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Transcript
INFORMATION TO USERS
This manuscript has been reproduced from the microfilm master. UMI films the
text directly fmm the original or copy submitted. Thus, some thesis and
dissertation copies are in typewriter face, while others may be from any type of
computer printer.
The quality of this reproduction is dependent upon the quality of the copy
submitted. Broken or indistinct print, &red or poor quality illustrations and
photographs, print bleedthrough, substandard margins, and improper alignment
can adversely affect reproduction.
In the unlikely event that the author did not send UMI a complete manuscript and
there are missing pages, these will be noted. Also, if unauthorized copyright
material had to be removed, a note will indicate the deletion.
Oversize materials (0.g . . maps, drawings, charts) am reproduced by sectioning
the original, beginning at the upper lefthand comer and continuing from left b
right in equal sections with small overlaps.
Photographs included in the original manuscript have been reproduced
xerographically in this copy. Higher quality 6" x 9" black and white photographic
prints are available for any photographs or illustrations appearing in this copy for
an additional charge. Contact UMI directly to order.
&I1 & H ~ l l Information and Learning 300 Nor(h Zeeb Road, Ann Arbor, MI 481061346 USA
ISLANDS OF RELIABILITY FOR HYBRID
TOPOLOGICAL-METRIC MAPPING
Shlomo Saul Simhon
Department of Computer Science
1 1 cGill University. MontrPal
September 1998
A Thesis submitted to the Faculty of Graduate Studies and Research
in partial fulfilment of the requirements for the degree of
1Llsster of Science
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ABSTRACT
This thesis describes a method for niapping unknown large scale static environrnetlts
using a hybrid of topological arid metric representations. -4 global map is f ~ r t w t l
from a set of local maps for sub-regions of the environments. Each local map corr-
tains quantitative environmetit information used to detinr a local reference frur~itl.
These maps are referred to as islunds 01 reliability because they are associated with
the sub-rcgions wilosc local structure is best matched to the sensors we are using. The
cunriectivity of these islands is represented topologically. The key niapping problem
we consider is where to place the islands of reliability and to what extent they should
ewer the environrrient. This is accomplished by defining the placement criteria in
terms of the task to be satisfied and the uncertainties of the mapping agent. Is-
lands are distributed about the environment at areas suitable For extracting metric
information relevant to a localization task.
RESUME
Cette tlil.se dccrit uue niPthode pour cartographier une iriconnu large Pchellr statique
environnement en u tilisant une hybrid de topologique et niCt rique repr6sentation. Cne
carte globale est crCes i partir des cartes local pour cies sous-region de l'environnement.
Chacune des ces cartes locales detiennent de l'information quantitative. utilisPe pour
difinir un cadrage tie reErence local. Elks sont r6f6rt;es h des iles de Jiubilzte' puisqu'elles
fournissent de l'informatim metrique tres precise de l'environnement. Ces iles sont
disposes par une structure topologique qrii inclus les descriptions tle lcurs conjonc-
tions. Nous cotaiderons que notre probl6me clef dans la cartographie est: ou placer
les iles de fiabilitP et B quel Ptendue elles devraient couvrir I'environnement. Ceci
cst accornplie en dCfinissant le critkt-c de placement selon les ternies des taches des
iles de fiabilit6 qui sont destinees B s a t i s h e et les incertitudes des cartographes. Les
iles sont clistribuPes vers I'environnement dam des regions approprii pour extraire de
l'information pertinentr pour une tache de localisat ion.
ACKNOWLEDGEMENTS
Sly thanks are to Gregory Dudek for providing outstanding supervision over this
work along with the brilliant insights and ideas that 1 couldn't have done rvittlout.
It is a pleasure to be apart of his team where I may expand nly knuwlcdgc and
uriderstanding in a dynamic and open envirunrnt.nt. I Further thank Greg Dud& for
his firiancial support over the past terms. I would also like to thank Paul Slacketizic
imrl Chi Zhang for their help and explanation on their thesis work. allowing me to
incorporate their software into mine.
DEDICATION
This dissertation is dedicated to my wife Stacy Silnho~i arid our hrnilies. I would
l i k ~ to thank Stacy for the grratt?it support that l could ever Iiaw ask for. Slaking
tkvery difficwlt challenge that seemed impassable a small hill to climb. I would not
have matic it this far had it not beer1 lor rriy Stacy. I especially want to thank niy
parents for being the greatest parents I can ever have. I find myself very lucky bcing
brought up by such noble parents. When it comes down to i t . all rriy learning and
studies are based on the foundation I was givcn by my parents. I rvoidd also like to
thank rny brothers for all those great times that we shared and am exited to see
rit lirns to navigate an unknown polygonal envirormient by dynamically co~istruct irlg
rhe visibility graph using sensors capable of detecting edges and corners of obsta-
&s. The global navigation algorithni corisists of increnieritally coristrnctirlg the
visibility graph while following a local navigation algorithm. Other work in topo-
logical maps deal with the problems of detection antl identification of noties to Form
a graph [6, 7, $1. In that work. maps are built without metric inforrnatioti: orily a
topological hierarchy of nodes specifying neighbourhooct relations amongst features.
Each node in t hr map is detected by a set of non-uniclue signatures. Csing a collect ion
uf these nodes. an extended signature is constructed to uniquely identify the nodes
antl avoid ambiguities. llataric [9] identifies nodes by an environment property that
is predefined by the designer along with a compass heading for additional reference.
Graph erplorat ion strategies using markers [lo] are described by traversing a graph
and placing markers at nodes. The markers identify previously visited nodes and de-
tect topological cycles. Even shape recognition problems [ll] are also formulated in a
topological mapping framework. In most of these cases. once the topological represen-
tation is defined. complex computational tasks can be formulated using graph-based
methods
Although current work in topological maps is theoretically sound. rnost limit the
ability to metrically represent important environment structure. -4 purely topoIogic.xl
representation does not include metric inforrnatioti. all measurements are symbolic.
Thus. a robot will not be able to extract metric information when needed (for instance
where position re-calibration is required). It is not clear that robots can only rely
on symbolic information. Furthermore. topological maps alonc are difficult to learn
and maintain. particularly when their configuration is arubigrious (31. The problem of
defining an unambiguous graph without using a metric representation is not a trivial
one.
1.2.2. Metric Maps. In orcicr to perform accurate positioning. Dudek arid
SIackenzie [I] construct sonar-based rriaps where explicit rriodrls arc built out of sonar
reading tlistribution in spacc The maps are used to deternlinc robot posc by fitting
new sensor data to the model. This is accornplishetl using a weighted voting of (:or-
rection uectors: computing vector tliffercnccs bctwetm olaervtvi data points and target
tnoclel in the map. Holenstein ct . rrl . [12] also build model based maps using ultrasonic
data coupled with a localization procedure. During localization. new sensory readings
are compared to the model map using clristering. Curran and Kyriakopoulos [13] con-
struct metric maps from range data. complementing their localization algorithm that
uses a n Extended Kalman Filter to combine dead reckoning. ultrasonic and infrared
sensor data. Dudek and Zhang (141 use a vision system to model the environrnent
and extract positioning information. The model consists of extracting appropriate
features from images and correlating them to pose. Position calibration is at, tained
by training a neural network. which allows accurate interpolation through the feature-
pose space. Krotkov [15] also uses a vision system to determine pose by establishing
correspondence between observed landmarks and map landmarks. The approach uses
objects commonly found in indoor environments as landmarks (in particular. verti-
cally oriented parts of fixed objects such as doors. desks and wall junctions).
While these traditional metric methods can determine a pose estimate without the
need of having artificial beacons placed about the environment, they use o ptiori maps
that are usually built using a single coordinate frame. Although such maps provide
accurate local correspondence. accumulated errors tend to warp the representation
over larger scale areas. Data rneasurements taken far apart are susceptible to largtt
errors. Csing such erroneous relations may mislead position estinlatio~l computations.
These triethods lack the ability to model large scale environmrrits without distortion.
especially in unstructured regions and rough terrains.
To compensate for the limitation of i~ccumulatrd error. there are mapping tech-
niques where semi-continuous localizat iorl is used. Leonard and Durrant-R'hyte [l6l
arltl Lu imd Llilios [17] employ such methods. The work provides a self consistent
description uf the envirorinlent by using a Kalrnan Filter ancl registration techr~iqucs
to compare predicted and perceived data while updating a map.
These methods. like many others. can lead to two key problems if used iniiis-
crirninatcly. Firstly. time and energy rnay he wasted in attempting to accurately
niap regions irrelevarlt to the tasks of interest. Secondly. they may attempt to detect
iimdrnarks and establish a reference coordirlate frame in regioris where the local strrlc-
cure is anibiguous or urirrliable. Consider a long whit($ hallway. where inforniation
gathered is irrelevant for a localization task. If pose estimation is to be estrected in
such a n area. it may result in an mrontwils ancl misleading soliitiotl. Furthtmiurt~.
metric relations between two rooms at eacfi end of the hallway cannot br acruratdy
determined. nor are they important. Thus. attempting to construct a single absolute
reference coordinate system can be problematic [18].
1.2.3. Topological-Metric Maps. It is not always beneficial to keep metric
relations over large scales (sinre the relation are usually erroneous). ;\ better alterna-
tive might be to provide topological or qualitative relations over such extents. while
storing metric relations over local areas. Prior work in cognitive science suggests
humans use a set of Local reference frames topologically connected to model large
scale environment. Yeap [19] shows that a module of the Cognitive Mapping Process
can be represented with a Relative Absolute (R-A) model. The model consists of a
global representat ion (referred to as Relative Space Representation. or RSR) which
1.1 -2 BXCKGRO C'ND
is qualitative composition of a sequence of local representations {S( 1 ). S(2) .... } called
Absolute Space Representations or .-\SRs. That is. the global map can be considered
as a set of clear and accurate patches of local inforniation linked topologically by
fuzzy. semi-unknown areas (Figure 1.1 ) .
This is easily exemplified by a person travelling down a street. While walking
on the uninteresting sidewalk. the person's attention is often diverted from the envi-
ronment (reallocated to other thoughts): the description of the environment is vagucl.
