A SPATIAL ONTOLOGY FOR HUMAN-ROBOT INTERACTION

Lamia Belouaer, Maroua Bouzid and Abdel-Illah Mouaddib

Universit

e de Caen - UFR des Sciences, D

epartement d’Informatique

Campus C

ote de Nacre, Bd Mar

echal Juin, BP 5186, 14032 Caen Cedex, France

Keywords:

Spatial Representation and Reasoning, Spatial Relations, Ontology, Planning, Human-robot Interaction.

Abstract:

Robotics quickly evolved in the recent years. This development widened the intervention ﬁelds of robots.

Robots interact with humans in order to serve them. Improving the quality of this interaction requires to

endow robots with spatial representation and/or reasoning system. Many works have been dedicated to this

purpose. Most of them take into account metric, symbolic spatial relationships. However, they do not consider

fuzzy relations given by linguistic variables in humans language in human-robot interaction. These relations

are not understood by robots. Our objective is to combine human representation (symbolic, fuzzy) of space

with the robot’s one to develop a mixed reasoning. More precisely, we propose an ontology to manage both

spatial relations (topological, metric), fuzziness in spatial representation. This ontology allows a hierarchical

organization of space which is naturally manageable by humans and easily understandable by robots. Our

ontology will be incorporated into a planner by extending the planning language PDDL.

1 INTRODUCTION

Robotics quickly evolved in the last decade and there

is an increasing demand for intelligent systems like

robots that can help in daily life. This development

widened the intervention ﬁelds of robots such as a

public area where robots interact with humans in or-

der to serve them. To improve the quality of this in-

teraction, robots should behave as much as possible

like humans. This requires to endow robots with rep-

resentations and/or systems of reasoning directly in-

spired by humans. We focus on human-robot interac-

tion (HRI) based on spatial organization of observed

structures, in order to plan robots actions.

Planner

Spaceontology

Problem :

initial state

goals

Spatial

information

Plan

Figure 1: Spatial Planner.

Our goal is to develop a planner allowing to

solve problems taking into account spatial informa-

tion. This planner, called Spatial Planner (Fig. 1),

consists of two sub-systems. The ﬁrst sub-system,

SpaceOntology allows a spatial representation and

reasoning model. As input, it takes a set of impre-

cise and incomplete spatial information. However,

as output, it provides a structured knowledge about

the environment to explored in planning. The second

sub-system, Planner, deﬁnes the set of actions to be

executed by the robot in order to achieve its mission.

In this paper, we focus on SpaceOntology that

models spatial representation and reasoning for better

mediation between humans and robots. This ontology

concerns:

• Hierarchical representation of space. The space

is structured to be manageable by humans and

robots.

• Numerical/Symbolic representation of space.

From the human’s point of view, the space is gen-

erally considered in a symbolic way (in, disjoint,

north, close, . . . ). From the robot’s point of view,

the space is considered in numerical way (angles,

distances, . . . ).

SpaceOntology gives a description of the environ-

ment (hierarchical organization, spatial relations) un-

derstandable by both humans and robots.

This paper is organized as follows. In section 2,

we place our work with regard to the state of art of the

spatial representation and ontologies. In section 3, we

present our framework to model spatial representation

and reasoning. In section 4, we present SpaceOntol-

ogy. In section 5, we present how we use ontology to

develop a mixed reasoning (from human to robot and

154

Belouaer L., Bouzid M. and Mouaddib A. (2010).

A SPATIAL ONTOLOGY FOR HUMAN-ROBOT INTERACTION.

In Proceedings of the 7th International Conference on Informatics in Control, Automation and Robotics, pages 154-159

DOI: 10.5220/0002948001540159

 SciTePress

from robot to human). In conclusion, we present our

future works.

2 RELATED WORK

2.1 Spatial Relations

The spatial relations have been developed in many do-

mains (image processing (Bloch and Ralescu, 2003),

GIS (Casati et al., 1998), . . . ). They can be di-

vided into topological, directional and distance rela-

tions (Kuipers and Levitt, 1988). In this paper, we

consider all these relations.

