Research ArticleDesign and Collaborative Operation of Multimobile InspectionRobots in Smart Microgrids

Nankai Chen and Yaonan Wang

College of Electrical and Information Engineering Hunan University Changsha 410082 China

Correspondence should be addressed to Nankai Chen chennkhnueducn

Received 19 November 2020 Revised 21 February 2021 Accepted 8 March 2021 Published 17 March 2021

Academic Editor Xin Li

Copyright copy 2021 Nankai Chen and Yaonan Wang is is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in anymedium provided the original work isproperly cited

is paper investigates the substation inspection problems of multimobile robots for large power stations in smart microgridsMost multirobot inspection robots generally face the challenge of path planning while the current widely used biologicalexcitation neural network (BENN) methods often have the defect of the neuronal active field near boundaries and obstacles Toend this we propose an improved biological excitation neural network (IBENN) method for path planning based on a detailedarchitecture and ontology framework through which the single-point inspection multipoint inspection and full-area inspectiontasks of substations in smart microgrids can be well completed Simulation results show that the designed IBENN-basedmultirobot collaboration inspection (MRCI) system can effectively shorten the path as well as the number of turns and then showbetter performance than most existing results when implementing various substation inspection tasks

1 Introduction

Safe and stable supply of electricity is of great significance toensure the sound and rapid development of the economyand society whereas the grid and substation generally sufferfrom long-term exposure to the wild during the transmis-sion and transformation process It is necessary to detect andmaintain transmission lines and substations regularly toprevent large-scale grid accidents among which substationequipment maintenance is an important mean to ensure safeoperation of smart microgrids improve the economy ofpower grid operation and provide good services [1ndash4]

Most of the current maintenance work still relies onmanual operation which has the disadvantage of dangerousworking environment and high maintenance cost More-over the factors of high intensity low efficiency and cannotwork around the clock are also the main difficulties thatmanual inspection must face In view of this intelligentautomation technology has gradually replaced manpower tobecome a new trend of inspection work due to the rapidtechnology development By simulating operation behavior

robots have been used in the detection process of smartgrids which cannot only reduce work risks and humanconsumption but also provide accurate data detection anddata collection However most inspection robots used inpower stations are manually remote-controlled rather thanautonomously operated and are used alone lacking coop-eration between multiple robots

Inspection robots often carry out comprehensive anddetailed inspection regularly for the equipment in thesubstation of smart microgrids to achieve all-weather no-dead and efficient inspection work erefore the multi-robot intelligent inspection system should possess thefunctions of (i) autonomic path planning (planning a safeand optimal path traverses all task points with known in-formation and information shared by other robots) (ii)environmental perception (sensing task points obstaclesetc) (iii) fault detection (it should be able to collect datathrough visible-light camera infrared thermal imager ul-trasonic device and other devices and transmit the acquiredinformation to the background through the communicationmodule for observation and analysis) (iv) remote operation

HindawiComplexityVolume 2021 Article ID 6695688 11 pageshttpsdoiorg10115520216695688

(the staff can realize the continuous monitoring of thespecific fault after the abnormal situation is found by theremote operation robot)

Inspection robots have been researched for more thanthirty years e substation inspection robot was first de-veloped by Mitsubishi Corporation of Japan Quek NorthHydro Corporation of Canada and University of Satildeo Paulo ofBrazil [5ndash7] A teleoperated robotic platform called LineScoutTechnology was introduced in [8] which has the capability toclear most obstacles that were found on the grid however themain functions and application modules were limited to thespecified platform Following this line a method of detectingpower grid lines by using the unmanned aerial vehicle (UAV)in the complex environment was presented in [9ndash11] Fur-thermore the inspection operations of flying robots andclimbing robots for power stations have also been madepreliminary attempts [12] although mobile robots were morewidely used in the field of intelligent inspection of powerstations of smartmicrogrids nomatter wheel-type or crawler-type robotse above methods were based on single robotswhich have become increasingly unable to meet the demandrequirement of operation with the increase of the number oftasks and operation difficulty Multirobot collaboration in-spection (MRCI) has become an important research directionin robot research because of the natural coordination ad-vantages however it is more complex and difficult than singlerobots in terms of scheduling and control especially for thechallenging path planning issues which is the focus of thisarticle Some research achievements have been made in pathplanning of multiple robots Yu and LaValle [13] investigatedon optimal multirobot path planning over four minimizationobjectives by combining the ILP model algorithm with theheuristic algorithmeir approach could achieve good levelsof efficiency Kelin and Pratihar [14] integrated the geneticalgorithm with the Alowast algorithm to design an approach usedto plan the paths of multiple robots Pradhan et al [15]researched the problem of multiple robots moving towardsindividual goals within a common workspace whereas themotion of every individual robot is deduced by a novelParticle Swarm Optimization-tuned Feed-Forward NeuralNetwork Luo et al [16] proposed a neural dynamics ap-proach for complete area coverage navigation by multiplerobots and achieved high computational efficiency Woosleyand Dasgupta [17] proposed an abstraction that models theuncertainty in the paths and aMarkov decision process-basedalgorithm that selects paths for themultirobots to find the taskordering that could reduce the overall distance In the studyby Rogers et al [18] they also developed an approach wherethe multiple robots were guided in their decision to select alocation by a utility function that combines Gaussian process-based distributions for information entropy and communi-cation signal strength In a study performed by Imeson andSmith [19] a framework for solving multirobot motionplanning problems with complex constraints had been in-troduced ey also proposed an algorithm that leveragesrecent advances in Satisfiability Modulo eory to combinestate-of-the-art SAT and TSP solvers Ayari and Bouamama[20] proposed a new dynamic distributed particle swarmoptimization algorithm for trajectory path planning of

multiple robots in order to find the collision-free optimal pathfor each robot in the environment More recently someheuristic intelligent algorithms were adopted for path plan-ning of the MRCI system including the path conflict-basedsearch algorithm [21] and the probability window-basedmultiobjective particle swarm optimization algorithm [22] toname just a few Nevertheless autonomous navigation is stillone of the most challenging abilities for mobile robots

Robot navigation consists of four parts perceptionpositioning decision-making and execution ie all robotsmust have the ability to sense the surrounding environmentthrough sensors and determine its own position then workout the motion strategy and finally control the motor outputto achieve the desired trajectory [23] Several typical robotnavigation methods include railway track magnetic navi-gation and pattern recognition Since the railway tracknavigation method lacks of flexibility and needs hard workfor the orbit construction [24] the magnetic navigation wasintroduced in [25 26] considering the substation environ-ment adaptability and cost where the RFID tag information(detected by the RFID reader) is uploaded to the controlsystem via the communication port to achieve the posi-tioning of the inspection robot parking or turning move-ments e pattern recognition-based navigation methodemploys noncontact sensors such as cameras and lidars toidentify the road and in turn determines the robotrsquosforehead posture the current road and the next location tobe inspected However it requires a large amount of cal-culation and has high uncertainty [27]

As the substation environment is relatively fixed thestatic map of the whole substation can be planned offline Inaddition since the substation studied in this paper is anoutdoor environment GPS navigation which has the ad-vantages of high positioning accuracy and a simple structureis adopted after comprehensive consideration of the mobilerobotrsquos path flexibility and comprehensive cost Based onthis this paper mainly studies the multirobot autonomousnavigation problem in power stations of smart microgridsand multimobile robots are used to complete the collabo-rative inspection operation in the outdoor large-scale sub-station In the following the inspection tasks are divided intothree categories single-point inspection multipoint in-spection and all-area inspection We will design differentMRCI algorithms to complete different inspection tasksefficiently

e rest of the parts are organized as follows Section 2formulates the multirobot collaborative inspection problemand the main IBENN-based navigation method is proposedin Section 3 Section 4 shows the implementation processand verifies the effectiveness of the established IBENN-basedMRCI system in three different inspection tasks and thepaper is concluded in Section 5

2 Problem Formulation and Modeling

We first establish the intelligent inspection robot systemmodeling in Subsection A and introduce three importantinspection tasks and the commonly used BENN methodrespectively in Subsections B and C

2 Complexity

21 Intelligent InspectionRobot SystemModeling e systemis divided into two parts remote control platform and robotbody as shown in Figure 1 e remote console is composedof a host PC and a database which realizes the functions ofinformation storage status display overall planning andcentralized control e remote control platform controlsthe inspection robot through a 24G wireless communica-tion module and the inspection robot sends the videos andimages of the inspection operation to the remote controlplatform through wireless Ethernet e video capture cardis connected to the on-board PC through the PCIE buswhich is used to collect the images of visible-light camerainfrared thermal imager and the front camera of the me-chanical arme motor driver is connected to the on-boardPC via the USB-CAN transfer card Auxiliary light sourcesystem ultrasonic ranging module differential GPS re-ceiving module and speed measurement block are con-nected to the industrial control computer through the RS485bus e robot is powered by the lithium battery and eachrobot realizes data sharing through the wireless commu-nication module

e substation inspection robot carries a visible-lightcamera and an infrared thermograph which is used to detectinvaders and equipmentsrsquo fault point respectively e hostPC plays a supervisory role such as reading the status fromeach subsystem recognizing the equipments from thethermal image planning the inspection path and displayingthe 3D map e on-board PC controls the behaviors of therobots such as movement obstacle avoidance and posi-tioning e associated multirobot collaborative systemadopts a hybrid layout as shown in Figure 2 e host PC isresponsible for computing planning and scheduling tasksInformation could be shared between the mobile robots overa wireless network

22 Task Classification We introduce three important in-spection tasks here which will be realized in Section 4 basedon the proposed control methods designed in Section 3

221 Single-Point Inspection ere are some importantareas or fault-prone areas that need to be monitored inlarge substations of smart microgrids For these areas theinspection robot sometimes needs to carry out a single-point inspection In this situation the multirobot systemassigns the task to a single robot according to the locationof the inspection point the location of each robot and itsability value and then converts the problem into the pathplanning problem of the single robot in the knownenvironment

222 Multipoint Inspection In real applications there aregenerally more than one important or fault-prone areas thatneed to be inspected simultaneously In this situation theinspection task can be assigned to several robots accordingto the position of the task points then the reasonable pathsare designed for each robot to complete the inspection task

223 All-Area Inspection If the entire equipment needs tobe inspected then the robot should move in the wholesubstation In this situation the basic process of multirobotinspection in a known environment includes the following(a) grouping of multimobile robots in pairs (b) design theopposite heuristic algorithm for each group of robots (c)start the inspection and when it falls into the dead zonechoose the IBENN method to jump out and (d) determinewhether the entire area has been inspected

In practical applications no matter what kind of in-spection task the multimobile robot system needs to de-compose and allocate tasks first then each robot separatelyformulates a reasonable inspection path e commonlyused path planning methods mainly include artificial po-tential field method A-star algorithm and fuzzy logicwhich however have certain defects for different practicalproblems [28] In order to accomplish various kinds ofinspection tasks the widely used BENN method will beintroduced in the next part and the IBENN algorithmwill beproposed in Section 3

23 Biological Excitation Neural Network (BENN) MethodIn the bioexcitation neural network method the motionspace of a mobile robot can be represented by a topologicalstate space composed of a neural network and the activityvalue of neurons represents environmental informationeactivity values of all neurons are generally initialized to 0while the changes in the activity values of each neuron aredescribed by the following shunting equation [29 30]

dxi

dt minusAxi + B minus xi( 1113857 Ii1113858 1113859

++ 1113944

k

j1wij xj1113960 1113961

+⎛⎝ ⎞⎠ minus D + xi( 1113857 Ii1113858 1113859minus

(1)

where xi is the neural activity of the ith neural parametersAB and D are nonnegative constants representing the passivedecay rate the upper and lower bounds of the neural activityrespectively k is the number of neurons in the neighbor-hood wij and xj represent the connection weight and ac-tivity of neurons in the neighborhood respectively E is anormal number much larger than B and Ii is the ith externalinput with the following form

Ii

E target

minusE obstacle

0 other

⎧⎪⎪⎨

⎪⎪⎩(2)

Excitation signal Sei [Ii]

+ + 1113936kj1 wij[xj]

+ and inputinhibition Si

i [Ii]minus e nonlinear threshold function [a]+

is defined as [a]+ max(a 0) and [a]minus max(minusa 0) Letdij is the Euclidean distance between neurons wij f(dij)and f(a) (u0a) u0 is a positive constant e robot startsfrom the starting point to the next position qn determined bythe following formula [31 32]

qnlArrxqn max xj j 1 2 3 k1113872 1113873 (3)

is method ensures that the positive neuronal activityvalue can spread outwards and affect the whole state space

Complexity 3

while the negative neuronal activity value can only act lo-cally e neuronal activity values of the target point and theobstacle are respectively at the crest and trough of the waveas shown in Figure 3 so the target point can attract the robotto move towards it while the obstacle can only repel therobot locally After the robot reaches the next location fromthe present location the next location becomes a newpresent location unless the present point is the target pointIf the found next location is the same as the present locationthe robot stays there without any movement

Although this method can solve the problem of robotpath planning it still has some problems such as nonoptimalpath wrong path judgment and easy to fall into the dead

zone To end this an improved bioexcitation neural networkalgorithm is designed next which will be applied for themultirobot to complete various types of smart grid in-spection tasks

3 Improved Biological Excitation NeuralNetwork (IBENN) Method

When calculating the neuron activity value near theboundary the traditional BENN method regards theboundary as an obstacle making it relatively low relative tothe surrounding nonboundary neuron activity value As aresult the best paths are often overlooked as shown inFigure 4 As seen it is better to choose the path along the leftboundary in Figure 4(a) and the optimal path is between thetwo obstacles in Figure 4(b) Moreover the original methodonly considers the activity value of surrounding neuronswhen choosing the next path point which ignores the ro-botrsquos steering in the form process However robot steeringrequires deceleration steering and acceleration whichgreatly increase the power consumption and travel time ofthe robot

Remote control platform

Host PC

Differential GPSbase station

Remote controlhandle

Front display ofrobotic arm

Inspectionimage display

Visible-light

cameradisplaywindow

Visible-light

cameradisplaywindow

Infraredthermalimagerdisplaywindow

24G wirelesscommunication

Power station inspection robort

Power supply and charging interface module

PClE

On-boardPC

Videocapture card

USB-CANconversion

card

Auxiliarylight source

system

Ultrasonicobstacle

avoidance system

DifferentialGPS

receiver

Speedmeasuring

device

Motor driver

Visible light camera

Infrared camera

Robotic arm front camera

Robotic driver

Inspection camera driver

Mobile platform driver

USB CAN

RS485

DifferentialGPS

communication

WirelessEthernet

Figure 1 Single robot system architecture in power stations of smart microgrids

LAN management

Host system

Cooperative system

Communicationsrsquo link

Robot 1

Robot 2Robot 3

WLAN

Host PCDatabase

Figure 2 Multirobot system architecture in power stations ofsmart microgrids

1 Target

05

0

ndash05

Act

ivity

ndash130

2520

1510X

Y5

0 0 5 10 15 20 25 30

Figure 3 Biological excitation neuronal active field of the BENNmethod

4 Complexity

In order to reduce the power consumption of the robotand to smooth the path of the robot the following pathdecision method is adopted

qnlArrxqn max xj + cyj j 1 2 3 k1113872 1113873 (4)

where xi is the active value at the current position c is apositive constant yj 1 minus Δθj π is a monotonically in-creasing function of the moving direction difference be-tween the current to the next robot and Δθj is the absoluteangle at which the robot moves from the current position tothe next position eg Δθj 0 (or Δθj π) when the robotmoves in a straight line (or turns around) Denote the co-ordinates of the current position qc (xqc

yqc) and the

previous position qp (xqp yqp

) then

Δθj θj minus θc

11138681113868111386811138681113868

11138681113868111386811138681113868 arctan yqjminus yqc

xqjminus xqc

1113874 1113875

minus arctan yqcminus yqp

xqcminus xqp

1113874 1113875

(5)

e path decision method takes into account the factorsof steering and selection of appropriate c which representsthe weight of steering in the path decision only then asmooth path can be planned In order to overcome thedrawbacks of ignoring the boundary optimal path as well asunreasonable path selection we propose the following im-provement strategies

Strategy (i) Map extension ie extend the activityrange of robot virtual neuronsStrategy (ii) Activity increasing ie increase the ac-tivity of neurons near the obstacle and boundaryStrategy (iii) Node deletion ie delete the redundantnodes that do not hinder the passage of robots

e boundary neurons of the original map are extendedoutward of one circle respectively ese areas are assumedto be virtual reachable (not treated as obstacles) with thepositive activity value and can also spread activity aroundduring the initialization process but are ignored when

choosing the actual path e main purpose of Strategies (i)and (ii) is to improve the activity value of the original mapboundary neurons which can be considered as a boundaryprotection for these neurons In addition if the robot canbypass the next adjacent node from a certain node withoutcolliding with an obstacle in a path the deletion of this nodecan effectively shorten the total length of the path thusStrategy (iii) can reduce the robotrsquos power consumption andimprove work efficiency To realize these improvements thefollowing Assumption and Definition are given

Assumption 1 Neurons outside the boundaries of theoriginal map are virtual nonobstacles which also have thefunction of spreading activity values and their activity valuesare the average activity values of nonobstacle points in theneighborhood

Definition 1 If a robot is on a nine-square grid map-centeredthe top and bottom left and right front left and back right andfront right and back left are respectively considered as foursets of symmetrical coordinates If any pair of symmetricalcoordinates are obstacles the robot is said to be between theobstacles

If the robot is between the obstacles the excitation inputof the neuron can be calculated by

Sei Ii1113858 1113859

++

n 1113936kj1 wij xj1113960 1113961

+

npos (6)

When the neuron is not located between the obstaclesthe excitation input of the neuron can be calculated by

Sei Ii1113858 1113859

++

n minus nneg1113872 1113873 1113936kj1 wij xj1113960 1113961

+

npos (7)

where n npos and nneg represent the numbers of neigh-borhood neurons nonobstacles and obstacles respectivelyLet Si

i [Ii]minus then system (1) can be rewritten as

9

8

7

6

5Y

X

4

3

2

1

1 2

Start

Target

3 4 5 6 7 8 9

(a)

Start

Target9

8

7

6

5Y

X

4

3

2

1

1 2 3 4 5 6 7 8 9

(b)

Figure 4 Unreasonable path planning under traditional methods (a) Path along the boundary (b) Obstacle intermediate path

Complexity 5

dxi

dt minusAxi + B minus xi( 1113857S

ei minus D + xi( 1113857S

ii (8)

Hence Strategies (i) and (ii) are used to increase theactivity value of neurons near the boundaries or obstacles Inpractical application one of these two strategies can beselected and used together with Strategy (iii) to achievebetter path planning

Figure 5 shows the comparison experiment usingStrategies (i) and (iii) with model parameters A 10B D 1 E 100 k 8 and c 1 e relevant datacomparison is shown in Table 1 It can be seen from Figure 5and Table 1 that the path length has been reduced from 1007to 841 and the times of turns have been changed from 4 to 1us the proposed strategies have obvious improvementeffects

In order to verify the superiority of Strategies (ii) and(iii) the simulation environment is set as a complex mazeand model parameters are also set as A 10 B D 1E 100 k 8 and c 1 e initial position of the robot is(6 3) and the target position is (1 30) e traditionalBENN method A-star algorithm and the proposed IBENNmethod are compared as shown in Figures 6 and 7 As seenthe proposed IBENNmethod cannot only solve the problemof path misjudgment but also reduce the path transitionsmooth the path and improve the path quality ree indexcomparisons of path length turn times and total rotationangle are concluded in Table 2 It can be seen that comparedwith the original BENNmethod the path length path turnsand total rotation angle of the proposed IBENN method arereduced by 612 412 and 643 respectively Com-pared with theA-star algorithm the number of turns and thetotal rotation angle can be reduced by 167 and 168respectively under the condition that the path length isunchanged It concludes that the improved IBENN methodshows better performance in terms of path quality and pathsmoothness than the other methods

4 Multirobot Cooperative Inspection(MRCI) System

In this section we will implement the proposed IBENNmethod to the MRCI system and complete the previouslyestablished three inspection tasks

41 Single-Point Inspection Assume that there are n iso-morphic inspection robots with different initial positionsand m areas that need to be monitored in a substation ofsmart microgrids and one of the areas needs to be con-tinuously monitored at a certain moment In this situationthe system needs to schedule a robot to complete the taskfollowing the principle of minimum cost or maximumbenefit We establish the following mathematical model

fi(L D) min εLij + ηDij j 1 2 3 gi1113872 1113873 (9)

TilArr cos ti min fi i 1 2 3 n( 1113857 (10)

where Lij and Dij represent the length and the turningnumber of the jth path for the ith robot respectively ε and ηrepresent the associated weights of Lij and Dij respectively

9

8

7

6

5Y

X

4

3

2

1

1 2

Start

Proposed IBENN method

Target

3 4 5 6 7 8 9

Figure 5 Single-robot path generated by the proposed IBENNmethod with Strategies (i) and (iii) in the situation of single-pointinspection

Table 1 Comparison results of BENN and IBENN methods

Evaluation index BENN IBENN with strategies (i) and (iii)Path length 1007 841Turn times 4 1

30

25

20

15Y

X

10

5

5

The A-star method

10 15 2520 30

Proposed IBENN method

Figure 6 Single-robot path generated by the traditional BENNmethod and A-star algorithm in the situation of single-pointinspection

6 Complexity

all robotsrsquo weights are the same by default in the path de-cision gi represents the number of paths available for the ithrobot to complete the task T and fi can be considered as theminimum cost of robot i to achieve taskTe objective hereis to find the robot i and the optimal path gi

To solve this problem the proposed IBENN method isused to calculate the minimum cost of each robot tocomplete the task and then compare the optimal cost of eachrobot It is necessary that the robot with the lowest costobtains the task and completes the task according to theoptimal path planned For example in the 30 times 30 mapshown in Figure 8 gray areas represent parallel devices andblack ones represent obstacles in the site and there are fourrobots Robot1 Robot2 Robot3 and Robot4 with initialpositions R1(1 1) R2(30 1) R3(1 30) and R4(30 30)respectively When inspection tasks are needed nearequipment Rtarget(14 15) (ie area no 9) according to theIBENNmethod the cost of each robot to complete the task iscalculated as shown in Table 3 and then each robot offers aquotation according to the above method with f1 14f2 1414 f3 1206 and f4 1533 which can be cal-culated according to (9) when the parameter is set asε η 05 According to the calculation we can choose

Robot3 as the best scheme to execute the task and otherrobots determine their priority as a backup according to thecost

42 Multipoint Inspection In the substation working areathere is occasionally a need to inspect multiple areas and theadvantages of the multirobot cooperation system can be wellreflected in this situation e cost equation of the systemcan be described as

F min cos t min1113944n

i1fi Li Di( 1113857

min1113944

n

i

min εLij + ηDij j 1 2 3 gi1113872 11138731113872 1113873

(11)

where gi represents the total number of paths that robot i

can choose to reach the target point Assume that there are n

robots with m areas that need to be inspected(ngt 1 andmgt 1) simultaneously and the collaborative workof robots needs to be determined according to the rela-tionship between the areas m and the robots n

30

25

20

15Y

X

10

5

5 10 15 2520 30

Proposed IBENN method

Figure 7 Single-robot path generated by the proposed IBENNmethod with Strategies (ii) and (iii) in the situation of single-pointinspection

Table 2 Comparison of the three methods

Index BENN A-star

IBENN with strategies (ii) and(iii)

Path length 4063 3814 3814Turn times 17 12 10Rotationangle 2199 943 785

30

25

20

15Y

X

10

5

5

Robot 1

10 15 2520 30

Robot 2Robot 3Robot 4

Figure 8 Four-robot path generated by the proposed IBENN-based MRCI system in the situation of single-point inspection

Table 3 Comparison of the four-robot path planning

Index Robot1 Robot2 Robot3 Robot4Path length 2173 2356 2097 2280Turn times 18 19 16 17Rotation angle 628 471 314 785

Complexity 7

Case 1 ngem assume that a robot can only complete onetask and it can ensure that each uninspected area can beassigned to a robot to perform tasks at the same time eallocation method is the same as the task allocation methodof the single-point robot mentioned above ie each robotputs forward an optimal quotation for each task and themaster robot determines the optimal decision-makingscheme based on the quotation of each robot combined withthe corresponding bidding algorithm and assigns subtasks toeach robot according to the scheme en the problem isfirst transformed into an assignment problem which can besolved by the classical Hungarian algorithm [33] For ex-ample let n 6 and m 4 their positions are shown inTable 4 and the minimum cost of each robot at each taskpoint is solved according to the above method According tothe above allocation method the following allocationscheme can be obtained A1⟶ R1 A2⟶ R2