When reaching a point of interest or distinction. such as an intersection. the persori
redirects his attention to the erivironnlent in ortier to accurately localize to the side-
walk edge. check the stnw names. signals etc. At this point. the environment's precise
structure is re-acquired. Thus. the Human cmgnitive map can be conceptualized in
both qualitatiw arid quantitative components. the quantitative coniponents are the
local patches of intercst (ASRs), used for computa t io~d purposes, while the global
hierarchy organization of the patches is the qualitative term (RSR). Furthcrrrlort.. the
hSR configuration is depentlent on the humans' cspclritwes ant1 goals. For twniple.
if the person walking on the sidewalk was a painter with a goal to pairit the sidewalk.
what is normally an uninteresting sitiewalk bccomes a part of the hSR.
FIGURE 1.1 . Global map composed of a set of local maps. Circles represent metrically accurate local maps. Edges represent qualitative informat ion.
Work by Nehrnzow [20] suggests that foundations of robust robot navigation
are based on using landmarks. canonical paths and topological models. Examples of
animal behaviour justifv this view. It was shown that animals use as set of landmarks
such as prominent trees, rocks etc.. as well as reference landmarks such as sun. stars
and magnetic senses to navigate. Furthermore, constant. well defined paths were
preferred even if it means longer travel distances.
Kuipcrs and Byun 1211 tlevelop a robot mapping and esploration strategy runi-
posed of both qualitative and qua~ititative conlponencs. Their method considers dis-
tinctiveness measures in terms of certain pre-defined sensory criteria that cat1 be
rnaxirnizrd. The map is cornposed of a set of edges (distinct paths) defined by 2-D
dist irictiveriess rneuure criteria. and a set of ~iodes (distinct places) defiried by 1-D
t1istinc:tivtms Ineastire criteria. in their work. a robot esplorrs an t~~~virorlrrirrlt by
following control strategies that maximize the 2-D criteria. This forrrls well defined
paths about the environment and constitute the edges of the topulugical map. During
t hr esploration. the robot gat ht?rs setwry iriforniatioti for the rrietric niap while also
looking for distinctive regions to include as nodes in the topological map. Once ill
the rieighbourhood of such a region. a hill climbing routine is executed to rnaciniize
the 1-D distinctiveness rneascre criteria and reach a distinct point.
-4 reheursul pmceduw uses geonwtrir infomiat ion girthereti along t tit. nodes to
distinguish new places from old ones. This is dorie by first assuming the new nodtl is
;in existing notle. Then srarching the graph u p to a crrtain depth to determint. if thr
assurription is valid. Thtl paptbr [21] . however. only indicates tentative guide1int.s to
construct tlic sensory criteria. Inappropriate sensory criteria can result in non-unique
solutions. the placenwnt of edges and nodes may not be clearly defined. Furthermore.
metric: information is gathertd in global correspondence. therefore accumulated dead
reckoning error may distort true metric relations resulting in an erroneous map.
Thrun produces hybrid topological-metric maps. similar to those of Kuipers anti
Byun using a subset of the Voronoi diagram computed from the rnetric map to define
the topological components [3]. First. the metric grid-based model of the environ-
ment is built by interpreting sensory data with an artificial neural network. This
maps the data into the probabilities of the occupancy. Bayed rule is used for inte-
grating multiple interpretations over time. Then. critical points that minimize ldcal
clearance of the occupancy grid are used to obtain critical lines that partition Free
space into disjoint regions. The partitioning is mapped to a graph. By combining
both topological and metric representations in this fashion. accurate/consistent and
efficient maps are constructed for navigation. Although. the metric component itself
is subject to large scale odometry errors and the topological points are distributed
arbitrarily ( they may be very numerous) .
1.3. Outline
The work tiescribed in this thesis is motivated by the way hunlans depict the
envirorirrleot as described in [19). The model we use consists o f a hybricl topologiral-
metric representation configured for a given task. We present this thesis iu follows:
chapter 2 tliscusses the approach we take to build a map and the necessary rnodulcs.
In chapter 3. we discuss the topological-metric nmtlei and its configuration. Chapter 4
describes the ~rwtlels used to represent ttw riodes in the topological map and chaptclr .I
defines the spatial configuration of nodes. Chapter 6 gives some experimental results
;md a discussion. \ \ i s then wparlcl on future work in ant1 conclude i r i chapter 7 .
CHAPTER 2
Approach
Providing a coririse descriptiori uf large sceltl environrrierlts proves to Ilc a clifficult
problem in the nmbile robotics field. Generally. a robot esplorcs arl environrnrtit
gathering data ( a t each sanlplirig position) using a single sensory systern. During the
esploration. the collected data is matched with internal odometric position measure-
rrlerits. typically using a single coorcliiiate frame. This describes the raw map. This
raw map is then etlcoded in accortlar~~: to predefined rnodellirig specifications. Stan-
tlard approaches of world niotlelling include fitting primitives or applying oprrirtcmi
to collected data. These approaches are often rncountereti in visiori where suprr-
ellipsoid or othrr parametric moclels are used to represent setlsory input 122, 14, 231.
Other work in data modelling includes forming nlotlels for sonar readings taking intu
account the intrinsic characteristics of the sensor [24, 1, 251. Once the raw map
is modelled. the final erivironment representation is stored to be used when ncces-
sary. This mapping architecture tias several drawbacks when dealing with real world
interactions.
Csing a single sensory modality is often not adequate to provide an acceptabltb
description of the environment. Many situations arise where certain sensory systems
are preferred over others. where one sensory system reveals no information while
another can extract useful features. Previous work in data fusion examines how to
match up noisy data from several sensing system to form a consistent map [26, 27,
CH-IPTER 2. APPROACH
13, 28, 291. Hackett and Shah [26] provide a sunrey of papers related to sensor
fusion and categorize them. They looked at a number of methods of sensor fusiori
that use simple set intersections. heuristic rules. non-linear least squares fits and
nlaviniuni likely-hood estimates. Other work [29] builds an architecture for fusing
sensory systems (range finder. camera and sonar) to autor~ornouslp drive a vehicle.
The work exploits sensor modality differences to produce complementar?; rather than
cornpetirig perceptual processes. The ability to fuse data or to automatically srlrct
the best sensory system a t a given location is a useful asset. Incorporating this wit hill
the mapping architecture improves the utility of the map.
X global reference frame ur large scale data correlation poses several problerrls
when rriappirlg a rral environment. While a single metric coordinate system is ir nat-
ural way to map space arid is effective over srriall areas. over large estents of space it
becotrws pro blenlatic. In particular, over large regions OF space irlcre~rirtltal posit iorl
errors car1 accrue to cause large errors in the global coordinate systerrl. Corrrlating
sensory <lati1 with erroneous dead reckoning tneasurerrients s k w s the represeritatio~l.
This can occur even when beacons or lantlrnarks are used to reduce otiornetry er-
ror. Further. this type of Prror ran causc inconsistmci~s in a map when updating
is perfortried. since updated information may be put in the wrong place. In many
rases. it is sufficient to create local coordinate frames only in selected regions. where
odornetry error must be nlinirnizcd. Kuipers. for example. considers this problem in
the context of building topological maps and proposes using reheursul procedures to
identify nodes. eliminating the effect of odomctric errors [21].
In this work. we are interested in mapping using a collection of local coordinate
frames organized topologically [30]. Data collected in separate coordinate frames
can he treated as independent local maps. each corresponding to a specific sensory
system and modelling method. This allows to select the best sensing system at a given
tocation. Furthermore, all metric relations are consistent with the real world since
they are gathered in local a r e s . avoiding large scale errors. Each frame is considered
CHAPTER 2. APPROACH
as a separate local metric map. The global hierarchal organization of these local maps
comprises the large scale map (figure 2.1).
Where and how should we attempt to create a local nietric niap so that it will
be accurate and effective:' To answer this. we must first determine what each node
represents. what cornpu tational procedure will be csecu ted a t each local map. \\is
consider how to evaluate the local enviro~iruerlt with rcspcct to an arbitrary local-
iz;rtiori procetl~lre. Candidate locations can be found where local metric maps are
gtbnerateci speritically for localization. Hmce. the mapping criteria are based upon
the best locations suitable for localization. However. this mapping franicwork rerrlains
generic in that it can be used to construct maps where other tasks are it~volvrcl. Lo-
calization baseci nodes wrrr chosen sincta they form an example of an ubiquitous and
challenging task of usiug rriaps. Furthermore. \w will st^ later that they are essential
coniponents for building ii navigation map.
In this work. we employ two localization nwthotls illustrating the use of two
drastically different classes of approach. \Ye show that for each method. we can
develop techniques that predict how appropriate a given region is for localizatiorl
(and hence for metric mapping). Thew t~chniques arc incorporatcvl within a mapping
architecture to produce a hybrid of topological and nietric representations.
We propose ;L mapping architecture as follows: -4 robot esplorrs the environment
using some esplorat ion strategy. While exploring, region select ion criteria are eval-
uated For each sensor modality to determine whether the robot should build a local
map at the rtirrmt location. Once the criteria are satisfied. the robot begins to gen-
erate the local map of the region using the best sensory modality. During this phase.
the robot also continues to evaluate the region to confirm its original decision. If the
criteria are continually satisfied and the local map is complete. the robot stores and
connects it within the global map. The robot then continues the next iteration.
The following lists the problems that are encountered in our mapping architecture:
Environment exploration
0 Region Selection
Local map generation
0 Topological connections
Although some of these problems are interrelated. to an extent. each one can be
treated independently. We can build separate modules to find solutions to these
problems where the complexity of the algorithms withi11 each rriodule can be treated
independently. However, a corripatible data model between certairi niodulcs is rth-
quired. For exaniple. the robot may be manually tiriveti in tlie expluratiori step or it
may use an existing exploration and control strategy to autonurrumdy drive (such as
[31, 32, 33, 34, 351). However. there must be a compatible record of the expluratiori
procedures executed such that the nodes may be cormected together appropriately
during thr topological conriection phase. Similarly. if the robot attrrnpts to build ir
local niap usirig a certain sensing system. thr region selection algorithm must urltier-
stand the inforrriation rrwtlt4 used such that it (:an rvaluirt~ the twvironrrlent proprrly.
The specific rr~odclling tnethods used to reprcsrrit the local rriaps artb assunied to rsist
in advance.