In robotics, quantitative representations of spatial

relations are commonly applied. Purely quantitative

representations have limitations particularly when im-

precise knowledge use spatial relations expressed in

linguistic terms, particular in HRI. Imprecision has to

be taken into account in such problems. It is often

inherent to human language. It may be caused by im-

precision about the objects to recognize due to the ab-

sence of crisp contours or by the imprecise semantics

of some relationships (eg. quite far, . . . ), or else by a

kind of task we would like fulﬁll in HRI. For exam-

ple, we may want a robot go towards a person while

remaining at security distance of it.

Our objective is to combine all symbolic represen-

tation with robotic numeric representation to develop

a mixed reasoning.

2.2 Ontologies and Spatial Dimension

Different techniques of spatial representation and rea-

soning have been proposed. Most are based on con-

straints, logical and algebraic approaches (Balbiani

et al., 1999). However, these approaches can not man-

age quantitative, qualitative and imprecise knowledge

at the same time. In HRI, we need to combine this

knowledge. For this reason, we must use an uniﬁed

framework to cover large classes of problems and po-

tential applications, and able to give rise to instanti-

ation adapted to each particular application. Ontolo-

gies (Gruber et al., 1995) appear as an appropriate tool

toward this aim.

Spatial ontologies can be found in some ﬁelds

such as GIS (Casati et al., 1998), Virtual Reality (Da-

siopoulou et al., 2005), Robotics (Dominey et al.,

2004), . . . All these ontologies are focused on the rep-

resentation of spatial concepts according to the ap-

plication domains. A major weakness of usual onto-

logical technologies is their inability to represent and

to reason with imprecision. An interesting work pre-

sented in (Hudelot et al., 2008) overcome this limit.

3 OUR FRAMEWORK

In our work, we set up an ontology to manage both

spatial relations, fuzziness in spatial representation.

Moreover, our ontology allows an organization of

space naturally manageable by human and easily un-

derstandable by the robot: hierarchical representation

of space.

3.1 Hierarchical Organization of Space

Hierarchical organization of space reduces the

amount of information considered for coping with a

complex, high-detailed world: concepts are grouped

into more general ones and these are considered new

concepts that can be abstracted again. The result is

a hierarchy of abstractions (or specialization) or a hi-

erarchy of concepts that ends when all information is

modeled by a single universal concept (or we reach

a desired level of specialization). Thus, we consider

this hierarchy to describe the considered space.

Our organization is made from the highest abstrac-

tion level to lowest (most detailed one) unlike the or-

ganization described in (Fern

andez-Madrigal et al.,

2004). The highest level represents the environment

with the maximum amount of detail available. The

lowest level represents the environment by a single

concept. Hierarchical representation of space allows

us to represent this space in a structure easily man-

ageable by human and robot. In addition, it provides

better performance than ﬂat representation in naviga-

tion or path planning.

3.1.1 Spatial Entity

All concepts in spatial representation are called Spa-

tial Entities. A spatial entity is localizable in a given

space by one of its attributes or by geometric trans-

formation. From a geometric point of view, a spatial

entity ε is deﬁned by a rectangle rect

corresponding

to its axis-aligned bounding rectangles.

From hierarchical organization of space, derives

two categories of spatial entities. Space represents a

global space. This entity is the highest abstraction and

the lowest level in the hierarchy organization. Region

represents any spatial entity belonging to different hi-

erarchical levels (intermediate and ﬁnal). A region is

a sub-space included in the given space. A region is

itself considered as a space that can be decomposed

into different sub-regions.

3.2 Spatial Relations

A spatial relation requires a reference frame. For ex-

ample, the relation bench is in front of coffee machine.

A SPATIAL ONTOLOGY FOR HUMAN-ROBOT INTERACTION

155

The semantic of the relation is not the same depend-

ing on whether the reference system is the coffee ma-

chine itself or an external observer. In order to have

an unique meaning and to remove the ambiguity, three

concepts have to be speciﬁed : the target object, the

reference object and the reference system (Hudelot,

2005). In our work, we consider both Intrinsic and

Egocentric reference frame.

3.2.1 Topological Relationships

We consider the ALBR relations deﬁned in ABLR

(Above Below West Right) (Laborie et al., 2006).

