From: AAAI Technical Report SS-02-04. Compilation copyright © 2002, AAAI (www.aaai.org). All rights reserved. Notes for the AAAISpring Syposiumon Intelligent Distributed and Embedded Systems, Stanford University, 2002 Deploymentand Localization for Mobile Sensor Networks Andrew Howard and MajaJ Matari~ and Gaurav S Sukhatme Robotics Research Laboratories, Departmentof ComputerScience, University of SouthernCalifornia, Los Angeles, CA90089-0781 ahoward@usc.edu, mataric @usc.edu, gaurav@usc.edu Abstract Thispaperbriefly sketchesa pair of algorithmsfor deploying andlocalizinga mobilesensornetwork.Weuse the term ’mobilesensornetwork’ to describea distributedcollection of nodes,eachof whichhas sensing, computation, communication andlocomotion capabilities. Fordeployment, wehave developed a potential-field-based approach that ensuresthat anycompactinitial configurationof nodeswill spreadout suchthat the area ’covered’by the networkis maximized. For localization, wehavedeveloped an approachthat makes use of the nodesthemselvesas landmarks.Through a combinationof maximum likelihoodestimationandnumericalo13timization,wecan,for eachnode,estimatethe relativerange, bearingandorientationof everyother nodein the network. This papersketchesthe basic formalismbehindthese algorithms,andpresentsomeexperimental results. 1 Introduction This paper briefly sketches a pair of algorithmsfor localizing and deploying a mobile sensor network. Weuse the term ’mobilesensor network’to describe a dis~ibuted collection of nodes, each of whichhas sensing, computation, communication and locomotioncapabilities. It is the latter capability that distinguishes a mobile sensor networkfrom its moreconventionalstatic cousins. Locomotion facilities a numberof useful networkcapabilities, includingthe ability to self-deployandself-repair. Weenvisage the use of such networks in applications ranging from urban combat, to search-and-rescueand emergency environment monitoring. Consider, for example, a search-and-rescue mission in which a sensor networkmust deployitself into a damaged structure, locate survivors, and guide rescuers to those survivors. This paper addresses two of the key problemsthat must be solved in order to conduct such missions: deploymentand localization. Thefirst problemwe consideris that of localization; i.e. howdoes each node determineits pose with respect to every other nodein the network.In the scenario wehavedescribed localization information cannot be obtained using GPSor landmark-basedtechniques; GPSis generally unavailable or unreliable in urbanenvironmentsdue to multi-path effects, while landmark-basedtechniques require prior modelsof the environmentthat are either unavailable, incompleteor inaccurate. For these reasons, we have developedan approachto localization that relies on using the nodesthemselves as landmarks. Nodesare equippedwith sensors that 27 allow themto measurethe relative pose of nearby nodes, and sensors that allow themto measurechangesin their own pose. Giventhe measurementsfrom these sensors, a combination of maximum likelihood estimation and numerical optimization is used to determinethe most probable pose for each node. Withthis approach,one can obtain goodlocalization informationin almost any environment,including those that are undergoingdynamicstructural changes. Our only requirementis that the nodes are able to maintain at least intermittent line-of-sight contactwithone another. The second problemwe consider is that of deployment; i.e. howdoes one control the motionof nodessuch that the networkas a wholemaintainsor optimizes somedesired set of properties. Twopropertiesare of particular interest: area coverageand line-of-sight connectivity. The former property is clearly useful in manyapplications, while he latter is required if the localization techniquedescribedaboveis to be effective. Aswith localization, the deployment algorithm is constrainedin that it cannotmakeuse of prior models of the environment. Therefore, we have developedan approachto deployment that relies entirely on sensed rather than stored data. This approachmakeuse of virtual potential fields; i.e., nodesare treated as virtual particles that are subject to virtual forces; these forces repell the nodesfromone other and fromobstacles. Theforces are such that an initial, compactconfigurationof nodeswill eventually spread out to cover a muchlarger area of the environment.Both area coverage and line-of-sight connectivityare emergentproperties of this algorithm. It should be noted that the localization and deployment algorithmsdescribedin this paperare entirely distributed. Weregard this as necessaryproperty for any algorithmthat must scale to networkswith thousandsor tens-of-thousands of nodes. The remainderof this paper is divided to two mainsections, the first of whichtreats the problemof localization, and the secondof whichtreats the problemof deployment. 