Research Article The COMRADE System for Multirobot ...

Research ArticleThe COMRADE System for Multirobot Autonomous LandmineDetection in Postconflict Regions

Prithviraj Dasgupta1 Joseacute Baca1 K R Guruprasad2

Angeacutelica Muntildeoz-Meleacutendez3 and Janyl Jumadinova4

1Computer Science Department University of Nebraska Omaha NE 68182 USA2Mechanical Engineering Department NIT Surathkal Karnataka 575025 India3Computer Science Department INAOE 72840 Puebla PUE Mexico4Computer Science Department Allegheny College Meadville PA 16335 USA

Correspondence should be addressed to Prithviraj Dasgupta pdasguptamailunomahaedu

Received 14 August 2014 Accepted 12 January 2015

Academic Editor Giovanni Muscato

Copyright copy 2015 Prithviraj Dasgupta et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

We consider the problem of autonomous landmine detection using a team of mobile robots Previous research on robotic landminedetectionmostly employs a single robot equippedwith a landmine detection sensor to detect landminesWe envisage that the qualityof landmine detection can be significantly improved if multiple robots are coordinated to detect landmines in a cooperativemannerby incrementally fusing the landmine-related sensor information they collect and then use that information to visit locations ofpotential landmines Towards this objective we describe a multirobot system called COMRADES to address different aspects ofthe autonomous landmine detection problem including distributed area coverage to detect and locate landmines informationaggregation to fuse the sensor information obtained by different robots and multirobot task allocation (MRTA) to enable differentrobots to determine a suitable sequence to visit locations of potential landmines while reducing the time required and batteryexpended We have used commercially available all-terrain robots called Coroware Explorer that are customized with a metaldetector to detect metallic objects including landmines as well as indoor Corobot robots both in simulation and in physicalexperiments to test the different techniques in COMRADES

1 Introduction

Humanitarian demining is a crucial effort for the safetyand sustenance of human lives in postconflict regionsUnfortunately recent surveys on landminemonitoring reportthat humanitarian demining efforts are considerably laggingbehind antipersonnel landmine planting activities due toseveral technological and economic reasons [1] This resultsin enormous loss to human lives for example in 2010 aloneexplosions of landmines and similar devices resulted in 4 191casualties with civilians accounting for 70 of the casu-alties One the major technological challenges in humani-tarian demining is to detect landmines rapidly and with rea-sonable accuracy while reducing the number of false posi-tives We envisage that automating landmine detection ope-rations using multiple off-the-shelf autonomous robots will

provide a reasonably accurate yet economical solution to theproblem of detecting landmines Towards this objective wedescribe a multirobot system called COMRADE (Cooper-ative Multirobot Automated Detection) System for human-itarian demining The central objective of COMRADES isto develop novel coordination techniques between multiplelow cost mobile robots which enable them to autonomouslyand collaboratively detect landmines with high accuracy inpostconflict regions COMRADES includes techniques thatallow each robot to explore an initially unknown regionwhilesearching for landmines recognize landmine-like objectson its sensors share and fuse the landmine-related sensorinformation with other robots and coordinate its actionswith other robots so that multiple robots can converge onthe object to analyze and confirm it as a landmine In thispaper we present the description and experimental results

Hindawi Publishing CorporationJournal of RoboticsVolume 2015 Article ID 921370 17 pageshttpdxdoiorg1011552015921370

2 Journal of Robotics

from different techniques for coverage task allocation andmultisensor information aggregation and sensor schedulingusingmultiple robots thatwe have developed as part of COM-RADES Specifically we describe the following aspects ofmultirobot autonomous landmine detection inCOMRADES

(i) A distributed area coverage technique allows a set ofrobots to dynamically partition an initially unknownenvironment into a set of nonoverlapping regionsand search for landmines within each region Thetechniques are robust to individual robot failures andare able to scale with the number of robots and size ofthe environment

(ii) A distributed information fusion technique aggre-gates landmine-related sensor information from dif-ferent robots using a prediction market-based tech-nique and a decision making technique that uses thefused information to allocate additional robots (sen-sors) to rapidly classify the object

(iii) A multirobot task allocation (MRTA) technique usesa spatial queueing model that enables a set of robotsto determine a suitable order or perform a set oflandmine detection related tasks while reducing thetime and energy spent in performing the tasks

To realize the above techniques we have customizedcommercially available all-terrain robots called CorowareExplorer with a metal detector to enable them to detectmetallic objects including landminesWehave also developeda user interface that allows shared autonomy between robotsand humans Humans can visualize information about thehealth and status of the robots and their progress in thelandmine detection operation on a control station and selec-tively supersede their autonomous operations by remotelycontrolling themovement and some operations of the robotsWe have verified the operation of the robots in differenttypes of outdoor terrain and different operational conditionsWe have also used indoor robots called Coroware Corobotswhich have very similar features to the outdoor Explorerrobots both in simulation and within an indoor arena to testthe different techniques used in COMRADES Our resultsshow that our proposed techniques offer suitable meansto rapidly perform autonomous landmine detection withinexpensive robots

The rest of our paper is structured as follows In thenext section we provide an overview of existing research onrobotic landmine detection In Section 3 we describe themain features of our proposed system the robots and thelandmine detector used and the user interface The speci-fic algorithms techniques and results related to the threemain technical aspects of COMRADES distributed area cov-erage distributed task allocation and information fusion areaddressed in Section 4 andfinallywe discuss future directionsof our work and conclude

2 Related Work

Autonomous landmine detection using robotic systems hasbeen an active research topic over the past decade Excellent

reviews of the state-of-the-art techniques in robotic landminedetection are available in [2 3] The research in this topiccan be divided into three major directions designing robotsattached with suitable sensor devices to detect and possiblyextract landmines developing data and information fusiontechniques to improve the accuracy of detecting landminesand computational techniques to coordinate multiple robotsand present the information collected by the robots in astructured and visualizable format to a human supervisor

Much of the recent research on autonomous landminedetection has been concentrated on developing robotic sys-tems for detecting landminesmost of these systems consist ofa single robot attached with appropriate sensors for landminedetection For example some of these robots include a mech-anism mounted on small robot platforms to flail the groundand detonate landmines along with vegetation clearing tools[4] Many deployed robotic systems for landmine detectionrely on teleoperation rather than autonomy Examples of suchsystems include a remote operated vehicle called MR-2 theenhanced teleoperated ordnance disposal system (ETODS)andTEMPEST robotThese robots benefit from the improvedprecision in detecting and neutralizing landmines due to ahumanrsquos presence in the loop but they require humans to bein the vicinity of landmines to teleoperate the vehicle Laterimprovements to some of these systems such as the MR-2have added partial autonomy in navigation and increasedthe teleoperation range to 5 km using feedback sensorsIn contrast to these larger robots researchers have alsoinvestigated smaller robots that are highly agile and havea small footprint and low weight to reduce the risk ofaccidental explosion of a landmine Examples of such robotsare the Ares Shrimps Pemexs Dervishs and Tridem robotsand legged robots such as the AMRU Shadow Deminer andCOMET [3] Despite their agility smaller robots are limitedin the weight of sensors that they can carry on board andare not suited for heavier more robust sensors like groundpenetrating radar (GPR) or large-coil metal detectors Toaccommodate such sensors robots such as the Titan [5]Gryphon [6] mine detection robot and mine hunter vehicle(MHV) [3] have been developedMost of the robots discussedabove are for detecting and locating landmines In contrastthe PEACE robot [7] and amechanical hand called theMine-hand [6] have been developed mainly to excavate detectedlandmines Researchers have also proposed unmanned aerialvehicles (UAVs) in landmine detecting robotic systems toaid in terrain mapping before deploying ground robots [2]or to unobtrusively detect landmines using a conceptualsystem of sensors attached to cables suspended from UAVs[8]

For detecting landmines a wide variety of sensors includ-ing metal detectors (MD) [9] ground penetrating radar(GPR) [10 11] infrared cameras [12] and chemical sensorsfor detecting plumes emanating from landmines [13] havebeen proposed For most research as well as commerciallydeployed applications metal detectors either individually orin combination with GPR [6 14] are the sensors of choice asthey provide reasonably accurate source localization and arerelatively straightforward to acquire as off-the-shelf compo-nents and integrate on robots For this reason we have used

Journal of Robotics 3

metal detectors on the robots for detecting landmines in oursystem

Yet another important aspect of landmine detection isfusing sensor readings obtained bymultiple sensorsThe JointMultisensor Mine-Signatures project was one of the earliestresearch efforts to collect landmine detection data usingmultiple sensors [15] Bloch et al [16] have proposed severalsensor fusion techniques based on Dempster-Shafer theoryincluding techniques for incorporating human confidencevalues with the data collected by sensors [17] A multisensordemining robot consisting of metal detector an infraredsensor and a chemical sensor is described in [18] In [11] theauthors report that Bayesian inference techniques for fusingdata using multiple sensors metal detector GPR infraredcamera and magnetometer can significantly improve thedetection rate of landmines The Advanced Landmine Imag-ing System (ALIS) uses signatures from metal detectorsand GPR to more accurately locate deep mines althoughthe sensors are operated manually and their signatures areinspected manually as well This idea has been extended torobotic landmine detection by collecting data from a metaldetector array and GPR mounted on a single robot andusing a combination of Bayesian inferencing and clusteringalgorithms depending upon the context of the collecteddata to get improved detection rate of landmines [19]Across the world several recent projects for humanitariandemining using robots are also utilizing multiple sensors toperform landmine detection more accurately The ongoingTIRAMISU project in the European Union [20] proposes touse multisensor data fusion techniques for combining infor-mation from a metal detector and a chemical sensor [21] toimprove the location and detection accuracy of landmines In[22] authors describe field tests with the ALIS and Gryphonsystems while using only metal detectors and metal detectorsalong with GPR for landmines buried in different typesof soil in test mine-fields in Croatia Similarly in [23] theauthor describes a mechanical system equipped with nucleardetectors for measuring gamma radiation and backscatteredthermal neutrons which is planned to be deployed in LibyaThe challenges reported in these projects include accuratelylocalizing a landminersquos depth and mitigating the false alarmrate subject to the probability of detection of the sensorused to detect the landmine Soil composition and clutter inthe soil are also important factors affecting the accuracy oflandmine detection [22]

Recently some researchers have proposed using multi-robot systems for landmine detection [22 24 25] The clearadvantage afforded by multiple robots is the ability to includesensors of different types on different robot platforms andmaking the system robust against the failure of single ormultiple robots In this direction the distributed field robotarchitecture (DFRA) [25] proposed a software framework forthe coordinated operation of an aerial and a wheeled groundrobot with visual and thermal sensors to detect landmineswhile in [24] the authors includedwheeled legged and aerialrobots using a combination of GPR metal detectors andvapour sensors for landmine detection Both these worksare mentioned to be preliminary research and mainly focuson a suitable software architecture for integrating multiple

robots into a single system for landmine detection Our workin this paper is mainly along this direction of coordinatingmultiple robots to perform landmine detection with a focuson specific techniques and algorithms that can be used bythe robots for performing various aspects of autonomouslandmine detection

3 Description of the COMRADE System

The central objective of the COMRADE (COoperativeMulti-Robot Automated DEtection) system for humanitarian dem-ining is to develop novel coordination techniques betweenmultiple low cost autonomous mobile robots which enablethem to collaboratively detect landmines in postconflictregions The robots used in the COMRADE system areoff-the-shelf relatively inexpensive autonomous robots thatare equipped with appropriate sensors for detecting land-mines We consider three main candidates for sensors metaldetectors (MD) IR-based multilocator device and groundpenetrating radar (GPR)The costs accuracy and capabilitiesof the different sensors are given in Table 1 Because ofthe differences between sensors across these three factorsit is important to deploy the sensors in a region basedon the possibility of existence of landmines and risks tohuman lives in that region For example in low-risk low-incidence areas more robots with low costlow accuracysensors (eg MD only) can be deployed using looselycoordinated robot teams that offer very coarse guaranteeson the time required to confirm a detected object as alandmine On the other hand in a high-risk high-incidencearea it would make sense to include more accurate andmore expensive sensors using tightly coupled robot teamsso that a potential landmine could be confirmed rapidly Toachieve this in the COMRADE system the area of interest(AOI) is classified by human experts into subareas basedon landmine incidence possibility and risks to human lifeand robots with appropriate sensors are deployed in eachsubarea An example classification of an AOI is given inTable 2 and a diagram showing the deployment of robotteams based on the AOI classification is shown in Figure 1As shown in Figure 1 for high-risk areas the entire AOIis covered using all sensor types For moderate-risk areasas a trade-off between landmine detection costs (time andenergy expended in detection) and accuracy higher accuracysensors are deployed at a certain location only when a loweraccuracy sensor has detected a suspicious object at thatlocation If 100 detection is required the entire AOI can beclassified as high-risk area to ensure that it is covered at leastonce by every sensor For the sake of legibility in the rest ofthe paper we refer to the subarea in which a team of robotsis deployed as their environment and consider algorithms forcoordinating the robots that are only within that subarea

We consider an initially unknown environment whoseboundaries are known but the locations of obstacles withinthe environment are initially not known or known withinaccuracies The environment contains landmines as wellas nonlandmine objects that are buried underground andcan be detected by the landmine detection sensors on therobots These objects are together referred to as objects of