The main focus of this thesis is on region selection. The robot r rwt autononioiisly
tlrtermin~ whether an area is appropriate for rnetric mapping. It will be seen that this
tiwision. the configliretion of the map and what information How is rtyuireci within
the above listed modules is based on the task the map is intended for along with the
liniitations of the agrnt constructing/tri~lrersing the map. The flow chart in figure 2.1
shows the architecture of our system.
CH-4PTER 2. APPROACH
/Local Maos \
Explore I election Criteria 'I
Reject 1 1 I Build Node 1
FIGURE 2 .1 . A global map composed of counected local maps (left) and a How chart of the map construction algorithm (right). The robot explores until the selection criteria are activated. .At that point. the robot builds a local map while intermittently confirming that the criteria evaluation is still positive. Once the local map is complete. it is iirlked to the hierarchy of local maps previously constnictecl.
CHAPTER 3
Islands of Reliability and Topology
In this work. the environment is represented by e set of accurate local maps. Each
local map is built using its w n lucid coordinate frame and rrdelling trwttiod. I r i
theory. any sensory system and rnodellirig rnerhoci can be tiseci to cereatr a locd
map. Hence. it is possible to [lave a set of local rrups where each map consists of
i~ifor~nation gathered wi th a differclnt serlsory system irrld trlodelled with ib tiiffermt
or rnudelled data that is in accurate correspondence to the real world. These local
maps are referred to as islunds of reliability. When the robot lies in the vicinity of an
island. it has the potential to perform local computational tasks involving real world
data and stored data with accurate results. The mviroriment is represented by a set
of these islands. where each island forms an independent coniputatiord component
of the global map.
The islands of reliability are organized in a topological structure. They constitute
nodes of a topological model of the worid. i.e.. a graph [21, 36, 371. Nodes are con-
nected together by edges of the graph that include descriptions of their ronriectivity.
An important note in describing the connectivity is to do so without use of u pnon
metric data of areas outside the nodes. otherwise it would not be consistent wit t.1 our
CHAPTER 3. ISLXXDS OF RELIABILITY AND TOPOLOGY
model. We defirie the global map. formed by the islands of reliability. as follows:
-11 = {K E }
C' = {c,,. Ul. .... u , }
L1, = {L. T }
E = {q.r2. .... e , }
r, = ( c , c , . S. K }
.\I is r h r glot)al 11liip. i r wrisists of a set of noclrs 1- and a set of 4 g r s E. A nodtl
c, corresporids to a local metric map L and the sensirig/niodelling type T used to
build the local map. An edge r , corresporitls to two corint'ctirig riutles i * , ~ ; . il sthr vf
instructions S tiescribing the connection anti a wight rr. Each t d g ~ carries a wight
that may btl related to the corresponding instruction set S ur to some properties of
tllr target riode. This tlcscribes the envirorment by ;I set of clear and accurate patches
of information that are organized topologically.
Consider a robot that lies at a node. 4 such. the environrnent structure is
iicquired in the form of a local map L of type 7'. When the robot veers away from thcl
node. following an edge e , . the environrnent is unknown until it reaches t h ~ next norlr
where environment structure is re-acquired. The robot must exit a node followirlg
and edge. If i t does not, it will no longer remain within the domain of the map ant1
may not find it's way to the next no& This niechanisni is similar to that of static
attention focus where the robot onlv diverts attention to certain environment features
while ignoring others. The features are unchangeable landmarks that can be used to
perform metric operations.
By using separate local reference Eiames. we avoid the need to perform large-sc&
enor integration. Metric data is gat hered only within restricted regions. At each
of these areas. data is mapped in an arbitrary way. forming independent local maps
(islands of reliability). The global map consists of a set of these local maps distributed
a bout the environment. selecting interesting regions for metric mapping and ignoring
others. (The robot does not wast time mapping uninteresting areas.) Ignoring the
3.3.1 TASK BASED DISTIYCTIVENESS 51E.ASL'RE
uninteresting areas causes voids in the global map. However. providi~ig procedures
that describe the connectivity between adjacent nodes (within the voids) eliminates
the need of an prior-i nietric rriap. These links may preclude any metric relations
between the notles. Nevertheless. it is not necessary to maintain these relations since
over large scales they are erroneous due to accu~rltilated error.
3.1. Task Based Distinctiveness Measure
The key issues in constructing the topological-metric representation described by
equation 3.1 are selecting where to place the nodes and how to connect them. That is.
we would like to determine rvherr good candidate locations for local reference frames
lie and record thr topologir*al conri~ction of these 1ocx.tions. U n w thr rtagions ilrd
their topology tare dcterniined. the map is fornied by botb the metric data gathered
at t ht> regions and t lie descriptions that relate c hese regions. This topological-metric
niodel. in the forrri of equation 3.1. det:omposes the twvironnlent into qualitative arid
quantitative components. In order to tieternline these cornponents. tile purpose of
the map must first be defined.
The niodcl's configuration is dependent on the task it facilitates. Without knowl-
edge of what goal the map is intended for. an appropriate configuration cannot be
determined. Once the task is defined. the task itself can be examined and deconi-
posed into qualitative and quantitative components. The quantitative components
describe computations involving (I prior+ nietric data and real world data, while the
qualitative components are high level instructions not requiring a priori metric data
of environment features. These coniponents define the configuration of the map. The
mapping procedure can then be accomplished in 2 steps: 1) Areas relevant to the
computational components are metrically mapped. generating the islands of relia-
bility ( V in equation 3.1). 2 ) The islands are connected together by including high
level instructions that are defined by the qualitative components of the task (E in
equation 3.1). The connecting instructions are subject to the model's u priori knowl-
edge constraint: they are expected to be executed without the need of u p i o n metric
information outside of nodes.
By defining the topological-metric configuration with relevance to a task. we
form a general framework to construct the model. This approach is necessary since
when looking for rnterestinq landmarks to insert as nodes. we must first defirie what
irltcrrstirig rllearls [38]. We definc interesting areas ifi arras that provitlr inforrriatiori
that satisfy the computatiorlal components of tlie given task. As such. tlie task can
be executed by traversing the graph. irpplying the metric cwnputations at the notirs
imtl following the instructioris ;it the edges.
This task based approach has analogirs to models of hunlari cogriit ion [19]. .Just
as the ASR configuration is dependent on person's goals (section 1.2). the node and
edge configuration of uur rnotlt4 is cltpxdtmt on t h ~ robot's goals. For t?xamplth. if the
robot is to paiut hallways. then thta map is configured to facilitate that task. Nodes
are placed at the hallways. such that the robot can accomplish the conlputational
painting tasks. The hallwrys become areas af interest. or distinction in the map.
Edges between the nocirs may describe the painting order. the nearest nrighbour
hallway. the complexity of the painting area. what color to paint the nest notlr.
etc.. This map is a painters map as prrreiv~d by t h ~ robot. I t stores and relates
inforrnatiori ac:cortling to a hallway painting task.
Different topological-rnrtrir configurations esist for different tasks. t w h with the
corresponding node placement and node connectivity. Ongoing work in our lab 1391
similarly produces a task-specific environment representation. In that work. the goal
at hand is to present a suitable configuration for a human observer. Therefore. the
nodal distribution is based on psychophysics. what catches a human's attention in
the environment.
This illustrates that the topoIogica1-metric model described is a general one and
can be used for many different mappiug goals. So long as the map is tagged with a
task. we can decompose the environment at areas computationally relevant to the task
and at uninteresting areas. Were those areas lie can be determined by a distinctiveness
measure. We define a general farm of the distinctiveness measure as follows:
Definition: The distinctiveness measure R for u uunrpututional tusk T ut un
ureu -4 is rneusure of how well the structure at area -4 allow the uceornplzshrnent of
the computcltzunal task T .
Given a computational task. we can evaluate arras of the environnirrit to predict
if the cornputatiori call be accomplished properly. Areas that show succcss art1 la-
belled with a high distinctiveness measure anci areas that fail are labelled with a low
tiistinctivenrss rrieasure. R car! br described as a lacierlcy measure of the envirormie~lt
that transforms explicit features to quantitative measures based on the usefulness of
data.
3.2. Navigation Map
The cunst rnirits for the spatial tlistribution of t hc islands of reliability (nodes) are
cleternlined by the computational task they facilitate. 111 this case. the map we intend
to build is a navigation map. In order to properly anci safely navigate. we should have
thc ability to localize [12]. That is. when an entity traversing the envirorment infers
it is lost. it should have the ability to compare sensory information with stored rriap
data in order to localize: to determine whrre it lies in the u p n o n map. Updating the
position estimate relative to environment features provides a. safer way to navigate
than by dead reckoning. This furitlamental computational task defines the islands of
reliability as localization based maps. Consequently. the computational component
for the navigation task. involving a pn'on' information and real world information.
is localization. Hence. islands are placed a t areas that provide good localization
information. Calculating the distinctiveness measure for the localization task provides
the constraints necessary For a beneficial distribution of the islands.
It is possible to form the islands of reliability using different sensory systems and
modelling methods. Furthermore. there exists many different localization techniques.
each with their own strengths and weaknesses. Therefore. the formulation of the dis-
tinct iveness measure R depends on the actual localization scheme and island models.
However, general guidelines car1 be provided in order to evaluate the environnlerit
and select distinctive regions. The general form of the distinctiveness measure R for
localization can be described as the following:
where I represents the reliability and strength of the response uf a serlsilig trchriicliitb
i r t d A I represerrts the ar~loilrit of spatial change uf that response (which may btb 0s-
pressed as spatial corlstraiut). / ( ) is some furictiori rnmotoriically pnqmrtional tu
both I ant1 11. Q, is ir quality measure sprcific to the propt~rtics uf the 1or;ilizatiot~
tectlriiquc anti A, is a corresponding weight. That is. to successfully perform localiza-
tion. there rrlust btl sufirierlt reliable infortnation I subject to spatial variation 1 I
along all degrees uf freedom. The addition of ad-hoc quality measures Q,. sptd ic*
to the techriiclut~. can iniprovcl region sekctiori. However. rrlost of the emphasis is on
searching for areas with enough reliable information subject to spatial cbhange (low
structural ambiguity). -4 good choice for f ( ) is one of the form I * 11. taken along
the dimension that results in the minimum value. As such. R is large if both I arid
-I1 are large in all degrees of freedom.