2 Localization Our approachto networklocalization relies on two basic assumptions.First, we assumethat each nodeis equippedwith a proprioceptive motiondetector such that it can measure changesin its ownpose (subject to somedegree of uncertainty). Suitable motiondetectors can be constructed using either odometryor inertial measurement units. Second,we Notes for the AAAISpring Syposiumon Intelligent Distributed and Embedded Systems, Stanford University, 2002 with respect to an arbitrary coordinate systemwhoserelationship with the external environment is undefined.Instead, each node uses these estimates to computethe pose of every other noderelative to itself, and uses this ego-cen~c viewpoint to coordinate activity. Wenote, however,that somesubset of the networkmaychooseto remain stationary, thereby’anchoring’the global coordinatesystemin the real world.In this case, the poseestimates in H maybe used as global coordinatesin the standardfashion. The detailed mathematicalformalismunderlying this approach can be found in (Howard, Matarid, & Sukhatme 2001a). Figure 1: Illustration of the basic formalism. The figure showstwo nodes,rl and r2, traveling fromleft to right; at time t~, node rl observes node r2. The vertices represent pose estimates; the edges represent observations. Twoobservations are highlighted: a motionobservation for node rl, and nodeobservationat time t2. assumethat each node is equippedwith a nodedetector such that it can measurethe relative pose of nearbynodesand determinetheir identity. Wefurther assumethat the identity of nodes is always measuredcorrectly (whicheliminates what wouldotherwise be a combinatoric labeling problem) but that there is someuncertainty in the relative pose measurements. Wediscuss someof the difficulties associated with the constructionof suitable nodedetectors in Section2.2. Giventhese assumptions,the networklocalization problem can be solved using maximum likelihood estimation. The basic methodis as follows. First, we construct a set of estimates H -- {h} in whicheach element h represents a pose estimate for a particular nodeat a particular time. Thesepose estimates are defined with respect to somearbitrary global coordinate system. Second,weconstruct a set of observations O = {o} in which each element o represents a relative pose measurement madeby either a motion or node detector. For motiondetectors, each observation o represents the measuredchangein pose of a single node; for node detectors, each observation o represents the measured pose of one noderelative to another. Finally, we use numerical optimizationto determinethe set of estimates H that is mostlikely to give rise to the set of observationsO. One can visualize the approach in terms of a directed graph, as shownin Figure 1. Weassociate each estimate h with a vertex in the graph, and each observation o with an edge. Each vertex can have both outgoing edges, correspondingto observations in whichthis vertex was the observer, and incomingedges, correspondingto observations in whichthis vertex was the observee. Eachedge also has a natural ’length’, correspondingto the measuredrelative pose of the twovertices. Numericaloptimization is used to determinethe configuration of vertices that mimimizesthe amountof ’stretching’ in the edges; i.e. to minimizethe difference betweenthe estimated and measuredrelative pose for eachpair of vertices. Note that, in general, we do not expect nodes to use the set of pose estimatesH directly; these estimates are defined 28 2.1 From Centralized to Distributed Implementations The formalismdescribedin the previous section can be readily implementedusing a centralized algorithm. Observations from all nodesare reported to a central base-station, wherean efficient numericaloptimization algorithmis applied to the data (wetypically use a conjugategradient algorithm). Estimated poses are communicatedback to the individual nodes. Whilethis