may vary in different tasks. Therefore, we use use 2 Normal-Distribution Normal-Distribution variables variables CCii ~N(µ, ~ N(μ,σσ2)) to to evaluate evaluate the the robots’ robots’ performance. performance. For For example, example, robot robotRRi i 2 which is the non-deterministic ability of robot R in tasks. is is associated associated with variable Cii ~~N(µ, N(μ, σσ2),),which is the non-deterministic ability of robot Ri in i tasks. Figure 9 gives an example of three heterogeneous robot capabilities, in which Figure Figure 9 gives an example of three heterogeneous robot capabilities, in which Figure 9a 9a reflects reflects the the task. The mean capability of team {r1 ,{r r21}, ris2}better than {r1 , {r r31}, rat3} themean meancapability capabilityofofthe therobots robotsinin the task. The mean capability of team is better than this time. Figure 9b uses distribution methodmethod to express distribution of robot capability at this time. Figure 9b the usesnormal the normal distribution to the express the distribution of robot in dynamicinscenes, where r2 has higher than r3 . Therefore, the new evaluation capability dynamic scenes, where r2 variance has higher variance than r3. according Therefore,toaccording to the new mechanism, {r1 , r3 } may {r surpass {r1 ,surpass r2 }. evaluation mechanism, 1, r3} may {r1, r2}.
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1.5 5.7 Ci～N(5.7, 12.6) Ci～N(1.5, 1.3) Figure 9. Capability graphs with three agents; (a) Values; (b) Normally-distributed variables. Figure 9. Capability graphs with three agents; (a) Values; (b) Normally-distributed variables. r2 r3 r2 r3
4.2. Modeling Task-Based Relationships 4.2. Modeling Task-Based Relationships (a)
(b)
In order to find out the best scheme of forming all of the robots, it is necessary to establish an Capability graphs with three (a) Values; variables.to establish an In order toFigure find9.out the best scheme of agents; forming all of (b) theNormally-distributed robots, it is necessary accurate social relationship model. In the field of social networking, a social graph is used for the accurate social relationship model. In the field of social networking, a social graph is used for the formation of multi-agent [29]. The vertices in the graph represent agents, and the vertices are 4.2. Modeling Task-Based teams Relationships formation teams [29]. The vertices in the graph agents, andindicates the vertices linkedof bymulti-agent edges to imply the social relationships between them.represent The weight of edges the are In order to find out the best relationships scheme of forming all of the robots, it isweight necessary to establish an linked by edges to imply the social between them. The of edges indicates strength of the relationship. The focus of this paper is to form a robot team with the best the accurate social relationship model. In the field of social networking, a social graph is used for the strength of the relationship. The focus of this paper is to form a model robot team with the best performance performance in tasks. Therefore, a task-based multi-robot graph is proposed. formation of multi-agent teams [29]. The vertices in the graph represent agents, and the vertices are The robot team is represented by the graph G = (V, E), where V represents robot in the team, in tasks.linked Therefore, a task-based multi-robot graph model is proposed. by edges to imply the social relationships between them. The weight of the edges indicates the and E reveals the task-based relationships between those robots (nodes), which is an edge Thein the Thestrength robot team represented the of graph = (V, where V represents robot of the isrelationship. Thebyfocus this G paper is E), to form a robot team withthe theset. best value e ij represents the communication efficiency between robots, which is used to calculate the team, and E revealsinthe task-based betweengraph thosemodel robots (nodes), which is an edge set. performance tasks. Therefore, relationships a task-based multi-robot is proposed. weighte of the edge (the strength of relationship between robots). The robot team is represented by the graph G = (V, E), where V represents theis robot in the team, The value represents the communication efficiency between robots, which used to calculate the ij Figure 10 shows an example of a robot team graph model.(nodes), In Figure 10a, a fully connected and E reveals the task-based relationships between those robots which is an edge set. The weight of the edge (the strength of relationship between robots). task-based is used represent the efficiency strength of task relationships among robots. Each pair value eij graph represents the to communication between robots, which is used to calculate the of Figure 10 shows an example of a robot team graph model. In Figure 10a, a fully connected vertices theedge graph has edge E connections, different edges give corresponding weightin of the (the strength of relationship betweenand robots). task-based graph isefficiency used strength task relationships among robots. Each pair of Figure 10 showstoanrepresent ofthe a robot team graph model. Ingraph Figureis 10a, connected communication eexample ij (relation strength). A of fully connected verya fully complex, i.e., the vertices in the graph has E represent connections, andisdifferent edges give among corresponding communication task-based graph is edge used to strength of task relationships robots.the Each pair of task-based relationship between the twothe robots completely independent, because relationship vertices in the graph has edge E connections, and different edges give corresponding efficiency e (relation strength). A fully connected graph is very complex, i.e., the task-based weightsijbetween robots are arbitrary. communication ij (relation strength). A fully connected graph is very complex, i.e., the relationship between efficiency the two erobots is completely independent, because the relationship weights task-based relationship between the two robots is completely independent, because the relationship between robots are arbitrary. weights between robots are arbitrary. r1 0.6
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Figure 10. Weighted task-based (b)connected task-based graph (a) graphs with three agents. (a) A fully with three agents; (b) A simplified task-based graph with three agents. Figure 10. Weighted task-based graphs with three agents. (a) A fully connected task-based graph
Figure 10. Weighted task-based graphs with three agents. (a) A fully connected task-based graph with In order to simplify the model used to describe the concept of relationship with three agents; (b) A simplified task-based graphthe withteam threerelationship, agents. three agents; A simplified task-based withtask-based three agents. transitivity is (b) introduced. Figure 10b is a graph simplified graph model based on the transitivity order to simplify the modelofused describe the team relationship, theisconcept of socialInrelations. The transitivity the to robots’ communication efficiency given of in relationship Equation (1).
