IMPROVED OCCUPANCY GRID LEARNING

The ConForM Approach to Occupancy Grid Mapping

Thomas Collins, J. J. Collins and Conor Ryan

Department of Computer Science and Information Systems, University of Limerick, Ireland

Keywords:

Robotics, Occupancy Grids, Machine Learning, Artiﬁcial Intelligence.

Abstract:

A central requirement for the development of robotic systems, that are capable of autonomous operation in

non-speciﬁc environments, is the ability to create maps of their operating locale. The creation of these maps is

a non trivial process as the robot has to interpret the ﬁndings of its sensors so as to make deductions regarding

the state of its environment. Current approaches fall into two broad categories: on-line and ofﬂine. An on-line

approach is characterised by its ability to construct a map as the robot traverses its operating environment,

however this comes at the cost of representational clarity. An ofﬂine approach on the other hand requires all

sensory data to be gathered before processing begins but is capable of creating more accurate maps. In this

paper we present a new means of constructing occupancy grid maps which addresses this problem.

1 INTRODUCTION

In recent times Occupancy Grids have become the

dominant paradigm for environmental modelling in

mobile robotics (D. Kortenkamp and Murphy, 1998).

An Occupancy Grid is a tessellated 2D grid in which

each cell stores ﬁne grained qualitative information

regarding which areas of a robots operating environ-

ment are occupied and which are empty (Moravec and

Elfes, 1985; Elfes, 1989). Speciﬁcally, each individ-

ual cell in the grid records a certainty factor relating

to the conﬁdence that the particular cell is occupied.

Such maps are extremely useful for mobile robotic

applications as they facilitate tasks such as naviga-

tion, path planning, localisation and collision avoid-

ance (Borenstein and Koren, 1991; Dissanayake et al.,

2001).

Currently in the Occupancy Grid mapping domain

there are two broad approaches: on-line and off-line.

The on-line approach is characterised by traditional

paradigms such as those from Moravec (Moravec and

Elfes, 1985), Matthies (Matthies and Elfes, 1988)

and Konolige (Konolige, 1997). The off-line ap-

proach has emerged from a more recent paradigm

from Thrun (Thrun, 2003). The on-line approach is

capable of generating maps in real-time as the robot

operates. However these maps often contain incon-

sistencies such as over estimation of occupied or free

space which is undesirable. The off-line approach on

the other hand, is capable of generating more consis-

tent maps but cannot do so in real time. These dia-

metric approaches give rise to a mode versus clarity

dilemma.

In this paper we introduce and empirically evaluate

a novel robotic mapping framework called ConForM

(Contextual Forward Modelling) which solves this

dilemma through combining the beneﬁcial aspects

of both existing approaches. Results from empirical

evaluations we have undertaken show that ConForM

provides maps that are of better quality than existing

paradigms.

2 ON-LINE VS. OFFLINE

OPERATION: THE ROBOTIC

MAPPING DILEMMA

Two types of model are available for sensory inter-

pretation in robotic mapping. These are the Inverse

and the Forward models (Thrun, 2003). An inverse

model attempts to describe an environment by trans-

492

Collins T., J. Collins J. and Ryan C. (2007).

IMPROVED OCCUPANCY GRID LEARNING - The ConForM Approach to Occupancy Grid Mapping.

In Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics, pages 492-497

DOI: 10.5220/0001651904920497

 SciTePress

(a) Ideal Map (b) Inverse model:

Moravec and Elfes 1985

1993

(d) Forward model:

Thrun 2001

Figure 1: Illustrating map generation using inverse/forward sensory models. Overall environmental size:

44m x 35m

. Corri-

dor width:

1.5m

lating from effects (sensory measurements) to causes

(obstacles). The forward model describes the charac-

teristics from causes to effects. The inverse model is

associated with on-line real-time paradigms such as

those mentioned previously and the forward with the

ofﬂine, non real-time approach.