A3⟶ R3 andA4⟶ R5 and the total costF 994 + 969 + 681 + 571 3215

Case 2 nltm it means that a robot needs to completemultiple tasks and there can also be a situation where one ormore robots are idle For multiple robots at different initialpositions the host computer needs to plan a reasonable pathso that all inspection areas can be visited by the robots andthe total cost is minimal We have designed a genetic al-gorithm to solve this problem e genetic algorithm adoptsthe following single-chain coding form as shown in Fig-ure 8 when decoding the Robot2 completes the inspectiontasks of Areas 1 and 3 in sequence and similarly Robot1 andRobot3 complete the tasks of Areas 4 and 6 and Areas 2 and 5in sequenceis coding method has the advantage of strongreadability however it is easy to produce infeasible solutionsduring crossover and mutation erefore different repairalgorithms are used to repair the infeasible solutions

Crossover Use Partial-Mapped Crossover (PMX) op-erator when generating a new gene chain If it is not afeasible solution then fix it e specific repair methodis to find the repetitive genes in gene chain A that causeinfeasible solutions (there may be multiple groups) oneof which must be in the cross-replacement gene se-quence then find the gene that maps to the gene in genechain B and use it to replace the repetitive genes inchain A that are not in the cross-replacement sequenceMutation Randomly select two genes in the gene chainand determine whether one of their positions is at theend of the gene chain If not exchange their positions inthe gene chainSelection e tournament selection method is usedthat is a certain number of individuals are removedfrom the population each time then the best one isselected to enter the offspring population Repeat thisoperation until the new population size reaches theoriginal population size

For example in a 30 times 30 map the initial positions of theRobots 1 minus 3 are Rstart

1 (1 10) Rstart2 (15 30) and

Rstart3 (30 10) and the positions of the 6 inspection points are

A1(11 27) A2(29 28) A3(3 18) A4(16 15) A5(13 3) andA6(26 6) e initial azimuth of the robot is (0 minusπ2 minusπ)Using the proposed IBENN method above the optimal pathand the minimum cost between each point can be calculatede genetic algorithm can draw the following distributionplan

R1⟶ A3⟶ A1⟶ A4⟶ A5 R2⟶ A2 R3⟶ A6

(12)

e total cost is 4528 and the multirobot multipointinspection path is shown in Figure 9 where the red starindicates the inspection point and the blue star indicates theinitial position of each robot

43 All-Area Inspection Since the substation of smartmicrogrids is exposed to the outdoors for a long time it iseasy to break into foreign objects or other dangerous goodsIt is necessary to conduct regular inspections of the entirepower station of smart microgrids for all-area coverageHowever performing this task by a single robot may take along time and is inefficient erefore a multirobot col-laborative whole-area inspection program is designed

Divide every two robots into a group and design aheuristic algorithm for each robot e priority of theheuristic algorithm of the robots in each group is oppositewhich ensures that each group of robots can start inspectionsfrom different directions When the robot enters the deadzone position according to the proposed IBENN methodabove the optimal path from the dead zone position to theuninspected area can be planned e robot moves to thisarea and continues to inspect according to the originalheuristic algorithm For example in a 30 times 30 map there areparallel devices and various obstacle points as shown inFigure 10 Two robots in the area are used to coordinate tocomplete the all-area inspection taske steering priority ofthe heuristic algorithm of Robot1 W minus S minus SW minus NW minus N minus

E minus SE minus NE and Robot2 E minus N minus NE minus SE minus S minus W minus NW

minusSW and the initial positions are (1 1) and (30 1)respectively

Simulation experiments were carried out in the ob-stacle-free and obstacle environments and the results areshown in Figures 11 and 12 and Table 5 where the red andblue represent Robots 1 and 2 respectively pink dotsexpress repeated path points dots mean the final positionof the robot when the task is completed and stars rep-resent the initial position It can be seen from Table 5 thatin a simple map when there are no other obstacles in theinspection area and only parallel substation equipment

Table 4 Comparison of the four-robot path planning

Position Area1(916) Area2(1616) Area3(227) Area4(2225)

R1(11) 994 1492 1488 1801R2(151) 1031 969 788 1688R3(301) 1596 1442 681 1523R4(130) 1101 1158 1987 1271R5(1530) 1060 956 1609 571R6(3030) 2518 1441 1551 1132

8 Complexity

this method can achieve 100 coverage without over-lapping areas When there are various obstacles in theinspection area this method can also achieve 100 full-

coverage inspection but there is a repetition rate of 23Hence compared with other inspection methods theproposed IBENN method does not need to set a templateoperator and has strong versatility Multirobot collabo-ration can complete the entire area and full-coverageinspection task

To further verify the effectiveness of the proposedcontrol schemes we carry out the simulation experimentwith Coppelia Sim Software in the space of 30mtimes 30m etwo inspection robots are in the initial position as t 0 asshown in Figure 13(a) in which the gray cube and dark bluecube represent the equipment area and the obstacle arearespectively e robot is supposed to inspect at a speed of1ms disregarding the inspection time Using the aboveinspection strategy the experimental results are shown inFigure 13 As seen the left robot and right robot fall intodead zones respectively as t 138 or t 365 inFigures 13(a) and 13(e) and t 357 or t 306 inFigures 13(c) and 13(d) However in these cases the in-spection machine can jump out of the dead zone by callingthe IBENN algorithm respectively Furthermore both ro-bots fall into the dead zone state when t 395 as shown inFigure 13(f ) Since there is no undetected area in this sit-uation it follows that the inspection task has been com-pleted erefore the experiment verifies the feasibility ofthe cooperation scheme

A1 A3 R2 A4 A6 R1 A2 A5 R3

Figure 9 Gene chain coding of the genetic algorithm

30

25

20

15Y

X

10

5

5

Start points

10 15 2520 30

Inspection points

Figure 10 ree-robot path generated by the proposed IBENNbased MRCI system in the situation of six-point inspection

30

25

20

15Y

X

10

5

5 10 15 2520 30

Figure 11 Two-robot path generated by the proposed IBENN-based MRCI system in the situation of all-area inspection withoutobstacle

30

25

20

15Y

X

10

5

5 10 15 2520 30

Figure 12 Two-robot path generated by the proposed IBENN-based MRCI system in the situation of all-area inspection complexobstacle

Table 5 Results in obstacle-free and obstacle environments

Evaluationindex

Obstacle-freeenvironment ()

Obstacleenvironment ()

Coverage rate 100 100Repetition rate 0 23

Complexity 9

5 Conclusion

In this paper a multimobile robot collaborative operatingsystem for power stations of the smart microgrids isdesigned and an improved IBENN method is proposedCompared with the traditional BENN method and A-staralgorithm the improved IBENN algorithm has an obviousoptimization effect in path length and turning times Basedon this method the multirobot cooperative operationstrategy is designed to realize the three classic tasks of single-point inspection multipoint inspection and full-coverageinspection in the substation of smart microgrids whichverifies the effectiveness of the main results

Data Availability

All of the data used to support the findings of this study areincluded within this article

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China under Grant nos 61733004 and61773158

References

[1] A Peyman and F Keynia ldquoLifetime efficiency index model foroptimal maintenance of power substation equipment based

on cuckoo optimisation algorithmrdquo IET Generation Trans-mission amp Distribution vol 11 no 11 pp 2787ndash2795 2017

[2] I Ullah Y Fang and R Khan ldquoPredictive maintenance ofpower substation equipment by infrared thermography usinga machine-learning approachrdquo Energies vol 10 no 12pp 1ndash13 1987

[3] X Lu J Lai X Yu Y Wang and J M Guerrero ldquoDistributedcoordination of islanded microgrid clusters using a two-layerintermittent communication networkrdquo IEEE Transactions onIndustrial Informatics vol 14 no 9 pp 3956ndash3969 2018

[4] X Lu J Lai X Yu Y Wang and J M Guerrero ldquoA novelsecondary power management strategy for multiple ACmicrogrids with cluster-oriented two-layer cooperativeframeworkrdquo IEEE Transactions on Industrial Informaticsvol 17 no 2 pp 1483ndash1495 2021

[5] H Takahashi Development of Patrolling Robot for Substationpp 10ndash19 Japan IERE CouncilSpecial Document R8903Japan 1989

[6] J Beaudry and S Poirier Vehicule teleopere pour inspectionvisuelle etthermographique dans les postes de ransformation2012

[7] J K C Pinto M Masuda L C Magrini J A Jardini andM V Garbelloti ldquoMobile robot for hot spot monitoring inelectric power substationrdquo in Proceedings of the IEEEPESTransmission and Distribution Conference and Expositionpp 1ndash5 Chicago Illinois April 2008

[8] N Pouliot P-L Richard and S Montambault ldquoLineScouttechnology opens the way to robotic inspection and main-tenance of high-voltage power linesrdquo IEEE Power and EnergyTechnology Systems Journal vol 2 no 1 pp 1ndash11 2015

[9] A Cantieri M Ferraz and G Szekir ldquoCooperative UAV-UGV autonomous power pylon inspection an investigationof cooperative outdoor vehicle positioning architecturerdquoSensors vol 20 no 6384 pp 1ndash22 2020

(a) (b)

(c) (d)

(e) (f )

Figure 13 Sequence diagram of cooperative operation of two inspection robots (a) T 0 (b) T138 (c) T 306 (d) T 357 (e) T 365(f ) T 395

10 Complexity

[10] Y Guang and P Yutian ldquoIntelligent inspection of marinedisasters based on UAV intelligent visionrdquo Journal of CoastalResearch vol 93 pp 410ndash416 2019

[11] S Jordan J Moore and S Hovet ldquoState-of-the-art tech-nologies for UAV inspectionsrdquo IET Radar Sonar amp Navi-gation vol 12 no 2 pp 151ndash164 2018

[12] J Katranik F Pernus and B Likar ldquoA survey of mobile robotsfor distribution power line inspectionrdquo IEEE Transactions onPower Delivery vol 25 no 1 pp 485ndash493 2010

[13] J Yu and S M LaValle ldquoOptimal multirobot path planningon graphs complete algorithms and effective heuristicsrdquo IEEETransactions on Robotics vol 32 no 5 pp 1163ndash1177 2016

[14] K Jose and D K Pratihar ldquoTask allocation and collision-freepath planning of centralized multi-robots system for indus-trial plant inspection using heuristic methodsrdquo Robotics andAutonomous Systems vol 80 pp 34ndash42 2016

[15] B Pradhan A Nandi N B Hui and D S Roy ldquoA novelhybrid neural network-based multirobot path planning withmotion coordinationrdquo IEEE Transactions on VehicularTechnology vol 69 no 2 pp 1319ndash1327 2020

[16] C Luo S X Yang and X Li ldquoNeural-dynamics-drivencomplete area coverage navigation through cooperation ofmultiple mobile robotsrdquo IEEE Transactions on IndustrialElectronics vol 64 no 1 pp 750ndash760 2017

[17] B Woosley and P Dasgupta ldquoIntegrated real-time task andmotion planning for multiple robots under path and com-munication uncertaintiesrdquo Robotica vol 36 no 3pp 353ndash373 2018

[18] B Woosley P Dasgupta J G Rogers and J Twigg ldquoMulti-robot information driven path planning under communica-tion constraintsrdquo Autonomous Robots vol 44 no 5pp 721ndash737 2020

[19] F Imeson and S L Smith ldquoAn SMT-based approach tomotion planning for multiple robots with complex con-straintsrdquo IEEE Transactions on Robotics vol 35 no 3pp 669ndash684 2019

[20] A Ayari and S Bouamama ldquoA new multiple robot pathplanning algorithm dynamic distributed particle swarmoptimizationrdquo Robotics and Biomimetics vol 4 no 1 p 82017

[21] B Banerjee and CE Davis ldquoMultiagent path finding withpersistence conflictsrdquo IEEE Transactions on ComputationalIntelligence and AI in Games vol 9 no 4 pp 402ndash409 2016

[22] S abit and A Mohades ldquoMulti-robot path planning basedon multi-objective particle swarm optimizationrdquo IEEE Accessvol 7 pp 2138ndash2147 2018

[23] R Siegwart ldquoIR nourbakhsh and D scaramuzza ldquoIntro-duction to autonomous mobile robotsrdquo Industrial Robotvol 2 no 6 pp 645ndash649 2004

[24] K Jiang Z Sun Y Liu and J Sui ldquoDevelopment and Ap-plication of the Rail-type Inspection Robot used in SubstationRoomsrdquo MATEC Web of Conferences vol 139 no 5 ArticleID 00210 2017

[25] H B Xu J H Liu and X Jia ldquoSubstation inspection systembased on RFID technologyrdquo Advanced Materials Researchvol 734-737 pp 2846ndash2850 2013

[26] S ZWang D Han and Q Dong ldquoe application of RFID insubstation inspection systemrdquo Applied Mechanics and Ma-terials vol 295-298 pp 2433ndash2436 2013

[27] J Zhu Y Sun and D Sun ldquoDesign of a laser navigationsystem for the inspection robot used in substationrdquo Pro-ceedings of the Spie vol 322 2017

[28] C-J Huang Y-W Wang H-M Chen et al ldquoApplication ofcellular automata and type-2 fuzzy logic to dynamic vehicle

path planningrdquo Applied Soft Computing vol 19 pp 333ndash3422014

[29] S X Yang and M Meng ldquoAn efficient neural network ap-proach to dynamic robot motion planningrdquo Neural Networksvol 13 no 2 pp 143ndash148 2000

[30] S X Yang and M Q-H Meng ldquoReal-time collision-freemotion planning of a mobile robot using a Neural Dynamics-based approachrdquo IEEE Transactions on Neural Networksvol 14 no 6 pp 1541ndash1552 2003

[31] S Yang and C Luo A Neural Network Approach to CompleteCoverage Path Planning pp 718ndash724 Systems Man andCybernetics 2004

[32] C Luo and S X Yang ldquoA bioinspired neural network for real-time concurrent map building and complete coverage robotnavigation in unknown environmentsrdquo IEEE Transactions onNeural Networks vol 19 no 7 pp 1279ndash1298 2008

[33] S Chopra G Notarstefano M Rice and M Egerstedt ldquoAdistributed version of the Hungarian method for multirobotassignmentrdquo IEEE Transactions on Robotics vol 33 no 4pp 932ndash947 2017

Complexity 11

21 Intelligent InspectionRobot SystemModeling e systemis divided into two parts remote control platform and robotbody as shown in Figure 1 e remote console is composedof a host PC and a database which realizes the functions ofinformation storage status display overall planning andcentralized control e remote control platform controlsthe inspection robot through a 24G wireless communica-tion module and the inspection robot sends the videos andimages of the inspection operation to the remote controlplatform through wireless Ethernet e video capture cardis connected to the on-board PC through the PCIE buswhich is used to collect the images of visible-light camerainfrared thermal imager and the front camera of the me-chanical arme motor driver is connected to the on-boardPC via the USB-CAN transfer card Auxiliary light sourcesystem ultrasonic ranging module differential GPS re-ceiving module and speed measurement block are con-nected to the industrial control computer through the RS485bus e robot is powered by the lithium battery and eachrobot realizes data sharing through the wireless commu-nication module

e substation inspection robot carries a visible-lightcamera and an infrared thermograph which is used to detectinvaders and equipmentsrsquo fault point respectively e hostPC plays a supervisory role such as reading the status fromeach subsystem recognizing the equipments from thethermal image planning the inspection path and displayingthe 3D map e on-board PC controls the behaviors of therobots such as movement obstacle avoidance and posi-tioning e associated multirobot collaborative systemadopts a hybrid layout as shown in Figure 2 e host PC isresponsible for computing planning and scheduling tasksInformation could be shared between the mobile robots overa wireless network

22 Task Classification We introduce three important in-spection tasks here which will be realized in Section 4 basedon the proposed control methods designed in Section 3

221 Single-Point Inspection ere are some importantareas or fault-prone areas that need to be monitored inlarge substations of smart microgrids For these areas theinspection robot sometimes needs to carry out a single-point inspection In this situation the multirobot systemassigns the task to a single robot according to the locationof the inspection point the location of each robot and itsability value and then converts the problem into the pathplanning problem of the single robot in the knownenvironment

222 Multipoint Inspection In real applications there aregenerally more than one important or fault-prone areas thatneed to be inspected simultaneously In this situation theinspection task can be assigned to several robots accordingto the position of the task points then the reasonable pathsare designed for each robot to complete the inspection task

223 All-Area Inspection If the entire equipment needs tobe inspected then the robot should move in the wholesubstation In this situation the basic process of multirobotinspection in a known environment includes the following(a) grouping of multimobile robots in pairs (b) design theopposite heuristic algorithm for each group of robots (c)start the inspection and when it falls into the dead zonechoose the IBENN method to jump out and (d) determinewhether the entire area has been inspected

In practical applications no matter what kind of in-spection task the multimobile robot system needs to de-compose and allocate tasks first then each robot separatelyformulates a reasonable inspection path e commonlyused path planning methods mainly include artificial po-tential field method A-star algorithm and fuzzy logicwhich however have certain defects for different practicalproblems [28] In order to accomplish various kinds ofinspection tasks the widely used BENN method will beintroduced in the next part and the IBENN algorithmwill beproposed in Section 3

23 Biological Excitation Neural Network (BENN) MethodIn the bioexcitation neural network method the motionspace of a mobile robot can be represented by a topologicalstate space composed of a neural network and the activityvalue of neurons represents environmental informationeactivity values of all neurons are generally initialized to 0while the changes in the activity values of each neuron aredescribed by the following shunting equation [29 30]

dxi

dt minusAxi + B minus xi( 1113857 Ii1113858 1113859

++ 1113944

k

j1wij xj1113960 1113961

+⎛⎝ ⎞⎠ minus D + xi( 1113857 Ii1113858 1113859minus

(1)

where xi is the neural activity of the ith neural parametersAB and D are nonnegative constants representing the passivedecay rate the upper and lower bounds of the neural activityrespectively k is the number of neurons in the neighbor-hood wij and xj represent the connection weight and ac-tivity of neurons in the neighborhood respectively E is anormal number much larger than B and Ii is the ith externalinput with the following form

Ii

E target

minusE obstacle

0 other

⎧⎪⎪⎨

⎪⎪⎩(2)

Excitation signal Sei [Ii]

+ + 1113936kj1 wij[xj]

+ and inputinhibition Si

i [Ii]minus e nonlinear threshold function [a]+

is defined as [a]+ max(a 0) and [a]minus max(minusa 0) Letdij is the Euclidean distance between neurons wij f(dij)and f(a) (u0a) u0 is a positive constant e robot startsfrom the starting point to the next position qn determined bythe following formula [31 32]

qnlArrxqn max xj j 1 2 3 k1113872 1113873 (3)

is method ensures that the positive neuronal activityvalue can spread outwards and affect the whole state space

Complexity 3

while the negative neuronal activity value can only act lo-cally e neuronal activity values of the target point and theobstacle are respectively at the crest and trough of the waveas shown in Figure 3 so the target point can attract the robotto move towards it while the obstacle can only repel therobot locally After the robot reaches the next location fromthe present location the next location becomes a newpresent location unless the present point is the target pointIf the found next location is the same as the present locationthe robot stays there without any movement

Although this method can solve the problem of robotpath planning it still has some problems such as nonoptimalpath wrong path judgment and easy to fall into the dead

zone To end this an improved bioexcitation neural networkalgorithm is designed next which will be applied for themultirobot to complete various types of smart grid in-spection tasks

3 Improved Biological Excitation NeuralNetwork (IBENN) Method

When calculating the neuron activity value near theboundary the traditional BENN method regards theboundary as an obstacle making it relatively low relative tothe surrounding nonboundary neuron activity value As aresult the best paths are often overlooked as shown inFigure 4 As seen it is better to choose the path along the leftboundary in Figure 4(a) and the optimal path is between thetwo obstacles in Figure 4(b) Moreover the original methodonly considers the activity value of surrounding neuronswhen choosing the next path point which ignores the ro-botrsquos steering in the form process However robot steeringrequires deceleration steering and acceleration whichgreatly increase the power consumption and travel time ofthe robot

Remote control platform

Host PC

Differential GPSbase station

Remote controlhandle

Front display ofrobotic arm

Inspectionimage display

Visible-light

cameradisplaywindow

Visible-light

cameradisplaywindow

Infraredthermalimagerdisplaywindow

24G wirelesscommunication

Power station inspection robort

Power supply and charging interface module

PClE

On-boardPC

Videocapture card

USB-CANconversion

card

Auxiliarylight source

system

Ultrasonicobstacle

avoidance system

DifferentialGPS

receiver

Speedmeasuring

device

Motor driver

Visible light camera

Infrared camera

Robotic arm front camera

Robotic driver

Inspection camera driver

Mobile platform driver

USB CAN

RS485

DifferentialGPS

communication

WirelessEthernet

Figure 1 Single robot system architecture in power stations of smart microgrids

LAN management

Host system

Cooperative system

Communicationsrsquo link

Robot 1

Robot 2Robot 3

WLAN

Host PCDatabase

Figure 2 Multirobot system architecture in power stations ofsmart microgrids

1 Target

05

0

ndash05

Act

ivity

ndash130

2520

1510X

Y5

0 0 5 10 15 20 25 30

Figure 3 Biological excitation neuronal active field of the BENNmethod

4 Complexity

In order to reduce the power consumption of the robotand to smooth the path of the robot the following pathdecision method is adopted

qnlArrxqn max xj + cyj j 1 2 3 k1113872 1113873 (4)

where xi is the active value at the current position c is apositive constant yj 1 minus Δθj π is a monotonically in-creasing function of the moving direction difference be-tween the current to the next robot and Δθj is the absoluteangle at which the robot moves from the current position tothe next position eg Δθj 0 (or Δθj π) when the robotmoves in a straight line (or turns around) Denote the co-ordinates of the current position qc (xqc

yqc) and the

previous position qp (xqp yqp

) then

Δθj θj minus θc

11138681113868111386811138681113868

11138681113868111386811138681113868 arctan yqjminus yqc

xqjminus xqc

1113874 1113875

minus arctan yqcminus yqp

xqcminus xqp

1113874 1113875

(5)

e path decision method takes into account the factorsof steering and selection of appropriate c which representsthe weight of steering in the path decision only then asmooth path can be planned In order to overcome thedrawbacks of ignoring the boundary optimal path as well asunreasonable path selection we propose the following im-provement strategies

Strategy (i) Map extension ie extend the activityrange of robot virtual neuronsStrategy (ii) Activity increasing ie increase the ac-tivity of neurons near the obstacle and boundaryStrategy (iii) Node deletion ie delete the redundantnodes that do not hinder the passage of robots

e boundary neurons of the original map are extendedoutward of one circle respectively ese areas are assumedto be virtual reachable (not treated as obstacles) with thepositive activity value and can also spread activity aroundduring the initialization process but are ignored when

choosing the actual path e main purpose of Strategies (i)and (ii) is to improve the activity value of the original mapboundary neurons which can be considered as a boundaryprotection for these neurons In addition if the robot canbypass the next adjacent node from a certain node withoutcolliding with an obstacle in a path the deletion of this nodecan effectively shorten the total length of the path thusStrategy (iii) can reduce the robotrsquos power consumption andimprove work efficiency To realize these improvements thefollowing Assumption and Definition are given

Assumption 1 Neurons outside the boundaries of theoriginal map are virtual nonobstacles which also have thefunction of spreading activity values and their activity valuesare the average activity values of nonobstacle points in theneighborhood

Definition 1 If a robot is on a nine-square grid map-centeredthe top and bottom left and right front left and back right andfront right and back left are respectively considered as foursets of symmetrical coordinates If any pair of symmetricalcoordinates are obstacles the robot is said to be between theobstacles

If the robot is between the obstacles the excitation inputof the neuron can be calculated by

Sei Ii1113858 1113859

++

n 1113936kj1 wij xj1113960 1113961

+

npos (6)

When the neuron is not located between the obstaclesthe excitation input of the neuron can be calculated by

Sei Ii1113858 1113859

++

n minus nneg1113872 1113873 1113936kj1 wij xj1113960 1113961

+

npos (7)

where n npos and nneg represent the numbers of neigh-borhood neurons nonobstacles and obstacles respectivelyLet Si

i [Ii]minus then system (1) can be rewritten as

9

8

7

6

5Y

X

4

3

2

1

1 2

Start

Target

3 4 5 6 7 8 9

(a)