This algebra balances between expressiveness and the

number of relations (reasoning/complexity). ABLR

reduces the number of relations while preserving the

directionality property of the representation deﬁned

in (Allen, 1983). A topological relation is an ABLR

relation. This relation is a couple hr

, r

i, where;

∈ {Le f t(L), OverlapsLe f t(O

),Contains(C

Inside(I

), OverlapsRightO

, Right(R)}

and

∈ {Above(A), OverlapsAbove(O

),Contains(C

Inside(I

), Overl pasBelow(O

), Below(B)}.

3.2.2 Metrical Relationships

Metrical relations concern distance and orientation re-

lations (Bloch, 2005). We consider a 2D representa-

tion of the space given by (O,

−→

i ,

−→

j ). The origin O

is a reference system that can be intrinsic or egocen-

tric. In the following, a rectangle denotd ε represents

a spatial entity. Its symmetry center will be known as

the spatial entity name. P

(ε) (resp. P

(ε)) denotes

the projection of ε on (

−→

i ) axis (resp. (

−→

j ) axis).

In HRI under spatial constraints, fuzzy informa-

tion is a key point as said in section 2. In this work,

vagueness and ambiguity concern the vagueness of

the relationship itself. Indeed, we don’t need to eval-

uate if a spatial entity is in north of a referent spatial

entity since spatial entities are crisp. The application

of fuzzy approach mainly concerns the distance rela-

tionship. The aim is to ﬁnd a way to represent the

symbolic direction and distance relationship (based

on linguistic variables) by a numerical direction and

distance and vice versa.

Directional Relationships. We describe directional

relations through cardinal direction : West of, North

of, East of and South of. We associate for every se-

mantic direction semantic West of, East of, North of

and South of following respective functions West

East

, North

(R is a referent object) and South

West

(ε) denotes ε is left of R given by West

(ε) =

(ε) − P

(R) 6 0}. East

(ε) denotes ε is right of R

given by East

(ε) = {P

(ε) −P

(R) > 0}. North

(ε)

denotes ε is in north of R given by North

(ε) =

(ε) − P

(R) > 0}. South

(ε) denotes ε is in south

of R given by South

(ε) = {P

(ε) −P

(R) 6 0}.

The representation of the 8 cardinal relationships

is possible by combining these four functions. Con-

sider the example of the directional relation the bench

b is north and east of coffee machine c

. This

corresponds to the combination of North

(b) and

East

(b):

North

(b) ⊕ East

(b) =



(b) − P

) > 0

(b) − P

) > 0

(1)

This representation allows us to express other direc-

tional relations (at the same level, between, . . . ).

Distance Relationships. We consider four linguis-

tic variables to describe distance relations: close to,

close to enough, far from enough, far from. We note

d(ε, r) in R

the euclidean distance between the point

of symmetry of two rectangles representing two re-

gions (r referent object and ε target object). The aim

is to ﬁnd a way to represent the four linguistic vari-

ables already deﬁned to evaluate distance by a nu-

meric value to evaluate it. To do so, we consider two

degrees, deﬁned in (Schockaert, 2008), N

(α,β)

(p, q)

( 2) and F

(α,β)

(p, q) ( 3). The degree N represents

two points p and q are near each other and the de-

gree F represents how p is far from q (α, β > 0). We

have deﬁned a hierarchical space organization. This

has an impact on the distance evaluation. Indeed, the

distance of 2m in a city is considered as near, how-

ever, 2m in an ofﬁce is considered as far. From these

information, we deﬁne for each hierarchical level an

α and a β depending on the scale of this level.

(α,β)

(p, q) =







1 if d(p,q) ≤ α

0 if d(p,q) ≥ α +β

α+β−d(p,q)

otherwise β 6= 0

(2)

(α,β)

(p, q) =







1 if d(p,q) > α +β

0 if d(p,q) ≤ α

d(p,q)−α

otherwise β 6= 0

(3)





d(p,q)

 ,

 p , q

 ,

 p , q

Figure 2: Graphical representation of relationship between

(α,β)

(p, q) and F

(α,β)

(p, q).

