Case-Based Indoor Navigation

Alessandro Micarelli and Giuseppe Sansonetti

Department of Computer Science and Automation

Artiﬁcial Intelligence Laboratory

Roma Tre University

Via della Vasca Navale, 79, 00146 Rome, Italy

Abstract. The purpose of this paper isto present a novel approach to the problem

of autonomous robot navigation in a partially structured environment. The pro-

posed solution is based on the ability of recognizing digital images that have been

artiﬁcially obtained by applying a sensor fusion algorithm to ultrasonic sensor

readings. Such images are classiﬁed in different categories using the well known

Case-Based Reasoning (CBR) technique, as deﬁned in the Artiﬁcial Intelligence

domain. The architecture takes advantage of fuzzy theory for the construction of

digital images, and wavelet functions for their analysis.

1 Introduction

In recent years, the problem of indoor robot navigation has been largely considered for

the challenges that issues in several technological ﬁelds. From the motion control sub-

strate to the artiﬁcial reasoning layer, many researchers have worked out solutions able

to perform complex navigation tasks in many application ﬁelds ranging from industry to

service robotics. In particular, a still open problem is the devising of efﬁcient strategies

able to cope with the problem of self localization in unstructured environments, i.e., the

ability of estimating the position of the mobile platform when no artiﬁcial landmarks

can be used to precisely indicate to the robot its position. Now, suppose to restrict the

problem and choose the environment in a particular class, still very wide: an ofﬁce-like

environment with corridors, corners and other similar features. Suppose also that only

low cost sonar sensors can be used: all localization information, that at this point have

a topological character, should be easily extracted from sensory data and used to guide

the platform along the path. Unfortunately, in a dynamic environment, those features

(natural landmarks) can vary and some unknown conﬁgurations could be found leav-

ing to the robot the choice on several strategies: one could consist in ﬁnding the nearest

matching topological element in a static library; an other one could include a supervised

learning stage in which the new pattern is used to increase the base library itself. This

second approach is often referred as Case-Based Reasoning (CBR) [1, 5], and tries to

catch all the learning opportunities offered both by the environment and, in an initial

phase, by an external supervisor, to improve robot skill in analyzing its exteroceptive

sensorial view.

Micarelli A. and Sansonetti G. (2007).

Case-Based Indoor Navigation.

In Robot Vision, pages 97-106

DOI: 10.5220/0002069300970106

 SciTePress

Fig.1. Map of a corridor.

Fig.2. Worldmark.

2 A Case-Based Approach

Autonomous navigation usually implies a recognition phase for each step taken by the

robot to estimate its position, or better, to understand the particular shape of the envi-

ronment (the topological feature) inside its actual range of view. In our case, this can

be done comparing the actual sonar output with a set of reference signals associated

with particular topological features. In most cases, association is done by comparing

the actual view with a static list of models obtained with a priori considerations on

the environment itself [4]. However, following a CBR philosophy, a learning approach

can be devised in which real-world cases obtained from a supervised navigation are

used to build and update a dynamic library. In this paper, we want to show how such

a method can be successfully applied to help the robot during navigation in dynamic

environments containing features that only partially correspond to previously known

cases. In particular, the problem we intend to address concerns the recognition of a

sonar-based digital image and its classiﬁcation under one category belonging to a set of

predetermined topological situations (Corridor, Corner, Crossing, End Corridor, Open

Space).

Basically, the surrounding of the robot is represented in terms of Fuzzy Local Maps

(FLM), i.e., Fuzzy Maps [7, 8], that turned out to be extremely useful in many sensor

fusion problems, obtained from a preprocessing stage applied to the sonar signals. Each

FLM consists of 40 x 40 cells and, for each cell of an FLM, two values specifying

the degree of membership to the set of empty cells and to the set of occupied cells are

computed. An FLM, usually derived at each step merging the last n sets of collected

data, is thereafter represented by two fuzzy sets: the empty cells set E, and the occupied

cells set O. As an example, in Fig. 1 the E set of a FLM obtained in a corridor is

reported. Different gray levels in the image represent different fuzzy values. Pixels with

darker gray levels correspond to lower values of membership to the empty cells set E,

white pixels are unexplored regions, with a fuzzy value of membership to E equal to 0.

