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
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