Note that it is not suffice to valuate R using a single one of these two demerits. I
or AI. both are necessary for localization. For example. if the evaluation is based only
on I. areas with reliable features in the form of a pattern. say a fence or wallpaper.
woulci show a high measure. However. localization at those areas is ambiguous (AI
is zero at the corresponding scale) and a node at those positions would not satisfy
the localization task. Similarly. if the evaluation was based only on 11. then features
with good spatial variance may show large 11. but the features themselves may not
be reliable sources of information. Therefore. we combine the strength of features
along with their spatial variance. Islands placed at areas with a high distinctiveness
measure render local maps with enough relevant features for accurate positioning
(avoids placing them in anlbiguous areas such as a long white hallway). -In iniportant
note about these two elements is that they reflect the two discussed limitations o f a
real robot: uncertainty in sensing and positioning.
To corriplete the topological-metric model. it is not suffice to present the envi-
ronrnent only by local niaps. As nientioried earlier. the local niaps form riodes of
the topological rrlodel that are linked together by edges. The edges are am importarit
cwnponent. providing instruction to follow between adjacent r i o d t ~ Tlir types d'
instructions requircci to accomplish our task are navigation ones. The rnap sl~oulti
provide the ability to navigate from one island to another. Hence. thtb edges must
include descriptioris that allow reliable navigation between corirwcting riodes. without
use of an u p i o n metric map. In this regard. the edge of a source node to a target
node entail a set of control strategies that navigate the robot from a given position
in the source frame to an estimated position in the target frame [21]. The idea of
using such canonical paths is justified by animal behwiour [20]. These instructiotls
may navigate a robot from orlr node to anotht~r. but cuc t ly whtw in the riorltb thtl
robot may rrid up is ~~ridett~rrriinid
DUP to aceumulat~d error. accurate robot positioning is not iwailahle whrn rs-
wuting an rtlgr's navigation instructions. We cannot assume that the robot would
fullow the instruction exactly. without errors. Furt herrriore. in accordanw with our
model. no environment data is gathered between nodes and no reference frrarnir~ is
given. It is not possible for computational position upclates using cwrironmcnt fra-
tures. All position estimates are based on internal measurements. such as dead reck-
oning. Thus. any attempt to extract a position estimate is subject to a degradation of
accuracy as the robot diverts further away from the node. However, an error bound
can be estimated among neighbouring nodes such that the robot's position can be
bounded within an error radius. The robot can blindly reach somewhere inside a
node (within a bound). Once the robot reaches the node. its position can be calcu-
lated more accurately using the corresponding computational metric map dedicated
for such a task.
This further relates the node and link distribution to the dead reckoning error.
To confidently navigate from node to node. the links should not be too long. The
error radius should remain small. coinciding with the connect irig island of reliability.
The robot nlusr avoid getting too lost in a link where it callriot find its way to the
next island. When required. position calibration can always be done by reaching the
cotinecting islands. Hence. the size of the i s l a~ds are proportiold to the accumulated
error. Furthermore, we enforce a lower bound on the error radius. The lower bound
prevents nodes froni being urlnecessarily close to each other when the qualitative
co~ltrol strategies suffice to navigate. -Attempts to build nodes arc. unly invoked uiirr
the robot infers its t i a s crossed the lower error b ~ u n d .
.issunling co~lsistericy of dead reckoning error for an exploring rubot. we call
define the node placenmit criteria as follows:
where 6 is the estimated accumulated error. Er,,,,, is the predefined l o w r rrror bound.
R, is the distinctiveness measure for model type 1 and T, is the predefined acceptable
tlistinctiwness measure threshold for sensing t y p ~ 1 . When the exploring robot infers
that it is lost (once the estimated acrumulatetl error has crossed the lower bound
error) the robot attempts to build an island of reliability using the available sensors.
IF the best [list inct iveness measure R, normalized by the curresponding acceptance
threshold is large enough. the island is inserted to the map. Otherwise. the robot
continues exploring. searching for a good area. Note that the more lost the robot is
the more willing it is to accept a potential island.
The size of the region mapped is related to the error the robot accumulated:
However. the islands should not grow too large such that they remain locally consis-
tent.
In surnnlary. the navigation task is decomposed into qualitative and quantitn-
tive (computational) components. The qualitative components consist of navigation
instructions that iufornl the robot where to go. what path to follow. The quantita-
tive components are the islands of reliability that allow tlie r o h t to rrposition itsdf.
The environment is mapped according to these components to form the topological-
metric nlotlc.1. Tlw configuration is constri~irlcd by t tie dist ilictivrric~ss rrlrasurc fur
tucalizatiotl a rd the accun~ulutecl error.
CHAPTER 4
Local Map Perception
This section discusses the methods used for representing the islands of reliability. The
r~iethocls rely or1 dead reckoning iriforniatiorl for pow-data currespondmcc. therefore
they are only locally consisterlt arid herice arc referred to as local maps. The niodelling
techniques irre tlt~vrlopetl in order to satisfy the corresponding locdization twhniques
which will also be discussed here. For a more complete description refer to [I] and [141.
We will briefly esarnine some of the details of these techniques since they describe the
local map perception and the tiistir~rtivcness measure corrrspond to thclir twoding.
4.1. Sonar Based Environmental Model
In order to perform localization. a model is constructed of how sensory data
varies as a function of the robot's position. The model resembles the layout of the
environment but is not a veridical map describing the layout of real objects. That
is. it describes the range sensor inputs as opposed to actual 2-D or 3-D occupancy.
The model is built by fitting primitives to sensory data. Line segment primitives are
considered efficient in nlodelling a collection of observations of the environment. Their
utility is appropriate given the characteristics of simple threshold- based sonar sensing
where even a small structure will produce collinear measurements. (Although. RCD
modelling may form a better representation but are cornputat ionally intense when
fitting to data.)
4.4.2 SONAR BASED POSE ESTIM4TIOY
The line fitting method is done in several steps. First. a spatial clustering algo-
rithm is employed to determine groups of neighbouring points that correspond to a
potential line segment. Then. by using a line titting procedure. a fitted line segnmt
is used to model each cluster. Finally. :a split and merge routine is applied to further
segment ant1 merge the lines at each cluster for a more proper fit. The final result is
a map composed our of line segments that may be usrd for locdization. -4 sanlplc.
map is shown in figure 4.1.
I? [CURE 4.1. .ill environment nlodeiled by line segment fits [II. .A robot ex- plored the environment. following the dotted pet 11. to build the line scgrrlerit rnociel.
4.2. Sonar Based Pose estimation
The pose ts imation problem is formulated as an optimization problem in terms
of the extent the map explains observed measurements. There are two phases involved
in position calibration: 1) Classification of Data Points and 2) Weighted Voting of
Correction Vectors. In the first phase. each measurement is associated to a line
segment in the model using a clustering algorithm. This allows to determine the
Correction Vector relative to the line segment in the second phase. An important note
is that only the perpendicular error of points are used to determine their Correction
4.4.3 L%IAGE BASED ENVIRONMENT.lL hIODELLING
\kctor. It is a one-dimensional posit ion constraint provided by each rrmisureriient
along the normal of the associated line segment. This Lack of constraint rlianifests
itself as what is called the long hallway effect. where observation of the position uf a
line segnierlt gives ouly information alorig its normal. l I ul t iple nwasurenients fror~l
non-parallel line segments are essential to const rairl t lie pro bleni in but tl dimensions.
The second phase is that of a non-uniform weighting of Correction C'ectors. Each
point is given a weight in relation to the distance it lies from the associated line
segnient. The weighting factor is defined as a sigmoid function:
Where d is thca tlistanw from t hr linca segment. r n ard (* arc1 constanrs. Points n t w
their lirw srgrricnt are weightrd rnorc than thoso that are f;rr sincr far ones artB probably
outliers. The overall Correction Vector is calculated as:
where c, is the perpendicular error vector br point r . The position estimate is resolved
after several i trrations of translating about the Correction Vector. Ideally the m a -
surements would be distributed equally in association to lines of both dimensions.
This would allow a position estimate in both dimensions with similar confidence.
Figure 4.2 illustrates the localization scheme.
4.3. Image Based Environment a1 Modelling
Building a description of the environment's structures using vision is known to be
a difficult problem. Generally. parameter or CAD type modelling of the environment
From a set of images entails solving the inverse problem defined by the surface ge-
ometry and reflectance. The method considered here differs in that is uses images in
4-4-3 LbIXGE BASED ENVIRONMENTAL MODELLIYG
Sonar points
Correction
Vector
Wall
FIGURE 4.2. Localixatiori by iterating about the Correction Vector consist- ing of ;L weighted sum of the error vectors.
creating its own implicit model optimized for localization. It avoitis the difficult prob-
lenis of computing a 3D model and forms a perception of structures by statisticidly
encoding irnagr katurrs as a Functio~i of pose.
For a camera nluunted on a mobile robot. the depmcltmy of the image and the
pose ti = (r . 9) is related by some function:
where i is im N-dinlensional vector of pixels. In order to solve the problem of com-
puting the camera position we must invert the function:
However. computing the inverse directly on images is cornputationally impractical.
in itself is not necessarily one-to-one and an inverse may not exist. To produce a
computationally tractable solution the images are modelled by a set of .\.l features:
4 . 4 VISION BASED POSE ESTIhIATIOX
This produces a lower dimensiorial space that relates the features and the pose with
a mapping:
At each smipling position. the robot takes a snapshot of the environment. Fea-
tures are then extracted and correlated with the odornetric readings. encoding the
rnviro~irrienr. reprrsentation in terms of a feature space. Given a r i t w image. it is rlow
computationally tractable to deterniirie its features G(i,,,,) and interpolate tiirough
the a. priori Feature space to extract a pose rstiniatt*. Thus. lorwring t l i r clin~tmiou-
ality of the problem allows us to solve it rriore efficirrltly.
Sleasurenient ftutures were cirrivrd from statistical propt>rties of idge images
(using t htb Carmy-Drriche optbrator) to rriininlize t hr effccts of' illuniination variation.