Now, with reference to the scheme depicted in Fig. 3, let us assume that the robot

has acquired a new FLM. As ﬁrst step, a feature-based representation of the new FLM

Fig.3. Navigation architecture with Case-Based Reasoning.

is evaluated by the feature extraction module. This representation constitutes the “new

case” of the proposed CBR system. The retrieval module shown in the ﬁgure will effect

a search in the case library containing the old cases, based on a <problem representa-

tion, solution> structure, which in this speciﬁc case will be <FLM based representa-

tion, topological category index>. The solution given in the old case can therefore be

seen as a pointer to the “Library of Objects”, containing the categories (i.e., “topolog-

ical features”) that could appear in the maps to be analyzed. The “recognized object”

is at this point taken into consideration by the robot navigation system to plan its mo-

tion. This object, which constitutes the old solution of the case retrieved from the Case

Library, will also be considered as a candidate solution of a new problem (basically,

there is no need for an adaptation of the old solution to suit the new case) and if the hu-

man supervisor accepts it, the pair <new FLM based feature representation, recognized

object index> can be inserted as a new case in the Case Library.

3 Image Recognition

For sake of clarity, the pseudo-code of a rather simpliﬁed version of the classiﬁcation

algorithm is reported in Table 1. The complete solution, employed for the experimental

performance assessment, was implemented in C language under the Linux operative

system, for reasons of porting and efﬁciency. To handle both the new case and any of

those cases dwelling in the Case Library, the use of a record structure comprising the

three ﬁelds below was adopted:

– a one-dimensional fuzzy worldmark summarizing the content of the FLM;

– object, designed to store the label associated to the recognized object;

– time, reserved to the storage of information regarding the utility of the case of

reference.

As indicated above, the ﬁrst ﬁeld is dedicated to the representation of the FLM. Speciﬁ-

cally, in order to guarantee the applicability of the current approach to real-time control,

a simpliﬁcation has been introduced: the bi-dimensional fuzzy map of Fig. 1 is replaced

with a one-dimensional fuzzy signal, named worldmark. The worldmark is computed

by determining, for each direction around the robot, the value of the cell with the high-

est matching score to the set of empty cells, or, in other words, the cell for which the

risk of belonging to a possible obstacle is minimum (see Fig. 2). Therefore the “new

case” that appears in Fig. 2 consists of a vector of N elements (typically N=360) with

values in the interval [0,1].

Before launching into the detailed description of the representation modalities of

the aforementioned three ﬁelds, we believe it useful to provide a general overview of

the entire algorithm. The domain expert’s possibility to intervene in the decision task is

possible both in the initial training phase of the system as well as during the veriﬁcation

phase for the retrieved solutions. Another aspect worthy of attention is the one related to

the adoption of a double similarity test. It is manifest that as the pertinence of the case

library increases, so does the probability of retrieving a candidate with a good value

of similarity to the case under examination and, therefore, that the associated solution

to will prove to be valid even in a contingent situation. On the other hand, a rather

voluminous library presents the two following inconveniences:

– more time necessary for the retrieval of the required information;

– a depletion in terms of available space.

In order to avoid, at least partially, this state of affairs, the proposed architecture uses

two different tests, respectively, named reliability test and identity test. The former pro-

vides indications on the possibility of successfully apply the solution of the retrieved

case to the new situation, the latter controls the insertion of the new case into the sys-

tem memory. The reason for the introduction of the identity test parameter is owed to

circumstances where it is useless to include a new case, “quite” similar to a case stored

in the library in the system memory. The reliability test is performed by comparing the

current similarity metric value s

with the reliability threshold S

, while the identity

test is performed by comparing the same value s

with an identity threshold S

. In

Tables 2 and 3 the threshold values determined by a heuristic procedure are reported

together with the percentage of coincidence between the responses given by the system

and those furnished by a domain expert. Speciﬁcally, for the setup of S

and S

, the

available memory space, the amount of resources necessary to keep in memory the pair

<representation of signal, represented object> and the statistics of the similarity index

were considered.