Table 1 Costs of different types of landmine detection sensors in the COMRADE system

Sensor Type Cost (USD) Prob of DetectionMaterial DetectedMetal Detector (MD) $100ndash$200 02ndash07only metalInfra-red based Multi Detector (IR) $2000ndash$5000 04ndash08metal and plasticGround Penetrating Radar (GPR) $20000ndash$30000 05ndash01metal and plastic

Table 2 Classification of different types of AOI in COMRADES depending on risk to human lives

Type of AOI Risk Category Number and Type of RobotsHigh Traffic low chance of landmine Low Individually moving robots mainly with MDModerate traffic high chance of landmine High Tightly coupled teams ndash most MD some IR few GPRLow traffic high chance of landmine Moderate Individually moving robots ndash some MD some IR few GPR

interest and their locations are not known a priori When arobot is in the vicinity of an object of interest we assumethat the robot is appropriately positioned so that the objectrsquossignature can be registered on its detection sensor We referto the operations performed by a robot to determine thesignature of a buried object of interest using its landminedetection sensor as a task The objective of the robots is tosearch for landmines using their landmine detection sensorsWhen an object of interest is detected on a robotrsquos sensorit calls other robots to the location at which the object wasdetected to analyse the objectrsquos signature using the otherrobotsrsquo sensors Finally the data collected from the object ofinterest by the robots has to be fused so that the object canbe classified as a landmine or nonlandmine To realize theseactivities the robots in COMRADES have to perform threemajor functions (1) Distributedly cover the free space in theenvironment to search for objects of interest (2) For eachrobot determine a schedule or order to perform tasks it isaware of so that the cost of the overall schedule in terms ofenergy expended by the robots is reducedThe set of tasks canchange dynamically as robots discover newobjects of interest(3) Fuse the information at an object of interest obtained bydifferent robots to classify it as a landmine or nonlandmineThe algorithms for realizing these functionalities withinCOMRADES are described in Section 4

31 COMRADES Robots We have used two robots called theExplorer and Corobot manufactured by Coroware Inc Bothrobots are four-wheeled and use a skid-steer mechanism formaneuvering The Explorer robot has rugged constructionwith a higher clearance and is suitable for outdoor navigationover rough terrains while the Corobot robot is a lighterscaled-down version of the Explorer robot and more suitedfor indoor usage and testing purposes Photographs of theExplorer and Corobot robots used in COMRADES areshown in Figure 2 Each robot is equipped with an on-board computer an AMDAthlonDual Core Processor 5050119890running at 26GHz with 187GB of RAM under WindowsXP Both robotsrsquo on-board sensors include a color VGAWebcam capable of 2MP resolution Wi-Fi to communicatewith the control station and a Hokuyo URG-04LX-UG01laser rangefinder with a detection range of 2 cm to 4m anda sweep angle of 240∘

TheCorobot robot is equippedwith aHagisonic Stargazerlocalization device that uses IR-based positioning using over-head markers to determine the location and heading of therobot with an accuracy of plusmn2 cm To avoid obstacles at closeproximity the Corobot robot is also fitted with two cross-beam IR sensorsmounted on the front bumper one IR sensoron each side oriented sixty degrees from the front of the vehi-cle the IR sensors provide proximity measurements withina range of 10ndash80 cm For the Corobot robots we used theirWebcams to detect specific objects or marks on the groundcorresponding to virtual landmines due to the complicationsin using landmine detectors such asmetal detectors in indoorenvironments (eg inside buildings with metal frames)

Additional on-board sensors on the Explorer robotinclude an inertial measurement unit (IMU) and a GarminGPS16x LVS differential GPS that provides localization withan accuracy of plusmn3m To localize the robot a Kalmanfiltering technique was used to combine the GPS IMUand encoder readings resulting in a localization accuracyof plusmn1m (Techniques to fuse localization data from multiplesensors [19] can be used to further improve the localizationaccuracy of detected landmines) The Explorer robots werealso customized with a metal detector attached with a fixedarm to the front of the robot as described in Figure 2

32 Metal Detector System Themetal detector (MD) systemused in COMRADES consists of an Infinium LSMetal Detec-tor manufactured by Garrett Inc attached to a fixed forwardfacing arm on the Explorer robot The MD is designed towork in moist and heavily mineralized environments Thedevice has been customized and integrated on the Explorerrobot via a USB interface to detect landmines over differentenvironments such as grass snow and rock based surfacesas shown in Figure 3 The metal detector implements pulseinduction (PI) technology which works by sending short(50 120583s) high current (20A) pulses to a search coil It thenlistens for the ldquoechordquo from a metallic object This echo isactually the residual magnetic field induced in an object nearthe coil and changes the decay rate from the natural decayof the coil If there is no metal near the coil this pulse willdecay rapidly and predictably When metal is near the coilit will decay at a different rate than the natural decay Thedifference between those two times indicates the presence of


Urban land with low risk tohumans from landmines Single robot with

metal detectorsearching in

low-risk region

Heterogeneous robots moving as ateam for high accuracy of landminedetection in high-risk areas

Agricultural land with high riskto humans from landmines

Robots with high capability sensorsconvening at an object of interestto confirm it following its initial

detection on a metaldetector sensor

Uncultivated land withmoderate risk to humans

from landmines

Robots searching individually forlandmines in moderate-risk area

Go

Go

Go

GoStop

Informationfilters

Logs

Analysistools

Ground stationUser interface

Robot with metaldetector located

landmine-likeobject of interest

Detect

Team

Robot withmetal detectorRobot withmultilocator device

Robot withGPR

Unnavigableregion

Control station

Figure 1 General schematic of the COMRADE system for landmine detection using multiple autonomous and mobile robots

GPS

IMU

Laser rangefinder

WebcamMetal detector

system

(a)

Webcam

Stargazer

IR sensors

(b)

Figure 2 Robots used in COMRADES along with their sensors (a) Explorer robot (b) Corobot robot

Figure 3 The Explorer robot searches for landmines in different types of environments It is possible to scan areas covered by grass snowand rocks due to the characteristics of the MDS


(a) (b)

0 20 40 60 80 1000

200

400

600

800

1000

1200

Depth (mm)

Met

al d

etec

tor d

ata (

raw

dat

a)

99680

38773

18241 16078 12241 10445

(c)

0 20 40 60 80 1000

05

1

15

2

25

3

35

4

Depth (mm)

Stan

dard

dev

iatio

n er

ror

326303

351323

306328

(d)

Figure 4 (a) A real action paintball mine is used to simulate mines made with few metallic parts (b) Landmine has been buried 100mm insoil with the purpose of mine detection analysis (c) Metal detector raw data for different buried depths of the paintball mine (d) Standarddeviation error for different depths at which the paintball mine is buried

metalThe slope rate of the curve will indicate how strong thesignal is from the metal An advantage of the pulse inductiontechnology over other comparable technologies is that it isaffected very little by mineralization in soil and water whichmeans it can be used in a broader range of soil types andlocations

To verify the operation of theMD we conducted a simpleexperiment we used a mockup landmine with a very littleamount of metal in its construction shown in Figure 4(a)Figure 4(b) shows the metal detector coil placed on thelandmine when it is placed on the surface and undergroundFigures 4(c) and 4(d) show the signal strength from themetaldetector and the standard deviation error when the mockuplandmine is placed at different depths below ground rangingfrom 0 to 100mm directly under the coil of the MD Thestrength of the signals shows that the MD used is able todetect the landmine and isolate it from nonmetallic materialdespite its low metal content

Controllers for a repertoire of low-level behaviors suchas obstacle avoidance wandering or random walk bound-ary following (both physical and virtual boundaries) andmine avoidance were programmed in C++ on each robotThese behaviors are utilized for implementing more complexcoordinated operations for coverage and task allocation onmultiple robots which are described later

33 Graphical User Interface A graphical user interface(GUI) has been designed using Java to interact with a teamof physical robots during a mission of collective detection oflandmines The primary goal of the GUI is to visualize inreal-time the state of a mission including the position andcurrent status of the robots their available battery powerand the location of potential landmines detected by robots asshown in Figure 5(a)The operator can also command robotsto do specific actions through the GUI such as to abort itscurrent operation and navigate to a specific location in theenvironment recall robots to the base station and stop andrestart the robots Figure 5(a) shows a snapshot of an exper-iment involving two physical robots deployed in an indoorenvironment of 35 times 5 square meters and the correspondingstate of theGUIThepaths followed by robots are dynamicallyrecorded and highlighted and the landmine-like objectsdetected by robots are represented with red spots in the GUI

Every two seconds each robot transmits data such asits pose and battery state to the control station Whena landmine-like object is detected the robot sends theestimated position of such object Landmine-like objectsare represented in indoor experiments by red pieces ofpaper detectable by the robotsrsquo camera The communicationbetween the robotsrsquo server and theGUI is established throughTCP ports The robot server periodically updates the state of


Maplocation of robots and mines

Directing robot 1 to new target position

Status of the missionRobot selection

Robot 1rsquos path

Robot 1

Robot 2

Detected mineMonitored mine

RobotMap

Inconclusive mine

RobotsRobot 2 Robot 1

Stop Reset

SummaryRobots deployed 2 Session time 0720Area covered 80

Mines Batteries

Mine detection efficiency

Robo

ts

Left

()

Robots

Mines

Robot coverage efficiency

Num

ber o

f min

es

Mine info

Red EmergencyGreen CoverageBlue DetectingPurple Found objectOrange On missionBlack Idle

Robot 1

Robot 2

444

(a)

Corobot1 Corobot2

Corobot3

Corobotn

Control station(GUI + robot server)

(b)

Figure 5 (a) Snapshot of the COMRADES graphical user interfaceThe image illustrates a panorama of the experimental environment usingtwo Corobot robots After 5 minutes of exploration the robots have detected 4 landmines shown by red circles The path followed by therobots is shown by the green trail (b) Communication architecture of the COMRADE system Dotted lines indicate wireless communicationvia Wi-Fi between the robots and the robot server at the control station

robots to the GUI Each robot receives and transmits datato the robot server located at the control station via Wi-Fias shown in Figure 5(b) Videos showing the operation ofCOMRADES along with its GUI are available at [26]

4 Robot Planning Techniques in COMRADES

Planning techniques form a central part of COMRADES toenable the deployed robots to navigate autonomously andreach objects of interests (potential landmines) while avoid-ing obstacles as well as other robots We consider two cat-egories of planning in COMRADES coverage path planningto ensure that the robots cover the entire free space within theenvironment using their landmine detection sensors whilesearching for landmines and task planning or task allocation

to determine the order inwhich a robot will visit the locationsat which objects of interests have been discovered by otherrobots

41 Distributed Terrain Coverage in COMRADES Coveragepath planning [27] techniques enable robots to plan theirpaths so that they can cover the entire free space of their envi-ronment using their coverage sensors Distributed coveragewith multiple robots offers several advantages over using asingle robot to perform coverage such as reduced time tocomplete coverage and improved robustness against singleor multiple robot failures However a challenging problemin distributed multirobot coverage is to ensure that differentrobots do not impede each otherrsquos movement or robots withthe same set of sensors repeatedly cover the same regionwhile


leaving portions of the environment uncovered Previousapproaches to multirobot distributed coverage assume thatthe environment is decomposed into a cellular or grid-likestructure before deploying the robots [28ndash31] They then usegraph traversal techniques to completely cover the environ-ment Robots sendmessages to each other with their coverageinformation to ensure that they cover disjoint regions In ourresearch we have usedVoronoi partitioning [32] to divide thefree space in the environment into disjoint cells or regionsThe robotsrsquo initial positions are used as the sites for generatingthe partition After partitioning each robot is responsible forcovering the Voronoi region it is situated in This removesthe overhead for avoiding repeated coverage and collisionbetween robots One issue with Voronoi partitioning is thatthe size of the Voronoi regions is dependent on the initialpositions of the robots and a bad initial spatial distribution ofthe robots (eg robots being very close to each other) mightresult in disproportionate regions To alleviate this situationwe propose to use simple dispersion strategies [33] betweenrobots to achieve a well-spaced initial spatial distribu-tion

411 Voronoi Partition Coverage (VPC) Algorithm Themaincontribution of our research on coverage in COMRADESis an algorithm called Voronoi Partition-Based Coverage(VPC) The detailed description of the algorithm is availablein [34] here we provide an overview of the key aspectsof the algorithm In the VPC algorithm each robot firstpartitions the environment into a set of disjoint regions givenby theVoronoi partition of the environment using the robotsrsquoinitial positions [35 36] The robots in the adjacent Voronoiregions of a robot are called its Voronoi neighbors In [37] wehave described a fully distributed technique for computingthe Voronoi partition using communication between a setof robots Once the partitions are determined each robotproceeds to cover the region in which it is situated For thisa robot decomposes the free space of its region using a grid-like cellular decomposition each cell of the grid correspondsto four times footprint size of the robotrsquos coverage tool(landmine detection sensor)