Start

Target9

8

7

6

5Y

X

4

3

2

1

1 2 3 4 5 6 7 8 9

(b)

Figure 4 Unreasonable path planning under traditional methods (a) Path along the boundary (b) Obstacle intermediate path

Complexity 5

dxi

dt minusAxi + B minus xi( 1113857S

ei minus D + xi( 1113857S

ii (8)

Hence Strategies (i) and (ii) are used to increase theactivity value of neurons near the boundaries or obstacles Inpractical application one of these two strategies can beselected and used together with Strategy (iii) to achievebetter path planning

Figure 5 shows the comparison experiment usingStrategies (i) and (iii) with model parameters A 10B D 1 E 100 k 8 and c 1 e relevant datacomparison is shown in Table 1 It can be seen from Figure 5and Table 1 that the path length has been reduced from 1007to 841 and the times of turns have been changed from 4 to 1us the proposed strategies have obvious improvementeffects

In order to verify the superiority of Strategies (ii) and(iii) the simulation environment is set as a complex mazeand model parameters are also set as A 10 B D 1E 100 k 8 and c 1 e initial position of the robot is(6 3) and the target position is (1 30) e traditionalBENN method A-star algorithm and the proposed IBENNmethod are compared as shown in Figures 6 and 7 As seenthe proposed IBENNmethod cannot only solve the problemof path misjudgment but also reduce the path transitionsmooth the path and improve the path quality ree indexcomparisons of path length turn times and total rotationangle are concluded in Table 2 It can be seen that comparedwith the original BENNmethod the path length path turnsand total rotation angle of the proposed IBENN method arereduced by 612 412 and 643 respectively Com-pared with theA-star algorithm the number of turns and thetotal rotation angle can be reduced by 167 and 168respectively under the condition that the path length isunchanged It concludes that the improved IBENN methodshows better performance in terms of path quality and pathsmoothness than the other methods

4 Multirobot Cooperative Inspection(MRCI) System

In this section we will implement the proposed IBENNmethod to the MRCI system and complete the previouslyestablished three inspection tasks

41 Single-Point Inspection Assume that there are n iso-morphic inspection robots with different initial positionsand m areas that need to be monitored in a substation ofsmart microgrids and one of the areas needs to be con-tinuously monitored at a certain moment In this situationthe system needs to schedule a robot to complete the taskfollowing the principle of minimum cost or maximumbenefit We establish the following mathematical model

fi(L D) min εLij + ηDij j 1 2 3 gi1113872 1113873 (9)

TilArr cos ti min fi i 1 2 3 n( 1113857 (10)

where Lij and Dij represent the length and the turningnumber of the jth path for the ith robot respectively ε and ηrepresent the associated weights of Lij and Dij respectively

9

8

7

6

5Y

X

4

3

2

1

1 2

Start

Proposed IBENN method

Target

3 4 5 6 7 8 9

Figure 5 Single-robot path generated by the proposed IBENNmethod with Strategies (i) and (iii) in the situation of single-pointinspection

Table 1 Comparison results of BENN and IBENN methods

Evaluation index BENN IBENN with strategies (i) and (iii)Path length 1007 841Turn times 4 1

30

25

20

15Y

X

10

5

5

The A-star method

10 15 2520 30

Proposed IBENN method

Figure 6 Single-robot path generated by the traditional BENNmethod and A-star algorithm in the situation of single-pointinspection

6 Complexity

all robotsrsquo weights are the same by default in the path de-cision gi represents the number of paths available for the ithrobot to complete the task T and fi can be considered as theminimum cost of robot i to achieve taskTe objective hereis to find the robot i and the optimal path gi

To solve this problem the proposed IBENN method isused to calculate the minimum cost of each robot tocomplete the task and then compare the optimal cost of eachrobot It is necessary that the robot with the lowest costobtains the task and completes the task according to theoptimal path planned For example in the 30 times 30 mapshown in Figure 8 gray areas represent parallel devices andblack ones represent obstacles in the site and there are fourrobots Robot1 Robot2 Robot3 and Robot4 with initialpositions R1(1 1) R2(30 1) R3(1 30) and R4(30 30)respectively When inspection tasks are needed nearequipment Rtarget(14 15) (ie area no 9) according to theIBENNmethod the cost of each robot to complete the task iscalculated as shown in Table 3 and then each robot offers aquotation according to the above method with f1 14f2 1414 f3 1206 and f4 1533 which can be cal-culated according to (9) when the parameter is set asε η 05 According to the calculation we can choose

Robot3 as the best scheme to execute the task and otherrobots determine their priority as a backup according to thecost

42 Multipoint Inspection In the substation working areathere is occasionally a need to inspect multiple areas and theadvantages of the multirobot cooperation system can be wellreflected in this situation e cost equation of the systemcan be described as

F min cos t min1113944n

i1fi Li Di( 1113857

min1113944

n

i

min εLij + ηDij j 1 2 3 gi1113872 11138731113872 1113873

(11)

where gi represents the total number of paths that robot i

can choose to reach the target point Assume that there are n

robots with m areas that need to be inspected(ngt 1 andmgt 1) simultaneously and the collaborative workof robots needs to be determined according to the rela-tionship between the areas m and the robots n

30

25

20

15Y

X

10

5

5 10 15 2520 30

Proposed IBENN method

Figure 7 Single-robot path generated by the proposed IBENNmethod with Strategies (ii) and (iii) in the situation of single-pointinspection

Table 2 Comparison of the three methods

Index BENN A-star

IBENN with strategies (ii) and(iii)

Path length 4063 3814 3814Turn times 17 12 10Rotationangle 2199 943 785

30

25

20

15Y

X

10

5

5

Robot 1

10 15 2520 30

Robot 2Robot 3Robot 4

Figure 8 Four-robot path generated by the proposed IBENN-based MRCI system in the situation of single-point inspection

Table 3 Comparison of the four-robot path planning

Index Robot1 Robot2 Robot3 Robot4Path length 2173 2356 2097 2280Turn times 18 19 16 17Rotation angle 628 471 314 785

Complexity 7

Case 1 ngem assume that a robot can only complete onetask and it can ensure that each uninspected area can beassigned to a robot to perform tasks at the same time eallocation method is the same as the task allocation methodof the single-point robot mentioned above ie each robotputs forward an optimal quotation for each task and themaster robot determines the optimal decision-makingscheme based on the quotation of each robot combined withthe corresponding bidding algorithm and assigns subtasks toeach robot according to the scheme en the problem isfirst transformed into an assignment problem which can besolved by the classical Hungarian algorithm [33] For ex-ample let n 6 and m 4 their positions are shown inTable 4 and the minimum cost of each robot at each taskpoint is solved according to the above method According tothe above allocation method the following allocationscheme can be obtained A1⟶ R1 A2⟶ R2

A3⟶ R3 andA4⟶ R5 and the total costF 994 + 969 + 681 + 571 3215

Case 2 nltm it means that a robot needs to completemultiple tasks and there can also be a situation where one ormore robots are idle For multiple robots at different initialpositions the host computer needs to plan a reasonable pathso that all inspection areas can be visited by the robots andthe total cost is minimal We have designed a genetic al-gorithm to solve this problem e genetic algorithm adoptsthe following single-chain coding form as shown in Fig-ure 8 when decoding the Robot2 completes the inspectiontasks of Areas 1 and 3 in sequence and similarly Robot1 andRobot3 complete the tasks of Areas 4 and 6 and Areas 2 and 5in sequenceis coding method has the advantage of strongreadability however it is easy to produce infeasible solutionsduring crossover and mutation erefore different repairalgorithms are used to repair the infeasible solutions

Crossover Use Partial-Mapped Crossover (PMX) op-erator when generating a new gene chain If it is not afeasible solution then fix it e specific repair methodis to find the repetitive genes in gene chain A that causeinfeasible solutions (there may be multiple groups) oneof which must be in the cross-replacement gene se-quence then find the gene that maps to the gene in genechain B and use it to replace the repetitive genes inchain A that are not in the cross-replacement sequenceMutation Randomly select two genes in the gene chainand determine whether one of their positions is at theend of the gene chain If not exchange their positions inthe gene chainSelection e tournament selection method is usedthat is a certain number of individuals are removedfrom the population each time then the best one isselected to enter the offspring population Repeat thisoperation until the new population size reaches theoriginal population size

For example in a 30 times 30 map the initial positions of theRobots 1 minus 3 are Rstart

1 (1 10) Rstart2 (15 30) and

Rstart3 (30 10) and the positions of the 6 inspection points are

A1(11 27) A2(29 28) A3(3 18) A4(16 15) A5(13 3) andA6(26 6) e initial azimuth of the robot is (0 minusπ2 minusπ)Using the proposed IBENN method above the optimal pathand the minimum cost between each point can be calculatede genetic algorithm can draw the following distributionplan

R1⟶ A3⟶ A1⟶ A4⟶ A5 R2⟶ A2 R3⟶ A6

(12)

e total cost is 4528 and the multirobot multipointinspection path is shown in Figure 9 where the red starindicates the inspection point and the blue star indicates theinitial position of each robot

43 All-Area Inspection Since the substation of smartmicrogrids is exposed to the outdoors for a long time it iseasy to break into foreign objects or other dangerous goodsIt is necessary to conduct regular inspections of the entirepower station of smart microgrids for all-area coverageHowever performing this task by a single robot may take along time and is inefficient erefore a multirobot col-laborative whole-area inspection program is designed

Divide every two robots into a group and design aheuristic algorithm for each robot e priority of theheuristic algorithm of the robots in each group is oppositewhich ensures that each group of robots can start inspectionsfrom different directions When the robot enters the deadzone position according to the proposed IBENN methodabove the optimal path from the dead zone position to theuninspected area can be planned e robot moves to thisarea and continues to inspect according to the originalheuristic algorithm For example in a 30 times 30 map there areparallel devices and various obstacle points as shown inFigure 10 Two robots in the area are used to coordinate tocomplete the all-area inspection taske steering priority ofthe heuristic algorithm of Robot1 W minus S minus SW minus NW minus N minus

E minus SE minus NE and Robot2 E minus N minus NE minus SE minus S minus W minus NW

minusSW and the initial positions are (1 1) and (30 1)respectively

Simulation experiments were carried out in the ob-stacle-free and obstacle environments and the results areshown in Figures 11 and 12 and Table 5 where the red andblue represent Robots 1 and 2 respectively pink dotsexpress repeated path points dots mean the final positionof the robot when the task is completed and stars rep-resent the initial position It can be seen from Table 5 thatin a simple map when there are no other obstacles in theinspection area and only parallel substation equipment

Table 4 Comparison of the four-robot path planning

Position Area1(916) Area2(1616) Area3(227) Area4(2225)

R1(11) 994 1492 1488 1801R2(151) 1031 969 788 1688R3(301) 1596 1442 681 1523R4(130) 1101 1158 1987 1271R5(1530) 1060 956 1609 571R6(3030) 2518 1441 1551 1132

8 Complexity

this method can achieve 100 coverage without over-lapping areas When there are various obstacles in theinspection area this method can also achieve 100 full-

coverage inspection but there is a repetition rate of 23Hence compared with other inspection methods theproposed IBENN method does not need to set a templateoperator and has strong versatility Multirobot collabo-ration can complete the entire area and full-coverageinspection task

To further verify the effectiveness of the proposedcontrol schemes we carry out the simulation experimentwith Coppelia Sim Software in the space of 30mtimes 30m etwo inspection robots are in the initial position as t 0 asshown in Figure 13(a) in which the gray cube and dark bluecube represent the equipment area and the obstacle arearespectively e robot is supposed to inspect at a speed of1ms disregarding the inspection time Using the aboveinspection strategy the experimental results are shown inFigure 13 As seen the left robot and right robot fall intodead zones respectively as t 138 or t 365 inFigures 13(a) and 13(e) and t 357 or t 306 inFigures 13(c) and 13(d) However in these cases the in-spection machine can jump out of the dead zone by callingthe IBENN algorithm respectively Furthermore both ro-bots fall into the dead zone state when t 395 as shown inFigure 13(f ) Since there is no undetected area in this sit-uation it follows that the inspection task has been com-pleted erefore the experiment verifies the feasibility ofthe cooperation scheme

A1 A3 R2 A4 A6 R1 A2 A5 R3

Figure 9 Gene chain coding of the genetic algorithm

30

25

20

15Y

X

10

5

5

Start points

10 15 2520 30

Inspection points

Figure 10 ree-robot path generated by the proposed IBENNbased MRCI system in the situation of six-point inspection

30

25

20

15Y

X

10

5

5 10 15 2520 30

Figure 11 Two-robot path generated by the proposed IBENN-based MRCI system in the situation of all-area inspection withoutobstacle

30

25

20

15Y

X

10

5

5 10 15 2520 30

Figure 12 Two-robot path generated by the proposed IBENN-based MRCI system in the situation of all-area inspection complexobstacle

Table 5 Results in obstacle-free and obstacle environments

Evaluationindex

Obstacle-freeenvironment ()

Obstacleenvironment ()

Coverage rate 100 100Repetition rate 0 23

Complexity 9

5 Conclusion

In this paper a multimobile robot collaborative operatingsystem for power stations of the smart microgrids isdesigned and an improved IBENN method is proposedCompared with the traditional BENN method and A-staralgorithm the improved IBENN algorithm has an obviousoptimization effect in path length and turning times Basedon this method the multirobot cooperative operationstrategy is designed to realize the three classic tasks of single-point inspection multipoint inspection and full-coverageinspection in the substation of smart microgrids whichverifies the effectiveness of the main results

Data Availability

All of the data used to support the findings of this study areincluded within this article

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China under Grant nos 61733004 and61773158

References

[1] A Peyman and F Keynia ldquoLifetime efficiency index model foroptimal maintenance of power substation equipment based

on cuckoo optimisation algorithmrdquo IET Generation Trans-mission amp Distribution vol 11 no 11 pp 2787ndash2795 2017

[2] I Ullah Y Fang and R Khan ldquoPredictive maintenance ofpower substation equipment by infrared thermography usinga machine-learning approachrdquo Energies vol 10 no 12pp 1ndash13 1987

[3] X Lu J Lai X Yu Y Wang and J M Guerrero ldquoDistributedcoordination of islanded microgrid clusters using a two-layerintermittent communication networkrdquo IEEE Transactions onIndustrial Informatics vol 14 no 9 pp 3956ndash3969 2018

[4] X Lu J Lai X Yu Y Wang and J M Guerrero ldquoA novelsecondary power management strategy for multiple ACmicrogrids with cluster-oriented two-layer cooperativeframeworkrdquo IEEE Transactions on Industrial Informaticsvol 17 no 2 pp 1483ndash1495 2021

[5] H Takahashi Development of Patrolling Robot for Substationpp 10ndash19 Japan IERE CouncilSpecial Document R8903Japan 1989

[6] J Beaudry and S Poirier Vehicule teleopere pour inspectionvisuelle etthermographique dans les postes de ransformation2012

[7] J K C Pinto M Masuda L C Magrini J A Jardini andM V Garbelloti ldquoMobile robot for hot spot monitoring inelectric power substationrdquo in Proceedings of the IEEEPESTransmission and Distribution Conference and Expositionpp 1ndash5 Chicago Illinois April 2008

[8] N Pouliot P-L Richard and S Montambault ldquoLineScouttechnology opens the way to robotic inspection and main-tenance of high-voltage power linesrdquo IEEE Power and EnergyTechnology Systems Journal vol 2 no 1 pp 1ndash11 2015

[9] A Cantieri M Ferraz and G Szekir ldquoCooperative UAV-UGV autonomous power pylon inspection an investigationof cooperative outdoor vehicle positioning architecturerdquoSensors vol 20 no 6384 pp 1ndash22 2020

(a) (b)

(c) (d)

(e) (f )

Figure 13 Sequence diagram of cooperative operation of two inspection robots (a) T 0 (b) T138 (c) T 306 (d) T 357 (e) T 365(f ) T 395

10 Complexity

[10] Y Guang and P Yutian ldquoIntelligent inspection of marinedisasters based on UAV intelligent visionrdquo Journal of CoastalResearch vol 93 pp 410ndash416 2019

[11] S Jordan J Moore and S Hovet ldquoState-of-the-art tech-nologies for UAV inspectionsrdquo IET Radar Sonar amp Navi-gation vol 12 no 2 pp 151ndash164 2018

[12] J Katranik F Pernus and B Likar ldquoA survey of mobile robotsfor distribution power line inspectionrdquo IEEE Transactions onPower Delivery vol 25 no 1 pp 485ndash493 2010

[13] J Yu and S M LaValle ldquoOptimal multirobot path planningon graphs complete algorithms and effective heuristicsrdquo IEEETransactions on Robotics vol 32 no 5 pp 1163ndash1177 2016

[14] K Jose and D K Pratihar ldquoTask allocation and collision-freepath planning of centralized multi-robots system for indus-trial plant inspection using heuristic methodsrdquo Robotics andAutonomous Systems vol 80 pp 34ndash42 2016

[15] B Pradhan A Nandi N B Hui and D S Roy ldquoA novelhybrid neural network-based multirobot path planning withmotion coordinationrdquo IEEE Transactions on VehicularTechnology vol 69 no 2 pp 1319ndash1327 2020

[16] C Luo S X Yang and X Li ldquoNeural-dynamics-drivencomplete area coverage navigation through cooperation ofmultiple mobile robotsrdquo IEEE Transactions on IndustrialElectronics vol 64 no 1 pp 750ndash760 2017

[17] B Woosley and P Dasgupta ldquoIntegrated real-time task andmotion planning for multiple robots under path and com-munication uncertaintiesrdquo Robotica vol 36 no 3pp 353ndash373 2018

[18] B Woosley P Dasgupta J G Rogers and J Twigg ldquoMulti-robot information driven path planning under communica-tion constraintsrdquo Autonomous Robots vol 44 no 5pp 721ndash737 2020

[19] F Imeson and S L Smith ldquoAn SMT-based approach tomotion planning for multiple robots with complex con-straintsrdquo IEEE Transactions on Robotics vol 35 no 3pp 669ndash684 2019

[20] A Ayari and S Bouamama ldquoA new multiple robot pathplanning algorithm dynamic distributed particle swarmoptimizationrdquo Robotics and Biomimetics vol 4 no 1 p 82017

[21] B Banerjee and CE Davis ldquoMultiagent path finding withpersistence conflictsrdquo IEEE Transactions on ComputationalIntelligence and AI in Games vol 9 no 4 pp 402ndash409 2016

[22] S abit and A Mohades ldquoMulti-robot path planning basedon multi-objective particle swarm optimizationrdquo IEEE Accessvol 7 pp 2138ndash2147 2018

[23] R Siegwart ldquoIR nourbakhsh and D scaramuzza ldquoIntro-duction to autonomous mobile robotsrdquo Industrial Robotvol 2 no 6 pp 645ndash649 2004

[24] K Jiang Z Sun Y Liu and J Sui ldquoDevelopment and Ap-plication of the Rail-type Inspection Robot used in SubstationRoomsrdquo MATEC Web of Conferences vol 139 no 5 ArticleID 00210 2017

[25] H B Xu J H Liu and X Jia ldquoSubstation inspection systembased on RFID technologyrdquo Advanced Materials Researchvol 734-737 pp 2846ndash2850 2013

[26] S ZWang D Han and Q Dong ldquoe application of RFID insubstation inspection systemrdquo Applied Mechanics and Ma-terials vol 295-298 pp 2433ndash2436 2013

[27] J Zhu Y Sun and D Sun ldquoDesign of a laser navigationsystem for the inspection robot used in substationrdquo Pro-ceedings of the Spie vol 322 2017

[28] C-J Huang Y-W Wang H-M Chen et al ldquoApplication ofcellular automata and type-2 fuzzy logic to dynamic vehicle

path planningrdquo Applied Soft Computing vol 19 pp 333ndash3422014

[29] S X Yang and M Meng ldquoAn efficient neural network ap-proach to dynamic robot motion planningrdquo Neural Networksvol 13 no 2 pp 143ndash148 2000

[30] S X Yang and M Q-H Meng ldquoReal-time collision-freemotion planning of a mobile robot using a Neural Dynamics-based approachrdquo IEEE Transactions on Neural Networksvol 14 no 6 pp 1541ndash1552 2003

[31] S Yang and C Luo A Neural Network Approach to CompleteCoverage Path Planning pp 718ndash724 Systems Man andCybernetics 2004

[32] C Luo and S X Yang ldquoA bioinspired neural network for real-time concurrent map building and complete coverage robotnavigation in unknown environmentsrdquo IEEE Transactions onNeural Networks vol 19 no 7 pp 1279ndash1298 2008

[33] S Chopra G Notarstefano M Rice and M Egerstedt ldquoAdistributed version of the Hungarian method for multirobotassignmentrdquo IEEE Transactions on Robotics vol 33 no 4pp 932ndash947 2017

Complexity 11

while the negative neuronal activity value can only act lo-cally e neuronal activity values of the target point and theobstacle are respectively at the crest and trough of the waveas shown in Figure 3 so the target point can attract the robotto move towards it while the obstacle can only repel therobot locally After the robot reaches the next location fromthe present location the next location becomes a newpresent location unless the present point is the target pointIf the found next location is the same as the present locationthe robot stays there without any movement

Although this method can solve the problem of robotpath planning it still has some problems such as nonoptimalpath wrong path judgment and easy to fall into the dead

zone To end this an improved bioexcitation neural networkalgorithm is designed next which will be applied for themultirobot to complete various types of smart grid in-spection tasks

3 Improved Biological Excitation NeuralNetwork (IBENN) Method

When calculating the neuron activity value near theboundary the traditional BENN method regards theboundary as an obstacle making it relatively low relative tothe surrounding nonboundary neuron activity value As aresult the best paths are often overlooked as shown inFigure 4 As seen it is better to choose the path along the leftboundary in Figure 4(a) and the optimal path is between thetwo obstacles in Figure 4(b) Moreover the original methodonly considers the activity value of surrounding neuronswhen choosing the next path point which ignores the ro-botrsquos steering in the form process However robot steeringrequires deceleration steering and acceleration whichgreatly increase the power consumption and travel time ofthe robot

Remote control platform

Host PC

Differential GPSbase station

Remote controlhandle

Front display ofrobotic arm

Inspectionimage display

Visible-light

cameradisplaywindow

Visible-light

cameradisplaywindow

Infraredthermalimagerdisplaywindow

24G wirelesscommunication

Power station inspection robort

Power supply and charging interface module

PClE

On-boardPC

Videocapture card

USB-CANconversion

card

Auxiliarylight source

system

Ultrasonicobstacle

avoidance system

DifferentialGPS

receiver

Speedmeasuring

device

Motor driver

Visible light camera

Infrared camera

Robotic arm front camera

Robotic driver

Inspection camera driver

Mobile platform driver

USB CAN

RS485

DifferentialGPS

communication

WirelessEthernet

Figure 1 Single robot system architecture in power stations of smart microgrids

LAN management

Host system

Cooperative system

Communicationsrsquo link

Robot 1

Robot 2Robot 3

WLAN

Host PCDatabase

Figure 2 Multirobot system architecture in power stations ofsmart microgrids

1 Target

05

0

ndash05

Act

ivity

ndash130

2520

1510X

Y5

0 0 5 10 15 20 25 30

Figure 3 Biological excitation neuronal active field of the BENNmethod

4 Complexity

In order to reduce the power consumption of the robotand to smooth the path of the robot the following pathdecision method is adopted

qnlArrxqn max xj + cyj j 1 2 3 k1113872 1113873 (4)

where xi is the active value at the current position c is apositive constant yj 1 minus Δθj π is a monotonically in-creasing function of the moving direction difference be-tween the current to the next robot and Δθj is the absoluteangle at which the robot moves from the current position tothe next position eg Δθj 0 (or Δθj π) when the robotmoves in a straight line (or turns around) Denote the co-ordinates of the current position qc (xqc

yqc) and the

previous position qp (xqp yqp

) then

Δθj θj minus θc

11138681113868111386811138681113868

11138681113868111386811138681113868 arctan yqjminus yqc

xqjminus xqc

1113874 1113875

minus arctan yqcminus yqp

xqcminus xqp

1113874 1113875

(5)

e path decision method takes into account the factorsof steering and selection of appropriate c which representsthe weight of steering in the path decision only then asmooth path can be planned In order to overcome thedrawbacks of ignoring the boundary optimal path as well asunreasonable path selection we propose the following im-provement strategies