Traditional approaches using inverse sensor mod-

els are prone to generating maps that are inconsis-

tent with the operational data from which they were

constructed (Thrun, 2003). This is because such

techniques decompose the high-dimensional mapping

problem into a number of one-dimensional estimation

problems, one for each cell in the map. In doing so

they do not consider the dependencies that exist be-

tween these cells. The forward sensory model ad-

dresses this deﬁcit by considering the dependencies

that exist between neighbouring grid cells thereby

generating more consistent maps.

Figure 1 presents some illustrative maps. Each

paradigm used identical sensory data in generating the

maps shown. As can be seen the map generated by the

forward model is more compatible with the ideal map.

This demonstrates the problem currently inherent in

the domain which we are addressing. That is, the

dilemma of selecting an on-line paradigm that yield

maps of lower accuracy versus an off-line paradigm

which produces better quality maps.

3 SPECULARITY AND

REDUNDANT INFORMATION

IN ROBOTIC MappINg

In addition to the type of sensory model used by

a mapping paradigm two other issues have a direct

correlation on the quality of map produced. These

are Specular Reﬂection and Redundant Information

(Murphy, 2000; Konolige, 1997).

• Specular Reﬂection: generally occurs when a

sonar beam hits a smooth surface and is reﬂected

off the surface at an obtuse angle. This results

in either no reading being returned to the sensor

or an erroneous reading being returned that has

bounced off many surfaces.

• Redundant Information: commonly arises when

the robot has been in the same pose for a period

of time and hence its sensors report multiple iden-

tical readings from that pose.

4 THE CONFORM APPROACH

TO ROBOTIC MAPPING

ConForM has two distinct aspects. These are:

1. The explicit modelling of sensory data to deal

with the specular and/or redundant information.

2. The use of an on-line forward sensory model to

translate the sensory readings into occupancy val-

ues for inclusion in the grid map.

4.1 Conform: Dealing With Specular

Readings

ConForM’s treatment of the problem of specularity

is novel as we consider it from two perspectives. The

ﬁrst is labelled Acceptability/Agreeability and the sec-

ond Trait Veriﬁcation. At each time-step Acceptabil-

ity/Agreeability consider solely the set of readings

currently received and evaluates each with respect to

its neighbouring readings. Trait veriﬁcation on the

other hand takes a wider perspective by evaluating

readings in relation to the current perceived state of

the environment.

4.1.1 Acceptability and Agreeability

Acceptability: Consider a reading s and let us assume

that it reports a range reading with a distance of d. As

operating environments are formed from regular fea-

tures and as the perceptual ﬁelds of neighbouring sen-

sors generally overlap we can assess the consistency

of a particular reading by evaluating its probabilistic

proﬁle in relation to its neighbours. A reading whose

measurement is corrupted by Gaussian noise of zero

IMPROVED OCCUPANCY GRID LEARNING - The ConForM Approach to Occupancy Grid Mapping

493

mean and variance σ

has the following probability

distribution where m is the map as illustrated in equa-

tion 1. This is based on the standard speciﬁcation of

a sensory model (Elfes, 1989).

p(s

|m) =

√

2πσ

−

(d)

(1)

Strictly speaking m is the local map corresponding to

the current perceptual ﬁeld and therefore a sub set of

the overall map that is produced.

Now consider the readings s

−1

and s

the neighbour-

ing readings on either side of the reading s. The prob-

abilistic proﬁle of these readings are used to support

or refute the reading s. If reporting an obstacle each

will have an associated distance d

−1

and d

. There-

fore we can calculate the probability distribution for

these readings using equation 1. These distributions

are compared to determine if the readings are con-

sistent. This is accomplished by translating the read-

ing s to the position of s

−1

. Upper and lower bound

proﬁles for s are calculated at this position through

scaling the original distance to the point of interest

d by the amount of translation required and also tak-

ing cognisance of the natural error range of the sen-

sor. If the readings are reporting on the same environ-

mental conditions the reading s will be encompassed

by the determined bounds. If this is so the reading

is deemed as being acceptable and subsequently al-

lowed to progress for further consideration. An iden-

tical procedure is utilised when considering the read-

ing s

. A reading s is discarded only when both ac-

ceptability tests indicate that it is unacceptable.