Thck perceptual structurp associated with a position in space consists of the following
c:Iass of rrwasurcments:
a First and second rnorncnts of the edge distributions
.\Iran r d g ~ orientation
a Densities of pirrallrl lines at four oritwtat.ions
These features conipromise the first ccritral nlonlents of the edge distribution in space
and are the natural choices For t~fficient encoding.
4.4. Vision Based Pose Estimation
Since it is inefficient to sample the environment at every possible location anti
sensory data is often noisy. it is important, to have the ability of robustly interpolating
within the feature space. For local areas this can be done by a linear interpolator:
I Gk-1 - GGd I (q2 - q1) Y = + Yr (4.7) 1 G ( L ) - G(i l ) 1
Empirical results showed that the linear interpolator is only applicable to very
restricted regions. In large regions or more complex areas. the linear interpolator fails.
4 . 4 . VISION BASED POSE ESTIMATION
In practice. a three layer back propagation neural network is used. The network
takes training examples and assigns appropriate weights to each network node by
minimizing training set errors. When a new feature set is used as input to the
network. the pose can be revealed by taking a linear combination of the output units.
Generally. if thc feature space is smooth. the interpolator would output good
results. On the other h a d . if tbr feature space c.onsisteti of r u t y gaps and rliscoti-
tinuities. interpolation between thrsr gaps may producr inac+curattb results. We haw
a trade off btween practical sanipling resolutiuti versus accuracy of the interpolator.
The sampling det~land is deterruiried by tlie coniplexity uf the environmerit. clioosirig
a sampling resolution for the most complex erlvironrrierlt (worst case scenario) rill1
be irxipractical. Althuugh. rrivirorinlcrit structure may also ilnlplify discolitinuities 110
matter the sanipling resolution.
CHAPTER 5
Local Map Distinctiveness Measure
Criteria
Wheri human observers are exploring new territories. their notion of the environrrient
can be described by a set of distinct landmarks. Once they veer off from tlw last
known landnlark. they set out to find ttir rlmt distinct Feature to t~r rrcordrd in
the cognitivr map. What is distinct to human o h s ~ r v ~ r s is i w w c i i r t ~ t l nit, h t hcir
goals and perception. Similarly, we seek out t h ~ best (most distinct) parts of the
environment corresponding to the robot's perception (which also corresponds to a
task). The task at hand is (s.y) position estiniatiorl anti the prrc.cption niodels
considered are the sonar and vision systems (described in the previous section). The
distinctiveness nie;uurr is derived accordingly. We derive methods to predict where
the robot can extract pose information for the (x.y) coordinates based on the general
guidelines of equation 3.2. The robot orientation 8 is not considered since only in
rare cases (the presence of circular symrnetrv) will the robot be able to localize its
(x.y) coordinates but not the rotation 8. That is. in most cases. the distinctiveness
nieasure for localization over (x.y) is the same as that for localization over (x.y.8).
3.5.1 MEXSC'RE CRITERI.4 FOR THE SON-4R SYSTEM
5.1. Measure Criteria for the Sonar System
.A good dist irict iveness measure for the sonar based localization and modelling
technique is one that assigns high values at areas well constrained (11) by near
line segments of significant length (I). That is. a local map with enough constraiuing
information reflects a region where the robot can localize. while uear line segments are
more reliable than distant unes. providing more dense serlsory ftdback. Furthcrnlorr.
it is desirable that the line rriodel shows siniilar orthogonal constrairlts along buth
kgrees of frecdonl. This rcsults in q u a 1 localizatiorl cutlfitlerlcr along the dinlensiuns.
h e p i ~ l g the error bound round. In the extrtmle case. a map coristitutirlg uf parallel
lines would r w ~ l t in ambiguities along one dimension arid will riot provide enough
information to adapt t tie full potential of tht! localization nirtllotl.
For the line rrlotiel niethotl. the distirltrtiveness mcwure R at a point p = (r . ! j )
over a square nt~ighbourhootl ( 2 0 ' can b t b calculated as:
where.
Q is a quality measure of the localization scheme. The functions fil and fL depict
the amount of reliable information I and spatial change of information LI along two
orthogonal directions. The smaller of the two represents / () in equation 3.2. choosing
the weaker dimension as a worst case scenario. We integrate over a rectangular area
defined by e and normalize.
The next and most important step is to define 4,. fL and Q. For these. we must
first derive I and AI in terms of the line model. In general cases, the reliability
5.5.1 MEASURE CRITEIIIA FOR THE SOX-IR SYSTEM
of iriforniation I is proportional to the distance of a sensed signal. Distarit lines
provide sparse and less reliable information due to a weaker. degraded sensory signal.
Furtherniore. a line segment provides strong constrainirig information 1 I only along
its normal. That is. an orthogonal positiori change with respect to the line guarantees
a sensory rrieasurenient change. We define A I to be the orthogonal component of a
serised line segment.
For each lirie segment. we iritrgrate the strength I allti the orthogonal constraint
1 1 to determine the cectur rn~luence along the nornial to the line. CVr compute the
vector influerice for each visible line segment (in the forrri o f 1 * 11) by:
I * I is the urtliogonal vector influmcr for line segtnerit i serri by point p arid .V, is
the unit nornial of linr segment i. 8 sweeps the visible viewing directions from the
point to the line segment. Only arigles within a reflect;~ncc threshold are taker! iri
to account in order to simulate specular reflection of real range siglials. p, is the
intersection point of line scgnient r and a l i w cwittcti fro111 point p idotlg the vitwiug
direction 8. The constraining relation for Vi is iri essence a projection of thtt vectors
fornietl from point p to linr segment points onto the nornial of the line segment (shown
in tigurt. 5.1 ) . IIv(..) espresscs the reduced probability of observing an object as a
function of distanct~. I I - is described by an esponential decay function:
k is the decay constant that is determined by the range of sensor confidence.
Once the vector influence is computed lor all visible line segments. we choose a
reference cector and determine the total number of components parallel and perpen-
dicular to it. These components determine the magnitude of constraint and reliability
d o n g two orthogonal directions and are calculated as:
5.5.1 ,LIE.L\SCRE CWTElU-4 FOR THE SON-IR SYSTEM
Pi Line Segment
Robot
FIGURE 5.1. Sweep over each line segment to tietern~ine tliu overall cun- straint axid reliability. Scanning resolution can be corltinuous or triirtch that of the real sensors.
A good choice for the reference vector is that of largest magnitude. since it de-
termines the dominating constraint. .I poor choice may lead to inaccurate results.
Consider a long line segment of slope I relative to a basis composed of a minute
line segment. The only constraint parallel to the long line segment is the projection
from the minute line segment. However. the computed parallel and perpendicular
constraints are almost equal (since the slope is I ) resulting in a high distinctiveness
measure. This is undesirable and to avoid it the dominating vector should always be
the reference basis.
The functions f L and fII describe the total strength and constraint of all the
line segments visible from point p. However, the numerical value of these functions
5.5.2 MEASURE CEUTERIA FOR THE VISION SYSTEhI
does not provide a decision threshold. To distinguish good valued from bad ones. we
re-map j, ( i heing I/ or 1) using a sigmoid filter as:
The cutoff threshold c and the decay rate rn can be found rmpirically. This allows
us to empirically coritrol the meaning of the numerical results. It provides a measure
ranging frorn 0- 1 ~d1c . r~ values above .5 cittl be considered acceptablr for localization.
The extra quality measure is iniplernentetl by evaluating the equality of the above
ternis along both directions. This determines whether the localizat i o ~ corifidenct~ is
equal along the two degrees of freedom. CVr compute a quality rneasure Q as:
Q rariges h r n 0 to L where 1 represents equal orthonormal constraints and O rrpre-
w i t s that only one direction forms a constraint.
5.2. Measure Criteria for the Vision System
111 terms of the vision based localization technique. good regions are denoted
by 3 properties of the feature space: a non-zero. non-constant and smooth feature
space. Feature values that are low or close to zero are indistinguishable to noise and
don't provide consistent reliability due to lack of environment information. (indicated
by a small value of I in equation 3.2). A flat feature space would result in not
enough spatial variance of' features. leading to positioning anibigui ties (indicated by
a small value of 11 in equation 3.2). A highly discontinuous space would reduce the
interpolatory accuracy for position estimation due to lack of sampling information.
Further~nore. equality of localization confidence along both degrees of Freedom is
desirable to keep the error bound circular.
5 - 5 2 UE.ASLW CRITERLA FOR THE VISION SYSTEM
For the vision system. the distinctiverless measure R at point p = (r. y) about a
viewing window (26) ' can be calculated as:
where.
and.
Ql is the quality measure for qua1 orthogonal constraints. Q2 is the smoothness of
the feature space arid / ( p ) represents I t 1 1 uf equariori 3.2.
Fur a featurr I iri the nornializrtl fcirturr space G. w (:an drtrrnlint. f at ;L p i n t
p along a directiori j ( j bring r or y ) as:
Figures :.'(a) to 5.2(d) show some sample scenes and their feature values. It can be
seen that the simple and noisy scene lias many locations with s n d feature values
that do rwt vary tiiuch. The details about the features uscd ran br Lurid iri the work
by Dudek and Zhang [U].
To properly evaluate the value of distinctiveness measure. For all the features we
average the values fl,, to form f, and map the result through a filter. We then need
to reduce the weight of areas with low slopes and weak features while accepting larger
slopes and stronger features. A sigrnoid is used for this mapping:
5.5.2 >IEXSCW CRJTERI-4 FOR THE VISION SYSTEM
W e compute Q l ( p ) as:
- if f&) > MP) otherwise
where a result of 0 implies unequal constraints and a result of 1 shows uniform con-
straint. We then derive the feature space snmothness nieasure as:
Further. a function is used to map Q2. This would increasr weight to areas: with low
values of V'G (smooth ones) ant1 recluw areas with large value of G'G (discontiriuous
ones). Again the sigmoid in another form car1 be used:
All paranieters are determined empirically (see appendix).
5.5.2 1LIE.UUR.E CFUTERI-4 FOR THE VISION SYSTEM
FIGURE 5.2. 5.2(a) shows the features of the sample image and 5.2(b) shows the leatures of an image taken at a slight offset using the same scene. 5.2(c) shows the features of another sample image (less visually interesting than the first) and 5.2(d) is the same scene taken at a small offset. It can be seen how the feature values are low and do not vary for the less interesting scene while the more interesting scene shows good features with significant varia- tion.