In order to simplify the model used describe task-based the team graph relationship, the concept of relationship is introduced. 10b is to a simplified model on the transitivity Thetransitivity eij represents the directFigure communication efficiency of the robots, and iebased ij represents the indirect transitivity is introduced. Figure 10bthe isofathe simplified task-based graph model based on thesatisfies transitivity of social relations. The transitivity robots’ efficiency is given in graph Equation (1). communication efficiency. When weight of communication the edges in the fully connected The e ij represents the direct communication efficiency of the robots, and ie ij represents the indirect of social relations. The transitivity of the robots’ communication efficiency is given in Equation Equation (2), the edge Eij is removed, that is, the weighted task-based graph model is simplified (1). communication When the weight of the edges in robots, the fullyand connected graph satisfies The eunder the efficiency. direct communication efficiency of the ieij represents the indirect the premise of keeping the best communication path. ij represents Equation (2), the edge Eij is removed, that is, the weighted task-based graph model is simplified communication efficiency. When the weight of the edges in the fully connected graph satisfies under the premise ofie keeping communication eik the best ekj , (i , j , k ) E ,path. i j k , eik , ekj 0 ,1 , (1) under Equation (2), the edge Eij is ijremoved, that is, the weighted task-based graph model is simplified k , jE , e e , ( i , j , k ) E , i j k , e , e 0 , 1 the premise of keeping the ie best communication path. ij ik kj ik kj (1)
k , jE
ieij = eik
∏
k,j∈ E
ekj , ∀(i, j, k) ∈ E, i 6= j 6= k, eik , ekj ∈ [0, 1],
(1)
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(2)
ieij ≤ eij , ∀(i, j) ∈ E,dimax 6= (j,ri e,ijrj∈) [0, 1],
(ri , rj )
φ (ri , r j ) =
(2)
dmax (ri , e r jij) , , i , jE ∑ eij
(3) (3)
i,j∈ E
In the weighted task-based graph, the maximum distance between vertices represents the best In the weighted task-based graph, the maximum vertices represents the best communication efficiency as different robots work distance together.between By introducing the Compatibility communication efficiency as different robots work together. By introducing Compatibility Function Function (Equation (3)), which shows the communication efficiency andthe social relations of robots, (Equation (3)), which shows the communication efficiency and social relations of robots, we can we can explicitly model task-based relational models. The Compatibility Function reflects the explicitly model task-based relational models. reflects the in compatibility compatibility between different robots, whereThe dmaxCompatibility (ri, rj) is the Function maximum distance the graph. between wherebetween dmax (ri , the rj ) iscommunication the maximum distance the compatibility graph. There is positive There is adifferent positiverobots, correlation efficiencyinand ofathe robot correlation between the communication efficiency and compatibility of the robot team, so Equation team, so Equation (3) is a monotone increasing function, and a longer distance corresponds to(3)a is a monotone increasing function, and a longer distance corresponds to a higher compatibility. higher compatibility. 4.3. Defining the Weighted Synergy Graph 4.3. Defining the Weighted Synergy Graph In the above sections, we have described in detail how the task-based relationship is represented In the above sections, we have described in detail how the task-based relationship is by a compatible function, which uses the distance between the vertices in the graph. Again, we have represented by a compatible function, which uses the distance between the vertices in the graph. also introduced how the robot’s ability is represented as a normal distribution variable. In this Again, we have also introduced how the robot’s ability is represented as a normal distribution section, we formally define the weighted synergy graph and introduce how it is used to calculate the variable. In this section, we formally define the weighted synergy graph and introduce how it is performance of the robot team in the task. The weighted synergy graph is defined as follows. used to calculate the performance of the robot team in the task. The weighted synergy graph is defined 1. G =as (V,follows. E) is a connected weighted graph. V ==(V, R =E){ris1 ,ar2connected , . . . }, i.e.,weighted the set ofgraph. vertices (V) that corresponds to the set of robots (R); and G E=R (ri=, r{r an i.e., edgethe between robots r(V) withcorresponds an efficiencytoweight . V set of vertices the setofofeijrobots (R); and E = (ri, j ,1e, ijr)2,is…}, i , rj that 2 rCj,i e~N ij) is(µ an edge between robots r i , r j with an efficiency weight of e ij . i , σi ) is robot ri ’s capability at the task. C i ~ N i, )σis i2)the is robot ri’s capability at distance the task.of a pair of vertices in a relational graph. dmax (r(μ , r maximum weighted i j dInmaxthe (ri, different rj) is the maximum weighted distance a relational weighted graphs G and G’, ifofRa=pair R’, of C vertices = C’ andinthe dmax (ri , rgraph. j ) of all vertices In the different weighted graphs G and G’, if R = R’, C = C’ and the d max (ri, rj) of all vertices are are the same, they are equivalent graphs. If Equation (2) is satisfied, the weighted graph of the same, theyEare equivalent graphs. If Equation (2) is satisfied, the weighted graph of non-maximum ij is removed as the simplified weighted synergy graph. non-maximum Eij is removed as the simplified weighted synergy graph. Figure Figure 11 11 shows showsthree threeexamples examplesofofweighted weightedsynergy synergygraphs graphswith withthree threerobots, robots,dmax dmax(r(r11,, rr22)) = = 0.5, 0.5, ddmax (r , r ) = 0.3, and d (r , r ) = 0.6 in all graphs. The three graphs have different structural forms. max 2 3 1 3 max (r2, r3) = 0.3, and dmax (r1, r3) = 0.6 in all graphs. The three graphs have different structural forms. In twotwo edges exist,exist, and the have three edges. Figure In 11b,c, especially In Figure Figure11a, 11a,only only edges andother the graphs other graphs have threeInedges. Figure 11b,c, the edge E23 Figure not used, to get better it is 12 to E 23 can especially theofedge E2310c of is Figure 10c isedge not Eused, edge E12betoused E23 can be aused to path get abecause better path between R and R . Therefore, in general, more than one graphic structure can be used to define 3 because it 2is between R2 and R3. Therefore, in general, more than one graphic structure can be used the social relationships between robots. When the corresponding robots in therobots three graphs to define the social relationships between robots. When the corresponding in the have three the same ability, they are equivalent weighted graphs, where Figure 11a is the simplified weighted graphs have the same ability, they are equivalent weighted graphs, where Figure 11a is the synergy graph. simplified weighted synergy graph. 2. 1. 2. 3. 3. 4. 4. 5. 5.
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Figure Three equivalent equivalentweighted weightedsynergy synergygraphs, graphs,i.e., i.e., the shortest distance between pairs Figure 11. 11. Three the shortest distance between pairs andand the the capability of robots is equivalent in three the three graphs. A simplified weighted synergy capability of robots is equivalent in the graphs. (a) A(a) simplified weighted synergy graph;graph; (b) A (b) A fully-connected weighted synergy graph; (c) other The other fully-connected weighted synergy graph. fully-connected weighted synergy graph; (c) The fully-connected weighted synergy graph.
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Using the weighted synergy graph, we quantify the performance of the robot team according to the following steps. Step 1: The robot in team R is composed of the minimum synergy team T = (ri , rj ) in every two units. Step 2: In each minimum synergy team T = (ri , rj ), the synergy ability of two robots is calculated according to the Synergy Function (Equation (4)). Due to the introduction of social relations, the working ability of each robot in the synergy team is independent, and it is also affected by compatibility. Therefore, the team working ability is the product of multiplying with the Synergy Function after adding the independent robot capability Ci and Cj . Step 3: The Synergy Function is used in the calculation of the working ability of any synergy team team Ri . The average working efficiency of robots in any team is given by the Efficiency Function (Equation (5)). Due to the connectivity of weighted synergy graph, the Synergy Function of two robots exists in any team. Therefore, any synergy team Ri of a robot team R can be constructed by one or more minimum synergy teams T. dmax (ri , r j ) · (Ci + Cj ), (4) ψ (ri , r j ) = ∑ eij i,j∈ E
η (Rx ) =
dmax (ri , r j ) 1 · (Ci + Cj ), | R x |(| R x | − 1) {r ,r∑}∈ R ∑ eij
(5)
dmax (ri , r j ) 1 · ( µ i + µ j ), ∑ | R x |(| R x | − 1) {r ,r }∈ R ∑ eij
(6)
i j
µ( R x ) =
i,j∈ E
i j
σ2 ( R x ) =
1 2
| R x | (| R x | − 1)
2
i,j∈ E
∑
φ2 (ri , r j ) · (σi2 + σj2 ),
(7)
{ri ,r j }∈ R
According to the definition of the weighted synergy graph, the average working efficiency of robot team R is a Normal-Distribution of random variables Cij ~N (µR , σR 2 ). The mathematical expectation of the working efficiency of the robot team is µR , with its variance being σR 2 . Their mathematical expressions are shown in Equations (6) and (7). 4.4. Optimization and Selection of Multi-Robot Team 4.4.1. Optimization of Robot Team The weighted synergy graph model introduces the variability of the transitivity of robot relations and the robot’s ability in tasks. In addition, we also define the process of forming the robot team and the method of calculating the average working efficiency of the robot in any team. However, the result of the Efficiency Function is a Normal-Distribution variable. In order to reasonably establish a task-based efficient robot team, these variables need to be sorted, and the following definitions are used. Definition 1: Assume that there is an optimized robot team Rξ ⊆ R, the probability that η(Rξ ) (team working efficiency) is higher than η o (objective task demand) is ξ, and the probability of any robot team Rx ⊆ R meeting objective task demand η o is no more than ξ. Equation (8) should be satisfied. P ( η R ξ ≥ η a ) = ξ ≥ P ( η ( R x ) ≥ η a ),
(8)
Inference 1: If there exists the probability ξ of the optimized team Rξ ⊆ R meeting the objective task demand η o of the task, ξ should satisfy Equation (9).