From equations 2 and 3 and organization given in

ﬁgure 2, it is easy to deduce that: (1) if d ∈ [0, α] then

ICINCO 2010 - 7th International Conference on Informatics in Control, Automation and Robotics

156

d is considered as close, (2) if d ∈]α, α +

] then d

is considered as close enough, (3) if d ∈]α +

, α +

β] then d is considered as far enough, (4) if d ∈]α +

β, +∞[ then d is considered as far.

4 IMPLEMENTATION

As a formal language, we opted for OWL DL formal-

ism (McGuinness et al., 2004; Baader et al., 2003).

This formalism beneﬁts from the compactness and

expressiveness of DL. Indeed, an important charac-

teristic of DL is their reasoning capabilities of in-

ferring implicit knowledge from the explicitly repre-

sented knowledge. In this section, we describe how

we present and reason about spatial knowledge.

4.1 Spatial Entities as Concepts

One of important concepts of SpaceOntology is the

concept Space (Spacev T) (T for Thing

). This con-

cept represents a global environment (i.e a country, a

city, . . . ). Also, we deﬁne a concept Regions. This

concept is a subclass of concept Space (Regionsv

Space). Thus, we can consider the hierarchical deﬁ-

nition of space. Indeed, a region itself is a space in the

next hierarchical level. Furthermore, the hierarchical

relationship between concepts Space and Regions is

given by subsumption. We offer the following links

consistsOf and isPartOf. The link consistsOf can ex-

press that space consists of one or more regions. The

link isPartOf can express one region may belong to

one or more spaces. These relationships are symmet-

rical and transitive.

Space v T u ∃ consistsOf.Regions u > 1

consistsOf

Regions v Space u ∃ isPartOf.Space u > 1

consistsOf

Space

building

Regions

region1 region11

Figure 3: Links between concepts and their instantiation.

From these links and their properties, we can com-

pose relationships between these two concepts. For

instance, the composite (2) relationship in ﬁgure 3, is

Thing is an OWL class that represents the set contain-

ing all individuals. Because of this all classes are subclasses

of OWL:Thing.

derived from the transitive links isPartOf (4) between

region1

with region1 and region1 with building.

Through this relationship we can deduce that region1

is part of the building.

4.2 Spatial Relations as Concepts

A spatial relation is not considered in our ontology

as a property between two regions but as a concept

on its own; SpatialRelations(SpatialRelationsv

T). This concept represents a set of all spatial rela-

tions between two regions. A SpatialRelations sub-

sumes TopologicalRelations and MetricRelations

which itself subsumes DirectionalRelations and Dis-

tanceRelations which itself subsumes DistanceAc-

cordingToActions and DistanceAccordingToHier-

archicalLevel.

4.2.1 HasRelation Concept

To deﬁne a spatial relationship between two regions

describing a given conﬁguration, we need to link

these regions with a spatial relationship.

SpatialRelations

DirectionalRelations

Left_Of

HasRelation

relation1

Space

Regions

Coffe machine

office

concernsSpatialRelation

hasReferent

hasTarget

Figure 4: Links between concepts and their instantiation.

As already deﬁned, a spatial relationship is given

by the concept SpatialRelations. We deﬁne the link

HasRelation as a concept which refers to the set of

spatial relations for which target and reference entities

are deﬁned. This concept is useful to describe spatial

conﬁgurations.

HasRelation v T u ∃

concernsSpatialRelation.SpatialRelations u = 1

concernsSpatialRelation u ∃

hasReferent.Regions u > 1 hasReferent u ∃

hasTarget.Regions u = 1 hasTarget

Consider as an example that human asks the

robot to enter into ”the ofﬁce left of the coffee ma-

chine”. In SpaceOntology, this expression is for-

malized as follows. First, identify this expression

by relation1. We note relation1:HasRelation

We consider that relation1 is an instantiation of

the concept HasRelation. Left

o f

is an instantia-

tion of the concept DirectionalRelations according

to a deﬁned reference system for spatial relations

(Left

o f

:DirectionalRelations). The ofﬁce and

These symbols are deﬁned in description logics syntax

and interpretation

A SPATIAL ONTOLOGY FOR HUMAN-ROBOT INTERACTION

157

the coffee machine are instantiations of the concept

Regions (office:Regions and coffee:Regions).