Strategy (i) Map extension ie extend the activityrange of robot virtual neuronsStrategy (ii) Activity increasing ie increase the ac-tivity of neurons near the obstacle and boundaryStrategy (iii) Node deletion ie delete the redundantnodes that do not hinder the passage of robots

e boundary neurons of the original map are extendedoutward of one circle respectively ese areas are assumedto be virtual reachable (not treated as obstacles) with thepositive activity value and can also spread activity aroundduring the initialization process but are ignored when

choosing the actual path e main purpose of Strategies (i)and (ii) is to improve the activity value of the original mapboundary neurons which can be considered as a boundaryprotection for these neurons In addition if the robot canbypass the next adjacent node from a certain node withoutcolliding with an obstacle in a path the deletion of this nodecan effectively shorten the total length of the path thusStrategy (iii) can reduce the robotrsquos power consumption andimprove work efficiency To realize these improvements thefollowing Assumption and Definition are given

Assumption 1 Neurons outside the boundaries of theoriginal map are virtual nonobstacles which also have thefunction of spreading activity values and their activity valuesare the average activity values of nonobstacle points in theneighborhood

Definition 1 If a robot is on a nine-square grid map-centeredthe top and bottom left and right front left and back right andfront right and back left are respectively considered as foursets of symmetrical coordinates If any pair of symmetricalcoordinates are obstacles the robot is said to be between theobstacles

If the robot is between the obstacles the excitation inputof the neuron can be calculated by

Sei Ii1113858 1113859

++

n 1113936kj1 wij xj1113960 1113961

+

npos (6)

When the neuron is not located between the obstaclesthe excitation input of the neuron can be calculated by

Sei Ii1113858 1113859

++

n minus nneg1113872 1113873 1113936kj1 wij xj1113960 1113961

+

npos (7)

where n npos and nneg represent the numbers of neigh-borhood neurons nonobstacles and obstacles respectivelyLet Si

i [Ii]minus then system (1) can be rewritten as

9

8

7

6

5Y

X

4

3

2

1

1 2

Start

Target

3 4 5 6 7 8 9

(a)

Start

Target9

8

7

6

5Y

X

4

3

2

1

1 2 3 4 5 6 7 8 9

(b)

Figure 4 Unreasonable path planning under traditional methods (a) Path along the boundary (b) Obstacle intermediate path

Complexity 5

dxi

dt minusAxi + B minus xi( 1113857S

ei minus D + xi( 1113857S

ii (8)

Hence Strategies (i) and (ii) are used to increase theactivity value of neurons near the boundaries or obstacles Inpractical application one of these two strategies can beselected and used together with Strategy (iii) to achievebetter path planning

Figure 5 shows the comparison experiment usingStrategies (i) and (iii) with model parameters A 10B D 1 E 100 k 8 and c 1 e relevant datacomparison is shown in Table 1 It can be seen from Figure 5and Table 1 that the path length has been reduced from 1007to 841 and the times of turns have been changed from 4 to 1us the proposed strategies have obvious improvementeffects

In order to verify the superiority of Strategies (ii) and(iii) the simulation environment is set as a complex mazeand model parameters are also set as A 10 B D 1E 100 k 8 and c 1 e initial position of the robot is(6 3) and the target position is (1 30) e traditionalBENN method A-star algorithm and the proposed IBENNmethod are compared as shown in Figures 6 and 7 As seenthe proposed IBENNmethod cannot only solve the problemof path misjudgment but also reduce the path transitionsmooth the path and improve the path quality ree indexcomparisons of path length turn times and total rotationangle are concluded in Table 2 It can be seen that comparedwith the original BENNmethod the path length path turnsand total rotation angle of the proposed IBENN method arereduced by 612 412 and 643 respectively Com-pared with theA-star algorithm the number of turns and thetotal rotation angle can be reduced by 167 and 168respectively under the condition that the path length isunchanged It concludes that the improved IBENN methodshows better performance in terms of path quality and pathsmoothness than the other methods

4 Multirobot Cooperative Inspection(MRCI) System

In this section we will implement the proposed IBENNmethod to the MRCI system and complete the previouslyestablished three inspection tasks

41 Single-Point Inspection Assume that there are n iso-morphic inspection robots with different initial positionsand m areas that need to be monitored in a substation ofsmart microgrids and one of the areas needs to be con-tinuously monitored at a certain moment In this situationthe system needs to schedule a robot to complete the taskfollowing the principle of minimum cost or maximumbenefit We establish the following mathematical model

fi(L D) min εLij + ηDij j 1 2 3 gi1113872 1113873 (9)

TilArr cos ti min fi i 1 2 3 n( 1113857 (10)

where Lij and Dij represent the length and the turningnumber of the jth path for the ith robot respectively ε and ηrepresent the associated weights of Lij and Dij respectively

9

8

7

6

5Y

X

4

3

2

1

1 2

Start

Proposed IBENN method

Target

3 4 5 6 7 8 9

Figure 5 Single-robot path generated by the proposed IBENNmethod with Strategies (i) and (iii) in the situation of single-pointinspection

Table 1 Comparison results of BENN and IBENN methods

Evaluation index BENN IBENN with strategies (i) and (iii)Path length 1007 841Turn times 4 1

30

25

20

15Y

X

10

5

5

The A-star method

10 15 2520 30

Proposed IBENN method

Figure 6 Single-robot path generated by the traditional BENNmethod and A-star algorithm in the situation of single-pointinspection

6 Complexity

all robotsrsquo weights are the same by default in the path de-cision gi represents the number of paths available for the ithrobot to complete the task T and fi can be considered as theminimum cost of robot i to achieve taskTe objective hereis to find the robot i and the optimal path gi

To solve this problem the proposed IBENN method isused to calculate the minimum cost of each robot tocomplete the task and then compare the optimal cost of eachrobot It is necessary that the robot with the lowest costobtains the task and completes the task according to theoptimal path planned For example in the 30 times 30 mapshown in Figure 8 gray areas represent parallel devices andblack ones represent obstacles in the site and there are fourrobots Robot1 Robot2 Robot3 and Robot4 with initialpositions R1(1 1) R2(30 1) R3(1 30) and R4(30 30)respectively When inspection tasks are needed nearequipment Rtarget(14 15) (ie area no 9) according to theIBENNmethod the cost of each robot to complete the task iscalculated as shown in Table 3 and then each robot offers aquotation according to the above method with f1 14f2 1414 f3 1206 and f4 1533 which can be cal-culated according to (9) when the parameter is set asε η 05 According to the calculation we can choose

Robot3 as the best scheme to execute the task and otherrobots determine their priority as a backup according to thecost

42 Multipoint Inspection In the substation working areathere is occasionally a need to inspect multiple areas and theadvantages of the multirobot cooperation system can be wellreflected in this situation e cost equation of the systemcan be described as

F min cos t min1113944n

i1fi Li Di( 1113857

min1113944

n

i

min εLij + ηDij j 1 2 3 gi1113872 11138731113872 1113873

(11)

where gi represents the total number of paths that robot i

can choose to reach the target point Assume that there are n

robots with m areas that need to be inspected(ngt 1 andmgt 1) simultaneously and the collaborative workof robots needs to be determined according to the rela-tionship between the areas m and the robots n

30

25

20

15Y

X

10

5

5 10 15 2520 30

Proposed IBENN method

Figure 7 Single-robot path generated by the proposed IBENNmethod with Strategies (ii) and (iii) in the situation of single-pointinspection

Table 2 Comparison of the three methods

Index BENN A-star

IBENN with strategies (ii) and(iii)

Path length 4063 3814 3814Turn times 17 12 10Rotationangle 2199 943 785

30

25

20

15Y

X

10

5

5

Robot 1

10 15 2520 30

Robot 2Robot 3Robot 4

Figure 8 Four-robot path generated by the proposed IBENN-based MRCI system in the situation of single-point inspection

Table 3 Comparison of the four-robot path planning

Index Robot1 Robot2 Robot3 Robot4Path length 2173 2356 2097 2280Turn times 18 19 16 17Rotation angle 628 471 314 785

Complexity 7

Case 1 ngem assume that a robot can only complete onetask and it can ensure that each uninspected area can beassigned to a robot to perform tasks at the same time eallocation method is the same as the task allocation methodof the single-point robot mentioned above ie each robotputs forward an optimal quotation for each task and themaster robot determines the optimal decision-makingscheme based on the quotation of each robot combined withthe corresponding bidding algorithm and assigns subtasks toeach robot according to the scheme en the problem isfirst transformed into an assignment problem which can besolved by the classical Hungarian algorithm [33] For ex-ample let n 6 and m 4 their positions are shown inTable 4 and the minimum cost of each robot at each taskpoint is solved according to the above method According tothe above allocation method the following allocationscheme can be obtained A1⟶ R1 A2⟶ R2

A3⟶ R3 andA4⟶ R5 and the total costF 994 + 969 + 681 + 571 3215

Case 2 nltm it means that a robot needs to completemultiple tasks and there can also be a situation where one ormore robots are idle For multiple robots at different initialpositions the host computer needs to plan a reasonable pathso that all inspection areas can be visited by the robots andthe total cost is minimal We have designed a genetic al-gorithm to solve this problem e genetic algorithm adoptsthe following single-chain coding form as shown in Fig-ure 8 when decoding the Robot2 completes the inspectiontasks of Areas 1 and 3 in sequence and similarly Robot1 andRobot3 complete the tasks of Areas 4 and 6 and Areas 2 and 5in sequenceis coding method has the advantage of strongreadability however it is easy to produce infeasible solutionsduring crossover and mutation erefore different repairalgorithms are used to repair the infeasible solutions

Crossover Use Partial-Mapped Crossover (PMX) op-erator when generating a new gene chain If it is not afeasible solution then fix it e specific repair methodis to find the repetitive genes in gene chain A that causeinfeasible solutions (there may be multiple groups) oneof which must be in the cross-replacement gene se-quence then find the gene that maps to the gene in genechain B and use it to replace the repetitive genes inchain A that are not in the cross-replacement sequenceMutation Randomly select two genes in the gene chainand determine whether one of their positions is at theend of the gene chain If not exchange their positions inthe gene chainSelection e tournament selection method is usedthat is a certain number of individuals are removedfrom the population each time then the best one isselected to enter the offspring population Repeat thisoperation until the new population size reaches theoriginal population size

For example in a 30 times 30 map the initial positions of theRobots 1 minus 3 are Rstart

1 (1 10) Rstart2 (15 30) and

Rstart3 (30 10) and the positions of the 6 inspection points are

A1(11 27) A2(29 28) A3(3 18) A4(16 15) A5(13 3) andA6(26 6) e initial azimuth of the robot is (0 minusπ2 minusπ)Using the proposed IBENN method above the optimal pathand the minimum cost between each point can be calculatede genetic algorithm can draw the following distributionplan

R1⟶ A3⟶ A1⟶ A4⟶ A5 R2⟶ A2 R3⟶ A6

(12)

e total cost is 4528 and the multirobot multipointinspection path is shown in Figure 9 where the red starindicates the inspection point and the blue star indicates theinitial position of each robot

43 All-Area Inspection Since the substation of smartmicrogrids is exposed to the outdoors for a long time it iseasy to break into foreign objects or other dangerous goodsIt is necessary to conduct regular inspections of the entirepower station of smart microgrids for all-area coverageHowever performing this task by a single robot may take along time and is inefficient erefore a multirobot col-laborative whole-area inspection program is designed

Divide every two robots into a group and design aheuristic algorithm for each robot e priority of theheuristic algorithm of the robots in each group is oppositewhich ensures that each group of robots can start inspectionsfrom different directions When the robot enters the deadzone position according to the proposed IBENN methodabove the optimal path from the dead zone position to theuninspected area can be planned e robot moves to thisarea and continues to inspect according to the originalheuristic algorithm For example in a 30 times 30 map there areparallel devices and various obstacle points as shown inFigure 10 Two robots in the area are used to coordinate tocomplete the all-area inspection taske steering priority ofthe heuristic algorithm of Robot1 W minus S minus SW minus NW minus N minus

E minus SE minus NE and Robot2 E minus N minus NE minus SE minus S minus W minus NW

minusSW and the initial positions are (1 1) and (30 1)respectively

Simulation experiments were carried out in the ob-stacle-free and obstacle environments and the results areshown in Figures 11 and 12 and Table 5 where the red andblue represent Robots 1 and 2 respectively pink dotsexpress repeated path points dots mean the final positionof the robot when the task is completed and stars rep-resent the initial position It can be seen from Table 5 thatin a simple map when there are no other obstacles in theinspection area and only parallel substation equipment

Table 4 Comparison of the four-robot path planning

Position Area1(916) Area2(1616) Area3(227) Area4(2225)

R1(11) 994 1492 1488 1801R2(151) 1031 969 788 1688R3(301) 1596 1442 681 1523R4(130) 1101 1158 1987 1271R5(1530) 1060 956 1609 571R6(3030) 2518 1441 1551 1132

8 Complexity

this method can achieve 100 coverage without over-lapping areas When there are various obstacles in theinspection area this method can also achieve 100 full-

coverage inspection but there is a repetition rate of 23Hence compared with other inspection methods theproposed IBENN method does not need to set a templateoperator and has strong versatility Multirobot collabo-ration can complete the entire area and full-coverageinspection task

To further verify the effectiveness of the proposedcontrol schemes we carry out the simulation experimentwith Coppelia Sim Software in the space of 30mtimes 30m etwo inspection robots are in the initial position as t 0 asshown in Figure 13(a) in which the gray cube and dark bluecube represent the equipment area and the obstacle arearespectively e robot is supposed to inspect at a speed of1ms disregarding the inspection time Using the aboveinspection strategy the experimental results are shown inFigure 13 As seen the left robot and right robot fall intodead zones respectively as t 138 or t 365 inFigures 13(a) and 13(e) and t 357 or t 306 inFigures 13(c) and 13(d) However in these cases the in-spection machine can jump out of the dead zone by callingthe IBENN algorithm respectively Furthermore both ro-bots fall into the dead zone state when t 395 as shown inFigure 13(f ) Since there is no undetected area in this sit-uation it follows that the inspection task has been com-pleted erefore the experiment verifies the feasibility ofthe cooperation scheme

A1 A3 R2 A4 A6 R1 A2 A5 R3

Figure 9 Gene chain coding of the genetic algorithm

30

25

20

15Y

X

10

5

5

Start points

10 15 2520 30

Inspection points

Figure 10 ree-robot path generated by the proposed IBENNbased MRCI system in the situation of six-point inspection

30

25

20

15Y

X

10

5

5 10 15 2520 30

Figure 11 Two-robot path generated by the proposed IBENN-based MRCI system in the situation of all-area inspection withoutobstacle

30

25

20

15Y

X

10

5

5 10 15 2520 30

Figure 12 Two-robot path generated by the proposed IBENN-based MRCI system in the situation of all-area inspection complexobstacle

Table 5 Results in obstacle-free and obstacle environments

Evaluationindex

Obstacle-freeenvironment ()

Obstacleenvironment ()

Coverage rate 100 100Repetition rate 0 23

Complexity 9

5 Conclusion

In this paper a multimobile robot collaborative operatingsystem for power stations of the smart microgrids isdesigned and an improved IBENN method is proposedCompared with the traditional BENN method and A-staralgorithm the improved IBENN algorithm has an obviousoptimization effect in path length and turning times Basedon this method the multirobot cooperative operationstrategy is designed to realize the three classic tasks of single-point inspection multipoint inspection and full-coverageinspection in the substation of smart microgrids whichverifies the effectiveness of the main results

Data Availability

All of the data used to support the findings of this study areincluded within this article

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China under Grant nos 61733004 and61773158

References

[1] A Peyman and F Keynia ldquoLifetime efficiency index model foroptimal maintenance of power substation equipment based

on cuckoo optimisation algorithmrdquo IET Generation Trans-mission amp Distribution vol 11 no 11 pp 2787ndash2795 2017

[2] I Ullah Y Fang and R Khan ldquoPredictive maintenance ofpower substation equipment by infrared thermography usinga machine-learning approachrdquo Energies vol 10 no 12pp 1ndash13 1987

[3] X Lu J Lai X Yu Y Wang and J M Guerrero ldquoDistributedcoordination of islanded microgrid clusters using a two-layerintermittent communication networkrdquo IEEE Transactions onIndustrial Informatics vol 14 no 9 pp 3956ndash3969 2018

[4] X Lu J Lai X Yu Y Wang and J M Guerrero ldquoA novelsecondary power management strategy for multiple ACmicrogrids with cluster-oriented two-layer cooperativeframeworkrdquo IEEE Transactions on Industrial Informaticsvol 17 no 2 pp 1483ndash1495 2021

[5] H Takahashi Development of Patrolling Robot for Substationpp 10ndash19 Japan IERE CouncilSpecial Document R8903Japan 1989

[6] J Beaudry and S Poirier Vehicule teleopere pour inspectionvisuelle etthermographique dans les postes de ransformation2012

[7] J K C Pinto M Masuda L C Magrini J A Jardini andM V Garbelloti ldquoMobile robot for hot spot monitoring inelectric power substationrdquo in Proceedings of the IEEEPESTransmission and Distribution Conference and Expositionpp 1ndash5 Chicago Illinois April 2008

[8] N Pouliot P-L Richard and S Montambault ldquoLineScouttechnology opens the way to robotic inspection and main-tenance of high-voltage power linesrdquo IEEE Power and EnergyTechnology Systems Journal vol 2 no 1 pp 1ndash11 2015

[9] A Cantieri M Ferraz and G Szekir ldquoCooperative UAV-UGV autonomous power pylon inspection an investigationof cooperative outdoor vehicle positioning architecturerdquoSensors vol 20 no 6384 pp 1ndash22 2020

(a) (b)

(c) (d)

(e) (f )

Figure 13 Sequence diagram of cooperative operation of two inspection robots (a) T 0 (b) T138 (c) T 306 (d) T 357 (e) T 365(f ) T 395

10 Complexity

[10] Y Guang and P Yutian ldquoIntelligent inspection of marinedisasters based on UAV intelligent visionrdquo Journal of CoastalResearch vol 93 pp 410ndash416 2019

[11] S Jordan J Moore and S Hovet ldquoState-of-the-art tech-nologies for UAV inspectionsrdquo IET Radar Sonar amp Navi-gation vol 12 no 2 pp 151ndash164 2018

[12] J Katranik F Pernus and B Likar ldquoA survey of mobile robotsfor distribution power line inspectionrdquo IEEE Transactions onPower Delivery vol 25 no 1 pp 485ndash493 2010

[13] J Yu and S M LaValle ldquoOptimal multirobot path planningon graphs complete algorithms and effective heuristicsrdquo IEEETransactions on Robotics vol 32 no 5 pp 1163ndash1177 2016

[14] K Jose and D K Pratihar ldquoTask allocation and collision-freepath planning of centralized multi-robots system for indus-trial plant inspection using heuristic methodsrdquo Robotics andAutonomous Systems vol 80 pp 34ndash42 2016

[15] B Pradhan A Nandi N B Hui and D S Roy ldquoA novelhybrid neural network-based multirobot path planning withmotion coordinationrdquo IEEE Transactions on VehicularTechnology vol 69 no 2 pp 1319ndash1327 2020

[16] C Luo S X Yang and X Li ldquoNeural-dynamics-drivencomplete area coverage navigation through cooperation ofmultiple mobile robotsrdquo IEEE Transactions on IndustrialElectronics vol 64 no 1 pp 750ndash760 2017

[17] B Woosley and P Dasgupta ldquoIntegrated real-time task andmotion planning for multiple robots under path and com-munication uncertaintiesrdquo Robotica vol 36 no 3pp 353ndash373 2018

[18] B Woosley P Dasgupta J G Rogers and J Twigg ldquoMulti-robot information driven path planning under communica-tion constraintsrdquo Autonomous Robots vol 44 no 5pp 721ndash737 2020

[19] F Imeson and S L Smith ldquoAn SMT-based approach tomotion planning for multiple robots with complex con-straintsrdquo IEEE Transactions on Robotics vol 35 no 3pp 669ndash684 2019

[20] A Ayari and S Bouamama ldquoA new multiple robot pathplanning algorithm dynamic distributed particle swarmoptimizationrdquo Robotics and Biomimetics vol 4 no 1 p 82017

[21] B Banerjee and CE Davis ldquoMultiagent path finding withpersistence conflictsrdquo IEEE Transactions on ComputationalIntelligence and AI in Games vol 9 no 4 pp 402ndash409 2016

[22] S abit and A Mohades ldquoMulti-robot path planning basedon multi-objective particle swarm optimizationrdquo IEEE Accessvol 7 pp 2138ndash2147 2018

[23] R Siegwart ldquoIR nourbakhsh and D scaramuzza ldquoIntro-duction to autonomous mobile robotsrdquo Industrial Robotvol 2 no 6 pp 645ndash649 2004

[24] K Jiang Z Sun Y Liu and J Sui ldquoDevelopment and Ap-plication of the Rail-type Inspection Robot used in SubstationRoomsrdquo MATEC Web of Conferences vol 139 no 5 ArticleID 00210 2017

[25] H B Xu J H Liu and X Jia ldquoSubstation inspection systembased on RFID technologyrdquo Advanced Materials Researchvol 734-737 pp 2846ndash2850 2013

[26] S ZWang D Han and Q Dong ldquoe application of RFID insubstation inspection systemrdquo Applied Mechanics and Ma-terials vol 295-298 pp 2433ndash2436 2013

[27] J Zhu Y Sun and D Sun ldquoDesign of a laser navigationsystem for the inspection robot used in substationrdquo Pro-ceedings of the Spie vol 322 2017

[28] C-J Huang Y-W Wang H-M Chen et al ldquoApplication ofcellular automata and type-2 fuzzy logic to dynamic vehicle

path planningrdquo Applied Soft Computing vol 19 pp 333ndash3422014

[29] S X Yang and M Meng ldquoAn efficient neural network ap-proach to dynamic robot motion planningrdquo Neural Networksvol 13 no 2 pp 143ndash148 2000

[30] S X Yang and M Q-H Meng ldquoReal-time collision-freemotion planning of a mobile robot using a Neural Dynamics-based approachrdquo IEEE Transactions on Neural Networksvol 14 no 6 pp 1541ndash1552 2003

[31] S Yang and C Luo A Neural Network Approach to CompleteCoverage Path Planning pp 718ndash724 Systems Man andCybernetics 2004

[32] C Luo and S X Yang ldquoA bioinspired neural network for real-time concurrent map building and complete coverage robotnavigation in unknown environmentsrdquo IEEE Transactions onNeural Networks vol 19 no 7 pp 1279ndash1298 2008

[33] S Chopra G Notarstefano M Rice and M Egerstedt ldquoAdistributed version of the Hungarian method for multirobotassignmentrdquo IEEE Transactions on Robotics vol 33 no 4pp 932ndash947 2017

Complexity 11

In order to reduce the power consumption of the robotand to smooth the path of the robot the following pathdecision method is adopted

qnlArrxqn max xj + cyj j 1 2 3 k1113872 1113873 (4)

where xi is the active value at the current position c is apositive constant yj 1 minus Δθj π is a monotonically in-creasing function of the moving direction difference be-tween the current to the next robot and Δθj is the absoluteangle at which the robot moves from the current position tothe next position eg Δθj 0 (or Δθj π) when the robotmoves in a straight line (or turns around) Denote the co-ordinates of the current position qc (xqc

yqc) and the

previous position qp (xqp yqp

) then

Δθj θj minus θc

11138681113868111386811138681113868

11138681113868111386811138681113868 arctan yqjminus yqc

xqjminus xqc

1113874 1113875

minus arctan yqcminus yqp

xqcminus xqp

1113874 1113875

(5)

e path decision method takes into account the factorsof steering and selection of appropriate c which representsthe weight of steering in the path decision only then asmooth path can be planned In order to overcome thedrawbacks of ignoring the boundary optimal path as well asunreasonable path selection we propose the following im-provement strategies

Strategy (i) Map extension ie extend the activityrange of robot virtual neuronsStrategy (ii) Activity increasing ie increase the ac-tivity of neurons near the obstacle and boundaryStrategy (iii) Node deletion ie delete the redundantnodes that do not hinder the passage of robots

e boundary neurons of the original map are extendedoutward of one circle respectively ese areas are assumedto be virtual reachable (not treated as obstacles) with thepositive activity value and can also spread activity aroundduring the initialization process but are ignored when

choosing the actual path e main purpose of Strategies (i)and (ii) is to improve the activity value of the original mapboundary neurons which can be considered as a boundaryprotection for these neurons In addition if the robot canbypass the next adjacent node from a certain node withoutcolliding with an obstacle in a path the deletion of this nodecan effectively shorten the total length of the path thusStrategy (iii) can reduce the robotrsquos power consumption andimprove work efficiency To realize these improvements thefollowing Assumption and Definition are given