The robot then uses a cellular coverage technique calledSpanning Tree Coverage (STC) [38] to cover the cells(althoughwe have used STC for implementing our algorithmany other single-robot coverage algorithm can be used inconjunction with VPC) The STC algorithm allows the robotto cover successive cells in its direction of motion Whenan obstacle is encountered the robot selects a previouslyuncovered cell from the neighbors of its current cell whilechecking the neighbors in a clockwise direction from itscurrent cell If no free neighboring cell is found (eg robotis in a cave) the robot backtracks to the previous cell fromwhich it had arrived at the current cell The STC algorithmterminates when the robot reaches its start cell by backtrack-ingWhen the robot completes coverage of itsVoronoi regionit broadcasts a coverage completion message to its Voronoineighbors We verified the operation of the VPC algorithmusing Corobot robots on the Webots simulator Figures 6(a)and 6(b) show snapshots from the simulation using 4 robotsin a 20 times 20m2 environment with no obstacles and an

X-shaped obstacle respectively the coverage paths followedby the different robots are marked with colored trails

The VPC algorithm is also robust to failure of individualor a few robots To ensure robustness each robot periodicallyexchanges alive messages with its Voronoi neighbors If anonresponsive neighbor that has not completed its coverageis discovered it is marked as a failed robot The Voronoiregions are recomputed while discarding the failed robotand the Voronoi neighbors of the failed robot then proceedto cover their new Voronoi regions after excluding alreadycovered portions in the region Figure 6(c) shows when therobot with the purple trail fails one of its Voronoi neigh-bors (robot with red trail) takes over and finishes coverageof its unfinished Voronoi region This process ensures thatthe entire environment will be covered as long as at leastone robot remains operational We have also shown analyt-ically that the VPC algorithm ensures complete nonoverlap-ping coverage provided the single-robot coverage algorithmachieves complete nonoverlapping coverage [34]

412 Repartitioning Coverage Algorithm In COMRADESbecause the environment is initially unknown we assumethat the robots are not aware of the location and geometryof obstacles A potential problem while using the VPCalgorithm in such a scenario is that a robot might discoverthat a portion of itsVoronoi region is occluded by obstacles asshown in Figure 7(a)The robot then has to use path planningtechniques to find a path to reach the inaccessible portionsof its Voronoi region such path planning technique caninvolve complex computations [27] and increase the robotsrsquotime and energy requirements To avoid excessive pathplanning costs we investigated an approach that adaptivelyrepartitions regions where coverage is impeded by obstaclesand reallocates the repartitioned portions to other robots thatcan complete the coverage as shown in Figure 7(b)

At the core of our repartitioning approach is an algorithmcalled repartition coverage [39] The main insight of thisalgorithm is that even if the Voronoi region that a robot iscovering gets disconnected due to obstacles because the freespace is connected the inaccessible portion of the regionmust be adjacent to at least one of the neighboring regionsand accessible to the robot in that region Consequentlythe robot performing coverage in the adjacent neighboringregion could be requested to augment its coverage with theinaccessible portion of the disconnected region as shownin Figure 7(b) While using the VPC algorithm if a robotdetermines that it cannot reach portions of its coverageregion due to obstacles it uses an auction-based protocolto systematically repartition and reallocate the inaccessibleregions to other robots We have shown analytically thatthe repartition coverage algorithm guarantees completenonoverlapping coverage and that it converges to terminationwithin a finite number of steps determined by the numberof robots in the environment The performance of the algo-rithm was also verified in Webots for different environmentsand different obstacle geometries to verify its completenessand coverage times for environments of different sizes anddifferent obstacle geometries Some of the results are shownin Figure 8


(a) (b)

(c)

Figure 6 4 robots marked by blue circles cover (a) a 20m times 20m square environment and (b) an X-shaped region within this environmentusing VPC algorithm (c) One robot fails in the same setting as in scenario (a) and an operational robot takes over coverage of the failedrobotrsquos Voronoi region

Initially inaccessibleregions

(a)

Robots reallocated torepartitioned cells

(b)

Figure 7 (a)The Voronoi cells of two robots are partially inaccessible due to obstacles The blue solid arrows show the path taken by a robotto reach the inaccessible portions of its cell using a bug-like path planning algorithm (b) Robots coordinate with each other to repartitionthe initial Voronoi cells so that each robot has a contiguous region to cover


(a) (b) (c)

Figure 8 Snapshots fromWebots showing repartition coverage by 7 robots in a 3times6m2 environmentwith different obstacle features (a) initialVoronoi partition (b) robots performing boundary coverage on Voronoi cell and blacklight blue boundaries show inaccessible regions (c)repartitioned cells and robots completing coverage of entire environment

42 Multirobot Task Allocation in COMRADES In COM-RADES when robots have detected objects of interest theyrequest other robots possibly with other types of sensors tovisit the location of the object and inspect it with their sen-sors Consequently each robot might receive requests to visitobjects of interest at different locations frommultiple robotsTo avoid expending excessive energy and time to visit theselocations and analyze the object the robots need to determinea suitable itinerary for visiting the locations Multirobot taskallocation (MRTA) techniques provide a structured methodto solve this problem how to find a suitable assignment oftasks to robots so that the tasks performed by the robotscan be completed in an efficient manner in terms of timeand energy expended by the robots We consider a categoryof MRTA problems called ST-MR-TA (single task robotmultirobot tasks time-extended assignment) [40] where STstands for single task robots that is each robot is able toexecute at most one task at a time MR means multirobottasks tasks that require multiple robots to be completed andTA means time-extended assignment problems where theinformation to allocate tasks to robots arrives over time Atask in the COMRADES scenario corresponds to a robotvisiting the location of a potential landmine (not necessarilyat the same time as other robots) to analyze the objectusing the robotsrsquo sensorsThe location of potential landminesarrives dynamically as they are detected using the coveragetechniques described in Section 41 MRTA in such a scenariocorresponds to the multiple traveling salesman problem(mTSP) that has been shown to be NP-hard [41] Previouswork in MRTA for ST-MR-TA problem considers local ormarket-based heuristics [42ndash44] In COMRADES we haveused a stochastic queueing-based technique to address theMRTA problem [45 46] Using spatial queueing is attractivefor our ST-MR-TA MRTA problem as it provides a formalframework for distributed decision making by the robotsso that they can respond efficiently to dynamic changesin the task distribution In the next section we give anoverview of a spatial queueing based MRTA algorithm usedin COMRADES details of the algorithm along with extensivesimulation results are available in [47 48]

421 Spatial Queueing for Multirobot Task Allocation Tomotivate our MRTA problem we consider an automatedlandmine detection scenario where a set of robots aredeployed within a bounded 2D environment with potentiallandmines The location of the landmines is not known a

priori Robots are equipped with sensors that are capable ofdetecting landmine-like objects albeit within a certain levelof uncertainty due to sensor noise Robots initially explorethe environment and when a robot finds an object of interestthat could potentially be a landmine it requests other robotspossibly with different sensor types to visit the location ofthe detection and confirm the object on their sensorsWithinthis setting a task corresponds to a set of robots visiting thelocation of an object of interest and recording the objectrsquos sig-nature on their sensors For legibility we have referred to eachrobotrsquos visit to the objectrsquos location and taking its readingas the robot performing its portion of the task Robots canperform a task asynchronously by performing their portionof the task at different times A task is considered to becomplete when a desired number of robots have performedtheir portion of the task Finally tasks can arrive dynamicallyas robots explore the environment and find objects of interestWithin this context the MRTA problem corresponds tofinding a suitable allocation of tasks to robots so that the totaltime required to complete the tasks is reduced

The MRTA problem described above corresponds to theMR-ST-TA setting [42] where MR (multirobot task) denotesthatmultiple robots are required to complete a task ST (singletask robot) denotes each robot can perform a single taskat a time and TA (time-extended assignment) denotes thateach robot can determine and update its schedule or orderof tasks to perform over a finite time window as opposed todetermining the task schedule instantaneously

We consider a set of mobile robots 119877 = 119903119894 119894 =

1 2 119898 that are deployed within a bounded environment119864 sub R2 We assume that each robot is capable of localizingitself with respect to the environment and its pose at anyinstant is given by 120588

119903119894 The environment also contains a set of

tasks 119879 = 120591119894 119894 = 1 2 119899 that are distributed arbitrarily

within the environment the location of task 120591119894is denoted by

120588120591119894 Robot and task positions are initially shared between the

robots and assumed to be common knowledgeThe objectiveof the robots is to visit the location of each task and performcertain operations related to the task We assume that task120591119894requires operations to be performed by 119889

120591119894le |119877| distinct

robots to be completed Because the focus of this paper is onthe task allocation algorithm we assume that techniques forappropriately positioning the robots to perform operations atthe locations of the tasks are already available The distancebetween two tasks 120591

119894and 120591119895 is denoted by 119889

119894119895= 120588120591119894minus 120588120591119895

while the distance between robot 119903119894and task 120591

119895is denoted by


119889119894119895= 120588119903119894minus 120588120591119895 Also we let 1205880

119894

denote the initial position ofrobot 119903

119894and we let 120591

1199031

119894

denote the first task selected by robot119903119894 Within this setting the MRTA problem can be formally

defined as the following

Definition 1 (multirobot task allocation) Given a set of robots119877 and a set of tasks 119879 find a suitable allocation 119860 2

119877

rarr 119879

such that forallR sube 119877 119903119894isinR

min sum

119903119894isin119877

(

10038171003817100381710038171003817100381710038171205880

119903119894

minus 120588120591

1199031

119894

1003817100381710038171003817100381710038171003817+ sum

(120591119895120591119896)isin119860(R)

100381710038171003817100381710038171003817120588120591119895minus 120588120591119896

100381710038171003817100381710038171003817)

subject to 120591119895= 120591119896

forall (120591119895 120591119896) isin 119860 (R)

forallR sube 119877 119903119894isinR forall119903

119894

|119860 (R)| = 119889120591119894

119860 (R) = 120591119894 R sube 119877 forall120591

119894

(1)

The above formulation of the MRTA problem attemptsto find an allocation for each robot such that the distancetraveled by the robots to perform the tasks is minimizedThetwo constraints of the problem ensure that the same task doesnot get allocated to the same robot more than once and thetotal number of robots allocated to perform a task equals thedemand for the task

The solution to the MRTA problem has been shown tobe an instance of the dynamic traveling salesman problemand proven to be NP-hard [49] In this paper we proposea spatial queue-based [50] solution for the MRTA problemusing a heuristic that represents the distances between robotsand tasks as an ordered queue based on the robotsrsquo locationsand intertask distances To achieve this is in a systematicmanner each robot utilizes the following four mathematicalconstructs

(1) Intertask Transition Matrix Intertask distances form thebasis of our method as the objective of the MRTA techniqueis to enable robots to find a suitable schedule or order ofnavigating between tasks so that the total distance traveledby them is reduced The intertask distances are representedas a transition matrix The transition matrix at time step119905 is denoted by 119872(119905) and given by the normalized inverseEuclidean distances between every task pair as shown in

119872(119905) =

[[[[[

[

1205871112058712sdot sdot sdot 1205871119899

1205872112058722sdot sdot sdot 1205872119899

sdot sdot sdot

12058711989911205871198992sdot sdot sdot 120587119899119899

]]]]]

]

(2)

where 120587119894119895= (1119889

119894119895)sum119895 =119894

(1119889119894119895)

Each entry 120587119894119895of 119872(119905) represents the probability of a

robot to select task 120591119895following 120591

119894 based on the distance

between the tasksrsquo locations Note that 120587119894119894= 0 and therefore

the diagonal elements of the matrix are zeros The transitionmatrix values are calculated independently by all robotsInitially the transition matrix is computed for all task pairsbut as time proceeds each robot recalculates the matrix

when it completes a task or when it receives information thata task has been completed by other robots The transitionprobabilities of completed tasks are set to zero and theprobability values in119872(119905) are renormalized

(2) Robot State Vector The state vector of a robot comprisesthe inverse Euclidean distances between the robot and eachtask in the environment The state vector for robot 119894 119881

119903119894 at

time step 119905 is given by

119881119903119894(119905) = (120587

1198941(119905) 1205871198942(119905) 120587

119894119899(119905)) (3)

where 120587119894119895(119905) = 1119889

119894119895(119905) and 119889

119894119895(119905) is the distance between

robot 119903119894and task 120591

119895at time step 119905

(3) Task ProximityVectorThe task proximity vector of a robot119903119894represents its preference for each task 120591

119895in the environment

based on performing task 120591119895first followed by the remaining

tasks It is calculated as the product of the robot 119903119894rsquos state

vector and the intertask transitionmatrixThe task proximityvector for robot 119903


119903119894(119905) is given by

119903119894(119905) = 119881

119903119894(119905) times 119872 (119905) (4)

(4) Robot Spatial Task Queue The spatial task queue of arobot denotes the order in which the robot plans to performthe tasks in the environment It is calculated by removing alltasks from the task proximity vector that are either occupiedor completed and sorting the remaining tasks in descendingorder based on their proximity vector values The task queuefor robot 119903

119894at time step 119905 119876

119903119894(119905) is given by

119876119903119894(119905) = 119902

1 1199022 119902

119899 119902119896ge 119902119896+1 forall119896 119902

119896isin 119903119894(119905) (5)