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ξ = 1 − Φ(
µo − µ( Rξ ) ), σ ( Rξ )
(9)
where Φ is the distribution function of the standard normal distribution, and µo is the mathematical expectation of objective task demand η o . The optimization probability ξ of the robot team indicates the probability that the robot optimization team Rξ exists, and also shows the cost performance and safety of Rξ in the task. The ξ of the robot team is negatively correlated with the risk of completing tasks; that is, the greater the ξ value, the greater the security of completing the task and the lower the risk. However, a low risk also means a high investment and low return. When the security is too high, the cost performance of the task will degrade. Before the formation of the robot team, the task’s cost performance and safety need to be considered in advance. Before the optimization of the robot team, the tolerance of the best team to the risk is set in advance according to the actual situation of the task, in order to balance the team’s cost and security. For example, when ξ = 0.6 is considered in the task, the best team performs the task in a compromising way. When ξ > 0.6, a team with high risk and high reward is more popular. When ξ < 0.6, a team with low risk and low economy is more popular. Definition 2: The task risk factor of robot optimization team is ρ ∈ (0, 1), and ρ satisfies Equation (10). ρ = 1 − ξ, ρ, ξ ∈ (0, 1)
(10)
4.4.2. Formation Algorithm of Multi-Robot Team The main target of our research is to find the best robot team under the given conditions: the task target risk factor (ρ*) and the mathematical expectation of objective task demand (µo ). Thus, we need to find that the team with better ability is composed of the minimum synergy teams T in the Weighted Synergy Graph. The following theorem is presented to analyze the computational complexity. Theorem 1. The problem of finding the best team of the MRCPS is non-deterministic polynomial-time hard (NP-hard). Proof of Theorem 1. By definition, a multi-robot team consists of one or more minimum synergy teams T. From the unweighted synergy graph, we need to figure out the maximum vertices’ values of the synergy teams. Thus, we turn the problem into a maximum clique problem (MCP) in graph theory to solve it. Suppose G = (V, E), where E = (vi , vj ), is an unweighted graph. The objective is to determine whether there is a clique of at least n sizes, i.e., a subgraph of n vertices that are completely connected. Through defining a weighted graph G’ = (V, E’), where E = (vi , vj , eij ), G can be regarded as a special case of G’ having equal weights, such as E = (vi , vj , 1). Hence, a clique in G corresponds to a clique in G’ that is fully connected with the edges of weight 1. Again, a clique has the greatest synergy (compared with other subsets of size n), because they have the largest number of edges and a weight of 1. Since the MCP is NP-complete, then that of the MRCPS is NP-hard. In the process of finding the best team, the optimization probability ξ of different team combinations can be calculated, and the task risk factor ρ of the robot optimization team is converted to Equation (10). Assuming that the task target risk factor is ρ*, the best robot team Rξ * ⊆ R is the optimization team of the task risk factor ρ matching the target risk factor ρ*. In view of the good performance of the simulated annealing algorithm in the maximum clique problem, we introduce it
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into a team formation algorithm. In order to optimize and sort the task risk factor ρ of the multi-robot team, a Multi-Robot Team Formation Algorithm (MTFA) based on the Simulated Annealing (SA) algorithm is proposed in this paper. The Simulated Annealing (SA) algorithm is designed to determine the global optimal solution of objective function [35,36]. The MTFA based on the SA does not depend on the selection of an initial value solution; rather, it can find the optimal solution of a target under any initial condition. If the complexity λ of the initial robot set R is large enough, then the global optimal solution can be determined. The MTFA is controlled by two layers of loop. The external loop is an iterative process. Given that the complexity λ0 of an initial robot set and the attenuation factor α is less than 1, a variable k is used to represent the number of loops of the external loop, and λk represents the complexity of the robot team in the kth loop. After each external loop, the system is iterated according to the attenuation factor α, so the risk factor λk satisfies Equation (11). λk > 0 lim λk = 0 , k→∞ λk = αλ0
(11)
In the internal loop, the MTFA follows the SA principle and ranks the objective function values. The smaller objective function value is retained in the iteration, the judgment condition is added, and the solution that may be deteriorated is subjected to probabilistic reception. The Metropolis acceptance guideline should be followed:
P=
n o exp f ( Rk )− f ( Rk−1 ) ,
f ( R k ) − f ( R k −1 ) > 0
1,
f ( R k ) − f ( R k −1 ) ≤ 0
λk
,
(12)
where f (x) is the objective function, Rk is the new solution, and Rk −1 is the old solution. The Objective Function of the solution is expressed by Equation (13), and it is the difference between the task risk factor ρ of the robot team, and the target risk factor ρ* after k iterations. µo − µ( Rk ) f ( Rk ) = ρ∗ − Φ( ) , σ( R )
(13)
k
The SA method can effectively sort the robot team risk factor ρ. However, the running time of the SA varies from tens of minutes to several hours, depending on the complexity of the robot set. Therefore, an adaptive improvement method (MTFA) is proposed by designing a single perturbation rule in the original SA. Equation (14) is the definition of a single perturbation rule: f num = max{2, int(πλ0 )} n o , f range = max 1, int(ελ0 C f num ) | R|
(14)
where fnum is the perturbation range of the robot’s number, frange is the neighborhood range of the MTFA perturbation, int() is an approximate rounding function, Cb a is the permutation combination of the robots set, and π and ε are custom adaptive strengths. Equation (14) associates the number of the perturbation number and neighborhood range of perturbation with the complexity of robot set. When the complexity is high, the perturbation neighborhood range is large, and the number of perturbation points is large, which can facilitate the convergence of the algorithm. With the decrease of complexity, the number of perturbation points of the algorithm is reduced, the perturbation neighborhood interval is reduced, and the detail optimization phase is entered. At this time, the optimization result can be further improved. Algorithm 1 shows the pseudo-code of the Multi-Robot Team Formation Algorithm (MTFA).