algorithm maybe suitable for applications in whichdistances are short and nodesare few, it does not scale well to large networks.This algorithmhas both computationand communicationbottlenecks. The basic formalism can, however, be implementedin an entirely distributed fashion. Consideronce again the directed-graphvisualization in Figure1. Wecan divide this graph into a set of fragments, each of which encompasses the poses estimates for a single node. Eachnode is then maderesponsible for its ’own’fragment,and conductsa separate numericaloptimization. The nodes must periodically broadcasttheir set of poseestimates(to ensureglobalconsistency) and must explicitly communicatenode observations (since the correspondingedgesare effectively ’shared’ by two fragments). Atpresent, this algorithmis largely speculative(it has not been implemented).Ourhope is that the algorithmwill have both constant-time and constant-bandwidthproperties, and will therefore scale to networksof any size. 2.2 On the Construction of Node Detectors Constructing a detector capable of measuringthe unique identity and relative pose of other nodes can be somewhat problematic, particularly as the numberof nodes becomes large. Wehave constructed one such detector using a SICK LMS200 scanning laser range-finder in combinationwith a bar-codemadefromalternating su’ips of retro-reflective and non-retro-reflective paper, as showin 2. The SICKlasers can be programmed to return range, bearing and intensity information,andwith a little post-processing,one can easily determinethe identity, range, bearingand orienation of the bar-code. Unfortunately,this solution does not scale particularly well. Since the angularresolutionof the laser is limited, andthe size of the bar-codecannotbe increasedwithout bound,the numberof uniqueid’s that can be used in practice is quite small (somewhere between16 and 32 for the particular setup we have used). In addition, these bar-codescan Notes/’or the AAAISpring Syposiumon Intelligent Disuibutedand Embedded Systems, Stanford University, 2002 (a) (b} (c) Figure 2: (a) and (b) A node detector constructed using a SICKLMS200 scanning laser range-finder and a retro-reflective bar-code. (c) Analternative node detector constructed using a SICKLMS200scanning laser range-finder and a pair of retmreflective ’totem-poles’. only be detected over limited tangs and fromcertain orientations; for reliable detection, the laser mustlie within 4 m of the bar-codecentroid and -4-60° of the bar-codesurface normal. Weare currently pursuingan alternative approachto node detection that should have improvedscaling and detection properties. In this approach, each node is equipped with a pair of non-uniquebeacons (two re~o-reflective ’totempoles’) and an omni-directional laser (two SICKLMS200 units back-to-back),as shownin Figure 2(c). Usingthe setup, each nodeis able to measurethe range and bearing, but not the orientation or identity, of other nodes. However, by communicatingtheir individual measurements,nodes can collectively infer orientationand identity by checkingfor geometric consistency. Imagine, for example, that both node A and nodeB have detected another node at a range of 3 m, and that no other nodehas beendetected at this range. Since the sensors are omni-directional,this necessarily implesthat nodeAis seeing B and nodeB is seeing nodeA. The relative orientation of the nodescan subsequentlybe determinedby comparingthe two bearing measurements. This approach is, of course, far from fool-proof. One can easily imaginepathologicalsituations in whichit is impossible to disambiguatemeasurements(such as whenthree nodesare placedat the vertices of an equilateral triangle). Suchsituations are relatively rare in real applications, however, and are easily detected and discarded. Of moreconcern is the mis-identificationthat will results fromthe failure of a laser to detect one of the beacons.Oursolution here is an engineering one: makethe beaconsvery easy to detect, and be very conservative wheninfering identities from geometric constraints. This is, in a sense, no different fromthe problems experienced with the bar-codes, which must be carefully engineeredto minimizethe chancesmis-identification. It shouldbe notedthat this nodedetection schemebenefits greatly fromthe use of local (short-range)rather than global (long-range)communications, since this naturally cuts down on the numberof geometricpossibilities that must be considered. 