Agreeability: The sister concept of acceptability is

Agreeability. It considers readings that report free

space. It is similar to Acceptability in that we evaluate

a reading in terms of its neighbours. Robotic sensors

are good at accurately reporting free space meaning

that we can use a direct comparison method with free

space readings as it is the detection of an obstacle or

not which is important, not the actual difference in

any distance reported. Therefore when determining

agreement, for efﬁciency, we do not construct prob-

abilistic proﬁles for the readings. Rather we use the

ranges reported instead. If one of a readings immedi-

ate neighbours is not in agreement with the reading it-

self we allow the reading s to proceed to the next stage

of the process where it will be checked in the context

of the generated map, using Trait Veriﬁcation. If nei-

ther of s’s immediate neighbours report a free-space

reading then the reading is discarded.

4.1.2 Trait Veriﬁcation

Agreeability and acceptability deal with specular

readings in a bottom up fashion at the local level.

Speciﬁcally this is in the context of a single reading

set. As outlined above there are cases when the relia-

bility of readings cannot be determined from purely

considering the local view of the reading set from

which they originated. Therefore we also need to con-

sider the top down, global, perspective which takes

into account the environmental features determined to

date and recorded in the map being constructed. This

is the basis of the Trait Veriﬁcation.

In its operation Trait Veriﬁcation makes use of the fact

that environments contain structural regularities and

symmetries such as walls that can be approximated

using line segments. This is used as a basis for the

construction of two environmental views:

• V: A temporary sonar view which consists of

traits, or line segments, that can be estimated from

the current set of sensory readings.

• L: A local view which contains a history of the

line segments estimated from past sensory read-

ings. Line segments are maintained for an area

covering four times the perceptual ﬁeld of the

robot along the path the robot has traversed.

L is used to form a hypothesis as to the probable state

of the environment from the robots current perspec-

tive. This is accomplished by extending L to cover

the current location of the robot using the historical

perspectives as a reference point.

Following this L and V are reconciled. Firstly, cer-

tainty values in the range 0 → 1 are calculated for the

readings that give rise to traits in V. This is accom-

plished through use of standard singular displacement

speciﬁcations presented in (Elfes, 1989).

Having determined certainty values in the readings, V

and L are reconciled. Two courses of action are ap-

plicable, depending on whether or not sufﬁcient state

was available for L’s construction.

If enough state was not present to provide four per-

ceptual lengths centred on the oath traversed by the

robot, v

’s attributes are considered. v

is a trait in V

and its attributes relate to the reading(s) that gave rise

to the trait. For example the certainty associated with

the reading(s) or whether the reading(s) were previ-

ously ﬂagged as potentially erroneous. If the reading

was ﬂagged as potentially erroneous from the Accept-

ability/Agreeability and Trait Veriﬁcation steps or the

reading certainty is below a determined threshold and

there is not an equivalent trait in L, where in this case

L has a size equivalent to maximum perceptual range

available, the reading is discarded.

If sufﬁcient state was available L and V are compared

directly. If traits coincide in both views the readings

that gave rise to those traits are accepted, provided

that they have not been ﬂagged as possibly erroneous.

If they have been ﬂagged the attributes of the trait v

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494

in V are considered. If two or more sensors agree on

the existence of the trait then the ﬂagged reading is

accepted. If the trait was detected by a single sen-

sor the certainty value associated with that reading is

consulted. If the certainty is below the threshold the

reading is rejected. Otherwise it is accepted. If a trait

occurs solely in V and not in L then the attributes of

the trait are considered. If the ﬂagged status and con-

ﬁdence value of the reading(s) that gave rise to the

trait are acceptable, the reading is allowed to proceed

for further utilisation. The problem of a reading relat-

ing to a trait solely in L and not in V is dealt with in

the same manner.

