Exploiting Robotic Swarm Characteristics for Adversarial Subversion in

31 Pages·2017·3.31 MB·English

Exploiting Robotic Swarm
Characteristics for Adversarial
Subversion in Coverage Tasks
NavyataSanghvi
CMU-RI-TR-17-60
August2017
Submittedinpartialfulfillmentoftherequirementsforthedegreeof
MasterofScienceinRobotics
RoboticsInstitute
CarnegieMellonUniversity
Pittsburgh,Pennsylvania15213
ThesisCommittee:
KatiaSycara,Chair
MaximLikhachev
SasankaNagavalli
Copyright(cid:13)c 2017NavyataSanghvi
For my parents
Abstract
Multi-robotsystems, suchasswarms, withlargenumberofmembersthatareho-
mogeneousandanonymousarerobusttodeletionandadditionofmembers. However,
thesesamepropertiesthatmakethesystemrobust,createvulnerabilitiesundercertain
circumstances. Inthiswork,westudysuchacase,namelytheinsertionbyadversarial
agents,calledmoles,thatsubverttheperformanceofthesystem. Theadversarymon-
itorstheswarm’smovementsduringsurveillanceoperationsforthepresenceofholes,
i.e. areasthatwereleftuncoveredbytheswarm. Theadversarythenaddsmolesthat
getpositionedintheswarm,insuchawayastodeceivetheswarmsregardingtheexis-
tenceofholesandthuspreventingtheswarmfromdiscoveringandrepairingtheholes.
This problem has significant military applications. Our contributions are as follows:
First,tothebestofourknowledge,thisisthefirstpaperthatstudiesthisproblem. Sec-
ond,weprovideaformalizationoftheproblem. Third,weprovideseveralalgorithms,
and characterizethem formallyand also experimentally. Finally, based ondeveloped
theoryandalgorithms, wepresentadynamicscenarioanddescribeadversarycontrol
lawstoleveragetheidentifiedswarmvulnerability.
I
Acknowledgements
I would like to begin by thanking my advisor, Professor Katia Sycara, for her
unerring guidance and enthusiasm. Her passion for the field of swarm robotics, as
well as her constant advice and insights have created for me a novel, exciting and
highlyinterestingjourneyinroboticsresearch. Throughallthetriumphsandfailures
accompanyingthisforay,Iamhonoredtohavehadhervastknowledgeandinvariable
supportbymyside.
IwouldalsoliketothankSasankaNagavalli,whoseexperienceandkeenintellect
havebothbeenaninspirationaswellasasteadyinghand.Hehasspentcountlesshours
with me on insightful discussions which have helped me overcome many a stressful
timeandhavealwayssteeredmyresearchinnew,fulfillingdirections.
IwouldliketothankmycommitteememberProfessorMaximLikhachevforinter-
estingquestionsandcomments,andtheopportunitytohavehisexperiencedjudgment
tocritiqueandbettermywork. IwouldliketothankProfessorNilanjanChakraborty,
ProfessorMichael Lewisand ChangjooNam fortheirexpert adviceduring manylab
meetings. I would also like to thank other members of our lab, Wenhao Luo, She-
hzamanKhatib, AnqiLi, JimitGandhi, and Ramitha Sundarformanyconversations,
lotsofhelp,laughterandsharing-in-strifeduringbothstudyandwork. Ithasbeenan
invaluableexperiencetowork,learnandgrowwiththisbunch.
Finally, I would like to express my endless thanks to my family and parents for
theirmanysacrifices,long-distancesupport,love,cheers,andboundlessfaith.