29 2.3 Results Figure 3 showsthe results for an experimentconductedusing a team of 7 nodes. Each node is comprised of a Pioneer 2DXmobile robot, a SICKLMS200 scanning laser range-finder and a retro-reflective bar-code. Motionobservations are providedby the robot’s on-boardodometry;node observationsare providedby the laser range-finder/bar-code combination. For this experiment, 6 of the 7 nodes were positioned at fixed locations in the corridors of a building, as shownin Figure 3(a); the remainingrobot wasthen ’joysticked’ aroundthe circuit, and wasthus ’seen’ by each of the stationary nodesin turn. Thestationary nodeswerepositioned outside each other’s sensor range, and hencethere are no observationsthat relate these nodesdirectly. Figure 3b shows the combinedlaser scans at t = 200 sec, after the mobilenodehas beenseen by all six stationary nodesexactlyonce. Notethat this is not a stored map:this is live laser data. Thecummulative error in the mobilenode’s odometryhas clearly manifesteditself as a ’bend’ in this plot. Figure 3(c) showsthe combinedlaser scans at t 220 sec, after the mobilenode has been seen by the first stationary noderz for a secondtime, thus ’closing the loop’. The cummulativeerror has been erased. These result were generated using a centralized algorithm. Moreplots, with associated quantafive analysis, can be found in (Howard, Matari~, & Sukhatme2001b) and (Howard,Matari6, &Sukhatme2001a). 2.4 Related Work Localization is an extremelywell studied area in the mobile robotics domain.Thevast majorityof this research has concentratedon twoproblems:localizing a single robot using an a priori mapof the environment(Leonard&DurrantWhyte 1991; Simmons& Koenig 1995; Fox, Burgard, & Thrun1999), or localizing a single robot whilst simultaneously building a map (Thrun, Fox, & Burgard 1998; Lu & Milios 1997; Yamaucbi, Shultz, & Adams1998; Duckett, Marsland, & Shapiro 2000; Golfarelli, Maio, & Rizzi 1998; Dissanayakeet al. 2001). Recently, someauthors have also consideredthe related problemof mapbuild- Notes for the AAAISpring Syposiumon Intelligent Distributed and Embedded Systems, Stanford University, 2002 I I J L ~ ’~!" %....’o __t ¯ .,i--..i ~ i-o !V:’ ~’0 " I ’ i o! ’~ (a) (b) (c) Figure 3: Anexperimentwith real nodes. (a) Experimentalset-up: six stationary nodes(rx to r6) are placed at at strategic locations; the seventhmobilenode(to) executesa circuit. (b) Combined laser scans at t -- 200sec, after the mobilenode beenseenby all six stationary nodesexactlyonce. Notethat this is not a stored map:this is live laser data. Poseestimatesand observationsare also shown,denotedby rectangles and lines respectively. (c) Combined laser scans at t = 220sec, after the mobilenodehas beenseen by the first stationary noderl for a secondtime, thus closing the loop. ing with multiple robots (Thrun2001). All of these authors makeuse of statistical or probabilistic techniquesof onesort or another; the common tools of choice are Kalmanfilters, maximum likelihood estimation, expectation maximization, and Markoviantechniques (using grid or sample-basedrepresentations for probability distributions). The networklocalization problemdescribed in this paper bears manysimilarities to the simultaneouslocalization and mapbuilding problem, and is amenableto similar mathematical treatmerits. Our mathematicalformalismis very similar, for example,to that described in (Lu &Milios 1997). A numberof authors have also considered the problem of localizing mobilerobot teams, whichis largely equivalent to the networklocalization problemdescribed in this paper. (Roumeliotis & Bekey2000) present an approach whichsensor data froma heterogeneouscollection of robots is combinedthrough a single Kaimanfilter to estimate the pose of each robot in the team. This methodrelies entirely on external landmarks; no attempt is madeto sense other robots or to use this informationto constrain the pose estimates. In contrast, (Foxet al. 2000) describe an approach in whicheach robot maintainsa probability distribution describing its ownpose (based on odometryand environment sensing), but is able to refine this distribution throughthe observation of other robots. It is not clear, however,that this techniquecan be applied to problemsin whichonly the robots are used as landmarks. A number of authors (Kurazume& Hirose 2000; Rekleitis, Dudek,&Milios 1997)havealso