Robots use the spatial queueing framework to select tasksusing the spatial queueing MRTA (SQ-MRTA) algorithmIn the SQ-MRTA algorithm each robot sorts the availabletasks using (2)ndash(4) The robot then selects the task at thehead of the spatial queue and announces a bid for that taskbased on its cost (distance) to perform that task It then waitsfor a certain time period to receive bids for the same taskfrom other robots If it is the highest bidder and the taskis still available it proceeds to perform the task otherwiseit selects the next available task from its spatial queue andrepeats the bidding process When it finishes performing thetask the robot broadcasts a task performed message Whenrobots receive a task performed message from another robotthat results in the task being completed (sufficient number ofrobots have visited the task) they rebuild their local copy ofthe transition matrix

We verified the performance of the SQ-MRTA (SQ)algorithm and compared it with three state-of-the-art MRTAalgorithms the Hungarian assignment (HA) based algorithm[51] a decentralized greedy (DG) allocation algorithm [47]and the repeated auctions (RA) algorithm [52] As before thealgorithm was implemented on Corobot robots within theWebots simulator We used 5 10 15 or 20 robots with 6 12


2015105

200

400

600

800

1000

Tim

e to

com

plet

e 24

task

s (s)

Number of robots

DGRA

SQHA

(a)

DGRA

SQHA

6 12 18Tasks

24

400

200

600

800

0

(b)

Figure 9 Completion times with fixed task load of 24 tasks for 5 10 15 and 20 robots (a) and with fixed number of 20 robots for 6 12 18and 24 tasks (b) for the compared MRTA approaches

18 or 24 tasks within a 20 times 20m2 environment Each taskwas required to be performed by 3ndash5 robots All results wereaveraged over 10 simulation runs We evaluated differentmetrics including the total time required to complete tasksand the average distance traveled per robot Two illustrativegraphs of our simulations are shown in Figures 9 and 10 InFigure 9 we see that the SQ-MRTA algorithm performs com-parably with the repeated auctions (RA) algorithm For morecombinations of robots and tasks Figure 10 shows that ourSQ-MRTA algorithm performs very closely in comparison tothe repeated auctions (RA) algorithm with their simulationtimes lying plusmn10 of each other On the other hand the HAalgorithmperforms poorly as the numbers of robots and tasksincrease because it assigns robots to tasks based on the initialplacement of robots and tasks delays in robots reaching tasksdue to interrobot collision avoidance are not considered byit while determining the robot to task assignments The DGalgorithm is inefficient in terms of task completion timeswhen the number of tasks greatly outweighs the number ofrobots as it allocates the closest task to a robot and is unableto calculate a suitable schedule when each robot needs toperform multiple tasks

43 Information Aggregation Techniques in COMRADES 2Acentral aspect of multirobot autonomous landmine detectionis to combine the information about the characteristics of apotential landmine fromdifferent types of sensors andmake adecision whether the object is indeed a landmine and identifyits characteristics if it is indeed one Previous researchers[17] have considered this problem from a static viewpointwhere all information about a landminersquos characteristics isassumed to be available and the main concept is to usestatistical inference techniques to classify the landminersquoscharacteristics with accuracy However in COMRADES theprocess of landmine detection is not an instantaneous one

0

05

25

15

1

2

Ratio

of s

imul

atio

n tim

es o

f diff

eren

t alg

orith

ms w

ithre

spec

t to

simul

atio

n tim

e of H

unga

rian

algo

rithm

DG algorithm

RA algorithm SQ-MRTA algorithm

5R 6

T

5R 1

8T5R

24T

10R

6T

10R

12T

10R

18T

10R

24T

15R

6T

15R

12T

15R

18T

15R

24T

20R

6T

20R

12T

20R

18T

20R

24T

5R 1

2T

Robot task combinations

Figure 10 Competitive ratio of simulation times using the Hun-garian method as the baseline Different robot and task numbersrsquocombinations used are shown on the 119909-axis

it continues over a period of time during which robots withappropriate sensors corresponding to a potential landminersquosinitially perceived characteristics need to be deployed tothe potential landminersquos location so that the cumulativeinformation gathered by the robotsrsquo sensors can improve theaccuracy of the landminersquos detection Because of this dynamicnature of landmine detection we consider the followingmultisensor information aggregation and sensor schedulingproblem in COMRADES given an initial signature perceivedby a certain type of sensor from a potential landmine whichis an appropriate set of sensors (robots) to deploy additionally


Sche

dulin

g de

cisio

n

Belief in objectbeing landmine(calculatedusing Bayesianinference

past beliefs)

Reportcalculatedusing exp

mechanismusing market‐based scoring

rule

Robotsensor scheduling

algorithm

Decisionmaker agent

Agg belief(from last time step)

Weightage of reports humanfrom sensor expert based on

Object(landmine)

Exp reward

Strategy

Senseddata

Belief

Report

Weight

Reports fromother agents

(sensors)

Sensor agent 1 Market maker agent

Bayesianinferenceand exp

maximization

Aggbelief

environment and operationalconditions

conditioned onutility

maximization

Prediction market

Aggregation

utility

bat

ra1t

Bt

Figure 11 Weightage of sensor reports from human expert based on environment and operational conditions

Mine Metallicobject

Nonmetallicobject

0

10

20

30

40

50

60

70

80

90

100

110

Object type

Cos

t

MDIR

GPR

(a)

0 1 2 3 4 5 6 7 8 9 100

01

02

03

04

05

Number of time steps

Aver

age R

MSE

MD

GPR

IR

(b)

Figure 12 (a) Cost to classify different types of objects mines andmetal but not mine and nonmetal using different types of sensors Relativecosts of sensing using MD IR and GPR were assumed to be in the ratio of 1 2 4 (b) Root mean square error from different types of sensorswhen used individually over time at the same object of interest Note that although using MDs along has a low cost their RMSE is higher(accuracy is lower)

to the location of the potential landmine so that the landmineis detected with higher accuracy Details of the operation ofthe information aggregation technique along with analyticaland experimental results of its performance are given in[53] we provide an overview of its main features and a fewsignificant results in the next section

To solve the information aggregation and sensor schedul-ing problem in COMRADES we have proposed a noveltechnique that uses a market-based information aggregation

mechanism called a prediction market Each robot participat-ing in the landmine detection task is provided with a softwareagent that uses the sensory input of the robot from a potentiallandmine and performs the calculations of the predictionmarket technique A schematic describing the technique isshown in Figure 11 When an agent records readings from apotential landmine on its sensors it associates a probabilityvalue called a belief 119887119886119905 to denote the agentrsquos confidence inidentifying the sensed object as a landmine The beliefs are


0 1 2 3 401

015

02

025

03

035

04

045

05

055


Aver

age R

MSE

MD

(a)

0 1 2 3 4 50

01

02

03

04

05


Aver

age R

MSE

MD

GPR

(b)

0 1 2 3 4 5 6 7 80

005

01

015

02

025

03

035

04

045

05


Aver

age R

MSE

MD

IR

GPR

(c)

0 05 1 15 2 25 3 35 4 45 50

01

02

03

04

05

06


Aver

age R

MSE

MD

IR

GPR

(d)

Figure 13 Average RMSE in the environment with 5MD sensors (a) 5MD and 1GPR sensor (b) 5MD 1 IR and 1GPR sensors (c) and2MD 2 IR and 2GPR sensors (d)

conditioned over past belief values to prevent wide variationsfrom the objectrsquos previous readings due to sensor noise orambient conditions using a Bayesian network Each agentthen strategically calculates a sensor report 119903119886119905 from itsbelief and expected rewards from making the report usinga utility maximization technique It then submits this reportto a central location called the aggregator or market makeragentThe information aggregation or fusion is implementedusing the aggregationmechanism that uses a technique calleda logarithmic market scoring rule (LMSR) This techniqueuses a utility-based formulation of the costs and value to eachsensor (robot) for identifying an object of interest as a land-mine It then assigns a score or virtual reward to each sensor(robot) if it correctly reports the probability distribution overthe different types of objects of interests such as landminemetal but not landmine and not landmine The details ofthis technique are given in [53] The aggregation mechanism

outputs a single aggregated belief value 119861119905 The aggregationmechanism also selectively includes weights of the sensorreports from a human expert about the accuracy of the sen-sorsrsquo reports based on the ambient conditions of the sensorsThe aggregated belief value is then passed on to a decisionmaker agent that makes decisions about which other robots(sensor types) should be deployed to the potential landminersquoslocation using a Bayesian inferencing based technique so thatthe landmine can be confirmed rapidly and accurately [53]

We simulated our algorithm using three different typesof sensors MD GPR and IR-based multisensor device Weperformed different experiments with data from differenttypes of sources (metallic low-metallic and nonmetallic)collected by different sensors at different times A fewexperimental results of our algorithm while using identicaldata distributions and settings are highlighted in Figures 12ndash14 Figure 12 shows the relative costs of deploying the sensors


0 2 4 6 8 100

005

01

015

02

025

03

035

04

045

05


RMSE

PM

D-S

DDF

(a)

0 2 4 6 8 10minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5


NM

SE

PM

D-S

DDF

(b)

0 2 4 6 8 10minus016

minus014

minus012

minus01

minus008

minus006

minus004

minus002

0


Info

rmat

ion

gain

PM

D-S

DDF

(c)

Figure 14 Comparsion between our prediction market-based information aggregation and Dempster-Shafer theory based fusion (DS) anddistributed fata fusion (DDF) (a) root mean square error (b) normalized root mean square error and (c) information gainThe results showthat over time the PM-based technique is able to perform better than the compared techniques

and the corresponding root mean square errors (RMSE)from the readings when using one type of sensor Figures13(a)ndash13(d) show the effect of deploying multiple sensors ofdifferent types over time For these experiments the data wasassumed to arrive from the same source object of interestDifferent sets of sensors were deployed over 7 time steps Wenotice that while using 5MDs (in Figure 13(a)) the RMSEreduces to 20 in 4 time steps but with a combination ofMD IR and GPR (in Figure 13(d)) the combined RMSEfrom the fused data from these sensors is reduced muchmore to around 6 Finally Figures 14(a)ndash14(c) illustratethe comparison of our proposed prediction market-basedtechniques for information aggregation with two techniquesThe results show that the information fusion performed using

our technique reduces the RMSE by 5ndash13 as comparedto a previously studied technique for landmine data fusionusing the Dempster-Shafer theory [17] and by 3ndash8 usingdistributed data fusion technique [54] We also conductedseveral experiments to test the effect of various parametersin our model and we found that using the combination ofdifferent sensors in the environment gives the best accuracyfor the objectrsquos type identification

5 Conclusions and Future Direction

In this paper we have described our experience with theCOMRADE system for autonomous landmine detectionusing multiple robots We have customized a Coroware


Explorer robot with a metal detector to detect landminesand performed tests with it on different terrains We havealso addressed various aspects of landmine detection such asmultirobot search and coverage multirobot task allocationand multisensor data fusion using different algorithms andvalidated our results using simulated indoor Corobot robots

As future work we are looking at several directions toimprove our proposed techniques Integration of awider suiteof sensor devices such as thermal sensors GPRs and chemi-cal sensors on outdoor robot platforms and test of the correctcombination of sensors for different ambient conditions suchas ambient temperature sunlight depth of landmines is anongoing work in our research We are also investigatingways to improve our coverage algorithm by sharing mapsbetween robots planning coverage paths based on expectedinformation gain about landmines and improved informa-tion fusion techniques for combining data from multiplesensors Finally we are also looking at using aerial robotsto help ground moving robots navigate more intelligently inthe environment Overall we envisage that our research willlay the foundation for further research and proliferation ofmultirobot systems for landmine detection nuclear sourcedetection unmanned search and rescue emergency responseservices and other high-risk applications

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The COMRADES project was supported by the US Office ofNaval Research Grant no N000140911174

References

[1] M Hiznay ldquoLandmine monitor reportrdquo Tech Rep 2011[2] M Acheroy ldquoMine action status of sensor technology for close-

in and remote detection of antipersonnel minesrdquo in Proceed-ings of the 3rd InternationalWorkshop onAdvancedGround Pen-etrating Radar (IWAGPR rsquo05) pp 3ndash13 May 2005

[3] M K Habib ldquoHumanitarian demining reality and the chal-lenge of technologymdashthe state of the artsrdquo International Journalof Advanced Robotic Systems vol 4 no 2 pp 151ndash172 2007

[4] H Stefan ldquoSome robotic approaches and technologiesforhumanitarian deminingrdquo in Humanitarian Demining K HMaki Ed InTech Open Access Publishing Vienna Austria2008

[5] P Debenest E F Fukushima Y Tojo and S Hirose ldquoA newapproach to humanitarian deminingrdquo Autonomous Robots vol18 no 3 pp 323ndash336 2005

[6] M Freese P Debenest E F Fukushima and S Hirose ldquoDevel-opment of deminer-assisting robotic tools at tokyo instituteof technologyrdquo in Humanitarian Demining M K Habib EdInTech Open Access Publishing Vienna Austria 2008

[7] Y Mori ldquoPeace an excavation-type demining robot for anti-personnel minesrdquo in Humanitarian Demining K H Maki EdInTech Open Access Publishing Vienna Austria 2008