II
Contents
1 Introduction 1
2 RelatedWork 2
3 ProblemFormulation 2
3.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
3.2 ProblemStatement . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
4 Algorithms 5
4.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
4.1.1 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . 5
4.1.2 MoleAgentsperCitizenAgent . . . . . . . . . . . . . . . . 6
4.1.3 Input,OutputandConstraints . . . . . . . . . . . . . . . . . 8
4.2 RandomScatterAlgorithm . . . . . . . . . . . . . . . . . . . . . . . 8
4.3 GridSearchAlgorithm . . . . . . . . . . . . . . . . . . . . . . . . . 8
4.3.1 MoleAgentInsertion . . . . . . . . . . . . . . . . . . . . . . 8
4.3.2 ProtrusionsGridSearchInsertion . . . . . . . . . . . . . . . 10
4.3.3 RandomizedGridSearchInsertion . . . . . . . . . . . . . . . 11
4.4 DiscreteArcCoverAlgorithm . . . . . . . . . . . . . . . . . . . . . 13
4.4.1 AlgorithmDescription . . . . . . . . . . . . . . . . . . . . . 13
4.4.2 Greedyversion . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.4.3 BoundsonSub-optimality . . . . . . . . . . . . . . . . . . . 14
4.5 ContinuousArcCoverAlgorithm. . . . . . . . . . . . . . . . . . . . 15
4.5.1 AlgorithmDescription . . . . . . . . . . . . . . . . . . . . . 15
4.5.2 Greedyversion . . . . . . . . . . . . . . . . . . . . . . . . . 16
5 AlgorithmResultsandDiscussion 16
5.1 CharacteristicsComparison . . . . . . . . . . . . . . . . . . . . . . . 16
5.2 AlgorithmAdvantage . . . . . . . . . . . . . . . . . . . . . . . . . . 17
5.3 Run-timeRatio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
5.4 OverallObservations . . . . . . . . . . . . . . . . . . . . . . . . . . 19
6 DynamicProblem 19
7 ConclusionsandFutureWork 23
III
1 Introduction
In recent years, there has been significant interest in distributed multi-robot systems
whosemembersactbasedoninformationacquiredthroughlocalsensingand/orcom-
municationwithotherrobotsintheirspatialneighborhood. Whentheselocalinterac-
tions result in global collective behaviors (e.g. rendezvous, flocking, dispersion), the
systemisknownasaroboticswarm[3,11]. Roboticswarmsarecomposedofalarge
numberofagents thatarehomogeneous. Additionally, swarms arerobusttoaddition
orsubtractionofagents, whichgivesthemthebeneficialpropertiesofscalabilityand
robustnesstoindividualrobotfailure. However, thesesamecharacteristicsalsomake
theswarmvulnerabletomanipulationbyagentsthatcouldbeinsertedintotheswarm
byanadversaryforthepurposeofsubvertingtheswarm’sperformance.
Swarms have great potential for many applications including search and rescue,
environmental monitoring, exploration, reconnaissance and surveillance. Particularly
formilitaryapplications,theyhavethepotentialtobeanexcellentassetwhenemployed
by allied forces or a dangerous threat when used by enemies. Robotic swarms are
envisionedtobecomposedofrelativelyinexpensive(evendisposable)robotssuchas
commercially available quadrotors that only cost tens or hundreds of dollars, which
makes them easily accessible to many parties — even those with limited monetary
resources. Based on current trends [16], [14], it is reasonable to expect that robotic
swarmswillcontinuetodecreaseincost. Thus,ithasbeenargued[17]inthemilitary
literature that when defending against a hostile swarm, it is not cost-effective to use
traditionalmeanstodisruptordestroytheswarm(e.g.ammunitionexpendedtodestroy
swarmmaybemoreexpensivethanswarmitself). Inthesesituations,abetterstrategy
wouldbetoexploitswarmvulnerabilitiestoinsertadversarialagentsforthepurposeof
disruptingswarmperformance,withtheaddedadvantagethattheenemystillthinksits
swarmworkscorrectly. Studyingsuchdeceptionstrategiesisalsonecessarytoguide
developmentofcounter-measuresagainstdisruptionofswarmbehaviorbyadversarial
agentsinfriendlyswarms.
Inthiswork, westudyascenarioinwhichahostileswarmisperformingsurveil-
lanceoperations. Eachrobotintheswarmisassumedtohaverange-limitedcommuni-
cationandsensing.Apointintheenvironmentisconsidered“covered”forsurveillance
ifitiswithinthesensingdiskofanyswarmrobot. Astheswarmrobotsslowlymove
ensuring that they maintain communication connectivity, holes in coverage dynami-
cally appear. The detection of “coverage” holes in sensor networks using both topo-
logicalapproaches[9]andmetricapproaches[20,12]hasbeenstudiedintheliterature
[1]. OneapproachbasedonlocalizedVoronoidiagrams[22]requiresonlylocalinfor-
mationandone-hopcommunicationbetweenmembersinthesensornetwork, soitis
particularlyapplicabletoswarmsandweassumetheswarmunderstudyusesthisap-
proach. Bymonitoringtheswarm’smovements,ourgoalistoperiodicallyidentifythe
numberandlocationwhereadversarial“mole”agentsmustbeinsertedintothehostile
swarmtopreventitsoriginal“citizen”agentsfromdetectinganyholesincoverage.
This research makes the following contributions. First, to the best of our knowl-
edge,thisisthefirstworkthatstudiesthisproblem.Second,weprovideaformalization
oftheproblem. Third,weprovideseveralalgorithms,andcharacterizethemformally
and also experimentally. In Section 3, we formalize this problem. In Section 4, we
1
present and characterize several algorithms to find the required number of moles and
their insertion locations. In Section 5, we present simulation results and discuss the
effectivenessofeachalgorithm. Finally,inSection6wedescribeadynamicscenario
andadversarycontrollawsbasedonthedevelopedtheoryandalgorithms.