Assumption 1 Neurons outside the boundaries of theoriginal map are virtual nonobstacles which also have thefunction of spreading activity values and their activity valuesare the average activity values of nonobstacle points in theneighborhood

Definition 1 If a robot is on a nine-square grid map-centeredthe top and bottom left and right front left and back right andfront right and back left are respectively considered as foursets of symmetrical coordinates If any pair of symmetricalcoordinates are obstacles the robot is said to be between theobstacles

If the robot is between the obstacles the excitation inputof the neuron can be calculated by

Sei Ii1113858 1113859

++

n 1113936kj1 wij xj1113960 1113961

+

npos (6)

When the neuron is not located between the obstaclesthe excitation input of the neuron can be calculated by

Sei Ii1113858 1113859

++

n minus nneg1113872 1113873 1113936kj1 wij xj1113960 1113961

+

npos (7)

where n npos and nneg represent the numbers of neigh-borhood neurons nonobstacles and obstacles respectivelyLet Si

i [Ii]minus then system (1) can be rewritten as

9

8

7

6

5Y

X

4

3

2

1

1 2

Start

Target

3 4 5 6 7 8 9

(a)

Start

Target9

8

7

6

5Y

X

4

3

2

1

1 2 3 4 5 6 7 8 9

(b)

Figure 4 Unreasonable path planning under traditional methods (a) Path along the boundary (b) Obstacle intermediate path

Complexity 5

dxi

dt minusAxi + B minus xi( 1113857S

ei minus D + xi( 1113857S

ii (8)

Hence Strategies (i) and (ii) are used to increase theactivity value of neurons near the boundaries or obstacles Inpractical application one of these two strategies can beselected and used together with Strategy (iii) to achievebetter path planning

Figure 5 shows the comparison experiment usingStrategies (i) and (iii) with model parameters A 10B D 1 E 100 k 8 and c 1 e relevant datacomparison is shown in Table 1 It can be seen from Figure 5and Table 1 that the path length has been reduced from 1007to 841 and the times of turns have been changed from 4 to 1us the proposed strategies have obvious improvementeffects

In order to verify the superiority of Strategies (ii) and(iii) the simulation environment is set as a complex mazeand model parameters are also set as A 10 B D 1E 100 k 8 and c 1 e initial position of the robot is(6 3) and the target position is (1 30) e traditionalBENN method A-star algorithm and the proposed IBENNmethod are compared as shown in Figures 6 and 7 As seenthe proposed IBENNmethod cannot only solve the problemof path misjudgment but also reduce the path transitionsmooth the path and improve the path quality ree indexcomparisons of path length turn times and total rotationangle are concluded in Table 2 It can be seen that comparedwith the original BENNmethod the path length path turnsand total rotation angle of the proposed IBENN method arereduced by 612 412 and 643 respectively Com-pared with theA-star algorithm the number of turns and thetotal rotation angle can be reduced by 167 and 168respectively under the condition that the path length isunchanged It concludes that the improved IBENN methodshows better performance in terms of path quality and pathsmoothness than the other methods

4 Multirobot Cooperative Inspection(MRCI) System

In this section we will implement the proposed IBENNmethod to the MRCI system and complete the previouslyestablished three inspection tasks

41 Single-Point Inspection Assume that there are n iso-morphic inspection robots with different initial positionsand m areas that need to be monitored in a substation ofsmart microgrids and one of the areas needs to be con-tinuously monitored at a certain moment In this situationthe system needs to schedule a robot to complete the taskfollowing the principle of minimum cost or maximumbenefit We establish the following mathematical model

fi(L D) min εLij + ηDij j 1 2 3 gi1113872 1113873 (9)

TilArr cos ti min fi i 1 2 3 n( 1113857 (10)

where Lij and Dij represent the length and the turningnumber of the jth path for the ith robot respectively ε and ηrepresent the associated weights of Lij and Dij respectively

9

8

7

6

5Y

X

4

3

2

1

1 2

Start

Proposed IBENN method

Target

3 4 5 6 7 8 9

Figure 5 Single-robot path generated by the proposed IBENNmethod with Strategies (i) and (iii) in the situation of single-pointinspection

Table 1 Comparison results of BENN and IBENN methods

Evaluation index BENN IBENN with strategies (i) and (iii)Path length 1007 841Turn times 4 1

30

25

20

15Y

X

10

5

5

The A-star method

10 15 2520 30

Proposed IBENN method

Figure 6 Single-robot path generated by the traditional BENNmethod and A-star algorithm in the situation of single-pointinspection

6 Complexity

all robotsrsquo weights are the same by default in the path de-cision gi represents the number of paths available for the ithrobot to complete the task T and fi can be considered as theminimum cost of robot i to achieve taskTe objective hereis to find the robot i and the optimal path gi

To solve this problem the proposed IBENN method isused to calculate the minimum cost of each robot tocomplete the task and then compare the optimal cost of eachrobot It is necessary that the robot with the lowest costobtains the task and completes the task according to theoptimal path planned For example in the 30 times 30 mapshown in Figure 8 gray areas represent parallel devices andblack ones represent obstacles in the site and there are fourrobots Robot1 Robot2 Robot3 and Robot4 with initialpositions R1(1 1) R2(30 1) R3(1 30) and R4(30 30)respectively When inspection tasks are needed nearequipment Rtarget(14 15) (ie area no 9) according to theIBENNmethod the cost of each robot to complete the task iscalculated as shown in Table 3 and then each robot offers aquotation according to the above method with f1 14f2 1414 f3 1206 and f4 1533 which can be cal-culated according to (9) when the parameter is set asε η 05 According to the calculation we can choose

Robot3 as the best scheme to execute the task and otherrobots determine their priority as a backup according to thecost

42 Multipoint Inspection In the substation working areathere is occasionally a need to inspect multiple areas and theadvantages of the multirobot cooperation system can be wellreflected in this situation e cost equation of the systemcan be described as

F min cos t min1113944n

i1fi Li Di( 1113857

min1113944

n

i

min εLij + ηDij j 1 2 3 gi1113872 11138731113872 1113873

(11)

where gi represents the total number of paths that robot i

can choose to reach the target point Assume that there are n

robots with m areas that need to be inspected(ngt 1 andmgt 1) simultaneously and the collaborative workof robots needs to be determined according to the rela-tionship between the areas m and the robots n

30

25

20

15Y

X

10

5

5 10 15 2520 30

Proposed IBENN method

Figure 7 Single-robot path generated by the proposed IBENNmethod with Strategies (ii) and (iii) in the situation of single-pointinspection

Table 2 Comparison of the three methods

Index BENN A-star

IBENN with strategies (ii) and(iii)

Path length 4063 3814 3814Turn times 17 12 10Rotationangle 2199 943 785

30

25

20

15Y

X

10

5

5

Robot 1

10 15 2520 30

Robot 2Robot 3Robot 4

Figure 8 Four-robot path generated by the proposed IBENN-based MRCI system in the situation of single-point inspection

Table 3 Comparison of the four-robot path planning

Index Robot1 Robot2 Robot3 Robot4Path length 2173 2356 2097 2280Turn times 18 19 16 17Rotation angle 628 471 314 785

Complexity 7

Case 1 ngem assume that a robot can only complete onetask and it can ensure that each uninspected area can beassigned to a robot to perform tasks at the same time eallocation method is the same as the task allocation methodof the single-point robot mentioned above ie each robotputs forward an optimal quotation for each task and themaster robot determines the optimal decision-makingscheme based on the quotation of each robot combined withthe corresponding bidding algorithm and assigns subtasks toeach robot according to the scheme en the problem isfirst transformed into an assignment problem which can besolved by the classical Hungarian algorithm [33] For ex-ample let n 6 and m 4 their positions are shown inTable 4 and the minimum cost of each robot at each taskpoint is solved according to the above method According tothe above allocation method the following allocationscheme can be obtained A1⟶ R1 A2⟶ R2

A3⟶ R3 andA4⟶ R5 and the total costF 994 + 969 + 681 + 571 3215

Case 2 nltm it means that a robot needs to completemultiple tasks and there can also be a situation where one ormore robots are idle For multiple robots at different initialpositions the host computer needs to plan a reasonable pathso that all inspection areas can be visited by the robots andthe total cost is minimal We have designed a genetic al-gorithm to solve this problem e genetic algorithm adoptsthe following single-chain coding form as shown in Fig-ure 8 when decoding the Robot2 completes the inspectiontasks of Areas 1 and 3 in sequence and similarly Robot1 andRobot3 complete the tasks of Areas 4 and 6 and Areas 2 and 5in sequenceis coding method has the advantage of strongreadability however it is easy to produce infeasible solutionsduring crossover and mutation erefore different repairalgorithms are used to repair the infeasible solutions

Crossover Use Partial-Mapped Crossover (PMX) op-erator when generating a new gene chain If it is not afeasible solution then fix it e specific repair methodis to find the repetitive genes in gene chain A that causeinfeasible solutions (there may be multiple groups) oneof which must be in the cross-replacement gene se-quence then find the gene that maps to the gene in genechain B and use it to replace the repetitive genes inchain A that are not in the cross-replacement sequenceMutation Randomly select two genes in the gene chainand determine whether one of their positions is at theend of the gene chain If not exchange their positions inthe gene chainSelection e tournament selection method is usedthat is a certain number of individuals are removedfrom the population each time then the best one isselected to enter the offspring population Repeat thisoperation until the new population size reaches theoriginal population size

For example in a 30 times 30 map the initial positions of theRobots 1 minus 3 are Rstart

1 (1 10) Rstart2 (15 30) and

Rstart3 (30 10) and the positions of the 6 inspection points are

A1(11 27) A2(29 28) A3(3 18) A4(16 15) A5(13 3) andA6(26 6) e initial azimuth of the robot is (0 minusπ2 minusπ)Using the proposed IBENN method above the optimal pathand the minimum cost between each point can be calculatede genetic algorithm can draw the following distributionplan

R1⟶ A3⟶ A1⟶ A4⟶ A5 R2⟶ A2 R3⟶ A6

(12)

e total cost is 4528 and the multirobot multipointinspection path is shown in Figure 9 where the red starindicates the inspection point and the blue star indicates theinitial position of each robot

43 All-Area Inspection Since the substation of smartmicrogrids is exposed to the outdoors for a long time it iseasy to break into foreign objects or other dangerous goodsIt is necessary to conduct regular inspections of the entirepower station of smart microgrids for all-area coverageHowever performing this task by a single robot may take along time and is inefficient erefore a multirobot col-laborative whole-area inspection program is designed

Divide every two robots into a group and design aheuristic algorithm for each robot e priority of theheuristic algorithm of the robots in each group is oppositewhich ensures that each group of robots can start inspectionsfrom different directions When the robot enters the deadzone position according to the proposed IBENN methodabove the optimal path from the dead zone position to theuninspected area can be planned e robot moves to thisarea and continues to inspect according to the originalheuristic algorithm For example in a 30 times 30 map there areparallel devices and various obstacle points as shown inFigure 10 Two robots in the area are used to coordinate tocomplete the all-area inspection taske steering priority ofthe heuristic algorithm of Robot1 W minus S minus SW minus NW minus N minus

E minus SE minus NE and Robot2 E minus N minus NE minus SE minus S minus W minus NW

minusSW and the initial positions are (1 1) and (30 1)respectively

Simulation experiments were carried out in the ob-stacle-free and obstacle environments and the results areshown in Figures 11 and 12 and Table 5 where the red andblue represent Robots 1 and 2 respectively pink dotsexpress repeated path points dots mean the final positionof the robot when the task is completed and stars rep-resent the initial position It can be seen from Table 5 thatin a simple map when there are no other obstacles in theinspection area and only parallel substation equipment

Table 4 Comparison of the four-robot path planning

Position Area1(916) Area2(1616) Area3(227) Area4(2225)

R1(11) 994 1492 1488 1801R2(151) 1031 969 788 1688R3(301) 1596 1442 681 1523R4(130) 1101 1158 1987 1271R5(1530) 1060 956 1609 571R6(3030) 2518 1441 1551 1132

8 Complexity

this method can achieve 100 coverage without over-lapping areas When there are various obstacles in theinspection area this method can also achieve 100 full-

coverage inspection but there is a repetition rate of 23Hence compared with other inspection methods theproposed IBENN method does not need to set a templateoperator and has strong versatility Multirobot collabo-ration can complete the entire area and full-coverageinspection task

To further verify the effectiveness of the proposedcontrol schemes we carry out the simulation experimentwith Coppelia Sim Software in the space of 30mtimes 30m etwo inspection robots are in the initial position as t 0 asshown in Figure 13(a) in which the gray cube and dark bluecube represent the equipment area and the obstacle arearespectively e robot is supposed to inspect at a speed of1ms disregarding the inspection time Using the aboveinspection strategy the experimental results are shown inFigure 13 As seen the left robot and right robot fall intodead zones respectively as t 138 or t 365 inFigures 13(a) and 13(e) and t 357 or t 306 inFigures 13(c) and 13(d) However in these cases the in-spection machine can jump out of the dead zone by callingthe IBENN algorithm respectively Furthermore both ro-bots fall into the dead zone state when t 395 as shown inFigure 13(f ) Since there is no undetected area in this sit-uation it follows that the inspection task has been com-pleted erefore the experiment verifies the feasibility ofthe cooperation scheme

A1 A3 R2 A4 A6 R1 A2 A5 R3

Figure 9 Gene chain coding of the genetic algorithm

30

25

20

15Y

X

10

5

5

Start points

10 15 2520 30

Inspection points

Figure 10 ree-robot path generated by the proposed IBENNbased MRCI system in the situation of six-point inspection

30

25

20

15Y

X

10

5

5 10 15 2520 30

Figure 11 Two-robot path generated by the proposed IBENN-based MRCI system in the situation of all-area inspection withoutobstacle

30

25

20

15Y

X

10

5

5 10 15 2520 30

Figure 12 Two-robot path generated by the proposed IBENN-based MRCI system in the situation of all-area inspection complexobstacle

Table 5 Results in obstacle-free and obstacle environments

Evaluationindex

Obstacle-freeenvironment ()

Obstacleenvironment ()

Coverage rate 100 100Repetition rate 0 23

Complexity 9

5 Conclusion

In this paper a multimobile robot collaborative operatingsystem for power stations of the smart microgrids isdesigned and an improved IBENN method is proposedCompared with the traditional BENN method and A-staralgorithm the improved IBENN algorithm has an obviousoptimization effect in path length and turning times Basedon this method the multirobot cooperative operationstrategy is designed to realize the three classic tasks of single-point inspection multipoint inspection and full-coverageinspection in the substation of smart microgrids whichverifies the effectiveness of the main results

Data Availability

All of the data used to support the findings of this study areincluded within this article

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China under Grant nos 61733004 and61773158

References

[1] A Peyman and F Keynia ldquoLifetime efficiency index model foroptimal maintenance of power substation equipment based

on cuckoo optimisation algorithmrdquo IET Generation Trans-mission amp Distribution vol 11 no 11 pp 2787ndash2795 2017

[2] I Ullah Y Fang and R Khan ldquoPredictive maintenance ofpower substation equipment by infrared thermography usinga machine-learning approachrdquo Energies vol 10 no 12pp 1ndash13 1987

[3] X Lu J Lai X Yu Y Wang and J M Guerrero ldquoDistributedcoordination of islanded microgrid clusters using a two-layerintermittent communication networkrdquo IEEE Transactions onIndustrial Informatics vol 14 no 9 pp 3956ndash3969 2018

[4] X Lu J Lai X Yu Y Wang and J M Guerrero ldquoA novelsecondary power management strategy for multiple ACmicrogrids with cluster-oriented two-layer cooperativeframeworkrdquo IEEE Transactions on Industrial Informaticsvol 17 no 2 pp 1483ndash1495 2021

[5] H Takahashi Development of Patrolling Robot for Substationpp 10ndash19 Japan IERE CouncilSpecial Document R8903Japan 1989

[6] J Beaudry and S Poirier Vehicule teleopere pour inspectionvisuelle etthermographique dans les postes de ransformation2012

[7] J K C Pinto M Masuda L C Magrini J A Jardini andM V Garbelloti ldquoMobile robot for hot spot monitoring inelectric power substationrdquo in Proceedings of the IEEEPESTransmission and Distribution Conference and Expositionpp 1ndash5 Chicago Illinois April 2008

[8] N Pouliot P-L Richard and S Montambault ldquoLineScouttechnology opens the way to robotic inspection and main-tenance of high-voltage power linesrdquo IEEE Power and EnergyTechnology Systems Journal vol 2 no 1 pp 1ndash11 2015

[9] A Cantieri M Ferraz and G Szekir ldquoCooperative UAV-UGV autonomous power pylon inspection an investigationof cooperative outdoor vehicle positioning architecturerdquoSensors vol 20 no 6384 pp 1ndash22 2020

(a) (b)

(c) (d)

(e) (f )

Figure 13 Sequence diagram of cooperative operation of two inspection robots (a) T 0 (b) T138 (c) T 306 (d) T 357 (e) T 365(f ) T 395

10 Complexity

[10] Y Guang and P Yutian ldquoIntelligent inspection of marinedisasters based on UAV intelligent visionrdquo Journal of CoastalResearch vol 93 pp 410ndash416 2019

[11] S Jordan J Moore and S Hovet ldquoState-of-the-art tech-nologies for UAV inspectionsrdquo IET Radar Sonar amp Navi-gation vol 12 no 2 pp 151ndash164 2018

[12] J Katranik F Pernus and B Likar ldquoA survey of mobile robotsfor distribution power line inspectionrdquo IEEE Transactions onPower Delivery vol 25 no 1 pp 485ndash493 2010

[13] J Yu and S M LaValle ldquoOptimal multirobot path planningon graphs complete algorithms and effective heuristicsrdquo IEEETransactions on Robotics vol 32 no 5 pp 1163ndash1177 2016

[14] K Jose and D K Pratihar ldquoTask allocation and collision-freepath planning of centralized multi-robots system for indus-trial plant inspection using heuristic methodsrdquo Robotics andAutonomous Systems vol 80 pp 34ndash42 2016

[15] B Pradhan A Nandi N B Hui and D S Roy ldquoA novelhybrid neural network-based multirobot path planning withmotion coordinationrdquo IEEE Transactions on VehicularTechnology vol 69 no 2 pp 1319ndash1327 2020

[16] C Luo S X Yang and X Li ldquoNeural-dynamics-drivencomplete area coverage navigation through cooperation ofmultiple mobile robotsrdquo IEEE Transactions on IndustrialElectronics vol 64 no 1 pp 750ndash760 2017

[17] B Woosley and P Dasgupta ldquoIntegrated real-time task andmotion planning for multiple robots under path and com-munication uncertaintiesrdquo Robotica vol 36 no 3pp 353ndash373 2018

[18] B Woosley P Dasgupta J G Rogers and J Twigg ldquoMulti-robot information driven path planning under communica-tion constraintsrdquo Autonomous Robots vol 44 no 5pp 721ndash737 2020

[19] F Imeson and S L Smith ldquoAn SMT-based approach tomotion planning for multiple robots with complex con-straintsrdquo IEEE Transactions on Robotics vol 35 no 3pp 669ndash684 2019

[20] A Ayari and S Bouamama ldquoA new multiple robot pathplanning algorithm dynamic distributed particle swarmoptimizationrdquo Robotics and Biomimetics vol 4 no 1 p 82017

[21] B Banerjee and CE Davis ldquoMultiagent path finding withpersistence conflictsrdquo IEEE Transactions on ComputationalIntelligence and AI in Games vol 9 no 4 pp 402ndash409 2016

[22] S abit and A Mohades ldquoMulti-robot path planning basedon multi-objective particle swarm optimizationrdquo IEEE Accessvol 7 pp 2138ndash2147 2018

[23] R Siegwart ldquoIR nourbakhsh and D scaramuzza ldquoIntro-duction to autonomous mobile robotsrdquo Industrial Robotvol 2 no 6 pp 645ndash649 2004

[24] K Jiang Z Sun Y Liu and J Sui ldquoDevelopment and Ap-plication of the Rail-type Inspection Robot used in SubstationRoomsrdquo MATEC Web of Conferences vol 139 no 5 ArticleID 00210 2017

[25] H B Xu J H Liu and X Jia ldquoSubstation inspection systembased on RFID technologyrdquo Advanced Materials Researchvol 734-737 pp 2846ndash2850 2013

[26] S ZWang D Han and Q Dong ldquoe application of RFID insubstation inspection systemrdquo Applied Mechanics and Ma-terials vol 295-298 pp 2433ndash2436 2013

[27] J Zhu Y Sun and D Sun ldquoDesign of a laser navigationsystem for the inspection robot used in substationrdquo Pro-ceedings of the Spie vol 322 2017

[28] C-J Huang Y-W Wang H-M Chen et al ldquoApplication ofcellular automata and type-2 fuzzy logic to dynamic vehicle

path planningrdquo Applied Soft Computing vol 19 pp 333ndash3422014

[29] S X Yang and M Meng ldquoAn efficient neural network ap-proach to dynamic robot motion planningrdquo Neural Networksvol 13 no 2 pp 143ndash148 2000

[30] S X Yang and M Q-H Meng ldquoReal-time collision-freemotion planning of a mobile robot using a Neural Dynamics-based approachrdquo IEEE Transactions on Neural Networksvol 14 no 6 pp 1541ndash1552 2003

[31] S Yang and C Luo A Neural Network Approach to CompleteCoverage Path Planning pp 718ndash724 Systems Man andCybernetics 2004

[32] C Luo and S X Yang ldquoA bioinspired neural network for real-time concurrent map building and complete coverage robotnavigation in unknown environmentsrdquo IEEE Transactions onNeural Networks vol 19 no 7 pp 1279ndash1298 2008

[33] S Chopra G Notarstefano M Rice and M Egerstedt ldquoAdistributed version of the Hungarian method for multirobotassignmentrdquo IEEE Transactions on Robotics vol 33 no 4pp 932ndash947 2017

Complexity 11

dxi

dt minusAxi + B minus xi( 1113857S

ei minus D + xi( 1113857S

ii (8)

Hence Strategies (i) and (ii) are used to increase theactivity value of neurons near the boundaries or obstacles Inpractical application one of these two strategies can beselected and used together with Strategy (iii) to achievebetter path planning

Figure 5 shows the comparison experiment usingStrategies (i) and (iii) with model parameters A 10B D 1 E 100 k 8 and c 1 e relevant datacomparison is shown in Table 1 It can be seen from Figure 5and Table 1 that the path length has been reduced from 1007to 841 and the times of turns have been changed from 4 to 1us the proposed strategies have obvious improvementeffects

In order to verify the superiority of Strategies (ii) and(iii) the simulation environment is set as a complex mazeand model parameters are also set as A 10 B D 1E 100 k 8 and c 1 e initial position of the robot is(6 3) and the target position is (1 30) e traditionalBENN method A-star algorithm and the proposed IBENNmethod are compared as shown in Figures 6 and 7 As seenthe proposed IBENNmethod cannot only solve the problemof path misjudgment but also reduce the path transitionsmooth the path and improve the path quality ree indexcomparisons of path length turn times and total rotationangle are concluded in Table 2 It can be seen that comparedwith the original BENNmethod the path length path turnsand total rotation angle of the proposed IBENN method arereduced by 612 412 and 643 respectively Com-pared with theA-star algorithm the number of turns and thetotal rotation angle can be reduced by 167 and 168respectively under the condition that the path length isunchanged It concludes that the improved IBENN methodshows better performance in terms of path quality and pathsmoothness than the other methods

4 Multirobot Cooperative Inspection(MRCI) System

In this section we will implement the proposed IBENNmethod to the MRCI system and complete the previouslyestablished three inspection tasks

41 Single-Point Inspection Assume that there are n iso-morphic inspection robots with different initial positionsand m areas that need to be monitored in a substation ofsmart microgrids and one of the areas needs to be con-tinuously monitored at a certain moment In this situationthe system needs to schedule a robot to complete the taskfollowing the principle of minimum cost or maximumbenefit We establish the following mathematical model

fi(L D) min εLij + ηDij j 1 2 3 gi1113872 1113873 (9)

TilArr cos ti min fi i 1 2 3 n( 1113857 (10)

where Lij and Dij represent the length and the turningnumber of the jth path for the ith robot respectively ε and ηrepresent the associated weights of Lij and Dij respectively