49
CHAPTER 6
Results and Discussion
111 this chapter. rvr evaluate the the distinctiveness criteria by comparing them to
the localization error. .-\ good clis t inctiwness measure should assign large values at
areas with low error and Ion w l u e s at high error locations. Cutnparirlg the pusitiori
estimate cotlfitlence with the distinctiveness measure allows us to confirm or reject
our ability to predict where importatit data lies arld where data should not be trusted.
We further proceed in discussing the results of building the topological-metric map
using the mapping criteria (equation 3.3).
6.1. Sonar System
For the sonar method. a line segment nludel tvas nianually constructed provicl-
ing the simulated environment shown in figure 6.2. The distinctiveness measure for
this sample environrrlent is plotted in figure 6.3(a). These results were obtained as
follows: First. at each sampling point in the map. conlples sinlulated sonar readings
w r c extracted using a robot controller/simulator developed in our labs. Then. the
distinctiveness measure operator (equation 5.1) was applied on the data to output the
plot. We can see how the long hallways show low measures while regions that are well
constrained aloug both dimensions (such as intersections and bounding areas) show
high measures. Furthermore. areas distant from line segments are of lower measure
due to the exponential decay (the decay constant k was set to 11200 cm to simulate
6.6-1 SONAR SYSTEM
a large scale region). The sigmoid constants were empirically set using a minimum
acceptable measure threshold as follows: an area with at least one line segment with
minimum length of jOcni seen no further than ll'kcnl along it's niid-line is considered
acceptable. If there are no otlier visible lines and the seen line segment is smaller and
further away. the rneasure will lie below the sigmoid cutoff. The neighbouring area
of the operator was set to zero (such that measures consist of only a single point
rather than an accunlulation of a neighbourhood) and the reflectance threshold set
to 30".
The nest step is to tlrterniine whether the robot car1 localize itself at the locations
associated with a large value of the distinctiveness measure. Figure 6.3(b) shows a
plot of the localization confidence for the sample map. The data for this plot was gen-
erated using the same robot controiler/simulator and the sonar localization/modelling
software. -At each sarnpling position. simulated sonar data was collected. thereafter
crriploying a position offset by a rantloni 6 ranging 10-15 cm along four tlirections. Ttw
localization technique was then esccuted to output a position estimate. T t i ~ error was
calculated as the difference between the initial posit ion to the tw i rna td orw. t akin#
the average of the errors from the four directions. Confidence is simply c - rrrcrr
where r is some constant. Similar to the value the exponential decay constant was
set to in the above, the sonar confidence r a n g was set 200 crn for consistency of wale
(k=200). The reffectance threshold for the simulated sonar data was also similar to
the previously set one.
When comparing the two plots (6.3(a) and 6.3(b)). we can seen how the confidence
plot is consistent with the distinctiveness measure. Regions where the distinctiveness
measure was high tends to be those with high localization confidence. Likewise.
Valleys where there was insufficient constraints and the localization confidence is
low are also those where the distinctiveness measure returns low values. When the
robot was far from the walls. simulated sonar data was of lower accuracy causing the
Localization confidence to drop. similar to the distinctiveness measure. This match
6.6.2 \'ISION SYSTEM
between the plots confirms our ability to appropriately evduate the environment in
relation to the sonar based localization method.
FIGURE 6.1. Residual plot for figtire 6.3(a) and 6.Y(b). there are N data points with differences greater than residual.
Figure 6.1 shows the residual plot betwren the distirictivc!ncss nwasure and local-
ization confidence. The plot displays the accumulated difference between both data
sets riornialized to orie arid provides a quantitative cornparison between the plots. It
shows how many data points have differences greater than the residual axis i .r!.. the
.V axis is the number uf data points that have a difference of a t least the residual
axis value. It can be seen that there are not many data points with residual greater
than 0.5 (about 20 V/c of the data).
6.2. Vision System
In order to test the distinctiveness measure for the vision system. a real sample
environment was constructed. It consisted of 3 t p e s of regions: one with substantial
constraints (visually interesting). one with limited constraints (little visual interest)
and one with no constraints (not visually interesting). show in figure 6.-l(a). Snapshots
of the scene were generated using a pan and tilt camera. The experiment was set
up to capture an image. extract the features and pan the camera by -5" for the next
iteration. An 18-D feature space was built using 17 features corresponding to each
pan position. The total scene extent had a viewing field of 30" at a distance of Im.
6.6.2 b?SION SYSTEM
FIGURE 6.2. A sirrrulated envirortrne~rt with hallways. iutersectiotls and bounding regions.
The distinctiveness nwasure (equation 5.10) was employed a t each point using a
window size r of LOQ. Every asis (for a total of 18. 16 features. I and y) of the feature
space were nornialized to L within each window to allow consistent thresholding. Tlic
sigmoid function (equation 3-14 parameters were empirically set such that t hr cutoff
c was I / & and rate nr was 3 For a slow transition (cubic sigmoid). That is. features
with intensity (I) of I and a variation (11) slope greater than 1 fi are acceptable.
For the other signloid (equation ?? for the smoothness constraint) the cutoff c was set
to .I7 (a nlavirnum of 10" slope change) and the cutoff rate rn was 3 (cubic sigmoid).
The distinctiveness measure for this contiguration is shown in figure 6.4(b). As we
move frotn left to right. it can be seen how the measure is large at the beginning.
where the image is visually complex. Then it immediately begins to drop clue to the
operator capturing the plain white area. The distinctiveness measure remains low
within this region and begins to rise when the features a t the end are within viewing
range.
Although the distinctiveness measure seems to describe what is visually inter-
esting to us as observers. we again must determine if it predicts whether the robot
can localize at those areas. Thus. we compute the localization errors by examining
6.6.2 VISIOK SYSTEM
the training confidence of the feature space interpolator (the neural network). Where
the training confidence is low. localization confiderlce is also Low due to the inability
to properly interpolate. If the training confidence is high then so is the localization
confidence. For this. we used the previously collected data from each window to
separately train the three layer back propagation neural network interpolator. The
neural network consisted of 17 input units. for the features. 6 hidden units and 5
output units for the pose. (The pose is decomposed into 5 corrponetits for the output
units that call later be linearly combined to re-compose the pose. ) Training was done
using a neural network suRware package S e r u m that was developecl at Cniversity of
Toronto. The training confidence for each window is shown in figure 6.4(c).
The distinctiveness measure and training confidence show similarities over r he
sample scene. The dist irlctiveness meiuurtx is high at areas r hat nertb intrrprrttd
interesting anti low itt nun-interesting areas. Tlir training confitlcr~t~ sliows ;I similar
pattern. This validates our irbilitv to pwdict whrrtl areas of the environnient provids
crluugh localizatiori iriforrrlatiuri for the vision system. A plot of the residual diffrrericr
betwen tile localization confidence and the distinctiveness measure is shown in ti gure
6.5.
One significant difference for both methods is where the localization confidence
exhibits sharp drops while the tiistinctiveness rnciuurr undergoes srriooth decay.
This is due to the localization t~chniques that are only accurate within a region
of convergence. Once the robot moves bevond that region the solution becomes
conipletely incorrect: there is a narrow mid-ground. The analytic distinctiveness
measure, on the other hand. is a smooth continuous function. This attest some of the
variational inconsistencies between the plots.
Keeping this in mind. a mapping threshold can be determined by the intersection
point of the distinctiveness measure and the confidence cutoff region. Areas where
the measure is less than the threshold are not reliabie and should not be mapped but
areas displaying larger measures are good candidates. Furthermore. the empirical
parameters can be determined more accurately by forming an optimization criterion
6.6.3 SL4PPING WITH LDE SEGMENT MODEL
to minimizing the residual plot. Searching the parameter space to minimize the
difference between distirictivrriess measure arid localization corifidenre car1 ir~ipruw
results.
6.3. Mapping with Line Segment Model
The goal of this experiment is to explore an environment and follow the mapping
criteria ( q u a t ion 13.3) to build a hybrid topological-metric repr~writ at ion ( q u a t io rb
3.1 ). -1 largt. scalt~ simu1att.d er~viron~rient was built using the robot curit roller a rd
siniulator. h simulated robot np lo r~c l this environnienr using a pre-defined set of
coritrol strategies extracted From a siniplr hall following procedure 1351. (.\It hough.
rriore corriplcs and au tonoruous esplorat ion st ratcgies may be used.) The robot was
initiated at a startirig node and Followecl the control strategies. while keeping an es-
timated ( ~ y ) accumulated error. Once the robot inferred it was lost. it atteniptcd
to build a line segment rnoclel: i.e.. an island of reliability using the sonar systtm.
For sirnplicitv. we did nut include the vision svstern for this cxperirnrnt. Each is-
land was built using a simple node building routine. It consisted of collecting sonar
data at four corners of a region mitliiri tlw rninirnurri visibility range (closest object
secri) while attempting; to constrain the size of the node to rover a square area uf
4 ( c + j):! We only map within the visibility range since the mapping algorithm does
not include collision avoidance. ( S h e advanced node building routines can easily be
incorporated to the structure.) While collecting data. the robot intermit tent ly calcu-
lates the distinctiveness measure to validattk the region. If the region is acceptable.
the new node is added to the map. including a link to the previous node and the
control strategies that were followed.
Figure 6.6(a) shows the simulated environment and the exploration path and
figure 6.6(b) shows the hybrid topological-metric map. As shown. the robot built
nodes a t well constrained areas that provide good localization information. Areas
such a s hallways were not included in the map since they lack in information along
one degree of freedom. Note that the robot almost missed an intersection at the top
6.6.3 LIXPPLXG WITH LINE SEGMENT MODEL
of the map (the last node). This is due to the specular properties of sonar data that
were incorporated to the measure and is consistent with localization confidence.
Figure 6.6(b) shows the line segment models within the nodes of the hybrid
topological-metric model. Each node represerits a separate local map with its own
co-ordinate system. no global reference is used. The spatial arrangement of nodes in
the figure are only set for clarity. Links between the nodes in the figure describe thr
topology and include a compilation of the control strategies used in the exploration
step. The esploratory control strategies were compiled in the appropriate reference
Franir t u Furni the riilvigation instrurtior~s ustd btmvrcn r~eighbouring nodes. T h y
are listed in table 6.1. Note that if t h t k robot is esploring a cyclical environment, a
procedure such as that in 121) may be used to identify new nodes from old ories.