2 Related Work
The problem of coverage hole discovery in sensor networks has been widely studied
intheliterature[1,21]. Avarietyofapproachestocoverageholediscoveryhavebeen
consideredforbothstaticandmobilenetworksincludingthosebasedoncomputational
geometry[22,12]andtopology[9,8]. Computationalgeometryapproachestypically
involvecomputingtheVoronoidiagram[2]andthen(formobilesensornetworks)fol-
lowingasimplemotionruletoheuristicallyminimizecoverageholes[20](e.g.moving
towardsthefurthestVoronoivertex,minimizingthemaximumdistanceofanypointto
thenearestVoronoivertex).Topologicalapproachesmakeminimalmetricassumptions
(e.g.theabilitytodistinguish‘near’and‘far’neighbors)andthenuseonlyinformation
basedontheconnectivityofthesensinggraphstofindandrepairholes[7]. Whilethe
previous literature has studied hole discovery, we study the novel problem of how to
placeagentstopreventholediscovery.
Whilethereissignificantliteratureonsecurityinsensornetworks[4,18],thatwork
hasfocusedonsecurityincommunicationsbasedon(a)attacksonsecrecyandauthen-
tication(e.g. unauthorizedsnoopingonprivatecommunicationchannels), (b)attacks
on network availability (e.g. overloading the network to cause distributed denial of
service)or(c)attacksonserviceintegrity(e.g. compromisingasensorinthenetwork
and injecting false data). That work is not relevant to our work since we do not try
tocompromisenetworksecurity,availabilityorintegritythroughcommunications. In-
stead,weexploitphysicalvulnerabilitiesintrinsictoroboticswarmsinordertoinsert
the minimum number of mole agents to prevent the hostile swarm from successfully
detectingcoverageholes.
PreviousworkonParticleSwarmOptimization(PSO) [15]defines‘deception’as
theaverageproportionofoptimizationiterationsinwhichtheselectedandtrueneigh-
borhood bests are different due to noise in particles’ personal best objective values,
leadingtosub-optimalparticlepropagation. Theactions,beliefsanddeceptionstrate-
gies of a deceiver robot against its mark have also been studied using game theory
[19],butinthecontextoftwoindividuals’interaction. Incontrasttosuchpriorwork
onroboticdeception,wearethefirsttoformadeliberate,structuredattackonacitizen
swarmthroughadversarialagentinsertiontosubvertitsperformance. Wedemonstrate
thisattackinthecontextofaswarmperformingsurveillanceoperations.
3 Problem Formulation
3.1 Preliminaries
Wepresentinthissub-sectionpreliminaryconcepts,definitionsandassumptionsused
todefineourproblem.
2
CitizenandMoleAgents: Assumethehostileswarmiscomposedofncitizenagents
P = {p ,p ,...,p }, p ∈ R2. We wish to insert a set of adversarial mole agents
1 2 n i
Q = {q ,q ,...},q ∈ R2 todisrupttheperformanceofthehostileswarm. Ourgoal
1 2 i
is to identify the quantity and locations of moles necessary to disrupt swarm perfor-
mance. Weassumemolescommunicateidenticallytocitizens. Thatis, messagesare
exchangedbetweenmolesinthesamemannerandformatasbetweencitizens.
Sensing, Communication and Agent Radius: We assume the sensing range r and
s
communication range r are identical for all agents (P ∪Q) (i.e. r = r = r). In
c s c
addition, we assume each agent occupies a disk of radius r . That is, ∀u ,u ∈
min i j
(P ∪Q) : (cid:107)u −u (cid:107) ≥ 2r . To make connectivity possible, r ∈ (cid:0)0,r(cid:3).
i j 2 min min 2
Weassumethecitizenswarmisconnected. Whenaddingmoles,wemustensurethat
the resulting network of agents (P ∪Q) is connected. If mole agents q are added
i
incrementally one-by-one, the following condition is both necessary and sufficient to
ensureglobalconnectivity: ∃v∈(P ∪Q):(cid:107)q −v(cid:107) ≤r.
i 2
Figure1: Voronoicellsof8agents. Agentp’scellis(cid:3)v v v v v .