9

8

7

6

5Y

X

4

3

2

1

1 2

Start

Proposed IBENN method

Target

3 4 5 6 7 8 9

Figure 5 Single-robot path generated by the proposed IBENNmethod with Strategies (i) and (iii) in the situation of single-pointinspection

Table 1 Comparison results of BENN and IBENN methods

Evaluation index BENN IBENN with strategies (i) and (iii)Path length 1007 841Turn times 4 1

30

25

20

15Y

X

10

5

5

The A-star method

10 15 2520 30

Proposed IBENN method

Figure 6 Single-robot path generated by the traditional BENNmethod and A-star algorithm in the situation of single-pointinspection

6 Complexity

all robotsrsquo weights are the same by default in the path de-cision gi represents the number of paths available for the ithrobot to complete the task T and fi can be considered as theminimum cost of robot i to achieve taskTe objective hereis to find the robot i and the optimal path gi

To solve this problem the proposed IBENN method isused to calculate the minimum cost of each robot tocomplete the task and then compare the optimal cost of eachrobot It is necessary that the robot with the lowest costobtains the task and completes the task according to theoptimal path planned For example in the 30 times 30 mapshown in Figure 8 gray areas represent parallel devices andblack ones represent obstacles in the site and there are fourrobots Robot1 Robot2 Robot3 and Robot4 with initialpositions R1(1 1) R2(30 1) R3(1 30) and R4(30 30)respectively When inspection tasks are needed nearequipment Rtarget(14 15) (ie area no 9) according to theIBENNmethod the cost of each robot to complete the task iscalculated as shown in Table 3 and then each robot offers aquotation according to the above method with f1 14f2 1414 f3 1206 and f4 1533 which can be cal-culated according to (9) when the parameter is set asε η 05 According to the calculation we can choose

Robot3 as the best scheme to execute the task and otherrobots determine their priority as a backup according to thecost

42 Multipoint Inspection In the substation working areathere is occasionally a need to inspect multiple areas and theadvantages of the multirobot cooperation system can be wellreflected in this situation e cost equation of the systemcan be described as

F min cos t min1113944n

i1fi Li Di( 1113857

min1113944

n

i

min εLij + ηDij j 1 2 3 gi1113872 11138731113872 1113873

(11)

where gi represents the total number of paths that robot i

can choose to reach the target point Assume that there are n

robots with m areas that need to be inspected(ngt 1 andmgt 1) simultaneously and the collaborative workof robots needs to be determined according to the rela-tionship between the areas m and the robots n

30

25

20

15Y

X

10

5

5 10 15 2520 30

Proposed IBENN method

Figure 7 Single-robot path generated by the proposed IBENNmethod with Strategies (ii) and (iii) in the situation of single-pointinspection

Table 2 Comparison of the three methods

Index BENN A-star

IBENN with strategies (ii) and(iii)

Path length 4063 3814 3814Turn times 17 12 10Rotationangle 2199 943 785

30

25

20

15Y

X

10

5

5

Robot 1

10 15 2520 30

Robot 2Robot 3Robot 4

Figure 8 Four-robot path generated by the proposed IBENN-based MRCI system in the situation of single-point inspection

Table 3 Comparison of the four-robot path planning

Index Robot1 Robot2 Robot3 Robot4Path length 2173 2356 2097 2280Turn times 18 19 16 17Rotation angle 628 471 314 785

Complexity 7

Case 1 ngem assume that a robot can only complete onetask and it can ensure that each uninspected area can beassigned to a robot to perform tasks at the same time eallocation method is the same as the task allocation methodof the single-point robot mentioned above ie each robotputs forward an optimal quotation for each task and themaster robot determines the optimal decision-makingscheme based on the quotation of each robot combined withthe corresponding bidding algorithm and assigns subtasks toeach robot according to the scheme en the problem isfirst transformed into an assignment problem which can besolved by the classical Hungarian algorithm [33] For ex-ample let n 6 and m 4 their positions are shown inTable 4 and the minimum cost of each robot at each taskpoint is solved according to the above method According tothe above allocation method the following allocationscheme can be obtained A1⟶ R1 A2⟶ R2

A3⟶ R3 andA4⟶ R5 and the total costF 994 + 969 + 681 + 571 3215

Case 2 nltm it means that a robot needs to completemultiple tasks and there can also be a situation where one ormore robots are idle For multiple robots at different initialpositions the host computer needs to plan a reasonable pathso that all inspection areas can be visited by the robots andthe total cost is minimal We have designed a genetic al-gorithm to solve this problem e genetic algorithm adoptsthe following single-chain coding form as shown in Fig-ure 8 when decoding the Robot2 completes the inspectiontasks of Areas 1 and 3 in sequence and similarly Robot1 andRobot3 complete the tasks of Areas 4 and 6 and Areas 2 and 5in sequenceis coding method has the advantage of strongreadability however it is easy to produce infeasible solutionsduring crossover and mutation erefore different repairalgorithms are used to repair the infeasible solutions

Crossover Use Partial-Mapped Crossover (PMX) op-erator when generating a new gene chain If it is not afeasible solution then fix it e specific repair methodis to find the repetitive genes in gene chain A that causeinfeasible solutions (there may be multiple groups) oneof which must be in the cross-replacement gene se-quence then find the gene that maps to the gene in genechain B and use it to replace the repetitive genes inchain A that are not in the cross-replacement sequenceMutation Randomly select two genes in the gene chainand determine whether one of their positions is at theend of the gene chain If not exchange their positions inthe gene chainSelection e tournament selection method is usedthat is a certain number of individuals are removedfrom the population each time then the best one isselected to enter the offspring population Repeat thisoperation until the new population size reaches theoriginal population size

For example in a 30 times 30 map the initial positions of theRobots 1 minus 3 are Rstart

1 (1 10) Rstart2 (15 30) and

Rstart3 (30 10) and the positions of the 6 inspection points are

A1(11 27) A2(29 28) A3(3 18) A4(16 15) A5(13 3) andA6(26 6) e initial azimuth of the robot is (0 minusπ2 minusπ)Using the proposed IBENN method above the optimal pathand the minimum cost between each point can be calculatede genetic algorithm can draw the following distributionplan

R1⟶ A3⟶ A1⟶ A4⟶ A5 R2⟶ A2 R3⟶ A6

(12)

e total cost is 4528 and the multirobot multipointinspection path is shown in Figure 9 where the red starindicates the inspection point and the blue star indicates theinitial position of each robot

43 All-Area Inspection Since the substation of smartmicrogrids is exposed to the outdoors for a long time it iseasy to break into foreign objects or other dangerous goodsIt is necessary to conduct regular inspections of the entirepower station of smart microgrids for all-area coverageHowever performing this task by a single robot may take along time and is inefficient erefore a multirobot col-laborative whole-area inspection program is designed

Divide every two robots into a group and design aheuristic algorithm for each robot e priority of theheuristic algorithm of the robots in each group is oppositewhich ensures that each group of robots can start inspectionsfrom different directions When the robot enters the deadzone position according to the proposed IBENN methodabove the optimal path from the dead zone position to theuninspected area can be planned e robot moves to thisarea and continues to inspect according to the originalheuristic algorithm For example in a 30 times 30 map there areparallel devices and various obstacle points as shown inFigure 10 Two robots in the area are used to coordinate tocomplete the all-area inspection taske steering priority ofthe heuristic algorithm of Robot1 W minus S minus SW minus NW minus N minus

E minus SE minus NE and Robot2 E minus N minus NE minus SE minus S minus W minus NW

minusSW and the initial positions are (1 1) and (30 1)respectively

Simulation experiments were carried out in the ob-stacle-free and obstacle environments and the results areshown in Figures 11 and 12 and Table 5 where the red andblue represent Robots 1 and 2 respectively pink dotsexpress repeated path points dots mean the final positionof the robot when the task is completed and stars rep-resent the initial position It can be seen from Table 5 thatin a simple map when there are no other obstacles in theinspection area and only parallel substation equipment

Table 4 Comparison of the four-robot path planning

Position Area1(916) Area2(1616) Area3(227) Area4(2225)

R1(11) 994 1492 1488 1801R2(151) 1031 969 788 1688R3(301) 1596 1442 681 1523R4(130) 1101 1158 1987 1271R5(1530) 1060 956 1609 571R6(3030) 2518 1441 1551 1132

8 Complexity

this method can achieve 100 coverage without over-lapping areas When there are various obstacles in theinspection area this method can also achieve 100 full-

coverage inspection but there is a repetition rate of 23Hence compared with other inspection methods theproposed IBENN method does not need to set a templateoperator and has strong versatility Multirobot collabo-ration can complete the entire area and full-coverageinspection task

To further verify the effectiveness of the proposedcontrol schemes we carry out the simulation experimentwith Coppelia Sim Software in the space of 30mtimes 30m etwo inspection robots are in the initial position as t 0 asshown in Figure 13(a) in which the gray cube and dark bluecube represent the equipment area and the obstacle arearespectively e robot is supposed to inspect at a speed of1ms disregarding the inspection time Using the aboveinspection strategy the experimental results are shown inFigure 13 As seen the left robot and right robot fall intodead zones respectively as t 138 or t 365 inFigures 13(a) and 13(e) and t 357 or t 306 inFigures 13(c) and 13(d) However in these cases the in-spection machine can jump out of the dead zone by callingthe IBENN algorithm respectively Furthermore both ro-bots fall into the dead zone state when t 395 as shown inFigure 13(f ) Since there is no undetected area in this sit-uation it follows that the inspection task has been com-pleted erefore the experiment verifies the feasibility ofthe cooperation scheme

A1 A3 R2 A4 A6 R1 A2 A5 R3

Figure 9 Gene chain coding of the genetic algorithm

30

25

20

15Y

X

10

5

5

Start points

10 15 2520 30

Inspection points

Figure 10 ree-robot path generated by the proposed IBENNbased MRCI system in the situation of six-point inspection

30

25

20

15Y

X

10

5

5 10 15 2520 30

Figure 11 Two-robot path generated by the proposed IBENN-based MRCI system in the situation of all-area inspection withoutobstacle

30

25

20

15Y

X

10

5

5 10 15 2520 30

Figure 12 Two-robot path generated by the proposed IBENN-based MRCI system in the situation of all-area inspection complexobstacle

Table 5 Results in obstacle-free and obstacle environments

Evaluationindex

Obstacle-freeenvironment ()

Obstacleenvironment ()

Coverage rate 100 100Repetition rate 0 23

Complexity 9

5 Conclusion

In this paper a multimobile robot collaborative operatingsystem for power stations of the smart microgrids isdesigned and an improved IBENN method is proposedCompared with the traditional BENN method and A-staralgorithm the improved IBENN algorithm has an obviousoptimization effect in path length and turning times Basedon this method the multirobot cooperative operationstrategy is designed to realize the three classic tasks of single-point inspection multipoint inspection and full-coverageinspection in the substation of smart microgrids whichverifies the effectiveness of the main results

Data Availability

All of the data used to support the findings of this study areincluded within this article

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China under Grant nos 61733004 and61773158

References

[1] A Peyman and F Keynia ldquoLifetime efficiency index model foroptimal maintenance of power substation equipment based

on cuckoo optimisation algorithmrdquo IET Generation Trans-mission amp Distribution vol 11 no 11 pp 2787ndash2795 2017

[2] I Ullah Y Fang and R Khan ldquoPredictive maintenance ofpower substation equipment by infrared thermography usinga machine-learning approachrdquo Energies vol 10 no 12pp 1ndash13 1987

[3] X Lu J Lai X Yu Y Wang and J M Guerrero ldquoDistributedcoordination of islanded microgrid clusters using a two-layerintermittent communication networkrdquo IEEE Transactions onIndustrial Informatics vol 14 no 9 pp 3956ndash3969 2018

[4] X Lu J Lai X Yu Y Wang and J M Guerrero ldquoA novelsecondary power management strategy for multiple ACmicrogrids with cluster-oriented two-layer cooperativeframeworkrdquo IEEE Transactions on Industrial Informaticsvol 17 no 2 pp 1483ndash1495 2021

[5] H Takahashi Development of Patrolling Robot for Substationpp 10ndash19 Japan IERE CouncilSpecial Document R8903Japan 1989

[6] J Beaudry and S Poirier Vehicule teleopere pour inspectionvisuelle etthermographique dans les postes de ransformation2012

[7] J K C Pinto M Masuda L C Magrini J A Jardini andM V Garbelloti ldquoMobile robot for hot spot monitoring inelectric power substationrdquo in Proceedings of the IEEEPESTransmission and Distribution Conference and Expositionpp 1ndash5 Chicago Illinois April 2008

[8] N Pouliot P-L Richard and S Montambault ldquoLineScouttechnology opens the way to robotic inspection and main-tenance of high-voltage power linesrdquo IEEE Power and EnergyTechnology Systems Journal vol 2 no 1 pp 1ndash11 2015

[9] A Cantieri M Ferraz and G Szekir ldquoCooperative UAV-UGV autonomous power pylon inspection an investigationof cooperative outdoor vehicle positioning architecturerdquoSensors vol 20 no 6384 pp 1ndash22 2020

(a) (b)

(c) (d)

(e) (f )

Figure 13 Sequence diagram of cooperative operation of two inspection robots (a) T 0 (b) T138 (c) T 306 (d) T 357 (e) T 365(f ) T 395

10 Complexity

[10] Y Guang and P Yutian ldquoIntelligent inspection of marinedisasters based on UAV intelligent visionrdquo Journal of CoastalResearch vol 93 pp 410ndash416 2019

[11] S Jordan J Moore and S Hovet ldquoState-of-the-art tech-nologies for UAV inspectionsrdquo IET Radar Sonar amp Navi-gation vol 12 no 2 pp 151ndash164 2018

[12] J Katranik F Pernus and B Likar ldquoA survey of mobile robotsfor distribution power line inspectionrdquo IEEE Transactions onPower Delivery vol 25 no 1 pp 485ndash493 2010

[13] J Yu and S M LaValle ldquoOptimal multirobot path planningon graphs complete algorithms and effective heuristicsrdquo IEEETransactions on Robotics vol 32 no 5 pp 1163ndash1177 2016

[14] K Jose and D K Pratihar ldquoTask allocation and collision-freepath planning of centralized multi-robots system for indus-trial plant inspection using heuristic methodsrdquo Robotics andAutonomous Systems vol 80 pp 34ndash42 2016

[15] B Pradhan A Nandi N B Hui and D S Roy ldquoA novelhybrid neural network-based multirobot path planning withmotion coordinationrdquo IEEE Transactions on VehicularTechnology vol 69 no 2 pp 1319ndash1327 2020

[16] C Luo S X Yang and X Li ldquoNeural-dynamics-drivencomplete area coverage navigation through cooperation ofmultiple mobile robotsrdquo IEEE Transactions on IndustrialElectronics vol 64 no 1 pp 750ndash760 2017

[17] B Woosley and P Dasgupta ldquoIntegrated real-time task andmotion planning for multiple robots under path and com-munication uncertaintiesrdquo Robotica vol 36 no 3pp 353ndash373 2018

[18] B Woosley P Dasgupta J G Rogers and J Twigg ldquoMulti-robot information driven path planning under communica-tion constraintsrdquo Autonomous Robots vol 44 no 5pp 721ndash737 2020

[19] F Imeson and S L Smith ldquoAn SMT-based approach tomotion planning for multiple robots with complex con-straintsrdquo IEEE Transactions on Robotics vol 35 no 3pp 669ndash684 2019

[20] A Ayari and S Bouamama ldquoA new multiple robot pathplanning algorithm dynamic distributed particle swarmoptimizationrdquo Robotics and Biomimetics vol 4 no 1 p 82017

[21] B Banerjee and CE Davis ldquoMultiagent path finding withpersistence conflictsrdquo IEEE Transactions on ComputationalIntelligence and AI in Games vol 9 no 4 pp 402ndash409 2016

[22] S abit and A Mohades ldquoMulti-robot path planning basedon multi-objective particle swarm optimizationrdquo IEEE Accessvol 7 pp 2138ndash2147 2018

[23] R Siegwart ldquoIR nourbakhsh and D scaramuzza ldquoIntro-duction to autonomous mobile robotsrdquo Industrial Robotvol 2 no 6 pp 645ndash649 2004

[24] K Jiang Z Sun Y Liu and J Sui ldquoDevelopment and Ap-plication of the Rail-type Inspection Robot used in SubstationRoomsrdquo MATEC Web of Conferences vol 139 no 5 ArticleID 00210 2017

[25] H B Xu J H Liu and X Jia ldquoSubstation inspection systembased on RFID technologyrdquo Advanced Materials Researchvol 734-737 pp 2846ndash2850 2013

[26] S ZWang D Han and Q Dong ldquoe application of RFID insubstation inspection systemrdquo Applied Mechanics and Ma-terials vol 295-298 pp 2433ndash2436 2013

[27] J Zhu Y Sun and D Sun ldquoDesign of a laser navigationsystem for the inspection robot used in substationrdquo Pro-ceedings of the Spie vol 322 2017

[28] C-J Huang Y-W Wang H-M Chen et al ldquoApplication ofcellular automata and type-2 fuzzy logic to dynamic vehicle

path planningrdquo Applied Soft Computing vol 19 pp 333ndash3422014

[29] S X Yang and M Meng ldquoAn efficient neural network ap-proach to dynamic robot motion planningrdquo Neural Networksvol 13 no 2 pp 143ndash148 2000

[30] S X Yang and M Q-H Meng ldquoReal-time collision-freemotion planning of a mobile robot using a Neural Dynamics-based approachrdquo IEEE Transactions on Neural Networksvol 14 no 6 pp 1541ndash1552 2003

[31] S Yang and C Luo A Neural Network Approach to CompleteCoverage Path Planning pp 718ndash724 Systems Man andCybernetics 2004

[32] C Luo and S X Yang ldquoA bioinspired neural network for real-time concurrent map building and complete coverage robotnavigation in unknown environmentsrdquo IEEE Transactions onNeural Networks vol 19 no 7 pp 1279ndash1298 2008

[33] S Chopra G Notarstefano M Rice and M Egerstedt ldquoAdistributed version of the Hungarian method for multirobotassignmentrdquo IEEE Transactions on Robotics vol 33 no 4pp 932ndash947 2017

Complexity 11

all robotsrsquo weights are the same by default in the path de-cision gi represents the number of paths available for the ithrobot to complete the task T and fi can be considered as theminimum cost of robot i to achieve taskTe objective hereis to find the robot i and the optimal path gi

To solve this problem the proposed IBENN method isused to calculate the minimum cost of each robot tocomplete the task and then compare the optimal cost of eachrobot It is necessary that the robot with the lowest costobtains the task and completes the task according to theoptimal path planned For example in the 30 times 30 mapshown in Figure 8 gray areas represent parallel devices andblack ones represent obstacles in the site and there are fourrobots Robot1 Robot2 Robot3 and Robot4 with initialpositions R1(1 1) R2(30 1) R3(1 30) and R4(30 30)respectively When inspection tasks are needed nearequipment Rtarget(14 15) (ie area no 9) according to theIBENNmethod the cost of each robot to complete the task iscalculated as shown in Table 3 and then each robot offers aquotation according to the above method with f1 14f2 1414 f3 1206 and f4 1533 which can be cal-culated according to (9) when the parameter is set asε η 05 According to the calculation we can choose

Robot3 as the best scheme to execute the task and otherrobots determine their priority as a backup according to thecost

42 Multipoint Inspection In the substation working areathere is occasionally a need to inspect multiple areas and theadvantages of the multirobot cooperation system can be wellreflected in this situation e cost equation of the systemcan be described as

F min cos t min1113944n

i1fi Li Di( 1113857

min1113944

n

i

min εLij + ηDij j 1 2 3 gi1113872 11138731113872 1113873

(11)

where gi represents the total number of paths that robot i

can choose to reach the target point Assume that there are n

robots with m areas that need to be inspected(ngt 1 andmgt 1) simultaneously and the collaborative workof robots needs to be determined according to the rela-tionship between the areas m and the robots n

30

25

20

15Y

X

10

5

5 10 15 2520 30

Proposed IBENN method

Figure 7 Single-robot path generated by the proposed IBENNmethod with Strategies (ii) and (iii) in the situation of single-pointinspection

Table 2 Comparison of the three methods

Index BENN A-star

IBENN with strategies (ii) and(iii)

Path length 4063 3814 3814Turn times 17 12 10Rotationangle 2199 943 785

30

25

20

15Y

X

10

5

5

Robot 1

10 15 2520 30

Robot 2Robot 3Robot 4

Figure 8 Four-robot path generated by the proposed IBENN-based MRCI system in the situation of single-point inspection

Table 3 Comparison of the four-robot path planning

Index Robot1 Robot2 Robot3 Robot4Path length 2173 2356 2097 2280Turn times 18 19 16 17Rotation angle 628 471 314 785

Complexity 7

Case 1 ngem assume that a robot can only complete onetask and it can ensure that each uninspected area can beassigned to a robot to perform tasks at the same time eallocation method is the same as the task allocation methodof the single-point robot mentioned above ie each robotputs forward an optimal quotation for each task and themaster robot determines the optimal decision-makingscheme based on the quotation of each robot combined withthe corresponding bidding algorithm and assigns subtasks toeach robot according to the scheme en the problem isfirst transformed into an assignment problem which can besolved by the classical Hungarian algorithm [33] For ex-ample let n 6 and m 4 their positions are shown inTable 4 and the minimum cost of each robot at each taskpoint is solved according to the above method According tothe above allocation method the following allocationscheme can be obtained A1⟶ R1 A2⟶ R2

A3⟶ R3 andA4⟶ R5 and the total costF 994 + 969 + 681 + 571 3215

Case 2 nltm it means that a robot needs to completemultiple tasks and there can also be a situation where one ormore robots are idle For multiple robots at different initialpositions the host computer needs to plan a reasonable pathso that all inspection areas can be visited by the robots andthe total cost is minimal We have designed a genetic al-gorithm to solve this problem e genetic algorithm adoptsthe following single-chain coding form as shown in Fig-ure 8 when decoding the Robot2 completes the inspectiontasks of Areas 1 and 3 in sequence and similarly Robot1 andRobot3 complete the tasks of Areas 4 and 6 and Areas 2 and 5in sequenceis coding method has the advantage of strongreadability however it is easy to produce infeasible solutionsduring crossover and mutation erefore different repairalgorithms are used to repair the infeasible solutions

Crossover Use Partial-Mapped Crossover (PMX) op-erator when generating a new gene chain If it is not afeasible solution then fix it e specific repair methodis to find the repetitive genes in gene chain A that causeinfeasible solutions (there may be multiple groups) oneof which must be in the cross-replacement gene se-quence then find the gene that maps to the gene in genechain B and use it to replace the repetitive genes inchain A that are not in the cross-replacement sequenceMutation Randomly select two genes in the gene chainand determine whether one of their positions is at theend of the gene chain If not exchange their positions inthe gene chainSelection e tournament selection method is usedthat is a certain number of individuals are removedfrom the population each time then the best one isselected to enter the offspring population Repeat thisoperation until the new population size reaches theoriginal population size

For example in a 30 times 30 map the initial positions of theRobots 1 minus 3 are Rstart

1 (1 10) Rstart2 (15 30) and

Rstart3 (30 10) and the positions of the 6 inspection points are

A1(11 27) A2(29 28) A3(3 18) A4(16 15) A5(13 3) andA6(26 6) e initial azimuth of the robot is (0 minusπ2 minusπ)Using the proposed IBENN method above the optimal pathand the minimum cost between each point can be calculatede genetic algorithm can draw the following distributionplan

R1⟶ A3⟶ A1⟶ A4⟶ A5 R2⟶ A2 R3⟶ A6

(12)

e total cost is 4528 and the multirobot multipointinspection path is shown in Figure 9 where the red starindicates the inspection point and the blue star indicates theinitial position of each robot

43 All-Area Inspection Since the substation of smartmicrogrids is exposed to the outdoors for a long time it iseasy to break into foreign objects or other dangerous goodsIt is necessary to conduct regular inspections of the entirepower station of smart microgrids for all-area coverageHowever performing this task by a single robot may take along time and is inefficient erefore a multirobot col-laborative whole-area inspection program is designed