[8] S Havlik ldquoLand robotic vehicles for deminingrdquo in Humanitar-ian Demining M K Habib Ed InTechOpen 2008

[9] S Masunaga and K Nonami ldquoControlled metal detectormounted on mine detection robotrdquo International Journal ofAdvanced Robotic Systems vol 4 no 2 pp 207ndash218 2007

[10] T Fukada Y Hasegawa Y Kawai S Sato Z Zyada and T Mat-suno ldquoGPR signal processingwith geography adaptive scanningusing vector radar for antipersonal landmine detectionrdquo Inter-national Journal of Advanced Robotic Systems vol 4 no 2 pp199ndash206 2007

[11] C Ratto P Torrione K Morton and L Collins ldquoContext-dependent landmine detection with ground-penetrating radarusing a hidden Markov context modelrdquo in Proceedings of the30th IEEE International Geoscience and Remote Sensing Sympo-sium (IGARSS rsquo10) pp 4192ndash4195 Honolulu Hawaii USA July2010

[12] E D Breejen K Schutte and F Cremer ldquoSensor fusion foranti personnel landmine detection a case studyrdquo in Proceedingsof the Detection and Remediation Technologies for Mines andMinelike Targets IV vol 3710 pp 1235ndash1245 April 1999

[13] S Bermudez i Badia U Bernardet A Guanella P Pyk and PF M J Verschure ldquoA biologically based chemo-sensing UAVfor humanitarian deminingrdquo International Journal of AdvancedRobotic Systems vol 4 no 2 pp 187ndash198 2007

[14] X Feng and M Sato ldquoLandmine imaging by a hand-heldGPR and metal detector sensor (ALIS)rdquo in Proceedings of theIEEE International Geoscience and Remote Sensing Symposium(IGARSS rsquo05) vol 1 IEEE July 2005

[15] P Verlinde M Acheroy G Nesti and A Sieber ldquoPreparingthe Joint Multi-sensor Mine-signatures project database fordata fusionrdquo in Proceedings of the International Geoscience andRemote Sensing Symposium (IGARSS rsquo01) vol 7 pp 3240ndash3242July 2001

[16] I Bloch N Milisavljevic and M Acheroy ldquoMultisensor datafusion for spaceborne and airborne reduction ofmine suspectedareasrdquo International Journal of Advanced Robotic Systems vol 4no 2 pp 173ndash186 2007

[17] N Milisavljevic and I Bloch ldquoSensor fusion in anti-personnelmine detection using a two-level belief function modelrdquo IEEETransactions on Systems Man and Cybernetics Part C Applica-tions and Reviews vol 33 no 2 pp 269ndash283 2003

[18] M Y Rachkov L Marques and A T De Almeida ldquoMultisensordemining robotrdquoAutonomous Robots vol 18 no 3 pp 275ndash2912005

[19] H Frigui L Zhang P Gader J N Wilson K C Ho and AMendez-Vazquez ldquoAn evaluation of several fusion algorithmsfor anti-tank landmine detection and discriminationrdquo Informa-tion Fusion vol 13 no 2 pp 161ndash174 2012

[20] 2015 httpwwwfp7-tiramisueu[21] J PradoG Cabrita and LMarques ldquoBayesian sensor fusion for

land-mine detection using a dual-sensor hand-held devicerdquo inProceedings of the 39th Annual Conference of the IEEE IndustrialElectronics Society (IECON rsquo13) pp 3887ndash3892 November 2013

[22] J Ishikawa K Furuta and N Pavkovic ldquoTest and evaluationof Japanese GPR-EMI dual sensor systems at the Benkovactest site in Croatiardquo in Anti-Personnel Landmine Detection forHumanitarian Demining K Furuta and J Ishikawa Eds pp63ndash81 Springer London UK 2009

[23] F A El Bakkoush ldquoCurrent research activities for landminedetection by nuclear technique in libyardquo 2009

[24] P Santana J Barata H Cruz AMestre J Lisboa and L FloresldquoAmulti-robot system for landmine detectionrdquo inProceedings ofthe 10th IEEE International Conference onEmerging Technologies


and Factory Automation (ETFA rsquo05) pp 721ndash728 September2005

[25] M Long A Gage R Murphy and K Valavanis ldquoApplication ofthe distributed field robot architecture to a simulated deminingtaskrdquo in Proceedings of the IEEE International Conference onRobotics and Automation pp 3193ndash3200 April 2005

[26] August 2014 httpcmanticunomahaeduprojectscomrades[27] H Choset W Burgard S Hutchinson et al Principles of Robot

Motion Theory Algorithms and Implementation MIT PressCambridge Mass USA 2005

[28] N Hazon and G A Kaminka ldquoOn redundancy efficiency androbustness in coverage for multiple robotsrdquo Robotics and Auto-nomous Systems vol 56 no 12 pp 1102ndash1114 2008

[29] S Hert andV Lumelsky ldquoPolygon area decomposition formult-iple-robot workspace divisionrdquo International Journal of Compu-tational Geometry and Applications vol 8 no 4 pp 437ndash4661998

[30] I Rekleitis A P New E S Rankin and H Choset ldquoEffi-cient Boustrophedon multi-robot coverage an algorithmicapproachrdquoAnnals ofMathematics and Artificial Intelligence vol52 no 2ndash4 pp 109ndash142 2008

[31] X Zheng S Koenig D Kempe and S Jain ldquoMultirobotforest coverage for weighted and unweighted terrainrdquo IEEETransactions on Robotics vol 26 no 6 pp 1018ndash1031 2010

[32] A Okabe B Boots K Sugihara and S N Chiu Spatial Tessella-tions Concepts and Applications of Voronoi Diagrams WileySeries in Probability and Statistics John Wiley amp Sons Chich-ester UK 2nd edition 2000

[33] M A Batalin and G S Sukhatme ldquoSpreading out a localapproach to multi-robot coveragerdquo in Proceedings of the 6thInternational Symposium on Distributed Autonomous RoboticSystems pp 373ndash382 2002

[34] KGuruprasad ZWilson andPDasgupta ldquoComplete coverageof an initially unknown environment by multiple robots usingvoronoi partitionrdquo in Proceedings of the 2nd International Con-ference on Advances in Control and Optimization of DynamicalSystems (ACODS 12) Bangalore India 2012

[35] J Cortes SMartınez T Karatas and F Bullo ldquoCoverage controlfor mobile sensing networksrdquo IEEE Transactions on Roboticsand Automation vol 20 no 2 pp 243ndash255 2004

[36] J W Durham R Carli P Frasca and F Bullo ldquoDiscrete parti-tioning and coverage control for gossiping robotsrdquo IEEE Trans-actions on Robotics vol 28 no 2 pp 364ndash378 2012

[37] K R Guruprasad and P Dasgupta ldquoDistributed Voronoi par-titioning for multi-robot systems with limited range sensorsrdquoin Proceedings of the 25th IEEERSJ International Conferenceon Robotics and Intelligent Systems (IROS rsquo12) pp 3546ndash3552Vilamoura Portugal October 2012

[38] Y Gabriely and E Rimon ldquoSpanning-tree based coverage ofcontinuous areas by amobile robotrdquoAnnals ofMathematics andArtificial Intelligence vol 31 no 1ndash4 pp 77ndash98 2001

[39] K Hungerford P Dasgupta and K R Guruprasad ldquoDis-tributed complete multi-robot coverage of initially unknownenvironments using repartitioningrdquo in Proceedings of the 13thInternational Confernece on Autonomous Agents and Multi-Agent Systems (AAMAS rsquo14) pp 1453ndash1454 2014

[40] B P Gerkey andM JMataric ldquoA formal analysis and taxonomyof task allocation in multi-robot systemsrdquo The InternationalJournal of Robotics Research vol 23 no 9 pp 939ndash954 2004

[41] P Oberlin S Rathinam and S Darbha ldquoA transformation fora heterogeneous multiple depot multiple traveling salesman

problemrdquo in Proceedings of the American Control Conference(ACC rsquo09) pp 1292ndash1297 June 2009

[42] B P Gerkey andM JMataric ldquoA formal analysis and taxonomyof task allocation in multi-robot systemsrdquo International Journalof Robotics Research vol 23 no 9 pp 939ndash954 2004

[43] M BDias R Zlot NKalra andA Stentz ldquoMarket-basedmult-irobot coordination a survey and analysisrdquo Proceedings of theIEEE vol 94 no 7 pp 1257ndash1270 2006

[44] L Liu and D Shell ldquoA distributable and computation-flexibleassignment algorithm from local task swapping to globaloptimalityrdquo in Proceedings of the Robotics Science and Systemspp 33ndash41 2012

[45] X Huang and R F Serfozo ldquoSpatial queueing processesrdquoMath-ematics of Operations Research vol 24 no 4 pp 865ndash886 1999

[46] F Bullo E Frazzoli M Pavone K Savla and S L SmithldquoDynamic vehicle routing for robotic systemsrdquo Proceedings ofthe IEEE vol 99 no 9 pp 1482ndash1504 2011

[47] A M Melendez P Dasgupta and W Lenagh ldquoA stochasticqueueing model for multi-robot task allocationrdquo in Proceedingsof the 9th International Conference on Informatics in ControlAutomation and Robotics (ICINCO 12) pp 256ndash261 2012

[48] W Lenagh Multi-robot task allocation a spatial queue-ing approach [MS thesis] University of Nebraska OmahaNebraska 2013

[49] P Dasgupta ldquoMulti-robot task allocation for performing coop-erative foraging tasks in an initially unknown environmentrdquo inInnovations in Defense Support Systemsmdash2 L Jain Ed pp 5ndash20 Springer 2011

[50] L Breuer ldquoSpatial queues with infinitely many serversrdquo in FromMarkov Jump Processes to Spatial Queues pp 119ndash138 SpringerDordrecht The Netherlands 2003

[51] H W Kuhn ldquoThe Hungarian method for the assignment prob-lemrdquo Naval Research Logistics Quarterly vol 2 no 1-2 pp 83ndash97 1955

[52] L Luo N Chakraborty and K Sycara ldquoDistributed algorithmdesign for multi-robot generalized task assignment problemrdquoin Proceedings of the 26th IEEERSJ International Conferenceon Intelligent Robots and Systems (IROS rsquo13) pp 4765ndash4771November 2013

[53] J Jumadinova and P Dasgupta ldquoMultirobot autonomouslandmine detection using distributed multisensor informationaggregationrdquo in Multisensor Multisource Information FusionArchitectures Algorithms and Applications vol 8407 of Pro-ceedings of the SPIE pp 1ndash12 Baltimore Md USA April 2012

[54] J Manyika and H Durrant-Whyte Data Fusion and SensorManagement A Decentralized Information-Theoretic ApproachPrentice Hall Upper Saddle River NJ USA 1995

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



from different techniques for coverage task allocation andmultisensor information aggregation and sensor schedulingusingmultiple robots thatwe have developed as part of COM-RADES Specifically we describe the following aspects ofmultirobot autonomous landmine detection inCOMRADES

(i) A distributed area coverage technique allows a set ofrobots to dynamically partition an initially unknownenvironment into a set of nonoverlapping regionsand search for landmines within each region Thetechniques are robust to individual robot failures andare able to scale with the number of robots and size ofthe environment

(ii) A distributed information fusion technique aggre-gates landmine-related sensor information from dif-ferent robots using a prediction market-based tech-nique and a decision making technique that uses thefused information to allocate additional robots (sen-sors) to rapidly classify the object

(iii) A multirobot task allocation (MRTA) technique usesa spatial queueing model that enables a set of robotsto determine a suitable order or perform a set oflandmine detection related tasks while reducing thetime and energy spent in performing the tasks

To realize the above techniques we have customizedcommercially available all-terrain robots called CorowareExplorer with a metal detector to enable them to detectmetallic objects including landminesWehave also developeda user interface that allows shared autonomy between robotsand humans Humans can visualize information about thehealth and status of the robots and their progress in thelandmine detection operation on a control station and selec-tively supersede their autonomous operations by remotelycontrolling themovement and some operations of the robotsWe have verified the operation of the robots in differenttypes of outdoor terrain and different operational conditionsWe have also used indoor robots called Coroware Corobotswhich have very similar features to the outdoor Explorerrobots both in simulation and within an indoor arena to testthe different techniques used in COMRADES Our resultsshow that our proposed techniques offer suitable meansto rapidly perform autonomous landmine detection withinexpensive robots

The rest of our paper is structured as follows In thenext section we provide an overview of existing research onrobotic landmine detection In Section 3 we describe themain features of our proposed system the robots and thelandmine detector used and the user interface The speci-fic algorithms techniques and results related to the threemain technical aspects of COMRADES distributed area cov-erage distributed task allocation and information fusion areaddressed in Section 4 andfinallywe discuss future directionsof our work and conclude

2 Related Work

Autonomous landmine detection using robotic systems hasbeen an active research topic over the past decade Excellent

reviews of the state-of-the-art techniques in robotic landminedetection are available in [2 3] The research in this topiccan be divided into three major directions designing robotsattached with suitable sensor devices to detect and possiblyextract landmines developing data and information fusiontechniques to improve the accuracy of detecting landminesand computational techniques to coordinate multiple robotsand present the information collected by the robots in astructured and visualizable format to a human supervisor