1 2 3 4 5
VoronoiPartition[2]: ConsidertheR2plane. Giventhesetofcitizenagentlocations
P ⊂ R2, a Voronoi partition of the plane divides it into convex polygons known as
Voronoi cells (one per agent). A Voronoi cell corresponding to agent p ∈ P is the
setofallpointsclosertopthantoanyotheragent. Formally,ifH(p ,p )represents
i j
thehalf-planedefinedbytheperpendicularbisectorofthelinesegmentjoiningagents
p ,p ∈P andcontainingp ,theVoronoicellofp isgivenbythefollowing.
i j i i
(cid:92)
cell (p )= H(p ,p ) (1)
vd i i j
pj∈P\{pi}
Voronoi Vertices: We represent the Voronoi cell corresponding to agent p ∈ P by
its set of vertices V (P) generated by the Voronoi partition of P. Figure 1 shows an
p
exampleofaVoronoipartitionwhere,foragentp,V (P)={v ,v ,v ,v ,v }.
p 1 2 3 4 5
BoundaryAgents: WhentheswarmincludesbothcitizensP andmolesQ,boundary
agents B (P) ⊆ P are the subset of citizens at the edge of a coverage hole. Since
Q
Voronoicellsaredefinedasthesetofpointsclosesttothecorrespondingagent,ifany
point is within an agent’s Voronoi cell but outside its sensing range, that point is not
withinanyagent’ssensingrange(i.e. thereisacoverageholeandthisagentisatthe
3
boundaryofthatcoveragehole). SinceVoronoicellsareconvex,aboundaryagentis
anycitizenwithoneormoreVoronoiverticesoutsideofitssensingranger.
B (P)={p∈P|∃v∈V (P ∪Q):(cid:107)v−p(cid:107) >r} (2)
Q p 2
Internal Agents: These are the subset of citizen agents I (P) ⊆ P which are not
Q
boundaryagents(i.e. I (P)=P \B (P)).
Q Q
3.2 ProblemStatement
Given a multi-agent configuration of citizen agents P performing an exploration and
surveillancemission,ourproblemisidentifyingnear-optimallythenumberandinser-
tionlocationsofmoleagentsQtopreventthediscoveryofcoverageholesinagiven
stateofthecitizensystem. Theseinsertionpointsareidentifiedsuchthateachcitizen
agent (after the insertion) believes that it is not on the edge of a hole (i.e. it is not a
boundaryagent)andthus,thatthesystemasawholehasachievedfullcoverage.
Figure2: Inthisfigure,circlesrepresentthesensingdiskofeachagentwithradii
equaltosensingrangesr,andsoliddisks(blueorred)representthephysicalarea
occupiedbyeachagentwithradii=r . Theleftpanelshowsthecitizenagent
min
formationinR2andtheirVoronoicells. Theareainpinkrepresentsholesinsensing.
Therighthandpaneldisplaysanexamplesolutionincludingcitizens(inblue),moles
(inred),andmoleagentplacementsandsensingdisks(alsoinR2). Theplacementof
themolesensuresthatnocitizenisaboundaryagent. Thiscanbeseenfromthe
resultingVoronoicellsofcitizens,shownviabluelines.
ConsiderunweightedundirectedgraphG=(V,E)withvertexsetV =P∪Q(i.e.
citizensandmolesarevertices)andedgesE ={(i,j)|v ,v ∈V :(cid:107)v −v (cid:107) ≤r}
i j i j 2
(i.e. anedgeconnectstwoagentsiftheyarewithinsensingrangeofeachother). Let
theLaplacianmatrixforthisgraphbegivenbyL(G). Itisknownthattheeigenvalues
of this matrix are non-negative (i.e. ∀k : 0 ≤ λ ≤ λ ). In addition, the second
k k+1
smallesteigenvalueisnon-zero(i.e. λ >0)ifandonlyifthegraphisconnected[13].
2
4
We must ensure this condition is true to ensure global connectivity of our network
of agents. If mole agents are incrementally inserted, incorporating sensing and agent
radiusconstraintsfromSection3.1givesusourobjective:
argmin |Q|
Q
subjectto B (P)=∅
Q
∀u ,u ∈(P ∪Q) : (cid:107)u −u (cid:107) ≥2r
i j i j 2 min
(cid:8) (cid:9)
λ(L(G))= λ ,λ ,...,λ :λ >0
1 2 |P∪Q| 2
InFigure2,anexampleofaformationofcitizenagentsisshownintheleftpanel,
along with an example solution (i.e. the near-optimal insertion locations of mole
agents) in red in the right panel. Also shown are the resulting Voronoi cells of the
citizenagentsaftermoleinsertion,whichareallwithintherespectiveagents’sensing
ranges, thus making the system of citizen agents conclude that there are no holes in
sensing.
4 Algorithms
4.1 Preliminaries
Weintroduceheresomepreliminaryterminology,definitionsandtheoremsrequiredto
understandouralgorithms.
4.1.1 Terminology
To illustrate the following concepts, consider the example boundary citizen agent in
Figure3. WeassumethattheplanecontainscitizensP andmolesQ.
Figure3: Exampleofacitizenagentp ,itsVoronoicell(cid:3)v v v v ,sensingdisk
1 1 2 3 4
sdisk(p ),protrusionsprot (p ),angleofprotrusion∠protandpiecedanglesof
1 k 1
protrusion∠prot fork ∈{1,2}.
k
5