Divide every two robots into a group and design aheuristic algorithm for each robot e priority of theheuristic algorithm of the robots in each group is oppositewhich ensures that each group of robots can start inspectionsfrom different directions When the robot enters the deadzone position according to the proposed IBENN methodabove the optimal path from the dead zone position to theuninspected area can be planned e robot moves to thisarea and continues to inspect according to the originalheuristic algorithm For example in a 30 times 30 map there areparallel devices and various obstacle points as shown inFigure 10 Two robots in the area are used to coordinate tocomplete the all-area inspection taske steering priority ofthe heuristic algorithm of Robot1 W minus S minus SW minus NW minus N minus

E minus SE minus NE and Robot2 E minus N minus NE minus SE minus S minus W minus NW

minusSW and the initial positions are (1 1) and (30 1)respectively

Simulation experiments were carried out in the ob-stacle-free and obstacle environments and the results areshown in Figures 11 and 12 and Table 5 where the red andblue represent Robots 1 and 2 respectively pink dotsexpress repeated path points dots mean the final positionof the robot when the task is completed and stars rep-resent the initial position It can be seen from Table 5 thatin a simple map when there are no other obstacles in theinspection area and only parallel substation equipment

Table 4 Comparison of the four-robot path planning

Position Area1(916) Area2(1616) Area3(227) Area4(2225)

R1(11) 994 1492 1488 1801R2(151) 1031 969 788 1688R3(301) 1596 1442 681 1523R4(130) 1101 1158 1987 1271R5(1530) 1060 956 1609 571R6(3030) 2518 1441 1551 1132

8 Complexity

this method can achieve 100 coverage without over-lapping areas When there are various obstacles in theinspection area this method can also achieve 100 full-

coverage inspection but there is a repetition rate of 23Hence compared with other inspection methods theproposed IBENN method does not need to set a templateoperator and has strong versatility Multirobot collabo-ration can complete the entire area and full-coverageinspection task

To further verify the effectiveness of the proposedcontrol schemes we carry out the simulation experimentwith Coppelia Sim Software in the space of 30mtimes 30m etwo inspection robots are in the initial position as t 0 asshown in Figure 13(a) in which the gray cube and dark bluecube represent the equipment area and the obstacle arearespectively e robot is supposed to inspect at a speed of1ms disregarding the inspection time Using the aboveinspection strategy the experimental results are shown inFigure 13 As seen the left robot and right robot fall intodead zones respectively as t 138 or t 365 inFigures 13(a) and 13(e) and t 357 or t 306 inFigures 13(c) and 13(d) However in these cases the in-spection machine can jump out of the dead zone by callingthe IBENN algorithm respectively Furthermore both ro-bots fall into the dead zone state when t 395 as shown inFigure 13(f ) Since there is no undetected area in this sit-uation it follows that the inspection task has been com-pleted erefore the experiment verifies the feasibility ofthe cooperation scheme

A1 A3 R2 A4 A6 R1 A2 A5 R3

Figure 9 Gene chain coding of the genetic algorithm

30

25

20

15Y

X

10

5

5

Start points

10 15 2520 30

Inspection points

Figure 10 ree-robot path generated by the proposed IBENNbased MRCI system in the situation of six-point inspection

30

25

20

15Y

X

10

5

5 10 15 2520 30

Figure 11 Two-robot path generated by the proposed IBENN-based MRCI system in the situation of all-area inspection withoutobstacle

30

25

20

15Y

X

10

5

5 10 15 2520 30

Figure 12 Two-robot path generated by the proposed IBENN-based MRCI system in the situation of all-area inspection complexobstacle

Table 5 Results in obstacle-free and obstacle environments

Evaluationindex

Obstacle-freeenvironment ()

Obstacleenvironment ()

Coverage rate 100 100Repetition rate 0 23

Complexity 9

5 Conclusion

In this paper a multimobile robot collaborative operatingsystem for power stations of the smart microgrids isdesigned and an improved IBENN method is proposedCompared with the traditional BENN method and A-staralgorithm the improved IBENN algorithm has an obviousoptimization effect in path length and turning times Basedon this method the multirobot cooperative operationstrategy is designed to realize the three classic tasks of single-point inspection multipoint inspection and full-coverageinspection in the substation of smart microgrids whichverifies the effectiveness of the main results

Data Availability

All of the data used to support the findings of this study areincluded within this article

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China under Grant nos 61733004 and61773158

References

[1] A Peyman and F Keynia ldquoLifetime efficiency index model foroptimal maintenance of power substation equipment based

on cuckoo optimisation algorithmrdquo IET Generation Trans-mission amp Distribution vol 11 no 11 pp 2787ndash2795 2017

[2] I Ullah Y Fang and R Khan ldquoPredictive maintenance ofpower substation equipment by infrared thermography usinga machine-learning approachrdquo Energies vol 10 no 12pp 1ndash13 1987

[3] X Lu J Lai X Yu Y Wang and J M Guerrero ldquoDistributedcoordination of islanded microgrid clusters using a two-layerintermittent communication networkrdquo IEEE Transactions onIndustrial Informatics vol 14 no 9 pp 3956ndash3969 2018

[4] X Lu J Lai X Yu Y Wang and J M Guerrero ldquoA novelsecondary power management strategy for multiple ACmicrogrids with cluster-oriented two-layer cooperativeframeworkrdquo IEEE Transactions on Industrial Informaticsvol 17 no 2 pp 1483ndash1495 2021

[5] H Takahashi Development of Patrolling Robot for Substationpp 10ndash19 Japan IERE CouncilSpecial Document R8903Japan 1989

[6] J Beaudry and S Poirier Vehicule teleopere pour inspectionvisuelle etthermographique dans les postes de ransformation2012

[7] J K C Pinto M Masuda L C Magrini J A Jardini andM V Garbelloti ldquoMobile robot for hot spot monitoring inelectric power substationrdquo in Proceedings of the IEEEPESTransmission and Distribution Conference and Expositionpp 1ndash5 Chicago Illinois April 2008

[8] N Pouliot P-L Richard and S Montambault ldquoLineScouttechnology opens the way to robotic inspection and main-tenance of high-voltage power linesrdquo IEEE Power and EnergyTechnology Systems Journal vol 2 no 1 pp 1ndash11 2015

[9] A Cantieri M Ferraz and G Szekir ldquoCooperative UAV-UGV autonomous power pylon inspection an investigationof cooperative outdoor vehicle positioning architecturerdquoSensors vol 20 no 6384 pp 1ndash22 2020

(a) (b)

(c) (d)

(e) (f )

Figure 13 Sequence diagram of cooperative operation of two inspection robots (a) T 0 (b) T138 (c) T 306 (d) T 357 (e) T 365(f ) T 395

10 Complexity

[10] Y Guang and P Yutian ldquoIntelligent inspection of marinedisasters based on UAV intelligent visionrdquo Journal of CoastalResearch vol 93 pp 410ndash416 2019

[11] S Jordan J Moore and S Hovet ldquoState-of-the-art tech-nologies for UAV inspectionsrdquo IET Radar Sonar amp Navi-gation vol 12 no 2 pp 151ndash164 2018

[12] J Katranik F Pernus and B Likar ldquoA survey of mobile robotsfor distribution power line inspectionrdquo IEEE Transactions onPower Delivery vol 25 no 1 pp 485ndash493 2010

[13] J Yu and S M LaValle ldquoOptimal multirobot path planningon graphs complete algorithms and effective heuristicsrdquo IEEETransactions on Robotics vol 32 no 5 pp 1163ndash1177 2016

[14] K Jose and D K Pratihar ldquoTask allocation and collision-freepath planning of centralized multi-robots system for indus-trial plant inspection using heuristic methodsrdquo Robotics andAutonomous Systems vol 80 pp 34ndash42 2016

[15] B Pradhan A Nandi N B Hui and D S Roy ldquoA novelhybrid neural network-based multirobot path planning withmotion coordinationrdquo IEEE Transactions on VehicularTechnology vol 69 no 2 pp 1319ndash1327 2020

[16] C Luo S X Yang and X Li ldquoNeural-dynamics-drivencomplete area coverage navigation through cooperation ofmultiple mobile robotsrdquo IEEE Transactions on IndustrialElectronics vol 64 no 1 pp 750ndash760 2017

[17] B Woosley and P Dasgupta ldquoIntegrated real-time task andmotion planning for multiple robots under path and com-munication uncertaintiesrdquo Robotica vol 36 no 3pp 353ndash373 2018

[18] B Woosley P Dasgupta J G Rogers and J Twigg ldquoMulti-robot information driven path planning under communica-tion constraintsrdquo Autonomous Robots vol 44 no 5pp 721ndash737 2020

[19] F Imeson and S L Smith ldquoAn SMT-based approach tomotion planning for multiple robots with complex con-straintsrdquo IEEE Transactions on Robotics vol 35 no 3pp 669ndash684 2019

[20] A Ayari and S Bouamama ldquoA new multiple robot pathplanning algorithm dynamic distributed particle swarmoptimizationrdquo Robotics and Biomimetics vol 4 no 1 p 82017

[21] B Banerjee and CE Davis ldquoMultiagent path finding withpersistence conflictsrdquo IEEE Transactions on ComputationalIntelligence and AI in Games vol 9 no 4 pp 402ndash409 2016

[22] S abit and A Mohades ldquoMulti-robot path planning basedon multi-objective particle swarm optimizationrdquo IEEE Accessvol 7 pp 2138ndash2147 2018

[23] R Siegwart ldquoIR nourbakhsh and D scaramuzza ldquoIntro-duction to autonomous mobile robotsrdquo Industrial Robotvol 2 no 6 pp 645ndash649 2004

[24] K Jiang Z Sun Y Liu and J Sui ldquoDevelopment and Ap-plication of the Rail-type Inspection Robot used in SubstationRoomsrdquo MATEC Web of Conferences vol 139 no 5 ArticleID 00210 2017

[25] H B Xu J H Liu and X Jia ldquoSubstation inspection systembased on RFID technologyrdquo Advanced Materials Researchvol 734-737 pp 2846ndash2850 2013

[26] S ZWang D Han and Q Dong ldquoe application of RFID insubstation inspection systemrdquo Applied Mechanics and Ma-terials vol 295-298 pp 2433ndash2436 2013

[27] J Zhu Y Sun and D Sun ldquoDesign of a laser navigationsystem for the inspection robot used in substationrdquo Pro-ceedings of the Spie vol 322 2017

[28] C-J Huang Y-W Wang H-M Chen et al ldquoApplication ofcellular automata and type-2 fuzzy logic to dynamic vehicle

path planningrdquo Applied Soft Computing vol 19 pp 333ndash3422014

[29] S X Yang and M Meng ldquoAn efficient neural network ap-proach to dynamic robot motion planningrdquo Neural Networksvol 13 no 2 pp 143ndash148 2000

[30] S X Yang and M Q-H Meng ldquoReal-time collision-freemotion planning of a mobile robot using a Neural Dynamics-based approachrdquo IEEE Transactions on Neural Networksvol 14 no 6 pp 1541ndash1552 2003

[31] S Yang and C Luo A Neural Network Approach to CompleteCoverage Path Planning pp 718ndash724 Systems Man andCybernetics 2004

[32] C Luo and S X Yang ldquoA bioinspired neural network for real-time concurrent map building and complete coverage robotnavigation in unknown environmentsrdquo IEEE Transactions onNeural Networks vol 19 no 7 pp 1279ndash1298 2008

[33] S Chopra G Notarstefano M Rice and M Egerstedt ldquoAdistributed version of the Hungarian method for multirobotassignmentrdquo IEEE Transactions on Robotics vol 33 no 4pp 932ndash947 2017

Complexity 11

Case 1 ngem assume that a robot can only complete onetask and it can ensure that each uninspected area can beassigned to a robot to perform tasks at the same time eallocation method is the same as the task allocation methodof the single-point robot mentioned above ie each robotputs forward an optimal quotation for each task and themaster robot determines the optimal decision-makingscheme based on the quotation of each robot combined withthe corresponding bidding algorithm and assigns subtasks toeach robot according to the scheme en the problem isfirst transformed into an assignment problem which can besolved by the classical Hungarian algorithm [33] For ex-ample let n 6 and m 4 their positions are shown inTable 4 and the minimum cost of each robot at each taskpoint is solved according to the above method According tothe above allocation method the following allocationscheme can be obtained A1⟶ R1 A2⟶ R2

A3⟶ R3 andA4⟶ R5 and the total costF 994 + 969 + 681 + 571 3215

Case 2 nltm it means that a robot needs to completemultiple tasks and there can also be a situation where one ormore robots are idle For multiple robots at different initialpositions the host computer needs to plan a reasonable pathso that all inspection areas can be visited by the robots andthe total cost is minimal We have designed a genetic al-gorithm to solve this problem e genetic algorithm adoptsthe following single-chain coding form as shown in Fig-ure 8 when decoding the Robot2 completes the inspectiontasks of Areas 1 and 3 in sequence and similarly Robot1 andRobot3 complete the tasks of Areas 4 and 6 and Areas 2 and 5in sequenceis coding method has the advantage of strongreadability however it is easy to produce infeasible solutionsduring crossover and mutation erefore different repairalgorithms are used to repair the infeasible solutions

Crossover Use Partial-Mapped Crossover (PMX) op-erator when generating a new gene chain If it is not afeasible solution then fix it e specific repair methodis to find the repetitive genes in gene chain A that causeinfeasible solutions (there may be multiple groups) oneof which must be in the cross-replacement gene se-quence then find the gene that maps to the gene in genechain B and use it to replace the repetitive genes inchain A that are not in the cross-replacement sequenceMutation Randomly select two genes in the gene chainand determine whether one of their positions is at theend of the gene chain If not exchange their positions inthe gene chainSelection e tournament selection method is usedthat is a certain number of individuals are removedfrom the population each time then the best one isselected to enter the offspring population Repeat thisoperation until the new population size reaches theoriginal population size

For example in a 30 times 30 map the initial positions of theRobots 1 minus 3 are Rstart

1 (1 10) Rstart2 (15 30) and

Rstart3 (30 10) and the positions of the 6 inspection points are

A1(11 27) A2(29 28) A3(3 18) A4(16 15) A5(13 3) andA6(26 6) e initial azimuth of the robot is (0 minusπ2 minusπ)Using the proposed IBENN method above the optimal pathand the minimum cost between each point can be calculatede genetic algorithm can draw the following distributionplan

R1⟶ A3⟶ A1⟶ A4⟶ A5 R2⟶ A2 R3⟶ A6

(12)

e total cost is 4528 and the multirobot multipointinspection path is shown in Figure 9 where the red starindicates the inspection point and the blue star indicates theinitial position of each robot

43 All-Area Inspection Since the substation of smartmicrogrids is exposed to the outdoors for a long time it iseasy to break into foreign objects or other dangerous goodsIt is necessary to conduct regular inspections of the entirepower station of smart microgrids for all-area coverageHowever performing this task by a single robot may take along time and is inefficient erefore a multirobot col-laborative whole-area inspection program is designed

Divide every two robots into a group and design aheuristic algorithm for each robot e priority of theheuristic algorithm of the robots in each group is oppositewhich ensures that each group of robots can start inspectionsfrom different directions When the robot enters the deadzone position according to the proposed IBENN methodabove the optimal path from the dead zone position to theuninspected area can be planned e robot moves to thisarea and continues to inspect according to the originalheuristic algorithm For example in a 30 times 30 map there areparallel devices and various obstacle points as shown inFigure 10 Two robots in the area are used to coordinate tocomplete the all-area inspection taske steering priority ofthe heuristic algorithm of Robot1 W minus S minus SW minus NW minus N minus

E minus SE minus NE and Robot2 E minus N minus NE minus SE minus S minus W minus NW

minusSW and the initial positions are (1 1) and (30 1)respectively

Simulation experiments were carried out in the ob-stacle-free and obstacle environments and the results areshown in Figures 11 and 12 and Table 5 where the red andblue represent Robots 1 and 2 respectively pink dotsexpress repeated path points dots mean the final positionof the robot when the task is completed and stars rep-resent the initial position It can be seen from Table 5 thatin a simple map when there are no other obstacles in theinspection area and only parallel substation equipment

Table 4 Comparison of the four-robot path planning

Position Area1(916) Area2(1616) Area3(227) Area4(2225)

R1(11) 994 1492 1488 1801R2(151) 1031 969 788 1688R3(301) 1596 1442 681 1523R4(130) 1101 1158 1987 1271R5(1530) 1060 956 1609 571R6(3030) 2518 1441 1551 1132

8 Complexity

this method can achieve 100 coverage without over-lapping areas When there are various obstacles in theinspection area this method can also achieve 100 full-

coverage inspection but there is a repetition rate of 23Hence compared with other inspection methods theproposed IBENN method does not need to set a templateoperator and has strong versatility Multirobot collabo-ration can complete the entire area and full-coverageinspection task

To further verify the effectiveness of the proposedcontrol schemes we carry out the simulation experimentwith Coppelia Sim Software in the space of 30mtimes 30m etwo inspection robots are in the initial position as t 0 asshown in Figure 13(a) in which the gray cube and dark bluecube represent the equipment area and the obstacle arearespectively e robot is supposed to inspect at a speed of1ms disregarding the inspection time Using the aboveinspection strategy the experimental results are shown inFigure 13 As seen the left robot and right robot fall intodead zones respectively as t 138 or t 365 inFigures 13(a) and 13(e) and t 357 or t 306 inFigures 13(c) and 13(d) However in these cases the in-spection machine can jump out of the dead zone by callingthe IBENN algorithm respectively Furthermore both ro-bots fall into the dead zone state when t 395 as shown inFigure 13(f ) Since there is no undetected area in this sit-uation it follows that the inspection task has been com-pleted erefore the experiment verifies the feasibility ofthe cooperation scheme

A1 A3 R2 A4 A6 R1 A2 A5 R3

Figure 9 Gene chain coding of the genetic algorithm

30

25

20

15Y

X

10

5

5

Start points

10 15 2520 30

Inspection points

Figure 10 ree-robot path generated by the proposed IBENNbased MRCI system in the situation of six-point inspection

30

25

20

15Y

X

10

5

5 10 15 2520 30

Figure 11 Two-robot path generated by the proposed IBENN-based MRCI system in the situation of all-area inspection withoutobstacle

30

25

20

15Y

X

10

5

5 10 15 2520 30

Figure 12 Two-robot path generated by the proposed IBENN-based MRCI system in the situation of all-area inspection complexobstacle

Table 5 Results in obstacle-free and obstacle environments

Evaluationindex

Obstacle-freeenvironment ()

Obstacleenvironment ()

Coverage rate 100 100Repetition rate 0 23

Complexity 9

5 Conclusion

In this paper a multimobile robot collaborative operatingsystem for power stations of the smart microgrids isdesigned and an improved IBENN method is proposedCompared with the traditional BENN method and A-staralgorithm the improved IBENN algorithm has an obviousoptimization effect in path length and turning times Basedon this method the multirobot cooperative operationstrategy is designed to realize the three classic tasks of single-point inspection multipoint inspection and full-coverageinspection in the substation of smart microgrids whichverifies the effectiveness of the main results

Data Availability

All of the data used to support the findings of this study areincluded within this article

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China under Grant nos 61733004 and61773158

References

[1] A Peyman and F Keynia ldquoLifetime efficiency index model foroptimal maintenance of power substation equipment based

on cuckoo optimisation algorithmrdquo IET Generation Trans-mission amp Distribution vol 11 no 11 pp 2787ndash2795 2017

[2] I Ullah Y Fang and R Khan ldquoPredictive maintenance ofpower substation equipment by infrared thermography usinga machine-learning approachrdquo Energies vol 10 no 12pp 1ndash13 1987

[3] X Lu J Lai X Yu Y Wang and J M Guerrero ldquoDistributedcoordination of islanded microgrid clusters using a two-layerintermittent communication networkrdquo IEEE Transactions onIndustrial Informatics vol 14 no 9 pp 3956ndash3969 2018

[4] X Lu J Lai X Yu Y Wang and J M Guerrero ldquoA novelsecondary power management strategy for multiple ACmicrogrids with cluster-oriented two-layer cooperativeframeworkrdquo IEEE Transactions on Industrial Informaticsvol 17 no 2 pp 1483ndash1495 2021

[5] H Takahashi Development of Patrolling Robot for Substationpp 10ndash19 Japan IERE CouncilSpecial Document R8903Japan 1989

[6] J Beaudry and S Poirier Vehicule teleopere pour inspectionvisuelle etthermographique dans les postes de ransformation2012

[7] J K C Pinto M Masuda L C Magrini J A Jardini andM V Garbelloti ldquoMobile robot for hot spot monitoring inelectric power substationrdquo in Proceedings of the IEEEPESTransmission and Distribution Conference and Expositionpp 1ndash5 Chicago Illinois April 2008

[8] N Pouliot P-L Richard and S Montambault ldquoLineScouttechnology opens the way to robotic inspection and main-tenance of high-voltage power linesrdquo IEEE Power and EnergyTechnology Systems Journal vol 2 no 1 pp 1ndash11 2015

[9] A Cantieri M Ferraz and G Szekir ldquoCooperative UAV-UGV autonomous power pylon inspection an investigationof cooperative outdoor vehicle positioning architecturerdquoSensors vol 20 no 6384 pp 1ndash22 2020

(a) (b)

(c) (d)

(e) (f )

Figure 13 Sequence diagram of cooperative operation of two inspection robots (a) T 0 (b) T138 (c) T 306 (d) T 357 (e) T 365(f ) T 395

10 Complexity

[10] Y Guang and P Yutian ldquoIntelligent inspection of marinedisasters based on UAV intelligent visionrdquo Journal of CoastalResearch vol 93 pp 410ndash416 2019

[11] S Jordan J Moore and S Hovet ldquoState-of-the-art tech-nologies for UAV inspectionsrdquo IET Radar Sonar amp Navi-gation vol 12 no 2 pp 151ndash164 2018

[12] J Katranik F Pernus and B Likar ldquoA survey of mobile robotsfor distribution power line inspectionrdquo IEEE Transactions onPower Delivery vol 25 no 1 pp 485ndash493 2010

[13] J Yu and S M LaValle ldquoOptimal multirobot path planningon graphs complete algorithms and effective heuristicsrdquo IEEETransactions on Robotics vol 32 no 5 pp 1163ndash1177 2016

[14] K Jose and D K Pratihar ldquoTask allocation and collision-freepath planning of centralized multi-robots system for indus-trial plant inspection using heuristic methodsrdquo Robotics andAutonomous Systems vol 80 pp 34ndash42 2016

[15] B Pradhan A Nandi N B Hui and D S Roy ldquoA novelhybrid neural network-based multirobot path planning withmotion coordinationrdquo IEEE Transactions on VehicularTechnology vol 69 no 2 pp 1319ndash1327 2020

[16] C Luo S X Yang and X Li ldquoNeural-dynamics-drivencomplete area coverage navigation through cooperation ofmultiple mobile robotsrdquo IEEE Transactions on IndustrialElectronics vol 64 no 1 pp 750ndash760 2017

[17] B Woosley and P Dasgupta ldquoIntegrated real-time task andmotion planning for multiple robots under path and com-munication uncertaintiesrdquo Robotica vol 36 no 3pp 353ndash373 2018

[18] B Woosley P Dasgupta J G Rogers and J Twigg ldquoMulti-robot information driven path planning under communica-tion constraintsrdquo Autonomous Robots vol 44 no 5pp 721ndash737 2020

[19] F Imeson and S L Smith ldquoAn SMT-based approach tomotion planning for multiple robots with complex con-straintsrdquo IEEE Transactions on Robotics vol 35 no 3pp 669ndash684 2019

[20] A Ayari and S Bouamama ldquoA new multiple robot pathplanning algorithm dynamic distributed particle swarmoptimizationrdquo Robotics and Biomimetics vol 4 no 1 p 82017

[21] B Banerjee and CE Davis ldquoMultiagent path finding withpersistence conflictsrdquo IEEE Transactions on ComputationalIntelligence and AI in Games vol 9 no 4 pp 402ndash409 2016

[22] S abit and A Mohades ldquoMulti-robot path planning basedon multi-objective particle swarm optimizationrdquo IEEE Accessvol 7 pp 2138ndash2147 2018

[23] R Siegwart ldquoIR nourbakhsh and D scaramuzza ldquoIntro-duction to autonomous mobile robotsrdquo Industrial Robotvol 2 no 6 pp 645ndash649 2004

[24] K Jiang Z Sun Y Liu and J Sui ldquoDevelopment and Ap-plication of the Rail-type Inspection Robot used in SubstationRoomsrdquo MATEC Web of Conferences vol 139 no 5 ArticleID 00210 2017

[25] H B Xu J H Liu and X Jia ldquoSubstation inspection systembased on RFID technologyrdquo Advanced Materials Researchvol 734-737 pp 2846ndash2850 2013