Much of the recent research on autonomous landminedetection has been concentrated on developing robotic sys-tems for detecting landminesmost of these systems consist ofa single robot attached with appropriate sensors for landminedetection For example some of these robots include a mech-anism mounted on small robot platforms to flail the groundand detonate landmines along with vegetation clearing tools[4] Many deployed robotic systems for landmine detectionrely on teleoperation rather than autonomy Examples of suchsystems include a remote operated vehicle called MR-2 theenhanced teleoperated ordnance disposal system (ETODS)andTEMPEST robotThese robots benefit from the improvedprecision in detecting and neutralizing landmines due to ahumanrsquos presence in the loop but they require humans to bein the vicinity of landmines to teleoperate the vehicle Laterimprovements to some of these systems such as the MR-2have added partial autonomy in navigation and increasedthe teleoperation range to 5 km using feedback sensorsIn contrast to these larger robots researchers have alsoinvestigated smaller robots that are highly agile and havea small footprint and low weight to reduce the risk ofaccidental explosion of a landmine Examples of such robotsare the Ares Shrimps Pemexs Dervishs and Tridem robotsand legged robots such as the AMRU Shadow Deminer andCOMET [3] Despite their agility smaller robots are limitedin the weight of sensors that they can carry on board andare not suited for heavier more robust sensors like groundpenetrating radar (GPR) or large-coil metal detectors Toaccommodate such sensors robots such as the Titan [5]Gryphon [6] mine detection robot and mine hunter vehicle(MHV) [3] have been developedMost of the robots discussedabove are for detecting and locating landmines In contrastthe PEACE robot [7] and amechanical hand called theMine-hand [6] have been developed mainly to excavate detectedlandmines Researchers have also proposed unmanned aerialvehicles (UAVs) in landmine detecting robotic systems toaid in terrain mapping before deploying ground robots [2]or to unobtrusively detect landmines using a conceptualsystem of sensors attached to cables suspended from UAVs[8]

For detecting landmines a wide variety of sensors includ-ing metal detectors (MD) [9] ground penetrating radar(GPR) [10 11] infrared cameras [12] and chemical sensorsfor detecting plumes emanating from landmines [13] havebeen proposed For most research as well as commerciallydeployed applications metal detectors either individually orin combination with GPR [6 14] are the sensors of choice asthey provide reasonably accurate source localization and arerelatively straightforward to acquire as off-the-shelf compo-nents and integrate on robots For this reason we have used






















low-risk region






from landmines


Go

Go

Go

GoStop

Informationfilters

Logs

Analysistools




Detect

Team


Robot withGPR

Unnavigableregion

Control station


GPS

IMU

Laser rangefinder


system

(a)

Webcam

Stargazer

IR sensors

(b)




(a) (b)

0 20 40 60 80 1000

200

400

600

800

1000

1200

Depth (mm)

Met

al d

etec

tor d

ata (

raw

dat

a)

99680

38773

18241 16078 12241 10445

(c)

0 20 40 60 80 1000

05

1

15

2

25

3

35

4

Depth (mm)

Stan

dard

dev

iatio

n er

ror

326303

351323

306328

(d)











Robot 1rsquos path

Robot 1

Robot 2


RobotMap

Inconclusive mine


Stop Reset


Mines Batteries


Robo

ts

Left

()

Robots

Mines


Num

ber o

f min

es

Mine info


Robot 1

Robot 2

444

(a)

Corobot1 Corobot2

Corobot3

Corobotn


(b)
















(a) (b)

(c)



(a)


(b)



(a) (b) (c)













120591119894le |119877| distinct


119894and 120591119895 is denoted by 119889

119894119895= 120588120591119894minus 120588120591119895


119895is denoted by


119889119894119895= 120588119903119894minus 120588120591119895 Also we let 1205880

119894


119894and we let 120591

1199031

119894




119877

rarr 119879


min sum

119903119894isin119877

(

10038171003817100381710038171003817100381710038171205880

119903119894

minus 120588120591

1199031

119894

1003817100381710038171003817100381710038171003817+ sum

(120591119895120591119896)isin119860(R)

100381710038171003817100381710038171003817120588120591119895minus 120588120591119896

100381710038171003817100381710038171003817)

subject to 120591119895= 120591119896

forall (120591119895 120591119896) isin 119860 (R)


119894

|119860 (R)| = 119889120591119894

119860 (R) = 120591119894 R sube 119877 forall120591

119894

(1)




119872(119905) =

[[[[[

[

1205871112058712sdot sdot sdot 1205871119899

1205872112058722sdot sdot sdot 1205872119899

sdot sdot sdot

12058711989911205871198992sdot sdot sdot 120587119899119899

]]]]]

]

(2)

where 120587119894119895= (1119889

119894119895)sum119895 =119894

(1119889119894119895)








119903119894 at


119881119903119894(119905) = (120587

1198941(119905) 1205871198942(119905) 120587

119894119899(119905)) (3)

where 120587119894119895(119905) = 1119889

119894119895(119905) and 119889


robot 119903119894and task 120591








119903119894(119905) is given by

119903119894(119905) = 119881

119903119894(119905) times 119872 (119905) (4)


119894at time step 119905 119876

119903119894(119905) is given by

119876119903119894(119905) = 119902

1 1199022 119902

119899 119902119896ge 119902119896+1 forall119896 119902

119896isin 119903119894(119905) (5)




2015105

200

400

600

800

1000

Tim

e to

com

plet

e 24

task

s (s)

Number of robots

DGRA

SQHA

(a)

DGRA

SQHA

6 12 18Tasks

24

400

200

600

800

0

(b)




0

05

25

15

1

2

Ratio

of s

imul

atio

n tim

es o

f diff

eren

t alg

orith

ms w

ithre

spec

t to

simul

atio

n tim

e of H

unga

rian

algo

rithm

DG algorithm


5R 6

T

5R 1

8T5R

24T

10R

6T

10R

12T

10R

18T

10R

24T

15R

6T

15R

12T

15R

18T

15R

24T

20R

6T

20R

12T

20R

18T

20R

24T

5R 1

2T





Sche

dulin

g de

cisio

n


past beliefs)



rule


algorithm

Decisionmaker agent



Object(landmine)

Exp reward

Strategy

Senseddata

Belief

Report

Weight


(sensors)



maximization

Aggbelief



maximization

Prediction market

Aggregation

utility

bat

ra1t

Bt


Mine Metallicobject

Nonmetallicobject

0

10

20

30

40

50

60

70

80

90

100

110

Object type

Cos

t

MDIR

GPR

(a)

0 1 2 3 4 5 6 7 8 9 100

01

02

03

04

05


Aver

age R

MSE

MD

GPR

IR

(b)






0 1 2 3 401

015

02

025

03

035

04

045

05

055


Aver

age R

MSE

MD

(a)

0 1 2 3 4 50

01

02

03

04

05


Aver

age R

MSE

MD

GPR

(b)

0 1 2 3 4 5 6 7 80

005

01

015

02

025

03

035

04

045

05


Aver

age R

MSE

MD

IR

GPR

(c)

0 05 1 15 2 25 3 35 4 45 50

01

02

03

04

05

06


Aver

age R

MSE

MD

IR

GPR

(d)






0 2 4 6 8 100

005

01

015

02

025

03

035

04

045

05


RMSE

PM

D-S

DDF

(a)

0 2 4 6 8 10minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5


NM

SE

PM

D-S

DDF

(b)

0 2 4 6 8 10minus016

minus014

minus012

minus01

minus008

minus006

minus004

minus002

0


Info

rmat

ion

gain

PM

D-S

DDF

(c)











Acknowledgment


References




























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation






























low-risk region






from landmines


Go

Go

Go

GoStop

Informationfilters

Logs

Analysistools




Detect

Team


Robot withGPR

Unnavigableregion

Control station


GPS

IMU

Laser rangefinder


system

(a)

Webcam

Stargazer

IR sensors

(b)




(a) (b)

0 20 40 60 80 1000

200

400

600

800

1000

1200

Depth (mm)

Met

al d

etec

tor d

ata (

raw

dat

a)

99680

38773

18241 16078 12241 10445

(c)

0 20 40 60 80 1000

05

1

15

2

25

3

35

4

Depth (mm)

Stan

dard

dev

iatio

n er

ror

326303

351323

306328

(d)











Robot 1rsquos path

Robot 1

Robot 2


RobotMap

Inconclusive mine


Stop Reset


Mines Batteries


Robo

ts

Left

()

Robots

Mines


Num

ber o

f min

es

Mine info


Robot 1

Robot 2

444

(a)

Corobot1 Corobot2

Corobot3

Corobotn


(b)
















(a) (b)

(c)



(a)


(b)



(a) (b) (c)













120591119894le |119877| distinct


119894and 120591119895 is denoted by 119889

119894119895= 120588120591119894minus 120588120591119895


119895is denoted by


119889119894119895= 120588119903119894minus 120588120591119895 Also we let 1205880

119894


119894and we let 120591

1199031

119894




119877

rarr 119879


min sum

119903119894isin119877

(

10038171003817100381710038171003817100381710038171205880

119903119894

minus 120588120591

1199031

119894

1003817100381710038171003817100381710038171003817+ sum

(120591119895120591119896)isin119860(R)

100381710038171003817100381710038171003817120588120591119895minus 120588120591119896

100381710038171003817100381710038171003817)

subject to 120591119895= 120591119896

forall (120591119895 120591119896) isin 119860 (R)


119894

|119860 (R)| = 119889120591119894

119860 (R) = 120591119894 R sube 119877 forall120591

119894

(1)




119872(119905) =

[[[[[

[

1205871112058712sdot sdot sdot 1205871119899

1205872112058722sdot sdot sdot 1205872119899

sdot sdot sdot

12058711989911205871198992sdot sdot sdot 120587119899119899

]]]]]

]

(2)

where 120587119894119895= (1119889

119894119895)sum119895 =119894

(1119889119894119895)








119903119894 at


119881119903119894(119905) = (120587

1198941(119905) 1205871198942(119905) 120587

119894119899(119905)) (3)

where 120587119894119895(119905) = 1119889

119894119895(119905) and 119889


robot 119903119894and task 120591








119903119894(119905) is given by

119903119894(119905) = 119881

119903119894(119905) times 119872 (119905) (4)


119894at time step 119905 119876

119903119894(119905) is given by

119876119903119894(119905) = 119902

1 1199022 119902

119899 119902119896ge 119902119896+1 forall119896 119902

119896isin 119903119894(119905) (5)




2015105

200

400

600

800

1000

Tim

e to

com

plet

e 24

task

s (s)

Number of robots

DGRA

SQHA

(a)

DGRA

SQHA

6 12 18Tasks

24

400

200

600

800

0

(b)




0

05

25

15

1

2

Ratio

of s

imul

atio

n tim

es o

f diff

eren

t alg

orith

ms w

ithre

spec

t to

simul

atio

n tim

e of H

unga

rian

algo

rithm

DG algorithm


5R 6

T

5R 1

8T5R

24T

10R

6T

10R

12T

10R

18T

10R

24T

15R

6T

15R

12T

15R

18T

15R

24T

20R

6T

20R

12T

20R

18T

20R

24T

5R 1

2T





Sche

dulin

g de

cisio

n


past beliefs)



rule


algorithm

Decisionmaker agent



Object(landmine)

Exp reward

Strategy

Senseddata

Belief

Report

Weight


(sensors)



maximization

Aggbelief



maximization

Prediction market

Aggregation

utility

bat

ra1t

Bt


Mine Metallicobject

Nonmetallicobject

0

10

20

30

40

50

60

70

80

90

100

110

Object type

Cos

t

MDIR

GPR

(a)

0 1 2 3 4 5 6 7 8 9 100

01

02

03

04

05


Aver

age R

MSE

MD

GPR

IR

(b)






0 1 2 3 401

015

02

025

03

035

04

045

05

055


Aver

age R

MSE

MD

(a)

0 1 2 3 4 50

01

02

03

04

05


Aver

age R

MSE

MD

GPR

(b)

0 1 2 3 4 5 6 7 80

005

01

015

02

025

03

035

04

045

05


Aver

age R

MSE

MD

IR

GPR

(c)

0 05 1 15 2 25 3 35 4 45 50

01

02

03

04

05

06


Aver

age R

MSE

MD

IR

GPR

(d)






0 2 4 6 8 100

005

01

015

02

025

03

035

04

045

05


RMSE

PM

D-S

DDF

(a)

0 2 4 6 8 10minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5


NM

SE

PM

D-S

DDF

(b)

0 2 4 6 8 10minus016

minus014

minus012

minus01

minus008

minus006

minus004

minus002

0


Info

rmat

ion

gain

PM

D-S

DDF

(c)











Acknowledgment


References




























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) (b)

0 20 40 60 80 1000

200

400

600

800

1000

1200

Depth (mm)

Met

al d

etec

tor d

ata (

raw

dat

a)

99680

38773

18241 16078 12241 10445

(c)

0 20 40 60 80 1000

05

1

15

2

25

3

35

4

Depth (mm)

Stan

dard

dev

iatio

n er

ror

326303

351323

306328

(d)











Robot 1rsquos path

Robot 1

Robot 2


RobotMap

Inconclusive mine


Stop Reset


Mines Batteries


Robo

ts

Left

()