consideredthe prob- 30 lem of team localization froma somewhat different perspective. Theseauthors describe cooperative approachesto localization, in whichteammembers actively coordinate their activities in order to reduce cumulativeodometricerrors. The basic methodis to keep one subset of the robots stationary, whilethe other robots are in motion;the stationary robots observethe robots in motion(or vice-versa), thereby providingmoreaccurate pose estimates than can be obtained using odometryalone. Whileour approachdoes not require such explicit cooperationon the part of networknodes, the accuracy of localization can certainly he improvedby the adoptionof such strategies. 3 Deployment Wehave developeda potential-field-based approachto deployment.In this approach,nodesare treated as virtual particles that are subject to virtual forces; these forces repell the nodes fromeach other and from obstacles. In addition, nodesare subject to a dissipativeviscousforce; this force is usedto ensurethat the networkwill eventuallyreach a state of static equilibrium;i.e. all nodeswill ultimatelycometo a completestop. Theviscous force does not, however,prevent the networkfromreacting to changesin the environment;if somethingis moved,the networkwill automatically reconfigure itself for the modifiedenvironmentbefore onceagain returning to a state of static equilibrium.Thus, nodesmove only whenit is necessaryto do so, whichsaves a great deal energy. Our only assumptionis that each node is equippedwith Notesfor the AAAISpringSyposium on Intelligent Distributedand Embedded Systems, StanfordUniversity, 2002 5 i i’ ’ ....................... ......... :--::::k’j~¢---~,’’, " (a) Figure4: (a) Potential field generatedby a simple environment; the contoursshowthe lines of equal potential. (b) Forcefields generatedby this potential; the arrowsindicate the direction (but not magnitude)of the force. a sensor, such as a scanning laser range-fioder or onmicamera, that allows it to determinethe range and bearing of both nearbynodesand obstacles. Usingthis information,the nodecan determinethe virtual forces acting it, and convert this informationinto a control vector to be sent its motors. Noother informationis required. It should be noted that this approachdoes not require global localization or communication betweennodes. While both capabilities mayin fact be present in the network,we wouldprefer to consu’uct a minimalist system that makes few assumptions about the environmentand relies on few capabilities on the part of the nodes.This is partly for the sake of producingan approachthat is robust, and partly for the sake of creating a base-line systemagainst whichmore complexand more capable techniques can be compared. The detailed mathemathicalformalismunderlying this approach can be found in (Howard, Matarit, & Sukhatme 2002). 3.1 Results Figure 5 showsa typical deploymentconductedin using the Stage multi-agent simulator (Gerkey, Vaughan,& Howard 2001). For this experiment, the simulated sensor network consisted of I00 nodes, each of whichis equipped with a scanninglaser rangefinder, a retro-reflective beaconand an omni-directionalmobilerobot base. The laser has a 360degree field-of-view and can determinethe range and bearing of objects out to a range of 4m. The laser can also distinguish betweennodes (whichcarry a retro-reflective beacon) and obstacles (whichdo not). The networkwas placed in large, complex,simulated hospital environment. Figures 5(a) and (b) showthe initial and final network configurationsfor this experiment.Fromtheir starting configuration (packed into a single room)the nodesspread out to cover a sizeable portion of the environment;the cover2, age area in the final configuration is in excess of 500 m a 10-fold improvement over the initial coverageof around 50 m2. The deploymentis also such that the networkmainrains completeline-of-sight connectivitythrought the duration of the experiment.That is, every node lies within the sensoryfield of at least oneother node,andany pair of nodes in the networkcan be connectedvia a series of such line-ofsight relationships. Full connectivity is an emergentprop- 31 erty of the deployment,and it is unclear at this time how reliably this propertyemerges.Whilethe potential field algnrithmis such that each node must remainwithin the sensory range of at least one other node (since a node cannot be repelledby a nodeit cannotsee), this