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Algorithm 1. MTFA for finding the optimization team. Robot team formation algorithm (R, ρ*, η o ) 1: if |R| > 2 then 2: Rk ← Random Team (R) 3: Calculating the objective function f (Rk ) 4: f (Rξ ) ← f (Rk ) 5: repeat () 6: Rk−1 ← Rk 7: f (Rk−1 ) ← f (Rk ) 8: Rk ← Neighbor Team (Rk− 1 ) 9: Calculating the objective function f (Rk ) 10: if accept (f (Rk−1 ), f (Rk )) then 11: Rk −1 ← Rk 12: f (Rk −1 ) ← f (Rk ) 13: f (Rξ ) ← f (Rk ) 14: end if 15: until done () 16: return f (Rξ ) 17: end if
Since the size of the target team (n) is not specified, the algorithm is run iteratively for increasing n and has a total run time of O(N3 ), where N is the size of a robot set. In particular, if the best team size is specified in advance, the algorithm runs in O(n2 ). In comparison, a brute force algorithm would take N O(( )). Compared with the traditional algorithm, MTFA based on a simulated annealing algorithm n can effectively reduce the running time and is more suitable for solving such NP-hard problems. 5. Results The previous sections describe the components, communication, and navigation methods of the Multi-Robot Cyber Physical System (MRCPS). Section 4 also researches the robot team weighted synergy graph model and proposes a Multi-robot Team Formation Algorithm (MTFA) based on graph theory and the Simulated Annealing (SA) algorithm. In this section, the aforementioned method is employed to capture the robot’s team performance in real-world scenarios. The organization of this chapter is as follows: Section 5.1 establishes a model of the robot team in a real-world scenario. Section 5.2 describes testing of mimic transmission line scenarios and provides an analysis and discussion of the experimental results. 5.1. Modeling and Simulation of the MRCPS The MRCPS should autonomously and periodically cover transmission lines to monitor environmental variables. This paper initiates a task-based multi-robot team model for the maintenance and monitoring of transmission lines. The system composition plan is changeable for different tasks. The inspection and communication capabilities of a multi-robot team should meet the objective task demand, and their values can be obtained by previous experience. In this paper, the inspection time t is used to describe the efficiency of robot inspection. The mathematical expectation of the robot team’s objective task demand in different inspection tasks satisfies Equation (15). The working ability of each independent robot is expected to satisfy Equation (16), and the variance of working ability can be obtained by previous experience. L , to | R x |
(15)
tw ≤ to , tw > to
(16)
µo (to , L, no ) = no ( µi =
vτ ttwo , vτ,
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Ce = Cs /Ct ,
(17)
In Equation (15), no denotes the number of targets for inspection tasks, L denotes the mileage of inspection routes, to denotes the required inspection time, and |Rx | = N denotes the number of robots in the team. Equation (15) is a function that takes the duration of inspection t as an independent variable. It can alter the objective demand of the task by changing the value of parameters. In Equation (16), v denotes the motion rate of a robot, tw denotes the nu-refueled inspection time, and τ denotes the average inspection time length for a single target. The communication efficiency between robots is obtained by Equation (17) where Ce denotes the communication efficiency, Cs denotes the communication control semaphore, and Ct denotes the total amount of communication. A task-based multi-robot team model aims at different task demands. The optimal team is formed on the basis of the weighted synergy graph and the algorithm of forming a robot team. The team performs real-time or delay tolerant communication with other wireless nodes in the inspection task. The uniform distribution of the motion model is used for the inspection of transmission lines. The specific steps for forming a multi-robot team are as follows. Step 1: Analyze and determine the objective demand of the robot inspection task of transmission lines. Step 2: Calculate the robots’ working ability and communication efficiency, and establish a weighted synergy graph of the multi-robot team based on the task. Step 3: Use the Multi-Robot Team Formation Algorithm (MTFA) to find the best team for an objective task demand. Step 4: Establish an inspect task database and assign the inspection task of each robot inspection task in the team. Step 5: Form a wireless dynamic sensor network with the heterogeneous multi-robot team and the static nodes for the transmission line monitoring. Step 6: The robots adopt a uniformly-distributed motion model BMI, and the transmission line inspection by multi-robot team is conducted. Equation (18) is used to calculate the effectiveness of forming the multi-robot team. E f f ectiveness( R x ) =
∗ ) [ ρ∗ −|ρ∗ − ρ( R x )|] − ρ( Rmin , ∗ ) ρ∗ − ρ( Rmin
(18)
where ρ* is the objective task risk factor, Rmin is the robot team with the minimum risk factor obtained under the objective task demand, and Rx is the select robot team. Then, the robot team formation effectiveness is a value from 0 to 1, where 1 is the target team and 0 is the worst performance team. We use the team formation effectiveness to measure the difference in task performance between the robot team and the target team to further evaluate the practical role of the weighted synergy graph model. Two experiments are designed to verify the effectiveness of the weighted synergy graph model and Multi-robot Team Formation Algorithm (MTFA). In the first experiment, a comparison is performed on the effect of the weighted synergy graph model and the unweighted synergy graph model on the robot team. The second experiment compares the performance of the MTFA with that of the original SA. The total number of robots in the robot set is N. For each N, the robot sets are tested 100 times. The MTFA parameters are configured as follows: complexity of initial robot set λ0 = N, attenuation factor α = 0.95, adaptive strength κ = 1, and adaptive strength ε = 0.1. Figures 12 and 13 show the effectiveness of the team found in the weighted and unweighted synergy graph, where Figure 12 uses 1000 iterations and Figure 13 uses 2000 iterations.
model on the robot team. Thenumber second experiment ofN, thethe MTFA of the original SA. The total of robots incompares the robot the set performance is N. For each robotwith setsthat are of the original SA. The total parameters number of robots in the robot set is N. For each N, the robot sets tested 100 times. The MTFA are configured as follows: complexity of initial robot setare λ0 tested 100 times.factor The MTFA parameters configured as follows: complexity initial robot set λ0 = N, attenuation α = 0.95, adaptive are strength κ = 1, and adaptive strength εof = 0.1. = N, attenuation factor = 0.95,the adaptive strength = 1,team and found adaptive ε = 0.1. Figures 12 and 13αshow effectiveness of κthe in strength the weighted and unweighted Figures 12 where and 13Figure show 12 theuses effectiveness of theand team found in the2000 weighted and unweighted synergy graph, 1000 iterations Figure 13 uses iterations. Sensors 2018, 18, 3146 20 of 29 synergy graph, where Figure 12 uses 1000 iterations and Figure 13 uses 2000 iterations. 1.0 1.0
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Figure 12. Effectiveness of teams found with the weighted or unweighted synergy graph and Figure 12. Effectiveness of teams found with the weighted or unweighted synergy graph and Figure 12. Effectiveness of teams found(MTFA), with the weighted or annealing unweighted synergy graph and Multi-Robot Team Formation Algorithm using simulated with 1000 iterations. Multi-Robot Team Formation Algorithm (MTFA), using simulated annealing with 1000 iterations. Multi-Robot Team Formation Algorithm (MTFA), using simulated annealing with 1000 iterations. 1.0 1.0
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Figure synergy graph graph and and MTFA, MTFA, Figure 13. 13. Effectiveness Effectiveness of of teams teams found found with with the the weighted weighted or or unweighted unweighted synergy using simulated annealing with 1000 and 2000 iterations. Figure 13. Effectiveness of teams found with theiterations. weighted or unweighted synergy graph and MTFA, using simulated annealing with 1000 and 2000
using simulated annealing with 1000 and 2000 iterations.