[26] S ZWang D Han and Q Dong ldquoe application of RFID insubstation inspection systemrdquo Applied Mechanics and Ma-terials vol 295-298 pp 2433ndash2436 2013

[27] J Zhu Y Sun and D Sun ldquoDesign of a laser navigationsystem for the inspection robot used in substationrdquo Pro-ceedings of the Spie vol 322 2017

[28] C-J Huang Y-W Wang H-M Chen et al ldquoApplication ofcellular automata and type-2 fuzzy logic to dynamic vehicle

path planningrdquo Applied Soft Computing vol 19 pp 333ndash3422014

[29] S X Yang and M Meng ldquoAn efficient neural network ap-proach to dynamic robot motion planningrdquo Neural Networksvol 13 no 2 pp 143ndash148 2000

[30] S X Yang and M Q-H Meng ldquoReal-time collision-freemotion planning of a mobile robot using a Neural Dynamics-based approachrdquo IEEE Transactions on Neural Networksvol 14 no 6 pp 1541ndash1552 2003

[31] S Yang and C Luo A Neural Network Approach to CompleteCoverage Path Planning pp 718ndash724 Systems Man andCybernetics 2004

[32] C Luo and S X Yang ldquoA bioinspired neural network for real-time concurrent map building and complete coverage robotnavigation in unknown environmentsrdquo IEEE Transactions onNeural Networks vol 19 no 7 pp 1279ndash1298 2008

[33] S Chopra G Notarstefano M Rice and M Egerstedt ldquoAdistributed version of the Hungarian method for multirobotassignmentrdquo IEEE Transactions on Robotics vol 33 no 4pp 932ndash947 2017

Complexity 11

this method can achieve 100 coverage without over-lapping areas When there are various obstacles in theinspection area this method can also achieve 100 full-

coverage inspection but there is a repetition rate of 23Hence compared with other inspection methods theproposed IBENN method does not need to set a templateoperator and has strong versatility Multirobot collabo-ration can complete the entire area and full-coverageinspection task

To further verify the effectiveness of the proposedcontrol schemes we carry out the simulation experimentwith Coppelia Sim Software in the space of 30mtimes 30m etwo inspection robots are in the initial position as t 0 asshown in Figure 13(a) in which the gray cube and dark bluecube represent the equipment area and the obstacle arearespectively e robot is supposed to inspect at a speed of1ms disregarding the inspection time Using the aboveinspection strategy the experimental results are shown inFigure 13 As seen the left robot and right robot fall intodead zones respectively as t 138 or t 365 inFigures 13(a) and 13(e) and t 357 or t 306 inFigures 13(c) and 13(d) However in these cases the in-spection machine can jump out of the dead zone by callingthe IBENN algorithm respectively Furthermore both ro-bots fall into the dead zone state when t 395 as shown inFigure 13(f ) Since there is no undetected area in this sit-uation it follows that the inspection task has been com-pleted erefore the experiment verifies the feasibility ofthe cooperation scheme

A1 A3 R2 A4 A6 R1 A2 A5 R3

Figure 9 Gene chain coding of the genetic algorithm

30

25

20

15Y

X

10

5

5

Start points

10 15 2520 30

Inspection points

Figure 10 ree-robot path generated by the proposed IBENNbased MRCI system in the situation of six-point inspection

30

25

20

15Y

X

10

5

5 10 15 2520 30

Figure 11 Two-robot path generated by the proposed IBENN-based MRCI system in the situation of all-area inspection withoutobstacle

30

25

20

15Y

X

10

5

5 10 15 2520 30

Figure 12 Two-robot path generated by the proposed IBENN-based MRCI system in the situation of all-area inspection complexobstacle

Table 5 Results in obstacle-free and obstacle environments

Evaluationindex

Obstacle-freeenvironment ()

Obstacleenvironment ()

Coverage rate 100 100Repetition rate 0 23

Complexity 9

5 Conclusion

In this paper a multimobile robot collaborative operatingsystem for power stations of the smart microgrids isdesigned and an improved IBENN method is proposedCompared with the traditional BENN method and A-staralgorithm the improved IBENN algorithm has an obviousoptimization effect in path length and turning times Basedon this method the multirobot cooperative operationstrategy is designed to realize the three classic tasks of single-point inspection multipoint inspection and full-coverageinspection in the substation of smart microgrids whichverifies the effectiveness of the main results

Data Availability

All of the data used to support the findings of this study areincluded within this article

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China under Grant nos 61733004 and61773158

References

[1] A Peyman and F Keynia ldquoLifetime efficiency index model foroptimal maintenance of power substation equipment based

on cuckoo optimisation algorithmrdquo IET Generation Trans-mission amp Distribution vol 11 no 11 pp 2787ndash2795 2017

[2] I Ullah Y Fang and R Khan ldquoPredictive maintenance ofpower substation equipment by infrared thermography usinga machine-learning approachrdquo Energies vol 10 no 12pp 1ndash13 1987

[3] X Lu J Lai X Yu Y Wang and J M Guerrero ldquoDistributedcoordination of islanded microgrid clusters using a two-layerintermittent communication networkrdquo IEEE Transactions onIndustrial Informatics vol 14 no 9 pp 3956ndash3969 2018

[4] X Lu J Lai X Yu Y Wang and J M Guerrero ldquoA novelsecondary power management strategy for multiple ACmicrogrids with cluster-oriented two-layer cooperativeframeworkrdquo IEEE Transactions on Industrial Informaticsvol 17 no 2 pp 1483ndash1495 2021

[5] H Takahashi Development of Patrolling Robot for Substationpp 10ndash19 Japan IERE CouncilSpecial Document R8903Japan 1989

[6] J Beaudry and S Poirier Vehicule teleopere pour inspectionvisuelle etthermographique dans les postes de ransformation2012

[7] J K C Pinto M Masuda L C Magrini J A Jardini andM V Garbelloti ldquoMobile robot for hot spot monitoring inelectric power substationrdquo in Proceedings of the IEEEPESTransmission and Distribution Conference and Expositionpp 1ndash5 Chicago Illinois April 2008

[8] N Pouliot P-L Richard and S Montambault ldquoLineScouttechnology opens the way to robotic inspection and main-tenance of high-voltage power linesrdquo IEEE Power and EnergyTechnology Systems Journal vol 2 no 1 pp 1ndash11 2015

[9] A Cantieri M Ferraz and G Szekir ldquoCooperative UAV-UGV autonomous power pylon inspection an investigationof cooperative outdoor vehicle positioning architecturerdquoSensors vol 20 no 6384 pp 1ndash22 2020

(a) (b)

(c) (d)

(e) (f )

Figure 13 Sequence diagram of cooperative operation of two inspection robots (a) T 0 (b) T138 (c) T 306 (d) T 357 (e) T 365(f ) T 395

10 Complexity

[10] Y Guang and P Yutian ldquoIntelligent inspection of marinedisasters based on UAV intelligent visionrdquo Journal of CoastalResearch vol 93 pp 410ndash416 2019

[11] S Jordan J Moore and S Hovet ldquoState-of-the-art tech-nologies for UAV inspectionsrdquo IET Radar Sonar amp Navi-gation vol 12 no 2 pp 151ndash164 2018

[12] J Katranik F Pernus and B Likar ldquoA survey of mobile robotsfor distribution power line inspectionrdquo IEEE Transactions onPower Delivery vol 25 no 1 pp 485ndash493 2010

[13] J Yu and S M LaValle ldquoOptimal multirobot path planningon graphs complete algorithms and effective heuristicsrdquo IEEETransactions on Robotics vol 32 no 5 pp 1163ndash1177 2016

[14] K Jose and D K Pratihar ldquoTask allocation and collision-freepath planning of centralized multi-robots system for indus-trial plant inspection using heuristic methodsrdquo Robotics andAutonomous Systems vol 80 pp 34ndash42 2016

[15] B Pradhan A Nandi N B Hui and D S Roy ldquoA novelhybrid neural network-based multirobot path planning withmotion coordinationrdquo IEEE Transactions on VehicularTechnology vol 69 no 2 pp 1319ndash1327 2020

[16] C Luo S X Yang and X Li ldquoNeural-dynamics-drivencomplete area coverage navigation through cooperation ofmultiple mobile robotsrdquo IEEE Transactions on IndustrialElectronics vol 64 no 1 pp 750ndash760 2017

[17] B Woosley and P Dasgupta ldquoIntegrated real-time task andmotion planning for multiple robots under path and com-munication uncertaintiesrdquo Robotica vol 36 no 3pp 353ndash373 2018

[18] B Woosley P Dasgupta J G Rogers and J Twigg ldquoMulti-robot information driven path planning under communica-tion constraintsrdquo Autonomous Robots vol 44 no 5pp 721ndash737 2020

[19] F Imeson and S L Smith ldquoAn SMT-based approach tomotion planning for multiple robots with complex con-straintsrdquo IEEE Transactions on Robotics vol 35 no 3pp 669ndash684 2019

[20] A Ayari and S Bouamama ldquoA new multiple robot pathplanning algorithm dynamic distributed particle swarmoptimizationrdquo Robotics and Biomimetics vol 4 no 1 p 82017

[21] B Banerjee and CE Davis ldquoMultiagent path finding withpersistence conflictsrdquo IEEE Transactions on ComputationalIntelligence and AI in Games vol 9 no 4 pp 402ndash409 2016

[22] S abit and A Mohades ldquoMulti-robot path planning basedon multi-objective particle swarm optimizationrdquo IEEE Accessvol 7 pp 2138ndash2147 2018

[23] R Siegwart ldquoIR nourbakhsh and D scaramuzza ldquoIntro-duction to autonomous mobile robotsrdquo Industrial Robotvol 2 no 6 pp 645ndash649 2004

[24] K Jiang Z Sun Y Liu and J Sui ldquoDevelopment and Ap-plication of the Rail-type Inspection Robot used in SubstationRoomsrdquo MATEC Web of Conferences vol 139 no 5 ArticleID 00210 2017

[25] H B Xu J H Liu and X Jia ldquoSubstation inspection systembased on RFID technologyrdquo Advanced Materials Researchvol 734-737 pp 2846ndash2850 2013

[26] S ZWang D Han and Q Dong ldquoe application of RFID insubstation inspection systemrdquo Applied Mechanics and Ma-terials vol 295-298 pp 2433ndash2436 2013

[27] J Zhu Y Sun and D Sun ldquoDesign of a laser navigationsystem for the inspection robot used in substationrdquo Pro-ceedings of the Spie vol 322 2017

[28] C-J Huang Y-W Wang H-M Chen et al ldquoApplication ofcellular automata and type-2 fuzzy logic to dynamic vehicle

path planningrdquo Applied Soft Computing vol 19 pp 333ndash3422014

[29] S X Yang and M Meng ldquoAn efficient neural network ap-proach to dynamic robot motion planningrdquo Neural Networksvol 13 no 2 pp 143ndash148 2000

[30] S X Yang and M Q-H Meng ldquoReal-time collision-freemotion planning of a mobile robot using a Neural Dynamics-based approachrdquo IEEE Transactions on Neural Networksvol 14 no 6 pp 1541ndash1552 2003

[31] S Yang and C Luo A Neural Network Approach to CompleteCoverage Path Planning pp 718ndash724 Systems Man andCybernetics 2004

[32] C Luo and S X Yang ldquoA bioinspired neural network for real-time concurrent map building and complete coverage robotnavigation in unknown environmentsrdquo IEEE Transactions onNeural Networks vol 19 no 7 pp 1279ndash1298 2008

[33] S Chopra G Notarstefano M Rice and M Egerstedt ldquoAdistributed version of the Hungarian method for multirobotassignmentrdquo IEEE Transactions on Robotics vol 33 no 4pp 932ndash947 2017

Complexity 11

5 Conclusion

In this paper a multimobile robot collaborative operatingsystem for power stations of the smart microgrids isdesigned and an improved IBENN method is proposedCompared with the traditional BENN method and A-staralgorithm the improved IBENN algorithm has an obviousoptimization effect in path length and turning times Basedon this method the multirobot cooperative operationstrategy is designed to realize the three classic tasks of single-point inspection multipoint inspection and full-coverageinspection in the substation of smart microgrids whichverifies the effectiveness of the main results

Data Availability

All of the data used to support the findings of this study areincluded within this article

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is work was supported by the National Natural ScienceFoundation of China under Grant nos 61733004 and61773158

References

[1] A Peyman and F Keynia ldquoLifetime efficiency index model foroptimal maintenance of power substation equipment based

on cuckoo optimisation algorithmrdquo IET Generation Trans-mission amp Distribution vol 11 no 11 pp 2787ndash2795 2017

[2] I Ullah Y Fang and R Khan ldquoPredictive maintenance ofpower substation equipment by infrared thermography usinga machine-learning approachrdquo Energies vol 10 no 12pp 1ndash13 1987

[3] X Lu J Lai X Yu Y Wang and J M Guerrero ldquoDistributedcoordination of islanded microgrid clusters using a two-layerintermittent communication networkrdquo IEEE Transactions onIndustrial Informatics vol 14 no 9 pp 3956ndash3969 2018

[4] X Lu J Lai X Yu Y Wang and J M Guerrero ldquoA novelsecondary power management strategy for multiple ACmicrogrids with cluster-oriented two-layer cooperativeframeworkrdquo IEEE Transactions on Industrial Informaticsvol 17 no 2 pp 1483ndash1495 2021

[5] H Takahashi Development of Patrolling Robot for Substationpp 10ndash19 Japan IERE CouncilSpecial Document R8903Japan 1989

[6] J Beaudry and S Poirier Vehicule teleopere pour inspectionvisuelle etthermographique dans les postes de ransformation2012

[7] J K C Pinto M Masuda L C Magrini J A Jardini andM V Garbelloti ldquoMobile robot for hot spot monitoring inelectric power substationrdquo in Proceedings of the IEEEPESTransmission and Distribution Conference and Expositionpp 1ndash5 Chicago Illinois April 2008

[8] N Pouliot P-L Richard and S Montambault ldquoLineScouttechnology opens the way to robotic inspection and main-tenance of high-voltage power linesrdquo IEEE Power and EnergyTechnology Systems Journal vol 2 no 1 pp 1ndash11 2015

[9] A Cantieri M Ferraz and G Szekir ldquoCooperative UAV-UGV autonomous power pylon inspection an investigationof cooperative outdoor vehicle positioning architecturerdquoSensors vol 20 no 6384 pp 1ndash22 2020

(a) (b)

(c) (d)

(e) (f )

Figure 13 Sequence diagram of cooperative operation of two inspection robots (a) T 0 (b) T138 (c) T 306 (d) T 357 (e) T 365(f ) T 395

10 Complexity

[10] Y Guang and P Yutian ldquoIntelligent inspection of marinedisasters based on UAV intelligent visionrdquo Journal of CoastalResearch vol 93 pp 410ndash416 2019

[11] S Jordan J Moore and S Hovet ldquoState-of-the-art tech-nologies for UAV inspectionsrdquo IET Radar Sonar amp Navi-gation vol 12 no 2 pp 151ndash164 2018

[12] J Katranik F Pernus and B Likar ldquoA survey of mobile robotsfor distribution power line inspectionrdquo IEEE Transactions onPower Delivery vol 25 no 1 pp 485ndash493 2010

[13] J Yu and S M LaValle ldquoOptimal multirobot path planningon graphs complete algorithms and effective heuristicsrdquo IEEETransactions on Robotics vol 32 no 5 pp 1163ndash1177 2016

[14] K Jose and D K Pratihar ldquoTask allocation and collision-freepath planning of centralized multi-robots system for indus-trial plant inspection using heuristic methodsrdquo Robotics andAutonomous Systems vol 80 pp 34ndash42 2016

[15] B Pradhan A Nandi N B Hui and D S Roy ldquoA novelhybrid neural network-based multirobot path planning withmotion coordinationrdquo IEEE Transactions on VehicularTechnology vol 69 no 2 pp 1319ndash1327 2020

[16] C Luo S X Yang and X Li ldquoNeural-dynamics-drivencomplete area coverage navigation through cooperation ofmultiple mobile robotsrdquo IEEE Transactions on IndustrialElectronics vol 64 no 1 pp 750ndash760 2017

[17] B Woosley and P Dasgupta ldquoIntegrated real-time task andmotion planning for multiple robots under path and com-munication uncertaintiesrdquo Robotica vol 36 no 3pp 353ndash373 2018

[18] B Woosley P Dasgupta J G Rogers and J Twigg ldquoMulti-robot information driven path planning under communica-tion constraintsrdquo Autonomous Robots vol 44 no 5pp 721ndash737 2020

[19] F Imeson and S L Smith ldquoAn SMT-based approach tomotion planning for multiple robots with complex con-straintsrdquo IEEE Transactions on Robotics vol 35 no 3pp 669ndash684 2019

[20] A Ayari and S Bouamama ldquoA new multiple robot pathplanning algorithm dynamic distributed particle swarmoptimizationrdquo Robotics and Biomimetics vol 4 no 1 p 82017

[21] B Banerjee and CE Davis ldquoMultiagent path finding withpersistence conflictsrdquo IEEE Transactions on ComputationalIntelligence and AI in Games vol 9 no 4 pp 402ndash409 2016

[22] S abit and A Mohades ldquoMulti-robot path planning basedon multi-objective particle swarm optimizationrdquo IEEE Accessvol 7 pp 2138ndash2147 2018

[23] R Siegwart ldquoIR nourbakhsh and D scaramuzza ldquoIntro-duction to autonomous mobile robotsrdquo Industrial Robotvol 2 no 6 pp 645ndash649 2004

[24] K Jiang Z Sun Y Liu and J Sui ldquoDevelopment and Ap-plication of the Rail-type Inspection Robot used in SubstationRoomsrdquo MATEC Web of Conferences vol 139 no 5 ArticleID 00210 2017

[25] H B Xu J H Liu and X Jia ldquoSubstation inspection systembased on RFID technologyrdquo Advanced Materials Researchvol 734-737 pp 2846ndash2850 2013

[26] S ZWang D Han and Q Dong ldquoe application of RFID insubstation inspection systemrdquo Applied Mechanics and Ma-terials vol 295-298 pp 2433ndash2436 2013

[27] J Zhu Y Sun and D Sun ldquoDesign of a laser navigationsystem for the inspection robot used in substationrdquo Pro-ceedings of the Spie vol 322 2017

[28] C-J Huang Y-W Wang H-M Chen et al ldquoApplication ofcellular automata and type-2 fuzzy logic to dynamic vehicle

path planningrdquo Applied Soft Computing vol 19 pp 333ndash3422014

[29] S X Yang and M Meng ldquoAn efficient neural network ap-proach to dynamic robot motion planningrdquo Neural Networksvol 13 no 2 pp 143ndash148 2000

[30] S X Yang and M Q-H Meng ldquoReal-time collision-freemotion planning of a mobile robot using a Neural Dynamics-based approachrdquo IEEE Transactions on Neural Networksvol 14 no 6 pp 1541ndash1552 2003

[31] S Yang and C Luo A Neural Network Approach to CompleteCoverage Path Planning pp 718ndash724 Systems Man andCybernetics 2004

[32] C Luo and S X Yang ldquoA bioinspired neural network for real-time concurrent map building and complete coverage robotnavigation in unknown environmentsrdquo IEEE Transactions onNeural Networks vol 19 no 7 pp 1279ndash1298 2008

[33] S Chopra G Notarstefano M Rice and M Egerstedt ldquoAdistributed version of the Hungarian method for multirobotassignmentrdquo IEEE Transactions on Robotics vol 33 no 4pp 932ndash947 2017

Complexity 11

[10] Y Guang and P Yutian ldquoIntelligent inspection of marinedisasters based on UAV intelligent visionrdquo Journal of CoastalResearch vol 93 pp 410ndash416 2019

[11] S Jordan J Moore and S Hovet ldquoState-of-the-art tech-nologies for UAV inspectionsrdquo IET Radar Sonar amp Navi-gation vol 12 no 2 pp 151ndash164 2018

[12] J Katranik F Pernus and B Likar ldquoA survey of mobile robotsfor distribution power line inspectionrdquo IEEE Transactions onPower Delivery vol 25 no 1 pp 485ndash493 2010

[13] J Yu and S M LaValle ldquoOptimal multirobot path planningon graphs complete algorithms and effective heuristicsrdquo IEEETransactions on Robotics vol 32 no 5 pp 1163ndash1177 2016

[14] K Jose and D K Pratihar ldquoTask allocation and collision-freepath planning of centralized multi-robots system for indus-trial plant inspection using heuristic methodsrdquo Robotics andAutonomous Systems vol 80 pp 34ndash42 2016

[15] B Pradhan A Nandi N B Hui and D S Roy ldquoA novelhybrid neural network-based multirobot path planning withmotion coordinationrdquo IEEE Transactions on VehicularTechnology vol 69 no 2 pp 1319ndash1327 2020

[16] C Luo S X Yang and X Li ldquoNeural-dynamics-drivencomplete area coverage navigation through cooperation ofmultiple mobile robotsrdquo IEEE Transactions on IndustrialElectronics vol 64 no 1 pp 750ndash760 2017

[17] B Woosley and P Dasgupta ldquoIntegrated real-time task andmotion planning for multiple robots under path and com-munication uncertaintiesrdquo Robotica vol 36 no 3pp 353ndash373 2018

[18] B Woosley P Dasgupta J G Rogers and J Twigg ldquoMulti-robot information driven path planning under communica-tion constraintsrdquo Autonomous Robots vol 44 no 5pp 721ndash737 2020

[19] F Imeson and S L Smith ldquoAn SMT-based approach tomotion planning for multiple robots with complex con-straintsrdquo IEEE Transactions on Robotics vol 35 no 3pp 669ndash684 2019

[20] A Ayari and S Bouamama ldquoA new multiple robot pathplanning algorithm dynamic distributed particle swarmoptimizationrdquo Robotics and Biomimetics vol 4 no 1 p 82017

[21] B Banerjee and CE Davis ldquoMultiagent path finding withpersistence conflictsrdquo IEEE Transactions on ComputationalIntelligence and AI in Games vol 9 no 4 pp 402ndash409 2016

[22] S abit and A Mohades ldquoMulti-robot path planning basedon multi-objective particle swarm optimizationrdquo IEEE Accessvol 7 pp 2138ndash2147 2018

[23] R Siegwart ldquoIR nourbakhsh and D scaramuzza ldquoIntro-duction to autonomous mobile robotsrdquo Industrial Robotvol 2 no 6 pp 645ndash649 2004

[24] K Jiang Z Sun Y Liu and J Sui ldquoDevelopment and Ap-plication of the Rail-type Inspection Robot used in SubstationRoomsrdquo MATEC Web of Conferences vol 139 no 5 ArticleID 00210 2017

[25] H B Xu J H Liu and X Jia ldquoSubstation inspection systembased on RFID technologyrdquo Advanced Materials Researchvol 734-737 pp 2846ndash2850 2013

[26] S ZWang D Han and Q Dong ldquoe application of RFID insubstation inspection systemrdquo Applied Mechanics and Ma-terials vol 295-298 pp 2433ndash2436 2013

[27] J Zhu Y Sun and D Sun ldquoDesign of a laser navigationsystem for the inspection robot used in substationrdquo Pro-ceedings of the Spie vol 322 2017

[28] C-J Huang Y-W Wang H-M Chen et al ldquoApplication ofcellular automata and type-2 fuzzy logic to dynamic vehicle

path planningrdquo Applied Soft Computing vol 19 pp 333ndash3422014

[29] S X Yang and M Meng ldquoAn efficient neural network ap-proach to dynamic robot motion planningrdquo Neural Networksvol 13 no 2 pp 143ndash148 2000

[30] S X Yang and M Q-H Meng ldquoReal-time collision-freemotion planning of a mobile robot using a Neural Dynamics-based approachrdquo IEEE Transactions on Neural Networksvol 14 no 6 pp 1541ndash1552 2003

[31] S Yang and C Luo A Neural Network Approach to CompleteCoverage Path Planning pp 718ndash724 Systems Man andCybernetics 2004

[32] C Luo and S X Yang ldquoA bioinspired neural network for real-time concurrent map building and complete coverage robotnavigation in unknown environmentsrdquo IEEE Transactions onNeural Networks vol 19 no 7 pp 1279ndash1298 2008

[33] S Chopra G Notarstefano M Rice and M Egerstedt ldquoAdistributed version of the Hungarian method for multirobotassignmentrdquo IEEE Transactions on Robotics vol 33 no 4pp 932ndash947 2017

Complexity 11