Keeping in mind an “intelligent” management of the resources available to the sys-

tem, a third test has been introduced. The idea that has, concretely, lead to its introduc-

tion, stems from the need to keep track, for all cases stored in memory, of the frequency

of their appearance and the effectiveness of the solution associated to them. The record

100

Table 1. Pseudo-code for CBR.

Function REC(NewImage) returns RecObject

inputs : NewImage; the input image

variables : CaseLib; the case library

; the generic old case

nouse

; the inactivity time

; the reliability threshold

; the identity threshold

local variables : D.image; the image representation

D.object; the recognized object

; the metric value

tempvalue; the temporary metric value

tempind; the temporary case index

D.image ← WAVELET(NewImage)

D.object ← 0

tempvalue ← 0

tempind ← 0

for each old case C

in CaseLib do

begin

← COMPARE CASE(D.image, C

.image )

if (tempvalue < s

) then

begin

tempvalue ← s

tempind ← j

end

if (tempvalue < S

) then

begin

D.object ← HumanExpertSolution

n+1

.image ← D.image

n+1

.object ← D.object

n+1

.time ← 0

end

else

begin

if (C

tempind

.object = HumanExpertSolution) then

begin

D.object ← C

tempind

.object

tempind

.time ← 0

end

else

D.object ← HumanExpertSolution

if (tempvalue < S

) then

begin

n+1

.image ← D.image

n+1

.object ← D.object

n+1

.time ← 0

end

CLEAN LIB(CaseLib,T

nouse

)

RecObject ← D.object

returns RecObject

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ﬁeld time was speciﬁcally introduced in consideration of these aims. Once more, the

clean library test compares this value with a threshold T

nouse

. If time exceeds T

nouse

the case is removed from the dictionary. For the determination of the optimal value to

assign to the indicator T

nouse

, the same considerations expressed above for the param-

eters S

and S

still apply.

However, for a full understanding of the architecture proposed in this article there

are still two major aspects that, as always, in any system based on cases, constitute the

heart around which all the rest revolves, that is,

– the signal representation;

– the similarity metric.

These aspects are, furthermore, strongly interrelated.

3.1 The Signal Representation

Choosing the most efﬁcient representation for a current problem constitutes the crucial

moment of any application of signal processing. Here, we resorted to a wavelet repre-

sentation of the worldmark. The wavelet representation expresses the signal of interest

as superimposed elementary waves and, therefore, in this respect does not introduce any

innovationcompared to traditional methods, such as Fourier series expansion. However,

the innovative aspect offered by wavelet functions consists in the possibility of subdi-

viding the available data in components with differing bandwidths and time durations.

Each of these components is subsequently analyzed by a resolution associated to its

scale. The advantages offered by this procedure are tangible, above all, in respect to

the analysis of physical situations where typical signals show discontinuity and sudden

peaks, exactly as happens with worldmarks. The advantages of adopting representa-

tions in similar situations through wavelet functions, instead of traditional methods, are

extensively expounded in the literature [3, 6,2].

3.2 The Similarity Metric

The last aspect to be examined concerns the choice of the metric necessary for the

evaluation of the similarity existing between case f in input and the generic case g be-

longing to the Case Library. Regardless of the application context, a good metric must

anyhow be able to guarantee an efﬁcient compromise between the two main requisites,

which are the quality of the recognition and the computational complexity. Accordingly,

during the experimental activity several different metrics were tested. Among them, the

relatively best results were obtained by using the cross-correlation factor as metric,

whose expression is:

M ax

θ∈[0,2π ]

hf(x), g(x − θ)i

hf(x), f(x)i hg(x), g(x)i

This quantity was calculated both in the time and frequency domains, respectively, ob-

taining in both cases signiﬁcant results with moderate processing time, through compu-

tation resources available on the market today.