As can be seen from Figure 12, the performance of the weighted graph model is superior to that of As can be seen from Figure 12, the performance of the weighted graph model is superior to the unweighted graph model. In addition, with the growth of the initial size of the robots’ set, the two Asthe canunweighted be seen from Figure 12, In theaddition, performance of the weighted is superior to that of graph model. with the growth of the graph initial model size of the robots’ set, models tend to exhibit similar properties, which are described below. As the growth of the robot set that of the unweighted model. Inproperties, addition, with theare growth of thebelow. initial size of the robots’ set, the two models tend tograph exhibit similar which described As the growth of the increased, the effectiveness of the two methods is firstly improved rapidly (in the range of the size of the two tendthe to effectiveness exhibit similar which is arefirstly described below. As the(in growth of the robot setmodels increased, ofproperties, the two methods improved rapidly the range of robots from two to four), and then relatively stabilized with a slight downward trend. robot setofincreased, thetwo effectiveness of the two methods is firstly with improved rapidly (in thetrend. range of the size robots from to four), and then relatively stabilized a slight downward As shown in Figure 13, the performance of a 2000 iteration is better than that of a 1000 iteration, the size robots two four), and then relatively stabilizediswith a slight downward As of shown in from Figure 13,tothe performance of a 2000 iteration better than that of a 1000trend. iteration, whether using the weighted graph model or the unweighted graph model. Furthermore, under different As shown in Figure 13, the performance of a 2000 iteration is better than that of a 1000 iteration, whether using the weighted graph model or the unweighted graph model. Furthermore, under conditions, the curves of effectiveness show a similar trend, i.e., first increasing rapidly and then whether the weighted graph model or the unweighted under different using conditions, the curves of effectiveness show a similar graph trend, model. i.e., firstFurthermore, increasing rapidly declining gently. different conditions, the curves of effectiveness show a similar trend, i.e., first increasing rapidly and then declining gently. While the size of the robots set is small, especially from two to four, the optimal solution and the and then declining While the sizegently. of the robots set is small, especially from two to four, the optimal solution and target have a large error, although the two methods can quickly find the optimal team, and the error of Whilehave the size of the robots set is the small, two to find four,the theoptimal optimalteam, solution the target a large error, although twoespecially methods from can quickly andand the the solution decreases gradually with the set increasing. Therefore, when the size of the robots set is the target have a large error, although the two methods can quickly find the optimal team, and the error of the solution decreases gradually with the set increasing. Therefore, when the size of from two to four, the effectiveness of the two models increases rapidly with the increase of the set. error of the solution decreases gradually with the set increasing. Therefore, when the size of the As the size of the set increases further, the difficulty of calculating the optimal solution is gradually increasing, and it is more and more constrained by the computational time and the number of iterations. Therefore, the effectiveness curve shows a slow downward trend, and the group with more iterations obviously perform better. Figures 14 and 15 show the relationship between the operation time and the effectiveness of the robot team. The size of the initial robot set is 15 and 35, respectively. In Figures 14 and 15, the convergence rate of the MTFA’s optimal solution is much better than that of the original SA. Furthermore, the larger the size of the robot set, the more obvious the advantage of MTFA. In addition, the results of a larger robot set can be improved after removing the restriction of the computation time and the number of iterations.
Figures 14 and 15 show the relationship between the operation time and the effectiveness of the robot team. The The size size of of the the initial initial robot robot set set isis 15 15 and and 35, 35, respectively. respectively. In In figures figures 14 14 and and 15, 15, the the the robot team. convergence rate of the MTFA’s optimal solution is much better than that of the original SA. convergence rate of the MTFA’s optimal solution is much better than that of the original SA. Furthermore, the the larger larger the the size size of of the the robot robot set, set, the the more more obvious obvious the the advantage advantage of of MTFA. MTFA. In In Furthermore, addition, the results of a larger robot set can be improved after removing the restriction of the addition, the results of a larger robot set can be improved after removing the restriction of the Sensors 2018, 18, 3146 21 of 29 computationtime timeand andthe thenumber numberof ofiterations. iterations. computation 1.0 1.0 0.9 0.9
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Figure14. 14.Effectiveness Effectiveness ofteams teams foundwith with theweighted weighted synergygraph graph andMTFA; MTFA; thesize size of the Figure Effectiveness of of teams found found with the the weighted synergy synergy graph and and MTFA; the the size of the initial robot set is 15. initial robot set is 15.
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Figure15. 15.Effectiveness Effectivenessof ofteams teamsfound foundwith withthe theweighted weightedsynergy synergygraph graphand andMTFA; MTFA;the thesize sizeof ofthe the Figure 15. Effectiveness of teams found with the weighted synergy graph and MTFA; the size of the Figure initialrobot robotset setis 35. initial robot set isis35. 35. initial
5.2. Result of Field Experiments 5.2.Result Resultof ofField FieldExperiments Experiments 5.2. These were conducted at theattest of Wuhan to verify thetoeffectiveness Theseexperiments experiments were conducted thesite test site of ofUniversity Wuhan University University verify the the These experiments were conducted at the test site Wuhan to verify of the MRCPS for sensing the environmental variables of a transmission line. This test site isThis usedtest to effectiveness of the MRCPS for sensing the environmental variables of a transmission line. effectiveness of the MRCPS for sensing the environmental variables of a transmission line. This test simulate theto working environment the inspection robot. siteisisused used simulate theworking workingof environment ofthe theinspection inspectionrobot. robot. site to simulate the environment of In order to simulate the open terrain around the overhead transmission line, a testing site with 50-m length and 30-m width is located on the top floor of the building. In addition, the analog line uses a more complex distribution than the actual power line. The transmission line of the test site integrates an adjustable number of on-line devices to cause spatial variations in environmental variables. Figure 16 shows an image of a field experiment.
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In order to simulate the open terrain around the overhead transmission line, a testing site with In order to simulate the open terrain around the overhead transmission line, a testing site with 50-m length and 30-m width is located on the top floor of the building. In addition, the analog line 50-m length and 30-m width is located on the top floor of the building. In addition, the analog line uses a more complex distribution than the actual power line. The transmission line of the test site uses a more complex distribution than the actual power line. The transmission line of the test site Sensors 2018, 18, 22 of 29 integrates an3146 adjustable number of on-line devices to cause spatial variations in environmental integrates an adjustable number of on-line devices to cause spatial variations in environmental variables. Figure 16 shows an image of a field experiment. variables. Figure 16 shows an image of a field experiment.