Robots

Mines


Num

ber o

f min

es

Mine info


Robot 1

Robot 2

444

(a)

Corobot1 Corobot2

Corobot3

Corobotn


(b)
















(a) (b)

(c)



(a)


(b)



(a) (b) (c)













120591119894le |119877| distinct


119894and 120591119895 is denoted by 119889

119894119895= 120588120591119894minus 120588120591119895


119895is denoted by


119889119894119895= 120588119903119894minus 120588120591119895 Also we let 1205880

119894


119894and we let 120591

1199031

119894




119877

rarr 119879


min sum

119903119894isin119877

(

10038171003817100381710038171003817100381710038171205880

119903119894

minus 120588120591

1199031

119894

1003817100381710038171003817100381710038171003817+ sum

(120591119895120591119896)isin119860(R)

100381710038171003817100381710038171003817120588120591119895minus 120588120591119896

100381710038171003817100381710038171003817)

subject to 120591119895= 120591119896

forall (120591119895 120591119896) isin 119860 (R)


119894

|119860 (R)| = 119889120591119894

119860 (R) = 120591119894 R sube 119877 forall120591

119894

(1)




119872(119905) =

[[[[[

[

1205871112058712sdot sdot sdot 1205871119899

1205872112058722sdot sdot sdot 1205872119899

sdot sdot sdot

12058711989911205871198992sdot sdot sdot 120587119899119899

]]]]]

]

(2)

where 120587119894119895= (1119889

119894119895)sum119895 =119894

(1119889119894119895)








119903119894 at


119881119903119894(119905) = (120587

1198941(119905) 1205871198942(119905) 120587

119894119899(119905)) (3)

where 120587119894119895(119905) = 1119889

119894119895(119905) and 119889


robot 119903119894and task 120591








119903119894(119905) is given by

119903119894(119905) = 119881

119903119894(119905) times 119872 (119905) (4)


119894at time step 119905 119876

119903119894(119905) is given by

119876119903119894(119905) = 119902

1 1199022 119902

119899 119902119896ge 119902119896+1 forall119896 119902

119896isin 119903119894(119905) (5)




2015105

200

400

600

800

1000

Tim

e to

com

plet

e 24

task

s (s)

Number of robots

DGRA

SQHA

(a)

DGRA

SQHA

6 12 18Tasks

24

400

200

600

800

0

(b)




0

05

25

15

1

2

Ratio

of s

imul

atio

n tim

es o

f diff

eren

t alg

orith

ms w

ithre

spec

t to

simul

atio

n tim

e of H

unga

rian

algo

rithm

DG algorithm


5R 6

T

5R 1

8T5R

24T

10R

6T

10R

12T

10R

18T

10R

24T

15R

6T

15R

12T

15R

18T

15R

24T

20R

6T

20R

12T

20R

18T

20R

24T

5R 1

2T





Sche

dulin

g de

cisio

n


past beliefs)



rule


algorithm

Decisionmaker agent



Object(landmine)

Exp reward

Strategy

Senseddata

Belief

Report

Weight


(sensors)



maximization

Aggbelief



maximization

Prediction market

Aggregation

utility

bat

ra1t

Bt


Mine Metallicobject

Nonmetallicobject

0

10

20

30

40

50

60

70

80

90

100

110

Object type

Cos

t

MDIR

GPR

(a)

0 1 2 3 4 5 6 7 8 9 100

01

02

03

04

05


Aver

age R

MSE

MD

GPR

IR

(b)






0 1 2 3 401

015

02

025

03

035

04

045

05

055


Aver

age R

MSE

MD

(a)

0 1 2 3 4 50

01

02

03

04

05


Aver

age R

MSE

MD

GPR

(b)

0 1 2 3 4 5 6 7 80

005

01

015

02

025

03

035

04

045

05


Aver

age R

MSE

MD

IR

GPR

(c)

0 05 1 15 2 25 3 35 4 45 50

01

02

03

04

05

06


Aver

age R

MSE

MD

IR

GPR

(d)






0 2 4 6 8 100

005

01

015

02

025

03

035

04

045

05


RMSE

PM

D-S

DDF

(a)

0 2 4 6 8 10minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5


NM

SE

PM

D-S

DDF

(b)

0 2 4 6 8 10minus016

minus014

minus012

minus01

minus008

minus006

minus004

minus002

0


Info

rmat

ion

gain

PM

D-S

DDF

(c)











Acknowledgment


References




























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













Robot 1rsquos path

Robot 1

Robot 2


RobotMap

Inconclusive mine


Stop Reset


Mines Batteries


Robo

ts

Left

()

Robots

Mines


Num

ber o

f min

es

Mine info


Robot 1

Robot 2

444

(a)

Corobot1 Corobot2

Corobot3

Corobotn


(b)
















(a) (b)

(c)



(a)


(b)



(a) (b) (c)













120591119894le |119877| distinct


119894and 120591119895 is denoted by 119889

119894119895= 120588120591119894minus 120588120591119895


119895is denoted by


119889119894119895= 120588119903119894minus 120588120591119895 Also we let 1205880

119894


119894and we let 120591

1199031

119894




119877

rarr 119879


min sum

119903119894isin119877

(

10038171003817100381710038171003817100381710038171205880

119903119894

minus 120588120591

1199031

119894

1003817100381710038171003817100381710038171003817+ sum

(120591119895120591119896)isin119860(R)

100381710038171003817100381710038171003817120588120591119895minus 120588120591119896

100381710038171003817100381710038171003817)

subject to 120591119895= 120591119896

forall (120591119895 120591119896) isin 119860 (R)


119894

|119860 (R)| = 119889120591119894

119860 (R) = 120591119894 R sube 119877 forall120591

119894

(1)




119872(119905) =

[[[[[

[

1205871112058712sdot sdot sdot 1205871119899

1205872112058722sdot sdot sdot 1205872119899

sdot sdot sdot

12058711989911205871198992sdot sdot sdot 120587119899119899

]]]]]

]

(2)

where 120587119894119895= (1119889

119894119895)sum119895 =119894

(1119889119894119895)








119903119894 at


119881119903119894(119905) = (120587

1198941(119905) 1205871198942(119905) 120587

119894119899(119905)) (3)

where 120587119894119895(119905) = 1119889

119894119895(119905) and 119889


robot 119903119894and task 120591








119903119894(119905) is given by

119903119894(119905) = 119881

119903119894(119905) times 119872 (119905) (4)


119894at time step 119905 119876

119903119894(119905) is given by

119876119903119894(119905) = 119902

1 1199022 119902

119899 119902119896ge 119902119896+1 forall119896 119902

119896isin 119903119894(119905) (5)




2015105

200

400

600

800

1000

Tim

e to

com

plet

e 24

task

s (s)

Number of robots

DGRA

SQHA

(a)

DGRA

SQHA

6 12 18Tasks

24

400

200

600

800

0

(b)




0

05

25

15

1

2

Ratio

of s

imul

atio

n tim

es o

f diff

eren

t alg

orith

ms w

ithre

spec

t to

simul

atio

n tim

e of H

unga

rian

algo

rithm

DG algorithm


5R 6

T

5R 1

8T5R

24T

10R

6T

10R

12T

10R

18T

10R

24T

15R

6T

15R

12T

15R

18T

15R

24T

20R

6T

20R

12T

20R

18T

20R

24T

5R 1

2T





Sche

dulin

g de

cisio

n


past beliefs)



rule


algorithm

Decisionmaker agent



Object(landmine)

Exp reward

Strategy

Senseddata

Belief

Report

Weight


(sensors)



maximization

Aggbelief



maximization

Prediction market

Aggregation

utility

bat

ra1t

Bt


Mine Metallicobject

Nonmetallicobject

0

10

20

30

40

50

60

70

80

90

100

110

Object type

Cos

t

MDIR

GPR

(a)

0 1 2 3 4 5 6 7 8 9 100

01

02

03

04

05


Aver

age R

MSE

MD

GPR

IR

(b)






0 1 2 3 401

015

02

025

03

035

04

045

05

055


Aver

age R

MSE

MD

(a)

0 1 2 3 4 50

01

02

03

04

05


Aver

age R

MSE

MD

GPR

(b)

0 1 2 3 4 5 6 7 80

005

01

015

02

025

03

035

04

045

05


Aver

age R

MSE

MD

IR

GPR

(c)

0 05 1 15 2 25 3 35 4 45 50

01

02

03

04

05

06


Aver

age R

MSE

MD

IR

GPR

(d)






0 2 4 6 8 100

005

01

015

02

025

03

035

04

045

05


RMSE

PM

D-S

DDF

(a)

0 2 4 6 8 10minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5


NM

SE

PM

D-S

DDF

(b)

0 2 4 6 8 10minus016

minus014

minus012

minus01

minus008

minus006

minus004

minus002

0


Info

rmat

ion

gain

PM

D-S

DDF

(c)











Acknowledgment


References




























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


















(a) (b)

(c)



(a)


(b)



(a) (b) (c)













120591119894le |119877| distinct


119894and 120591119895 is denoted by 119889

119894119895= 120588120591119894minus 120588120591119895


119895is denoted by


119889119894119895= 120588119903119894minus 120588120591119895 Also we let 1205880

119894


119894and we let 120591

1199031

119894




119877

rarr 119879


min sum

119903119894isin119877

(

10038171003817100381710038171003817100381710038171205880

119903119894

minus 120588120591

1199031

119894

1003817100381710038171003817100381710038171003817+ sum

(120591119895120591119896)isin119860(R)

100381710038171003817100381710038171003817120588120591119895minus 120588120591119896

100381710038171003817100381710038171003817)

subject to 120591119895= 120591119896

forall (120591119895 120591119896) isin 119860 (R)


119894

|119860 (R)| = 119889120591119894

119860 (R) = 120591119894 R sube 119877 forall120591

119894

(1)




119872(119905) =

[[[[[

[

1205871112058712sdot sdot sdot 1205871119899

1205872112058722sdot sdot sdot 1205872119899

sdot sdot sdot

12058711989911205871198992sdot sdot sdot 120587119899119899

]]]]]

]

(2)

where 120587119894119895= (1119889

119894119895)sum119895 =119894

(1119889119894119895)








119903119894 at


119881119903119894(119905) = (120587

1198941(119905) 1205871198942(119905) 120587

119894119899(119905)) (3)

where 120587119894119895(119905) = 1119889

119894119895(119905) and 119889


robot 119903119894and task 120591








119903119894(119905) is given by

119903119894(119905) = 119881

119903119894(119905) times 119872 (119905) (4)


119894at time step 119905 119876

119903119894(119905) is given by

119876119903119894(119905) = 119902

1 1199022 119902

119899 119902119896ge 119902119896+1 forall119896 119902

119896isin 119903119894(119905) (5)




2015105

200

400

600

800

1000

Tim

e to

com

plet

e 24

task

s (s)

Number of robots

DGRA

SQHA

(a)

DGRA

SQHA

6 12 18Tasks

24

400

200

600

800

0

(b)




0

05

25

15

1

2

Ratio

of s

imul

atio

n tim

es o

f diff

eren

t alg

orith

ms w

ithre

spec

t to

simul

atio

n tim

e of H

unga

rian

algo

rithm

DG algorithm


5R 6

T

5R 1

8T5R

24T

10R

6T

10R

12T

10R

18T

10R

24T

15R

6T

15R

12T

15R

18T

15R

24T

20R

6T

20R

12T

20R

18T

20R

24T

5R 1

2T





Sche

dulin

g de

cisio

n


past beliefs)



rule


algorithm

Decisionmaker agent



Object(landmine)

Exp reward

Strategy

Senseddata

Belief

Report

Weight


(sensors)



maximization

Aggbelief



maximization

Prediction market

Aggregation

utility

bat

ra1t

Bt


Mine Metallicobject

Nonmetallicobject

0

10

20

30

40

50

60

70

80

90

100

110

Object type

Cos

t

MDIR

GPR

(a)

0 1 2 3 4 5 6 7 8 9 100

01

02

03

04

05


Aver

age R

MSE

MD

GPR

IR

(b)






0 1 2 3 401

015

02

025

03

035

04

045

05

055


Aver

age R

MSE

MD

(a)

0 1 2 3 4 50

01

02

03

04

05


Aver

age R

MSE

MD

GPR

(b)

0 1 2 3 4 5 6 7 80

005

01

015

02

025

03

035

04

045

05


Aver

age R

MSE

MD

IR

GPR

(c)

0 05 1 15 2 25 3 35 4 45 50

01

02

03

04

05

06


Aver

age R

MSE

MD

IR

GPR

(d)






0 2 4 6 8 100

005

01

015

02

025

03

035

04

045

05


RMSE

PM

D-S

DDF

(a)

0 2 4 6 8 10minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5


NM

SE

PM

D-S

DDF

(b)

0 2 4 6 8 10minus016

minus014

minus012

minus01

minus008

minus006

minus004

minus002

0


Info

rmat

ion

gain

PM

D-S

DDF

(c)











Acknowledgment


References




























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) (b) (c)













120591119894le |119877| distinct


119894and 120591119895 is denoted by 119889

119894119895= 120588120591119894minus 120588120591119895


119895is denoted by


119889119894119895= 120588119903119894minus 120588120591119895 Also we let 1205880