5 OPERATING SPACEONTOLOGY

In this section, we present the exploitation of our on-

tology and the methods for reasoning. As already

mentioned, we developed an ontology to provide a ba-

sis spatial data to be used after in planning problems

to improve HRI. Exploitation of ontology is neces-

sary for path planning between two positions. In this

paper, we present how and by which methods from

ontology we can extract the paths between two posi-

tions even if the information is incomplete. Work on

path planing is the subject of future work.

5.1 Example

Consider an HRI problem in a building. A human

asks the robot to fetch a bottle near the coffee ma-

chine located in the hallway of the third ﬂoor. Then,

to bring back the bottle to the human who is on the

ﬁrst ﬂoor (initial robot position’s). Speciﬁcally, robot

should compute the path between its position and bot-

tle position’s, catching the bottle and after to give it to

human. To explain the reasoning, we consider in the

following only the ﬁrst part of the task, namely; fetch-

ing the bottle.

5.2 Reasoning

In SpaceOntology, we insisted on two key notions:

hierarchy of space and spatial relationships. Thus, we

rely on these notions for reasoning.

Consider the example given in section 5.1. By

giving a map with all the corridors and all access,

deﬁning a path by considering the size of the map be-

comes quickly expensive. Hierarchical organization

of space simpliﬁes the path computation. Indeed, it

helps to decompose the problem into 3 sub-problems:

(1) from initial position reach an access point to the

third ﬂoor, (2) from this access point plan to reach the

third ﬂoor and (3) from arrival position on the third

ﬂoor, plan to reach the coffee machine.

Reasoning for the ﬁrst and last steps requires more

detailed information than the second step. For this

step, we must ignore the details given in two other

steps. However, considering ﬂoors like black boxes

does not guarantee the path quality. Consider that

quality is related to speed. Passing through certain

corridors with big distances can be faster than through

the ones with short distances but with many obstacles.

Thus, hierarchical organization of a space, involves

reasoning at each level.

Thus, we can construct a path between any two

given locations in an accurate (i.e in room number 3)

or approximate ( i.e somewhere on the ﬁrst ﬂoor). In

this paper, we do not present an algorithm for ﬁnd-

ing paths, but rather we present a structure generated

from the ontology providing a set of possible paths

between two positions by considering the space hier-

archy. For the target object, in our case the bottle, we

deﬁne the concept of target zone. Considering the hi-

erarchy of the environment, we deﬁne the target zone

as T

(o), where l is the hierarchy level and o the ob-

ject or region targeted. Thus, we can deduce from

SpaceOntology a hierarchy for the target zone. This

allows us to determine the most abstract target zone

(o) = building) and the more detailed one (T

(o)=

region of coffee machine).

Another key knowledge in this work are spatial re-

lationships. They allow, given an environment, to de-

scribe its spatial conﬁguration (obstacle position’s).

For instance, we can describe that the corridor H is

adjacent to the door doorB of the ofﬁce B. Here, an

example from SpaceOntology.owl allowing to illus-

trate the example.

</intersectionresult>

</hasTarget>

</hasReferent>

</TopologicalRelations>

</concernsSpatialRelation>

</HasRelationWithIntersection>

As already mentioned, our strategy of searching a

path is to ﬁnd a path divided into different portions.

Each part belongs to a single hierarchical level. To

do this, we need a structure for this type of dedicated

research. This structure is generated from SpaceOn-

tology. Thus, we deﬁne the Crossing Network Graph.

5.2.1 Crossing Network Graph

A Crossing Network Graph(Γ

) is a directed graph.

A node in this graph represents a network of passage.

The nodes are organised hierarchically. The arcs rep-

resent relationships between nodes as described in

SpaceOntology.

ICINCO 2010 - 7th International Conference on Informatics in Control, Automation and Robotics

158

A Crossing Network(Γ) is a graph whose nodes

are Crossing Network. Edges represent spatial ad-

jacency relations between two nodes described in

SpaceOntology giving a contact point between these

nodes, known as gateways. A gateway (i.e door, pass-

ing lane, . . . ) allows transitions between adjacent

spaces and between spaces adjacent in different hier-

archical levels. Edges are labeled by a couple (pass,

dist), where pass gives the gateway connecting these

regions (or networks) and dist is the distance sep-

arating these regions (or networks) passing through

this gateway. There are two types of crossing net-

works: (1) Low-level crossing Networks are crossing

networks whose nodes are crossing networks. It used

such a network mainly as we have not reached the

level of specialization wanted (or ﬁxed). (2) High-

level crossing Networks are crossing networks whose

nodes are the regions. It used when level of special-

ization desired (or ﬁxed) is reached.