Power line Power line UAV UAV
TIR TIR CIR CIR
Vegetation Vegetation On-line Device On-line Device
Figure 16. 16. The field field experiments, i.e., i.e., the Multi-Robot Multi-Robot Cyber Physical Physical System (MRCPS) (MRCPS) composed of of Figure Figure 16. The The field experiments, experiments, i.e., the the Multi-Robot Cyber Cyber Physical System System (MRCPS) composed composed of TIR, CIR and UAV performs an inspection task. TIR, TIR, CIR CIRand andUAV UAVperforms performsan aninspection inspectiontask. task.
this work, work, both both effects effects were were fully fully validated: validated: the effectiveness of collaborative work of the the In this In this work, both effects were fully validated: the effectiveness of collaborative work of the in MRCPS, MRCPS, and multi-robot in and the the balance balance performance performance of the economy and collaboration capability of multi-robot in MRCPS, and the balance performance of the economy and collaboration capability of the multi-robot multi-robot team team in in the the multiple multiple scenarios. scenarios. the multi-robot team in the multiple scenarios. Firstly, the the inspection inspection robot robot carries carries the the laser laser scanner scanner and and the the Inertial Inertial Measurement Measurement Unit Unit ((IMU) Firstly, IMU) Firstly, the inspection robot carries the laser scanner and the Inertial Measurement Unit (IMU) equipment to measure the space parameters. The basic spatial data of the test site is obtained, such equipment to measure the space parameters. The basic spatial data of the test site is obtained, such as equipment to measure the space parameters. The basic spatial data of the test site is obtained, such as the number of transmission the length each type, and number, andof location of the number of transmission lines, lines, the length of eachof line, theline, type,the number, location devices on as the number of transmission lines, the length of each line, the type, number, and location of devices and the vegetation obtained spatial data,system a multi-robot system the line, on andthe theline, vegetation distance. Withdistance. obtainedWith spatial data, a multi-robot inspection map devices on the line, and the vegetation distance. With obtained spatial data, a multi-robot system inspection mapdatabase and inspection are then constructed. The obtained point cloud data and and inspection are thendatabase constructed. The obtained point cloud data and map are shown in inspection map and inspection database are then constructed. The obtained point cloud data and map are shown in Figure 17 from (these data are cited from our previous articles [24–26], which have Figure 17 (these data are cited our previous articles [24–26], which have described the acquisition map are shown in Figure 17 (these data are cited from our previous articles [24–26], which have described theresults acquisition process and results in 17a detail), in which Figuredata 17a is the point data process and in detail), in which Figure is the bycloud the robot, described the acquisition process and results in detail), in point whichcloud Figure 17a collected is the point cloud data collected by the robot, and Figure 17b is the constructed inspection map. and Figureby17b the constructed collected theisrobot, and Figureinspection 17b is the map. constructed inspection map. Power line (Walking Path) Power line (Walking Path)
Power line Power line
Edge of the site Edge of the site
Foreign body Foreign body
On-line Device On-line Device
Vegetation Vegetation
(a) (a)
(b) (b)
Figure 17. The obtained point cloud data and map of field testing site. (a) The point cloud data Figure17. 17.The Theobtained obtained point cloud of testing field testing The point cloud data Figure point cloud datadata and and map map of field site. (a)site. The (a) point cloud data collected collected by the inspection robot; (b) The inspection map. collected by the inspection robot; (b) The inspection map. by the inspection robot; (b) The inspection map.
Subsequently, scenario 1 was designed for verifying the effectiveness of the multi-robot team of the MRCPS. Table 5 shows the default experimental parameters of scenario 1. Tables 6–9 shows the variation rules of the sub-scenarios 1.1–1.4. In the multiple scenarios, different objective task
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Subsequently, scenario 1 was designed for verifying the effectiveness of the multi-robot team of the MRCPS. Table 5 shows the default experimental parameters of scenario 1. Tables 6–9 shows Sensors 2018, 18, 3146 23 oftask 29 the variation rules of the sub-scenarios 1.1–1.4. In the multiple scenarios, different objective demands are proposed by changing the inspection distance, the number of inspection objectives, and the required inspection time. demands are proposed by changing the inspection distance, the number of inspection objectives, and the required inspection time. Table 5. Default parameters of field experiment for scenario 1. Table 5. Default Parameter parameters of field experiment for scenario 1. Default Value
Test area size (m × m) 50 × 30 Parameter Default Value Required inspection time to (s) 1200 Test area size (m × m) 50 × 30 Inspection distance L (m) 1000 Required inspection time to (s) 1200 Number of inspection objectives n o Inspection distance L (m) 1000 10 Objective taskobjectives demand nμoo Number of inspection 10 8.3 Objective task demand 8.3 0.6 Task risk factorµρ o Task 0.6 6 Sizerisk of factor robotsρ set N Size of robots set N
6
Table 6. Parameters of Scenario 1.1. Table 6. Parameters of Scenario 1.1.
Parameter Parameter L (m)
Setting 1 Setting 2 Setting 3 Setting 4 Setting 5 Setting 6 Setting 7 Setting 2 Setting 3 Setting 4 Setting 5 Setting 6 Setting 7 25 50 75 100 200 500 1000
Setting 1
L (m)
25 0.02 0.02 × L×
tot(s) o (s)
50 0.02 0.02 × L×
L
75
100
200
500
1000
L 0.020.02 0.02 ×L × L × L 0.02 0.02 × L × L 0.02 × L × L0.02 ×0.02 L × L0.02 × 0.02 L
Table7.7.Parameters Parametersof ofScenario Scenario1.2. 1.2. Table
Parameter Parameter nno o
Setting Setting 1 1 55
Setting Setting 2 77
2 Setting Setting Setting Setting 5Setting Setting 6Setting Setting 7 3 3 Setting 4 4 Setting 5 6 7 10 15 20 25 30 10 25 30 15 20
Table8.8.Parameters Parametersof ofScenario Scenario1.3. 1.3. Table
Parameter Parameter
Setting Setting 1 1
Setting Setting 2
to t(min) o (min)
30 30
2525
2 Setting Setting Setting Setting 5Setting Setting 6Setting Setting 7 3 3 Setting 4 4 Setting 5 6 7 2020
15 15
10
10
7
7
5
5
Table Table9.9.Parameters Parametersof ofScenario Scenario1.4. 1.4. Parameter Parameter
Setting 1 1 Setting
Setting 2 Setting
ρρ
0.1
0.2
0.1
3 3 Setting 4 4 Setting 5 6 7 2 Setting Setting Setting Setting 5Setting Setting 6Setting Setting 7 0.4
0.2
0.6
0.4
0.7
0.6
0.8
0.7
0.9
0.8
0.9
Figure results of of the themulti-robot multi-robotteam teamwith withthose thoseof Figure18 18shows showsthe the comparison comparison of of the inspection results ofthe theindividual individualrobot robotininScenario Scenario 1. 1. In In Figure Figure 18a–d, 18a–d, the objective task task demand demand and and the thetask taskrisk risk factor factorare areadjusted adjustedtotoobtain obtainthe theduration durationofofthe themulti-robot multi-robotteam teamand andthe theindividual individualrobot robotunder under different differentconditions. conditions.
5.7
100
200
Inspection distance (m)
25.4
42.3 24.8
40.5 23.4
37.9
35.4 22.1
19.3
18.6
11.3
20
21.5
31.4
33.4
35.4
75
2.1
4.5
1.64
3.4
50
30
4.2
8.8
25
1.13
2.4
10
21.5
18.9
40
20
0
Single Robot
50
Inspection time (min)
Multi-Robot Team Single Robot
30
0.52
Inspection time (min)
40
48.6
(b) Inspection time with different Number of inspection objectives 60 Multi-Robot Team
(a) Inspection time with different Inspection distance
10 500
1000
0
5
Figure 18. Cont.