119894


119894and we let 120591

1199031

119894




119877

rarr 119879


min sum

119903119894isin119877

(

10038171003817100381710038171003817100381710038171205880

119903119894

minus 120588120591

1199031

119894

1003817100381710038171003817100381710038171003817+ sum

(120591119895120591119896)isin119860(R)

100381710038171003817100381710038171003817120588120591119895minus 120588120591119896

100381710038171003817100381710038171003817)

subject to 120591119895= 120591119896

forall (120591119895 120591119896) isin 119860 (R)


119894

|119860 (R)| = 119889120591119894

119860 (R) = 120591119894 R sube 119877 forall120591

119894

(1)




119872(119905) =

[[[[[

[

1205871112058712sdot sdot sdot 1205871119899

1205872112058722sdot sdot sdot 1205872119899

sdot sdot sdot

12058711989911205871198992sdot sdot sdot 120587119899119899

]]]]]

]

(2)

where 120587119894119895= (1119889

119894119895)sum119895 =119894

(1119889119894119895)








119903119894 at


119881119903119894(119905) = (120587

1198941(119905) 1205871198942(119905) 120587

119894119899(119905)) (3)

where 120587119894119895(119905) = 1119889

119894119895(119905) and 119889


robot 119903119894and task 120591








119903119894(119905) is given by

119903119894(119905) = 119881

119903119894(119905) times 119872 (119905) (4)


119894at time step 119905 119876

119903119894(119905) is given by

119876119903119894(119905) = 119902

1 1199022 119902

119899 119902119896ge 119902119896+1 forall119896 119902

119896isin 119903119894(119905) (5)




2015105

200

400

600

800

1000

Tim

e to

com

plet

e 24

task

s (s)

Number of robots

DGRA

SQHA

(a)

DGRA

SQHA

6 12 18Tasks

24

400

200

600

800

0

(b)




0

05

25

15

1

2

Ratio

of s

imul

atio

n tim

es o

f diff

eren

t alg

orith

ms w

ithre

spec

t to

simul

atio

n tim

e of H

unga

rian

algo

rithm

DG algorithm


5R 6

T

5R 1

8T5R

24T

10R

6T

10R

12T

10R

18T

10R

24T

15R

6T

15R

12T

15R

18T

15R

24T

20R

6T

20R

12T

20R

18T

20R

24T

5R 1

2T





Sche

dulin

g de

cisio

n


past beliefs)



rule


algorithm

Decisionmaker agent



Object(landmine)

Exp reward

Strategy

Senseddata

Belief

Report

Weight


(sensors)



maximization

Aggbelief



maximization

Prediction market

Aggregation

utility

bat

ra1t

Bt


Mine Metallicobject

Nonmetallicobject

0

10

20

30

40

50

60

70

80

90

100

110

Object type

Cos

t

MDIR

GPR

(a)

0 1 2 3 4 5 6 7 8 9 100

01

02

03

04

05


Aver

age R

MSE

MD

GPR

IR

(b)






0 1 2 3 401

015

02

025

03

035

04

045

05

055


Aver

age R

MSE

MD

(a)

0 1 2 3 4 50

01

02

03

04

05


Aver

age R

MSE

MD

GPR

(b)

0 1 2 3 4 5 6 7 80

005

01

015

02

025

03

035

04

045

05


Aver

age R

MSE

MD

IR

GPR

(c)

0 05 1 15 2 25 3 35 4 45 50

01

02

03

04

05

06


Aver

age R

MSE

MD

IR

GPR

(d)






0 2 4 6 8 100

005

01

015

02

025

03

035

04

045

05


RMSE

PM

D-S

DDF

(a)

0 2 4 6 8 10minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5


NM

SE

PM

D-S

DDF

(b)

0 2 4 6 8 10minus016

minus014

minus012

minus01

minus008

minus006

minus004

minus002

0


Info

rmat

ion

gain

PM

D-S

DDF

(c)











Acknowledgment


References




























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










119889119894119895= 120588119903119894minus 120588120591119895 Also we let 1205880

119894


119894and we let 120591

1199031

119894




119877

rarr 119879


min sum

119903119894isin119877

(

10038171003817100381710038171003817100381710038171205880

119903119894

minus 120588120591

1199031

119894

1003817100381710038171003817100381710038171003817+ sum

(120591119895120591119896)isin119860(R)

100381710038171003817100381710038171003817120588120591119895minus 120588120591119896

100381710038171003817100381710038171003817)

subject to 120591119895= 120591119896

forall (120591119895 120591119896) isin 119860 (R)


119894

|119860 (R)| = 119889120591119894

119860 (R) = 120591119894 R sube 119877 forall120591

119894

(1)




119872(119905) =

[[[[[

[

1205871112058712sdot sdot sdot 1205871119899

1205872112058722sdot sdot sdot 1205872119899

sdot sdot sdot

12058711989911205871198992sdot sdot sdot 120587119899119899

]]]]]

]

(2)

where 120587119894119895= (1119889

119894119895)sum119895 =119894

(1119889119894119895)








119903119894 at


119881119903119894(119905) = (120587

1198941(119905) 1205871198942(119905) 120587

119894119899(119905)) (3)

where 120587119894119895(119905) = 1119889

119894119895(119905) and 119889


robot 119903119894and task 120591








119903119894(119905) is given by

119903119894(119905) = 119881

119903119894(119905) times 119872 (119905) (4)


119894at time step 119905 119876

119903119894(119905) is given by

119876119903119894(119905) = 119902

1 1199022 119902

119899 119902119896ge 119902119896+1 forall119896 119902

119896isin 119903119894(119905) (5)




2015105

200

400

600

800

1000

Tim

e to

com

plet

e 24

task

s (s)

Number of robots

DGRA

SQHA

(a)

DGRA

SQHA

6 12 18Tasks

24

400

200

600

800

0

(b)




0

05

25

15

1

2

Ratio

of s

imul

atio

n tim

es o

f diff

eren

t alg

orith

ms w

ithre

spec

t to

simul

atio

n tim

e of H

unga

rian

algo

rithm

DG algorithm


5R 6

T

5R 1

8T5R

24T

10R

6T

10R

12T

10R

18T

10R

24T

15R

6T

15R

12T

15R

18T

15R

24T

20R

6T

20R

12T

20R

18T

20R

24T

5R 1

2T





Sche

dulin

g de

cisio

n


past beliefs)



rule


algorithm

Decisionmaker agent



Object(landmine)

Exp reward

Strategy

Senseddata

Belief

Report

Weight


(sensors)



maximization

Aggbelief



maximization

Prediction market

Aggregation

utility

bat

ra1t

Bt


Mine Metallicobject

Nonmetallicobject

0

10

20

30

40

50

60

70

80

90

100

110

Object type

Cos

t

MDIR

GPR

(a)

0 1 2 3 4 5 6 7 8 9 100

01

02

03

04

05


Aver

age R

MSE

MD

GPR

IR

(b)






0 1 2 3 401

015

02

025

03

035

04

045

05

055


Aver

age R

MSE

MD

(a)

0 1 2 3 4 50

01

02

03

04

05


Aver

age R

MSE

MD

GPR

(b)

0 1 2 3 4 5 6 7 80

005

01

015

02

025

03

035

04

045

05


Aver

age R

MSE

MD

IR

GPR

(c)

0 05 1 15 2 25 3 35 4 45 50

01

02

03

04

05

06


Aver

age R

MSE

MD

IR

GPR

(d)






0 2 4 6 8 100

005

01

015

02

025

03

035

04

045

05


RMSE

PM

D-S

DDF

(a)

0 2 4 6 8 10minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5


NM

SE

PM

D-S

DDF

(b)

0 2 4 6 8 10minus016

minus014

minus012

minus01

minus008

minus006

minus004

minus002

0


Info

rmat

ion

gain

PM

D-S

DDF

(c)











Acknowledgment


References




























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










2015105

200

400

600

800

1000

Tim

e to

com

plet

e 24

task

s (s)

Number of robots

DGRA

SQHA

(a)

DGRA

SQHA

6 12 18Tasks

24

400

200

600

800

0

(b)




0

05

25

15

1

2

Ratio

of s

imul

atio

n tim

es o

f diff

eren

t alg

orith

ms w

ithre

spec

t to

simul

atio

n tim

e of H

unga

rian

algo

rithm

DG algorithm


5R 6

T

5R 1

8T5R

24T

10R

6T

10R

12T

10R

18T

10R

24T

15R

6T

15R

12T

15R

18T

15R

24T

20R

6T

20R

12T

20R

18T

20R

24T

5R 1

2T





Sche

dulin

g de

cisio

n


past beliefs)



rule


algorithm

Decisionmaker agent



Object(landmine)

Exp reward

Strategy

Senseddata

Belief

Report

Weight


(sensors)



maximization

Aggbelief



maximization

Prediction market

Aggregation

utility

bat

ra1t

Bt


Mine Metallicobject

Nonmetallicobject

0

10

20

30

40

50

60

70

80

90

100

110

Object type

Cos

t

MDIR

GPR

(a)

0 1 2 3 4 5 6 7 8 9 100

01

02

03

04

05


Aver

age R

MSE

MD

GPR

IR

(b)






0 1 2 3 401

015

02

025

03

035

04

045

05

055


Aver

age R

MSE

MD

(a)

0 1 2 3 4 50

01

02

03

04

05


Aver

age R

MSE

MD

GPR

(b)

0 1 2 3 4 5 6 7 80

005

01

015

02

025

03

035

04

045

05


Aver

age R

MSE

MD

IR

GPR

(c)

0 05 1 15 2 25 3 35 4 45 50

01

02

03

04

05

06


Aver

age R

MSE

MD

IR

GPR

(d)






0 2 4 6 8 100

005

01

015

02

025

03

035

04

045

05


RMSE

PM

D-S

DDF

(a)

0 2 4 6 8 10minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5


NM

SE

PM

D-S

DDF

(b)

0 2 4 6 8 10minus016

minus014

minus012

minus01

minus008

minus006

minus004

minus002

0


Info

rmat

ion

gain

PM

D-S

DDF

(c)











Acknowledgment


References




























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Sche

dulin

g de

cisio

n


past beliefs)



rule


algorithm

Decisionmaker agent



Object(landmine)

Exp reward

Strategy

Senseddata

Belief

Report

Weight


(sensors)



maximization

Aggbelief



maximization

Prediction market

Aggregation

utility

bat

ra1t

Bt


Mine Metallicobject

Nonmetallicobject

0

10

20

30

40

50

60

70

80

90

100

110

Object type

Cos

t

MDIR

GPR

(a)

0 1 2 3 4 5 6 7 8 9 100

01

02

03

04

05


Aver

age R

MSE

MD

GPR

IR

(b)






0 1 2 3 401

015

02

025

03

035

04

045

05

055


Aver

age R

MSE

MD

(a)

0 1 2 3 4 50

01

02

03

04

05


Aver

age R

MSE

MD

GPR

(b)

0 1 2 3 4 5 6 7 80

005

01

015

02

025

03

035

04

045

05


Aver

age R

MSE

MD

IR

GPR

(c)

0 05 1 15 2 25 3 35 4 45 50

01

02

03

04

05

06


Aver

age R

MSE

MD

IR

GPR

(d)






0 2 4 6 8 100

005

01

015

02

025

03

035

04

045

05


RMSE

PM

D-S

DDF

(a)

0 2 4 6 8 10minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5


NM

SE

PM

D-S

DDF

(b)

0 2 4 6 8 10minus016

minus014

minus012

minus01

minus008

minus006

minus004

minus002

0


Info

rmat

ion

gain

PM

D-S

DDF

(c)











Acknowledgment


References




























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 1 2 3 401

015

02

025

03

035

04

045

05

055


Aver

age R

MSE

MD

(a)

0 1 2 3 4 50

01

02

03

04

05


Aver

age R

MSE

MD

GPR

(b)

0 1 2 3 4 5 6 7 80

005

01

015

02

025

03

035

04

045

05


Aver

age R

MSE

MD

IR

GPR

(c)

0 05 1 15 2 25 3 35 4 45 50

01

02

03

04

05

06


Aver

age R

MSE

MD

IR

GPR

(d)






0 2 4 6 8 100

005

01

015

02

025

03

035

04

045

05


RMSE

PM

D-S

DDF

(a)

0 2 4 6 8 10minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5


NM

SE

PM

D-S

DDF

(b)

0 2 4 6 8 10minus016

minus014

minus012

minus01

minus008

minus006

minus004

minus002

0


Info

rmat

ion

gain

PM

D-S

DDF

(c)











Acknowledgment


References




























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 2 4 6 8 100

005

01

015

02

025

03

035

04

045

05


RMSE

PM

D-S

DDF

(a)

0 2 4 6 8 10minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5


NM

SE

PM

D-S

DDF

(b)

0 2 4 6 8 10minus016

minus014

minus012

minus01

minus008

minus006

minus004

minus002

0


Info

rmat

ion

gain

PM

D-S

DDF

(c)











Acknowledgment


References




























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














Acknowledgment


References




























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Research Article The COMRADE System for Multirobot ...

Documents

Transcript of Research Article The COMRADE System for Multirobot ...