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4 Experimental Results

For our tests, we used the simulator of Nomad200 by Nomadic Technologies, a mo-

bile robot equipped with a ring of 16 equally spaced ultrasonic sensors. The procedure

consists of tracing a number of global maps of hypothetical ofﬁce-like environments,

simulating the robot dynamics and, ﬁnally, collecting the output data. For these op-

erations we used the real time navigation software A.N.ARCH.I.C. [9] which, together

with the aforementioned simulator, made the robot virtual navigation inside the mapped

environment possible producing the sequence of FLMs and corresponding worldmark,

each pair related to a different position taken during the followed path. Each sequence,

therefore, includes hundreds of FLMs and worldmarks, which constitute the input for

the tests that we performed on our classiﬁer. The values reported below were obtained

by using a machine equipped with a Pentium M processor, 1700 MHz, and 512 MB

RAM. During the testing phase, we initialized the system through representations re-

lated to four different conﬁgurations:

– corridor

– crossing

– end of corridor

– angle

providing, for each of these, three different standard schemes, in practice as it appears

in the initial phase, at its basic level, and in the ﬁnal phase.

Tables 2 and 3 show, in particular, the results recorded during two different series of

tests of the system. The ﬁrst illustrates the results obtained by performing the similarity

evaluation between the input signal and the generic one inside the case library directly

in the temporal domain. Instead, for the second one, the same operation was effected in

the wavelet domain, i.e., the matching evaluation of the two signals was not made by es-

timating the cross-correlation between sequences of temporal samples, but between the

corresponding residual low-frequency components, obtained through Discrete Wavelet

Transform (DWT). Consequently, it is possible to appreciate in a more tangible way

the extent of the possible advantages granted by the expansion of signals in series of

waveform, perfectly located in time and in frequency.

To perform this experimentation, we simulated the robot navigation in an environ-

ment that Fig. 4 illustrates as a global map. In the same ﬁgure we have also traced the

path followed by the robot, planned on the basis of speciﬁc methods for which further

explanation is out of the scope of this paper. A sequence of 636 FLMs is thus gen-

erated, as well as a corresponding number of worldmarks. In order to streamline the

experimental procedure, without, however, penalizing its efﬁciency, since the variation

between one FLM and the subsequent one was practically insigniﬁcant, we decided to

consider only one over three samples and to discard the others. As a result, the map

effectively input to the system consists of only 212 FLMs.

Initially, we shall examine the values reported in Table 2. As anticipated earlier,

the tests were performed by running the system beforehand through the same training

session, for each test series. This fact becomes apparent by looking at the data in the

column, since the same value recurs systematically in each line (12 cases). Actually,

the coincidence does not only concern the number of cases used, but also the samples

103

Fig.4. Global map.

themselves. In this way, we attempted to guarantee the same initial condition in each

test series.

A reading of the data discloses the consistency of the recorded ﬂuctuations, in re-

spect to the varying values assigned to the two similarity thresholds. For example, it

is noticeable that when the reliability threshold S

decreases, there is a proportional

decrease in the number of interventions required of the domain expert by the system.

Similarly, there is a clear increase in the number of cases inserted in the relative library

matching an increase in the identity threshold S

. However, the phenomenon of major

importance and interest relates to the trend recorded by the factor indicated in the ta-

ble as coincidence percentage. This factor was gathered by a comparison between the

system responses and those that would have been given by the same expert who per-

formed the training, when examining the corresponding FLM. Clearly, such a strategy

is inevitably damaged by the loss of information that occurs during the passage from a

bi-dimensional fuzzy map (FLM) to the corresponding polar map (worldmark). How-

ever, notwithstanding this additional source of uncertainty, the results obtained may be

considered more than satisfactory.

Proceeding with the analysis of the data reported in Table 3, which refer to the

same experimental tests, but performed on the wavelet coefﬁcients and not on their

corresponding original signals, the gain is noteworthy, both in terms of coincidence

percentage as well as computational complexity. In particular, it can be observed how

the ﬁrst factor is affected to a signiﬁcant lesser degree by the variation of the values

assigned to the two thresholds S

and S

Although we do not wish to dwell upon too many details of the experimentation, it

should be noted, however, that to obtain the wavelet coefﬁcients relating to sequences

of 360 temporal samples we used a simple DWT with four levels and analysis ﬁlters of

the type belonging to the Daubechies family (speciﬁcally, the version with four coefﬁ-

cients).