7
10
15
20
Number of inspection objectives
25
30
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6.9
5
7
10
15
20
Required inspection time (min)
25
30
20
34.8 23.6
22.8
22.1
21.5
20.3
30
35.1
35.4
35.8
35.4
35.6
40
35.4
Multi-Robot Team Single Robot
20.1
36.3
8.3
11.5
20
Inspection time (min)
30.5 24.2
16.1
21.5
30
0
35.9
34.9
35.9
35.4
34.2
Inspection time (min)
40
10
(d) Inspection time with different Task risk factor
50
Multi-Robot Team Single Robot
19.6
(c) Inspection time with different Inspection time demand
36.1
50
24 of 29 24 of 29
10 0
0.1
0.2
0.4
0.6
Task risk factor
0.7
0.8
0.9
Figure 18. Results of scenario 1; inspection time with different parameters. (a) Inspection time with Figure 18. Results of scenario 1; inspection time with different parameters. (a) Inspection time different inspection distance; (b) Inspection time with different number of inspection objectives; (c) with different inspection distance; (b) Inspection time with different number of inspection objectives; Inspection time with different required inspection times; (d) Inspection time with different task risk (c) Inspection time with different required inspection times; (d) Inspection time with different task factors. risk factors.
The comparison comparison between individual robot is shown in Figure 13. The The between the therobot robotteam teamand andthethe individual robot is shown in Figure 13. following properties are summarized. The following properties are summarized. • • •
Under the same conditions, the multi-robot team completed the inspection task in a much Under the same conditions, the multi-robot team completed the inspection task in a much shorter shorter time than the single robot. time than the single robot. The inspection time of the multi-robot team was most affected by required inspection time to The inspection time of the multi-robot team was most affected by required inspection time to and and inspection distance L. The inspection time of the single robot was most affected by inspection distance L. The inspection time of the single robot was most affected by inspection inspection distance L and the number of inspection objectives no. distance L and the number of inspection objectives no . The higher the required inspection time to, the harder it was for the robot team to achieve the The goal.higher the required inspection time to , the harder it was for the robot team to achieve the goal.
Firstofofall,all, collaborative inspection of MRCPS reduces the timeforrequired for First thethe collaborative inspection of MRCPS greatly greatly reduces the time required completing completing the task. Secondly, to directly restricts the time of the team and has the the task. Secondly, to directly restricts the inspection timeinspection of the robot team androbot has the greatest impact greatest impact on test the ofresults. In the the testcollaborative of the L change, the rate collaborative rate is on the results. In the the L change, inspection is constant,inspection and to is changed constant, and to ismakes changed indirectly, which time makes the actual inspection time the change obviously. indirectly, which the actual inspection change obviously. However, single robot is However, theby single robot is affected only by the difficulty of the inspection (L, no). of Finally, due affected only the difficulty of the inspection task (L, no ). Finally, due to thetask limitation the initial to the of the size of theisrobot set, the team capability is constrained, higher size of limitation the robot set, the initial team capability constrained, i.e., the higher the requirement,i.e., the the worse the the requirement, performance will the be. worse the performance will be. Finally,the the default experimental parameters for scenario 2 are shown Table 10. The Finally, default experimental parameters for scenario 2 are shown in Table 10.inThe performance performance of cost and capability collaboration capability of theteam multi-robot team in MRCPS adjustedthe by of cost and collaboration of the multi-robot in MRCPS is adjusted byischanging changingtask the demand objective and taskthe demand andfactor. the task risk11factor. Tables and 12 shows the range of objective task risk Tables and 12 shows11the range of variation of the variation of the experimental parameters for 2.1 and 2.2. experimental parameters for sub-scenarios 2.1sub-scenarios and 2.2. Table10. 10.Default Defaultparameters parametersofoffield field experiment experiment for 2. 2. Table forscenario scenario
Parameter Default Value Parameter Default Value Test area size (m × m) 50 × 30 Test area size (m × m) 50 × 30 Required inspection timetime to (s)to (s) 1200 Required inspection 1200 Inspection distance L (m) 1000 Inspection distance L (m) 1000 Number of inspection objectives no 15 Number of inspection objectives no 15 Objective task demand µo 12.5 Objective demand μo Task risktask factor ρ 0.612.5 Task risk factor Size of robots set N ρ 6 0.6 Size of robots set N 6 Table 11. Parameters of scenario 2.1.
Parameter
Parameter Variation Range
Parameter Variation Amplitude
μo
10–22.5
0.1
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Table 11. Parameters of scenario 2.1. Parameter
Parameter Variation Range
Parameter Variation Amplitude
10–22.5
0.1
µo Sensors Sensors 2018, 2018, 18, 18, xx FOR FOR PEER PEER REVIEW REVIEW
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Table 12. Parameters of Scenario 2.2.
Table Scenario 2.2 2.2.. Table 12. 12. Parameters Parameters of of Scenario
Parameter Parameter Parameter ρ ρρ
Parameter Variation Range Parameter Variation Range Parameter Variation Range 0.01–0.99 0.01–0.99 0.01–0.99
ParameterVariation VariationAmplitude Amplitude Parameter Parameter Variation Amplitude 0.01 0.01 0.01
Similar to the effectiveness of the formation, the effectiveness of multi-robot team Similar effectiveness of of the the team team the effectiveness of the the team in in Similar to to thethe effectiveness teamformation, formation, the effectiveness of multi-robot the multi-robot team in collaboration capability is calculated by the relationship between the actual inspection time and collaboration capability is calculated by the relationship between the actual inspection time and the the collaboration capability is calculated by the relationship between the actual inspection time and the required required inspection inspection time. time. The The effectiveness effectiveness of of the the multi-robot multi-robot team team in in practical practical work work is is shown shown in in required inspection time. The effectiveness of the multi-robot team in practical work is shown in Equation Equation (19). (19).
Equation (19).
ess Effectiven ess EEffectiven f f ectiveness =
t[tooto−| || ttoto o− ttRxRxt Rx || |] , ttooto
(19) (19)
,,
(19)
where to is the required inspection time, and tRx is the actual inspection time of the multi-robot team. where where ttoo is is the the required required inspection inspection time, time, and and ttRx Rx is is the the actual actual inspection inspection time time of of the the multi-robot multi-robot team. team. Figure 19 shows the effectiveness of multi-robot team with differentobjective objective taskdemands, demands, and the Figure Figure 19 19 shows shows the the effectiveness effectiveness of of multi-robot multi-robot team team with with different different objective task task demands, and and effectiveness of different task risk factors is shown in in Figure 20. the Figure the effectiveness effectiveness of of different different task task risk risk factors factors is is shown shown in Figure 20. 20. Effeciveness Effeciveness
0.0.98 98 00.9.966
00.8.844 00.8.822 00.8.800
1 14 4
1 12 2
ess veness eciven Effeci Eff
00.9.944 00.9.922 00.9.900 00.8.888 00.8.866
33
2222
2020
1818
1616
Objective Objective task task demand demand
11
22
44
55
6 6
Number Number of of robots robots
Figure 19.19. of scenario2.1, 2.1, effectiveness of multi-robot team with objective differenttask objective Figure Results the effectiveness of team different Figure 19.Results Results of of scenario scenario 2.1, thethe effectiveness of multi-robot multi-robot team with with different objective task taskdemands. demands. demands. Effeciveness Effeciveness
0.0.98 98 00.9.966
ss eness ecivene Effeciv Eff
00.9.944 00.9.922 00.9.900 00.8.888 00.8.866
4 4
0 0. .1 1
00.8.844 00.8.822 00.8.800
0 . 0 .5 5
0. 0.3 3
33
22
0.0.9 9
0. 0.7 7
Task Task risk risk factor factor
11
Number Number of of robots robots
Figure 20. 20. Results of scenario 2.2,2.2, thethe effectiveness of of multi-robot Figure Results of scenario effectiveness multi-robotteam teamwith withdifferent differenttask taskrisk riskfactors. Figure 20. Results of scenario 2.2, the effectiveness of multi-robot team with different task risk factors. factors.