is not sufficient to guaranteefull connectivity. Onecould, for example,imagine a situation in whichthe networkbreaksinto multipledisconnectedislands. This topic remainsthe subject of further investigation. For completeness, Figure 5(c) showsan occupancygrid generatedusing laser scans capturedfromthe final configuration: areas that can be seen by the networkare shownin black (for obstacles) or white (for open space); unseen eas are shownin gray. Note that there are no gaps or breaks in the coverage. Thehigh quality of this coveragecan be attributed to the even spacing of nodes, combinedwith the fact that the averagenodeseparation is about half the sensor range. Thiseffectively creates a dense, highly redundent network. Futher information on this experiment can be found in (Howard, Matari~, & Sukhatme 2002). Animations of this and other experiments can be found at: http : I/robotics. usc. edu/~ahowardlmovies, html 3.2 Related Work Potential field techniquesfor robotic applicationswerefirst described by Khafib (Khafib 1986) and have since been widely used in the mobile robotics communityfor tasks such as local navigation and obstacle avoidance. The related conceptof ’motorschemas’,whichutilizes the superposition of spatial vector fields to generatebehaviorwasintroducedby Arkin(Arkin 1989). Both techniqueshave since beenapplied to the problemof formationcontrol for groups of mobile robots (Scheider, Wildermuth, & Wolf 2000; Balch &Hybinette 2000). The formation problem is similar, in somerespects, to the deployment problemdescribed in this paper, in that the robots will attempt to maintaina formation based on local sensing and computation. A key difference, however,is that there is no requirementthat the formationreach a state of static equilibrium. The deploymentproblemalso is also similar, in somerespects, to the multi-robot exploration and mappingproblem. Here, the aim is to build a global mapof the environ- Notes for the AAAISpring Syposiumon Intelligent Distributed and Embedded S’ ~stems,Stanford University, 2002 ...m:-Xl. (a) (b) (c) Figure 5: A pinto-typical deploymentexperimentfor a 100-nodenetwork.(a) Initial networkconfiguration. (b) Final configuration after 300seconds. (c) Occupancy grid generatedfor the final configuration; visible space is markedin black (occupied) or white (free); unseenspaceis markedin gray. mentby sequentially visiting each location with one or more robots. This problem has been considered by a numberof authors (Dedeoglu&Sukhatme2000; Simraonset al. 2000; Burgardet aL 2000)whouse a variety of techniquesranging from topological matching (Dedeoglu&Sukhatme2000) fuzzy inference (L6pez-S~inchezet al. 1998) and particle filters (Thrunet al. 2001). Finally, we note that the concept of coverage as a paradigmfor evaluating many-robotsystems was introduced by Gage(Gage1992). Gagedefines three basic types of coverage: blanket coverage,wherethe objective is to achieve a static arrangementof robots that maximizes the total detection area; barrier coverage, wherethe objective is to minimizethe probability of undetectedpenetration throughthe barrier; and sweepcoverage, whichis more-or-less equivalent to a movingbarrier. Accordingto this taxonomy,the deploymentproblemdescribed in this section is a blanket coverage problem. 32 4 Future Directions To date, we have treated the problemsof localization and deploymentquite separately. There is muchscope, however, for combiningthese twoproblems;for example,one can design deploymentstrategies that explicitly maximize the accuracyof localization by reasoningaboutuncertainty. Weare also considering two additional problems: networkrecoveryand self-repair. Ideally, oncethe networkhas performedits task, wewouldlike to be able to recover, or ’un-deploy’the network.Interestingly, this is a moredifficult task than deployingthe networkin the first place (one can see that this is likely to be the case using a basic entropy argument). Similarly, since the networkis intended for hostile environmentsin which nodes maybe destroyed (either by accident or maliciousactivity), wewouldlike the networkto be able to repair itself. This can be doneby reposition nodes to patch the ’holes’ formedby the destroyed nodes. Notes for the AAAI Spring Syposium on Intelligent Distributed and EmbeddedSystems, Stanford University, 2002 References Arkin, R. C. 1989. 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