.-
Link I Control Strategies
F w d 660 1 F w d 78. Rot 90. F w d 360 1
Rot 190. Fwrd 682 I I 1 3 1 Rot N O . Fwrd 40. Rot -LOO. F w d 340 I I -I 1 Rot 90, Fwrci 'LO, Rot -90. Fwrd 650 1
TABLE 6.1. Control strategies for inter-node navigation
Each control strategy is initiated at coordinates (r. I/. O) = (0.0.0) in the corre-
sponding reference kame. Therefore. to navigate from node to node. the robot milst
first localize at (0.0.0) then follow the control i~istructions. These control strategies
form a simplistic way to navigate the environment. .-\lthough they are not purely
qualitative controls. they do form instructions that navigate the robot from one node
to the next without the need of a pion' data gathered at the links. Furthermore.
they can be replaced by purely qualitative controls strategies such as Follow WUIL 10
next node (or such as those listed in [21]). Here, sensory criteria can be defined to
execute these purely qualitative instructions. For example. the robot can execute a
wall following procedure. intermittently comparing sensory data and node data to see
if it has reached the next node.
6.6.3 SI-4PPING WITH LINE SEGMENT MODEL
Since rotational error was not included in this simulation, all coordinate frames
were parallel. If rotational error is included. then each node would be slightly rotated.
the control strategies would vary accordingly and the acc~irnulated ermr would grow
more rapidly. However. the tlistinrtiveriess rueasure used did not iriclude a criterion
For rotational degree of freedom. On the rare occasions. it is possible to choose a
hati area for angle estimation using the current distinctiverless measure (such as ttlc
centrc of a rowid roorn). Figurer 6.7(a) and 6.7(b) shows a topological map of a real
environment. The robot was set to extract the first 3 rlotles of the h~llways near
our laboratory. It is easy to set. how the robot only recorded local artbas that art1
well constrained anti igrloreci the long hallways. Tht! links are bitiirrctiorial sirice the
corltrol striltegies can be irlvrrtetl. Again they originate at ( r , y. O) = (0.0.0) in each
local reference frame. Table 6.2 shows the links.
I Link I Control Strategies I Fwrd 1'25. Rot 270. Fwrd 652
Rot 270. Fwrd 28. Rot 90. Fwrri 832
TABLE 6.2. Control strategies for inter-rwdo navigation
6.6.3 X4PPING WITH LINE SEGMENT MODEL
FIGURE 6 -3. Sonar based distinctiveness measure 6.3(a) and localization confidence 6.3(b) for the simulated environment 6.2.
6.6.3 %fAPPLYG WITH LIYE SEGMEYT MODEL
FIGURE 6 -4. Vision based distinctiveness measure 6 4 b ) and localization confidence 6.4(c) for a real environment 6.-L(a) with real object. room divider (shading is difficult to observe) and background clutter.
6.6.3 MAPPING WITH LIXE SEGMENT MODEL
FIGURE 6.5. Residual plot for figure 6.4(b) iuid 6.4(c). there ;Lrr .V data points with differences greater than res.iduul.
6.6.3 MAPPING WITH LINE SEGMENT MODEL
FIGURE 6.6. Simulated map and the exploration path 6.6(a) and the topological-metric map 6.6(b). Large dots in the exploration path show where the robot attempted to place an island but immediately failed due to low measure. The lull star like paths show where the robot had successf'ully completed to build an island. The partial star Like paths show an attempt that partially built a node but was dismissed due to later discovery of low distinct iveaess measure.
6.6.3 MAPPING WITH LIXE SEGMENT MODEL
FIG u RE 6.7. -4 map of a real environment 6.7(a) and the topological-metric map 6.7(b). The dots in the topological map show the origin of the local frame.
CHAPTER 7
Conclusion
This thesis describes an important step in the creation of large scalt. maps that com-
bine both metric and topological knowledge. The main idea was to build a global map
by connecting several local metric maps together. We formed a mapping criteria that
configured the distribution and connectivity of the local metric maps. Specifically.
wr describe how the locations of individual localization regions or rsluntls r ~ f r u l w
b l f i t y can be selected. Our general concept is illustrated using two specific yet very
different types of localization procedure: a sonar system and a vision system. The
distinctiveness measure showed consistency with localization confidence. making it a
good nieasure of the utility of environment information for localization. We further
examined the niapping criteria using the sonar system with a siniulated and a real
environment. The results showed that the nodes were connected appropriately and
placed at itreas where their utility is established. The thesis was put in context to
high level mapping goals that require the framework of environment evaluation.
7.1. Future Work
The two sensory and localization systems described in this thesis form an instance
of our generic mapping scheme. To improve robustness. other localization methods
can be incorporated into the architecture. This would allow a robot to select between
many different schemes when building a local island of reliability (a node). Hence.
-." t i . FUTURJZ WORK
it is possible that an area. where the two (vision/sonar) serising methods show a low
distinctiveness measure. is included in the map due to a high distinctiveness measure
of another method. Other localization nlethotls may use information in a better way
at chat region. even when the same sensory system is ustd. This opens a broad rangcl
of work in developing evaluation criteria and formulatirig the distinctiveriess r~wasurc.
for localization scherlies. Each localization scheme can he analysetl to forniulate the
distinctivent!~~ rrtt1iWure as clescribd in this t lieuis.
Further work car1 include optimizing the distinctiveness measure by variation of
parameters within its forniulatiori to niinirnize the differences between the predicted
nieilsure and the actual localization errors. Evaluating different functional forms of
combining hot h I anti AI may d s o improve the nleasure. The tlistirictivt!rit~ss rlit.asurtb
operator scale also remains an open problem. An advantage in txxttwfirlg this work
is that each localizirt iorl met hod (:an be anal y r d and opt iniizeci separately to lw
inclutird as ari rs tra coniponrnt in the architwturt!.
Thc mapping irrchitecturc itself opens room for much espansion. One main issue
is to derive a suitable method for identifying new riotles from old ones. This can be
considered as a global localization task within the topological representation. Issut?s
to be considered are problems of detccting visited nodes from ntlw ones. geonietricdly
identical but separate nodes and partially intersectirig nodes.
hlorr work can txparitl on the no& building mechanism. In this thesis. wr simply
collected data from four corners defined by f . unless an obstacle was in the way i.e..
map within the minimum visibility. This does not guarantee that the size of the nodes
will be large enough so that the robot can reach them. Obstacles may obstruct the
node building routine and limit the node size. Thus. a more intelligent routine can
be developed to map around obstacles and assure metric mapping of a given size.
The use of more sophisticated exploration strategies can also improve the mapping
procedure. An exploration strategy directed by the distinctiveness measure can be
developed to explore the environment specifically looking for good regions. A hill
climbing technique could be incorporated within the exploration strategy such that
the mapping criteria will not be threshold based but will search for neighbourhood
optimality of distinctive regions. Future work on navigation can help develop an
optimal navigation procedure coupled to our environment representation. With our
model. the navigation problem now falls within the topological frarncwork where WE>
can use graph search algorithms.
The topological-metric environment representation described in this thesis pro-
vides a framework for developing maps For niary purposes. Thtwfore. it is possiblt~
tu investigate different mapping goals arid ( l w ~ l o p a tlistirirtivruess rwasurr i ~ r l ( l thta
associated algorithm for each. The general approach is to decompose a task into corn-
ponents requiring nietrir data. Theri. to cittfine the rkodr placrnw~t criteria by deriving
the distinctivpness measure most appropriate For the coniputational t a sk . The robot
can then follow these criteria to construct the nodes and connect them appropriately.
It is also possible to investigate a method for cornbiriing several task-based rnaps. For
example. combining a navigation map anti a painter's map (figure 7.1) can provitlth a
conlplere map where the robot can navigate and paint an environrrier~t. Thtb problcrri
then becorri~s how to niatch and connect the two maps together.
Merged
Painter ("--J Map
Painter
.Map
FIGURE 7.1. An example of 2 task-based maps. A navigation map consisting of connected localization maps and a painter map consisting of connected surface maps (describing the surfaces to be painted). The merged map allows the robot to navigate and paint the environment.
REFERENCES
[ I ] P. SlilcKenzie arid G. Dud&. *'Precise positioning using nwdel-based nlaps".
in IEEE In tenut ional Conference on Robotzcs arid .-lutomution. Sari Diego.
California. May 1994. pp. 1615-1621.
[ 2 ] G. Dudek. .-Environnlerit mapping using nlultiplr abstraction levels". in Pro-
ceedirqs of the IEEE. Nov. 1996. vol. 84.
[3] S. Thruri. "Ltwning rrwtric-topological maps for indoor mobile robot naviga-
polygons". .-llgonthrrricu. vol. -I. pp. 14 1 135. 1989.
[j] N. Rao. S. Iyngar. and G. tleSaussurr. "The visit problem: visibility graph-
baseti solution". in 1988 hf. Conf. o n Robotics und .4utorrrution. 1988. pp.
1650- 1635.
[6! G. Dudek. P. Freedman. and S. Hadjres. **Signatures and extended signatures
for topological mapping using graphs". TR-193-231-34. UcGill Research Cen-
ter for Intelligent hlachines. October 1992.
[7] G. Dudek. P. Freedman. and S. Hadjres. "Mapping in unknown graph-like
worlds". .Journal uf Robotic Systems. vol. 13. no. 8. pp. 539-559. August 1996.
[S] G. Dudek. P. Freedman. and S. Hadjres. *'Using local information in a non-
local way for mapping graph-like worlds". in Proceedfngs of the Thirteenth
International Conference on ..lrtzficzul Intelligence. Charnbery. France. August
1993. pp. 1639-1645, Internation .Joint Conf. on Artificial Intelligence Inc.
[9] M. hlataric. "Navigating v.rith a rat brain: A neurobiologically-inspired model
for robot spatial representat ion" . in Proc. 1 st I71 t enu t ionu l Curt f. on Sitrrulu-
tian of .idup tiuc Be/u+uzour: 199 1.