It is seen from Figure 19 that the effectiveness of the robot team is negatively related to the objectiveItIttask demand µo ; corresponding to the specified of robots, the taskto is is from 19 of robot team negatively the is seen seen from Figure Figure 19 that that the the effectiveness effectiveness of the theset robot team is is especially negatively related related todemand the objective objective task task demand demand μμoo;; corresponding corresponding to to the the specified specified set set of of robots, robots, especially especially the the task task demand demand is is too low or too high, the variation of the working efficiency of the robot team is more obvious. too low or too high, the variation of the working efficiency of the robot team is more obvious. For For
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too low or too high, the variation of the working efficiency of the robot team is more obvious. For the moderate value of µo , little change is observed in the effectiveness of the multi-robot team, and it can maintain a high efficiency (0.89–0.93). In addition, with the difficulty of the target task increasing, the number of robots is gradually increasing, that is, the economic efficiency declines the execution of the robot team. The changing of the effectiveness of the MRCPS is more obvious under the influence of task risk factor ρ (as shown in Figure 20). The effectiveness of robot team is also negatively related to the task risk factors. There is no stable phase in the efficiency curve, and the change rate is large compared with the result in Figure 19. With the increase of task risk factor, the number of robots has steadily declined, and the economic efficiency has been gradually enhanced. That is, the higher the risk, the greater the return; the lower the risk, the greater the cost. 6. Discussion The Multi-Robot Cyber Physical System (MRCPS) is derived from the rapid development and extensive application of robots, multi-agent theory, and the WSN. The most significant characteristic of the MRCPS is the dynamic monitoring of transmission lines by multiple mobile WSNs composed of heterogeneous robots and static nodes along a ground line. The monitoring mode of MRCPS is different from that of the traditional WSN with low flexibility and high cost of operation and maintenance; it is also different from single robot inspection system, whose fault tolerance is poor, and wireless signal could be frequently blocked by vegetation. WSN and multi-robot technologies have been rapidly developing in recent years, especially in terms of the light weight and cost-effectiveness of the hardware. Thus, it has become possible to build a multi-robot team and propose a new method for monitoring high-voltage transmission lines. The MRCPS, combining the characteristics of robots, WSN, and multi-agent theory, is a very distinctive system. Firstly, the system structure is changeable and flexible for mobile robots as the information sensing center; secondly, the system has the properties of high inspection quality and effectiveness; thirdly, as fewer nodes are deployed, the deployment cost is decreased, and the system’s fault-tolerant performance is improved. These characteristics of the MRCPS provide a strong technological support for the effective inspection of the transmission line. The main contribution of the proposed method is to improve the intelligent level of the power grid monitoring system and the quality of the inspected data. At present, the single robot control and communication mode is commonly used for inspecting transmission lines. That is, there is only one robot per inspection task. Thus, such control and communication modes seriously restrict the large-scale application of the robotic line inspection. In this paper, a highly practical Multi-Robot Cyber Physical System (MRCPS) is proposed. The proposed method can greatly reduce the workload of operators and improve the intelligent level. Further, this research makes a new attempt in theory: the relationship model of the multi-robot is analyzed and summarized; the method of normal distribution is introduced to the statistics and calculation of robot task-based ability; the mathematical model of the multi-robot weighted graph is also introduced. Under the premise of guaranteeing working efficiency, by setting risk factors, the number of robots is reduced, and the economic effectiveness of tasks is improved. Finally, based on the mathematical model and simulated annealing algorithm, a Multi-robot Team Formation Algorithm (MTFA) is designed. It balances the relationship between the global optimal solution and the operation time, and also optimizes the working efficiency and operation cost. Therefore, the reliability and practicability of the MRCPS are greatly improved. The proposed method improves the practical applications in the following aspects. Firstly, the simulation results verify that the multi-robot weighted graph model can effectively improve the efficiency of the robot team. Secondly, the Multi-robot Team Formation Algorithm (MTFA) can facilitate the convergence rate of the global optimal solution and improve the actual performance in application. Thirdly, through field experiments, it is found that the multi-robot team can effectively reduce the inspection time and improve the working efficiency. Finally, the multi-robot team can effectively balance the relationship between the inspection effectiveness and operation cost of the
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task by adjusting the task risk factors. To sum up, the proposed Multi-Robot Cyber Physical System (MRCPS) can efficiently monitor transmission lines and environmental variables. 7. Conclusions This paper proposes a novel method of a Multi-Robot Cyber Physical System (MRCPS) for the inspection of transmission lines. The main conclusions are summarized as follows: (1)
(2)
(3)
The MRCPS is able to act as a new type of intelligent monitoring system to automatically inspect the transmission lines. Since the robot team can adapt to different scenarios by changing the organization structure and task assignment, it is more flexible and fault-tolerant than a single robot or WSN sensor system. In addition, the robot team can call on more resources to complete the task, which makes the system more efficient. When a robot team is replaced with a large number of static nodes, the availability and the cost of the monitoring system can be improved. The proposed method mainly includes two parts, i.e., the multi-robot weighted graph model and the MTFA. In the first part, the composition and structure of the robot team are introduced. Then, the characteristics of the relationship between robots are analyzed, and the weighted graph model is proposed. Finally, a new mathematical model for the robot team is proposed. The proposed model fully considers the characteristics of the relationship and ability of robots, and a scheme is designed to balance the working efficiency and operation cost. In the next part, a new algorithm (MTFA) is designed. The MTFA is similar to the Simulated Annealing algorithm, as it is designed to find the global optimal solution of the objective function. Then, the mathematical model is combined to update the weight of the links and conversion to objective function. Finally, the robot team risk factors are ranked. In simulations and experiments, multiple experimental scenarios are performed for verifying the two kinds of effectiveness. It not only verifies the effectiveness of the weighted synergy graph model and the MTFA, but also the effectiveness of the multi-robot team in different scenarios. The experimental results show that the multi-robot weighted synergy graph and MTFA can find the optimal robot team, and they perform better than other methods. In the comparison experiment, the inspection efficiency of robot team for transmission line is much better than that of a single robot. Furthermore, the multi-robot team can effectively balance the performance of work effectiveness and operation cost.
Further research should mainly focus on two aspects. One is that the weighted graph model has not designed the variability of the transitivity of the relations among robots. As the relations (communication efficiency) change, the optimal result is less reliable. In addition, more factors are need to be calculated to regulate the relation link between robots. The other is that the MTFA sometimes cannot achieve ideal result rapidly; it is more difficult to find the optimal robot team if the initial robot set is huge. Multivariate analysis is required to control the convergence of the global optimal solution. Author Contributions: F.F. proposed and developed the research design, designed the simulation experiment, collected the experimental data, performed the data analysis, results interpretation and manuscript writing. G.W. assisted with developing the research design and results interpretation. M.W. assisted with refining the manuscript writing and coordinating the revision activities. Q.C. and S.Y. assisted with process of experiments. Funding: This work was supported by a Guangdong Robot Special Project (2015B090922007), a Foshan Technical Innovation Team Project (2015IT100143), and a State Grid Jilin Electric Power Co., Ltd. Project, China (JDK2015-21). Conflicts of Interest: The authors declare no conflict of interest.
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