4.2 Conform: Addressing Redundant

Information

To deal with the problem of redundant informa-

tion ConForM makes use of pose buckets (Konolige,

1997). With pose buckets a map has a dual repre-

sentation where each cell represents both the occu-

pancy of the area and the pose of readings that have

affected that cell. Therefore a record is maintained

stating whether a reading from a given distance and

angle has affected a particular cell. This means that

the ﬁrst reading received from a speciﬁc pose will be

utilised, and all following readings from that pose for

this cell are discarded, as they merely duplicate infor-

mation already in the model.

4.3 Conform: Sensor Model

As per the original formulation, ConForM’s forward

model it also based on optimisation using the EM al-

gorithm (Dempster et al., 1977). It is a mixture model,

which accounts for the potential causes of a reading

(Thrun, 2003). A measurement may correspond to

the detection of an obstacle somewhere in the per-

ceptual ﬁeld of the sensor, failure to detect any ob-

stacle thereby reporting freespace, or indeed, a ran-

dom ﬂuctuation of a sensor. Each case has an associ-

ated probability. The model convolves these potential

causes and associated Gaussian noise into an amalga-

mated probability distribution which is subsequently

optimised by the EM algorithm to determine the most

likely cause of the received reading.

Our model differs from the original in that operates

on-line and in real-time. The on-line and real-time

use of the EM algorithm in ConForM is facilitated

through a two step approach. The ﬁrst step consists of

explicitly dealing with potentially erroneous or redun-

dant information through Acceptability/Agreeability,

Trait Veriﬁcation and Pose Buckets. As such the read-

ings available for the second stage encompass more

accurately the true state of the perceived environment

meaning that EM can be applied to a search space that

is tractable during real-time operation.

Using the EM algorithm to determine a map

1. Initialisation: Unlike traditional occupancy grid

mapping algorithms using inverse sensor models

EM does not estimate posteriors. Therefore maps

resulting from EM are discrete with each cell be-

ing either occupied or empty. As such the cells

in the map being constructed are initialised to an

occupancy of 0.5.

2. E-step: The E-Step calculates the expectations for

the potential causes of readings conditioned on the

map m and the current set of readings S.

3. M-step: The M-step assumes all expectations are

ﬁxed and calculates the most likely map based on

these expectations. The probability distributions

calculated in the E-Step encapsulate all potential

causes of the readings in S when determining a

new map m. Maximisation of these distributions

are performed by hill climbing in the space of all

maps. The search is terminated when the target

function is no longer increasing.

4. Incorporating Uncertainty: EM calculates only a

single map not an entire posterior. An approxi-

mation which conditions the posterior on the map

generated by EM is utilised to incorporate uncer-

tainty into the map, thereby providing useful in-

formation for real-time operation.

5. Finally we integrate the map generated by EM

into the overall map using a Bayesian based in-

tegration.

5 EMPIRICAL EVALUATION

Real world and simulated environments were used to

empirically evaluate ConForM. The simulator used

was the Saphira architecture with the associated Pio-

neer simulator. For simulated experiments odometry

error was turned off so that wheel slippage would not

be a factor thus allowing us to focus on evaluating the

performance of the mapping paradigms in large cyclic

environments such as those illustrated earlier. For real

world experimentation we used relatively small ofﬁce

environments purely for the reason that wheel slip-

page and thus odometric error is minimal over such

short distances.

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495

5.1 Benchmarking Technique

To evaluate the maps generated during our exper-

iments we use an extensible suite of benchmarks

which allow for the empirical evaluation of map

building paradigms (Collins et al., 2004; Collins et al.,

2005).

1. Correlation: As a generated map is similar to an

image it is possible to use a technique from image

analysis known as Baron’s cross correlation coef-

ﬁcient (Baron, 1981) as a basis for evaluating the

map.

2. Map Score: This is a technique which calcu-

lates the difference between a generated map and

an ideal map of the environment (Martin and

Moravec, 1996).

3. Map Score of Occupied Cells This metric is simi-

lar to the previous one but only tests those cells in

the map that are occupied.

4. Path Based Analysis: To fully evaluate a gener-

ated map its usefulness to a mobile robot must be

considered.