[lo] G. Dudek. M. Jenkin. E. Mlios. and D. Wilkes. -*Csing nlultiple ~ r i a r h r s in
graph exploration". in Pn.x Sgrnposiutrr on .-ldcunces :rr Iritelltycrrt Rubuttcs
Sgstems: CorrJwence on Mobile Robotics. Philadelphia. PA. 1989. Interna-
tional Socitlty fur Optical Enginewing.
1111 L. llassonr G. Sanclini anti V. Tagliasco. .srFor~r~-Invariant' topological rr iap
ping strategy fur 2 r l sliapc recognition". CVGIP. vol. 30, pp. 165 188. 1985.
[12] A. A. Holenstein. SI. .A. Nillet. and E. Badrecldiu. 9lobile robot localization
in a structured environrrlent cluttered with obstacles". iri Proc u j the lEEE In-
tenwtionul Conference o n Robotics and ..luta?rrution. Nice. France. May 1992.
pp. 25i'6--%8 1.
[13] A. Curran and L I . Kyriakopoulos. .*Sensor-Based Self-Localization for
Kheeled !dobile Robots". in Proc o/ the IEEE Internationul Conference o n
Robotics and .-I utornulion. Atlanta. Georgia. May 1993. pp. 8- 13.
jl4] G. Dudek and C. Zllang. "Vision based robot localization without explicit ob-
ject models'.. in IEEE Internutiorrul Conference on Robotics arrd .-lutomution.
.Ilinneapolis. SIN. .LIw 1996. pp. 76-82.
[ lz] Eric Krotkov. -%obile robot localization using a single image". in Proueedinys
1989 IEEE Intenrutional Conference on Robotics and rlrrtomution. pp. 918-
983. 1989.
[16] J. Leonard and H. F. Durrant-Whpte. "Mobile robot localization by tracking
geometric beacons". IEEE Tmnsactions on Robotics und Automation. vol. 7 .
no. 3. pp. 376-382. June 1991.
REFERENCES
[I 71 F. Lu and E. Milios. "Optimal global pose estimation for consistent sensor data
registration". in ~EJ??E hternutional Con ferencr on Robotics urrd .-l utomution.
1995. pp. 93-100.
[18] R. Smith and P. Cheeseman. *'On the representation and estimation of spatial
uncertainty". The internutiortul jounrul of Robotics Reseurch. vol. j (4 ) . pp.
56--68. Winter 1986.
[XI] L'. Nernzow. .*Animal and robot navigation". in Robotics und .-lutononrous
Systems. .July 1995. vol. 15. pp. 71-81.
[21] B. Kuipers and Em-T. Byun. "A robot exploration and mapping strategy based
on a semantic hierarchy of spatial representations". Robotics urrd .-l~utunurrruu.s
Sgstems. vol. Y. pp. 47-63, 1991.
[El P. Whaitr and F. P. Ferrie. "From uncertainty to visual rsploration". in
Proceedings of the :Id I n t e . ~ d o n d Conference on Compvtrr CTi.srun. Tokyo.
.Japan. November 1990.
[23] A. Witkin. LI. Kass. and D. Terzopoulos. "Physic:ally based m o d t h g for vision
and graphics". in Proceedings u f the h u g e Lhferstunding bVorkshop. 1985. pp.
254-278.
[%I S. Lange. L. Korba. and A. Wmg. "Characterizing and nlodelling a sonar
ring". in Proc. SPlE Mobile Robotics IV. Philadelphia. 1989. pp. 291--304.
[Xi] D. Wilkes. G. Dudek. M. Jenkin, and E. Milios. "?vlodelling sonar range sen-
sors". in .-ldvancrs in machine uision: strategies and applications. C. Archibald
and E. Petriu. Eds. World Scientific Press. Singapore. 1992.
[26] .J. K. Hackett and M. Shah. "Multi-sensor fusion: a perspective". in Pmceed-
ings 1990 IEEE International Conference on Robotics and rlutomation, pp.
1324-1330. 1990.
REFERESCES
[27] S. Lang and -1. Wong. "Building geometric world models with graph synthesis
for sensor fusion in mobile robots'?. Computat iond Intelligence. vol. 6. pp.
91-10;. 1990.
[28] H. Moravec. 5ensor fusion in certainty grids for mobile robots.'. .4 I !Cluyurinr.
pp. 61 7 4 . Summer 1988.
[29] S. Shafer. -4. Strntz. and C. Thorpr. "An architecture for sensor fusion in
a mobile robot". iri lEEE h t . Conf. o n Robotrcs a n d .-latorrratzon. 1986. pp.
2002-2011.
[30] G. Dudek. 11. Jenkin. E. Milios. and D. Wlkes. "On building and navigat-
ing with ir globally topological hut lorally metric niap" . in Pmr:. 3rd ECPD
I d . Cunf. un .4drlur~crd Rabotzc.~. htrl l iyent .-!utunrutlon und .-ktr,ue Sptems .
Brrmen. Germany. 1997. pp. 132 - 136.
[31] R. DP Almeida anti C. hIelin. ~*Esploratiori of unknown erwironnients by a
mobile robot". lrrtellzyent -4 utonomous S?/stems 2, pp. 715- 725. 1989.
[32] N. Roy and G. Dudek. "Learning to rendezvous during multi-agent explu-
rat ion". in Proc. 6th Europmn Workshop on Leurning Robots. Brighton. Eng-
land. Aug. 1997.
[33] I. Rekleitis. G. Dudek. and E. SIilios. "Multi-robot exploration of an unknown
environment. efficiently reducing the odomet ry error". in Int. Jornt Cod. on
.-1.I. (see also CIM Tech. Report TR-CIM-97-01). .lug. 1997.
[34] G. Dudek. 11. Jenkin. E. hlilios. and D. Wilkes. "Robotic exploration as graph
construction". Transactions on Robotics and .4 utomatiorr. vol. 7. no. 6. pp.
559-865. December 1991.
[Xi] P- Ciaravola. *'3Iaze exploration*', Tech. Rep., Centre for Intelligent Machines.
YcGill University. 1996.
REFEREYCES
[36] G. Dudek and J . K. Tsotsos. *'Shape representation and recognition from cur-
vature". in Pmeeedinys of the 1991 Conference on Cuntp-uter. Vision arid Pat-
tern Recoyrrrtron. Slaui. Hawaii. .June 1991. pp. 35-41. IEEE.
[37] G. Dudek. M. .Jenkin. E. Slilios. and D. Wilkes. taxonomy for multi-agent
robotics". .-Lutonunruus Robots. vol. 3. pp. 375-39'7. 1996.
(381 I. Park and -1. R. Kender. "Topologcal direction-giving and visual navigation
in large environnients". .41-tifieid fntelligerrce. vol. 78. no. 1-2. pp. 355-395.
October 1995.
[39] E. Bourque and G. Dutlek. 9.iewpoi1it select ion an autonorrious n) botir
system for virtual environment creation". in IEEE I n t e m u ~ i o n u l Currfrrence
on h te l l i yen t Robotic Sgsterns. 1998.
APPENDIX A
Implement at ion
The architecture of the map building routine cor~sisteti of several coniponents rlinrling
in parallel. .At the top level lies the main map building motlule which mlsists of ceom-
puting the disti~ictiveness n w . w m . building and corlriectirig the notlcs following our
rnappirg criteria. Tile niairi mapping tnodulr rornlrnmicates wi th five other processes:
robot corit roller/simulator.
0 robot.
exploration module.
0 vision system server.
sonar system server.
It directly communicates with a robot corttroIl~r/simulator developed in our labs.
wliich opens a connection to a real or simulated robot. I t also connects to an rsplo-
ratioti module arid the two rriudel based mapping modules (sonar and vision system
packages converted to servers) which also connect to the robot controller/simulator.
Figure .I. 1 shows the How chart for these modules and Figure -4.2 shows the nlodules
running.
These modules were all written in the C programming lariguage along with sorue
scripts. written in Perl. for data analysis and conversions.
APPEXDL,Y -4. IMPLEMENT-ATION
FIGURE A . 1 . Flow chart of software rrloduies.
FIGURE -4.2. This screen shot shuws the software rrmdules running together. On the top left is the robot controller with a socket connection to the other modules. The bottom left window shows the output of the sonar system module after executirig the Iirie fitting algorithm (in the dark xterm window). The three upper to middle right windows show the vision system module. one window shows the captured image. another window shows the edge map and the last window shows a histogram of the extracted feature values.
APPENDIX B
The sigrrioid function is a function that provides a gradual charge t'rorrl a low plateau
to a high m e . I t is used often as a a weighed normalizing function. I t was shown
in chapter 4 that it can also be used to describe the characteristics of sonar signal
degradation (although. we used an esponcntiai decay). The parameters of the func-
tiurl control thr transition point ( c ) imd the trarisition rate ( r n ) . Figure B. 1 show
;r plot of the high pass Function and figure 8.2 shows the low pass furlction. W t b
use this functiorl to provide a consistent thresshoid based nieaure based on the pa-
rameters. For example. for the vision system. we considered that the slope between
good features and the position should be about 45'. so we set the cutoff value of c
accordingly. This was chosen such that desired features are ones that vary a t least
at t tiat rate over the operators scale where all axis are rlormalized. If the axis were
not normalized. a slope of 45" over the operator scale would be meaningless. Thus
we must vary the parameters with respect to some normalizing factor a r d a clesircd
target result. Similarly. the numerical result of the integral for the vector influence
(equation 5.4) is dependent on the quantization of the seen line segment. i.e.. the
sensory resolution. We set the value of c according to a minimum line length seen
a t a certain distance. normalizing with the sensory resolution. If only a single line
segment is seen that is further away or smaller than the measure would lie below
APPENDLY B. SIGMOID FUNCTION
the cutoff. Thus the meaning of these values can be portrayed by remapping them
through the normaher and setting the parameters accordingly.
B. 1. Sigrrloid furict iou passing Large values: d"/(xrn + P" ) with rri = 7 and u = 1. The vertical axis shows the
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
B.2. Sigmoid functiou passing low vd ues : 1 - rm/ ( rm + cm) with m = 7 and c = 1.The vertical axis shows the function and the horizontal axis shows x.