The construction of Crossing Network Graph is

done from the abstract level to ﬁxed detailed level.

First, we consider the target zone of the most abstract

level. In the same way, we consider the initial zone

of the most abstract level in the ontology. We select

the most abstract target zone and initial zone targeted

areas as these two zones are included in the same re-

gion. For instance, we consider the third ﬂoor (target

zone) and the ﬁrst ﬂoor (initial). It requires setting

different gateways allowed to exit the initial zone and

enter to the target zone. From the spatial relationships

of adjacency deﬁned SpaceOntology, we can ﬁnd with

backward mechanism all possible paths to reach the

initial region.

6 CONCLUSIONS

This paper presents a spatial representation using an

ontology allowing us to represent and reason on spa-

tial objects represented from different point of views

(human and robot). Future work will concern to in-

tegrate it in planning by extending the planning lan-

guage PDDL. This is an innovative concept. In this

paper, several aspects are still cause for thought as the

assessment of a relationship without a ﬁxed target or

the implementation of an algorithm to generate a path

according to some optimality criteria. These points

will be the subject of future work.

REFERENCES

Allen, J. (1983). Maintaining knowledge about temporal

intervals.

Baader, F., Calvanese, D., McGuinness, D., Patel-

Schneider, P., and Nardi, D. (2003). The description

logic handbook: theory, implementation, and applica-

tions. Cambridge Univ Pr.

Balbiani, P., Condotta, J.-F., and del Cerro, L. F. (1999).

A new tractable subclass of the rectangle algebra. In

IJCAI, pages 442–447.

Bloch, I. (2005). Fuzzy spatial relationships for image pro-

cessing and interpretation: a review. Image and Vision

Computing, 23:89–110.

Bloch, I. and Ralescu, A. (2003). Directional relative posi-

tion between objects in image processing: a compari-

son between fuzzy approaches. Pattern Recognition.

Casati, R., Smith, B., and Varzi, A. (1998). Ontological

tools for geographic representation. (FOIS’98).

Dasiopoulou, S., Mezaris, V., Kompatsiaris, I., Papastathis,

V., and Strintzis, M. (2005). Knowledge-assisted se-

mantic video object detection. IEEE Transactions on

Circuits and Systems for Video Technology.

Dominey, P., Boucher, J., and Inui, T. (2004). Building

an adaptive spoken language interface for perceptu-

ally grounded human–robot interaction. In Proceed-

ings of the IEEE-RAS/RSJ international conference on

humanoid robots.

Fern

andez-Madrigal, J., Galindo, C., and Gonz

alez, J.

(2004). Assistive navigation of a robotic wheelchair

using a multihierarchical model of the environment.

Integrated Computer-Aided Engineering.

Gruber, T. et al. (1995). Toward principles for the design of

ontologies used for knowledge sharing. International

Journal of Human Computer Studies.

Hudelot, C. (2005). Towards a cognitive vision platform

for semantic image interpretation; application to the

recognition of biological organisms.

Hudelot, C., Atif, J., and Bloch, I. (2008). Fuzzy spatial

relation ontology for image interpretation. Fuzzy Sets

and Systems.

Kuipers, B. (2000). The spatial semantic hierarchy. Artiﬁ-

cial Intelligence, 119:191–233.

Kuipers, B. and Levitt, T. (1988). Navigation and mapping

in large scale space. AI magazine, 9:25.

Laborie, S., Euzenat, J., and Layaıda, N. (2006). A spatial

algebra for multimedia document adaptation. SMAT.

McGuinness, D., Van Harmelen, F., et al. (2004). OWL web

ontology language overview. W3C recommendation.

Schockaert, S. (2008). Reasoning about fuzzy temporal and

spatial information from the web. PhD thesis, Ghent

University, 2008.

A SPATIAL ONTOLOGY FOR HUMAN-ROBOT INTERACTION

159