• The degree to which the paths created in the

generated map would cause the robot to collide

with an obstacle in the real world, and are there-

fore invalid. False Positives.

• The degree to which the robot should be able to

plan a path from one position to the another us-

ing the generated map, but cannot. False Nega-

tives.

5.1.1 Determining an Overall Score

To allow an overall score to be determined we have

developed an amalgamation technique which can be

used to rank the overall performance of mapping

paradigms relative to each other as outlined in equa-

tion 2.

map

∈M

map

+ P

map

(2)

map

(1−MapScore

all

) + (1−MapScore

occ

) + B

300

map

= 1−

(FP) + (FN)

200

map

∈M

is the overall classiﬁcation score obtained, M

is the set of maps generated in an experiment,

map

is a

particular map within the set of maps M. MapScore

all

and MapScore

all

are the normalised result from the

Map Score metrics, B

is the normalised Correlation

result. FP is the normalised False Positive result and

FN is the normalised False Negative result.

5.2 Results

In determining the performance of ConForM we em-

pirically evaluated it in relation to its peer mapping

paradigms, the original Forward Modelling paradigm

of Thrun (Thrun, 2003) and an on-line paradigm

from Konolige (Konolige, 1997) which has proven to

have the best performance of the inverse model based

paradigms (Collins et al., 2005).

Benchmarking consisted of completing a number of

data acquisition runs in the environments and using

this data in conjunction with the mapping paradigms

to generate the grid maps. Our experiment used four

differing environments, two simulated and two real

world, with three data acquisition runs being com-

pleted per environment. Therefore the results pre-

sented here are derived from evaluating a total of

thirty six individual grid maps. Table 5.2 presents the

amalgamated score for the mapping paradigms ob-

tained using the benchmarks outlined above. A larger

Table 1: Evaluating the ConForM approach to robotic map-

ping.

Mapping Paradigm Result

Moravec and Elfes 1985 0.67

Matthies and Elfes 1988 0.65

Konolige 1997 0.76

Thrun 2001 0.84

ConForM 0.87

evaluation recently completed and to be reported on,

which consisted of ten differing environments and

3600 individual maps, reported trends consistent with

those outlined here.

(a) Konolige

1997

(b) ConForM (c) Thrun 2003

Figure 2: Illustrative maps from the ConForM evaluation.

5.3 Analysis

Overall the results show that ConForM has outper-

formed the other approaches. ConForM outperforms

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496

the inverse model based approaches because of its

improved sensor model and the manner in which it

tackles the problem of specularity in addition to its

use of pose buckets. In dealing with specularity,

the multi-faceted approach consisting of Acceptability

and Agreeability and Trait Veriﬁcation is capable of a

ﬁner reading set analysis when compared to inverse

model based approaches. This also has the knock-

on effect of making the operation of the pose buckets

more accurate as they suffer less from the problem of

spurious readings giving rise to false hypothesis re-

garding the perceived state of the environment.

ConForM outperforms the original Forward Mod-

elling approach because of its pro-active approach to

the problems of specularity and redundant informa-

tion. That original approach addressed the problems

of seemingly conﬂicting information through the EM

algorithm. The likelihood of the reading was evalu-

ated in a global context meaning that some localised

accuracy may be sacriﬁced. In ConForM the Forward

Model used considers the local perspective meaning

that it is capable of capturing and retaining more sub-

tle characteristics that may be dismissed in the ofﬂine

approach.

6 SUMMARY

Overall ConForM overcomes the problems inherent

in traditional approaches such as the need for assump-

tion of cell independence or the need for ofﬂine op-

eration. It also overcomes the issue of the existing

forward model approach not being applicable in an

on-line context. In addition it generates maps that

are more consistent then existing approaches. The ar-

eas for further consideration and research in relation

to ConForM include reﬁning the threshold used with

trait veriﬁcation, investigating the use of EM as a ba-

sis for reﬁning already generated portions of the map

and investigating alternative EM formulations such as

Bayesian based approximations.

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