Another observation should be made on the processing time. In order to ﬁnalize this

experimentation, for sake of clarity, we decided to operate on the group of worldmarks

104

Table 2. First experimental set.

Input Expert Coincidence Cases Cases Processing

cases interventions percentage before after Time (s)

0.90 0.93 212 14 84.0% (178) 12 51 10.31

0.88 0.93 212 12 84.0% (178) 12 51 10.16

0.85 0.93 212 5 81.6% (173) 12 51 9.46

0.91 0.93 212 23 94.3% (200) 12 51 10.46

0.91 0.95 212 19 94.3% (200) 12 74 13.86

0.89 0.91 212 14 88.7% (188) 12 37 8.21

Table 3. Second experimental set.

Input Expert Coincidence Cases Cases Processing

cases interventions percentage before after Time (s)

0.90 0.93 212 12 94.3% (200) 12 43 0.47

0.88 0.93 212 7 93.9% (199) 12 43 0.53

0.85 0.93 212 5 92.4% (196) 12 43 0.43

0.91 0.93 212 15 94.3% (200) 12 43 0.48

0.91 0.95 212 13 94.3% (200) 12 64 0.59

0.89 0.91 212 12 94.8% (201) 12 51 0.38

generated during the course of the overall navigation inside the simulated environment.

Consequently, the time necessary to operate in real-time is decidedly less than that

reported as the sum over all input cases in the table and, above all, signiﬁcantly lower

than the time allowed during the robot actual navigation.

5 Conclusions

Generally, the normal pattern recognition techniques require models of the objects that

must be recognized and classiﬁed. The collection of models available to the classiﬁer

clearly reﬂects the original knowledge of the situation to be analyzed. However,in most

cases, as for the robot autonomous navigation, there exists practically no prior infor-

mation whatsoever. Our proposed architecture includes a feature extraction algorithm

incorporated into a CBR shell, which allows a constant increase in the knowledge of

the surrounding environment. We remark, however, that the possibility of updating the

Object Library as well as the Case Library, although left open and in principle with no

limit to the number and complexity of information that may be collected, is constrained

to real-time restrictions linked to the technology that is available on the market today.

Future developments will be focused on introducing the possibility of fusing more

information coming from different kind of sensors (e.g., laser scanners or cameras) into

a more detailed worldmark to provide the classiﬁer with a better and more robust input

data.

105

References

1. Aamodt, A., and Plaza, E. Case-Based Reasoning: Foundational Issues, Methodological

Variations, and System Approaches. AI Communications, 7(1), pp. 39–59, 1994.

2. Chui, C.K. An Introduction to Wavelets. Academic Press, London, England, 1992.

3. Daubechies, I. Orthonormal bases of compactly supported wavelets. Comm. Pure Appl.

Math., 41(7), pp. 909–996, 1988.

4. Fabrizi, E., Panzieri, S., and Ulivi, G. Extracting topological features of indoor environment

from sonar-based fuzzy maps. Proceedings of the 6th International Conference on Intelligent

Autonomous Systems, Venice, Italy, 2000.

5. Kolodner, J. Case-Based Reasoning. Morgan Kaufmann, San Mateo, CA, 1993.

6. Mallat, S.G. A Theory for Multiresolution Signal Decomposition: the Wavelet Representa-

tion. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(7), pp. 674–693,

1989.

7. Oriolo, G., Vendittelli, M., and Ulivi, G. Real-Time Map Building and navigation for Au-

tonomous Robots in Unknown Environments. IEEE Transactions on Systems, Men and Cy-

bernetics - Part B: Cybernetics, 28(3), pp. 316–333, 1998.

8. Panzieri, S., Petroselli, D., and Ulivi, G. Topological localization on indoor sonar-based

fuzzy maps. Intelligent Autonomous System, IOS Press, Amsterdam, Netherlands, pp. 596–

603, 2000.

9. Panzieri, S., Pascucci, F., and Petroselli, D. Auton. Navigation ARCHitecture for Intelligent

Control, www.dia.uniroma3.it/autom/labrob/anarchic, 2002.

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