HANDLING SPATIAL VAGUENESS IN VIRTUAL AGENT

CONTROL

Spyros Vosinakis, Nikos Pelekis, Yannis Theodoridis and Themis Panayiotopoulos

Department of Informatics, University of Piraeus, 80 Karaoli & Dimitriou str, Piraeus, Greece

Keywords: Fuzzy Logic, Computer Animation, Virtual Reality, Virtual Agents.

Abstract: Virtual agents are an important element of virtual environments that enhance their believability and

autonomy. Nowadays, there are a number of architectures and languages for designing virtual agents and

scripting their control process, but the majority of them cannot cope with the vagueness that characterizes a

designer’s description of a location or direction using natural language, and, thus, fail to demonstrate

complex spatial behavior in dynamic environments. We propose a framework for handling spatial

vagueness in virtual agent control, which uses binary fuzzy relations to represent vague location

descriptions and a fuzzy rule-based system for the agent control. We present a prototype implementation

and a case study, in which the proposed framework is successfully used for a virtual agent’s locomotion in a

dynamic environment.

1 INTRODUCTION

Virtual Agents are autonomous entities in synthetic

environments that aim to enhance the believability

of virtual reality applications (Aylett and Luck,

2000). To satisfy this need for autonomy, they are

equipped with mechanisms for monitoring changes

in the environment (sensors), for executing actions

upon it (effectors), and for taking decisions about

their actions.

One problem in current agent control

architectures, which is a consequence of their need

to combine both an abstract representation and a

concrete model of the virtual world, is spatial

vagueness, i.e. the inability to translate abstract

descriptions of locations and areas into crisp

coordinates as needed by the control mechanism.

Most agent control languages in the literature

represent locations as specific points in space, i.e. as

2D or 3D coordinates. In some cases, locations can

be determined by areas predefined by the designer,

or they can be dynamically assigned to the position

of another object or agent (Arafa and Mamdani,

2003). Such representations are adequate for simple

instructions such as ‘go to the door’ or ‘look at

John’. However, in the case of dynamic and non-

deterministic environments, the agent’s locomotion

and spatial behavior in general (gaze, object

placement, etc.) cannot be based on predefined

locations or simply on the position of another object.

Fuzzy logic is an effective means of representing

vague and imprecise knowledge, and has already

been used successfully in the field of robotics

(Benreguieg et al, 1997). It can, therefore, be used

for representing vague descriptions of locations and

areas, and for building a virtual agent control

mechanism that can operate with vague data.

In this paper, we present a framework for

handling spatial vagueness in virtual environments,

which could extend existing agent control languages

and increase their autonomy and adaptability. We

define vague locations as a representation scheme

that supports linguistic descriptions of locations and

propose an agent control architecture that is using a

fuzzy rule-based system to take low-level decisions

concerning the agent’s spatial behavior. We have

implemented a language for scripting the agent’s

control mechanism using vague locations and we

present a case study of an agent operating in a

dynamic environment using the proposed

architecture.

2 VAGUE LOCATIONS

The problem of spatial vagueness (Hazarika and

Cohn, 2001) is that people think and reason about

locations and areas in a qualitative manner in

contrast to software agents operate with crisp

Vosinakis S., Pelekis N., Theodoridis Y. and Panayiotopoulos T. (2007).

HANDLING SPATIAL VAGUENESS IN VIRTUAL AGENT CONTROL.

In Proceedings of the Second International Conference on Computer Graphics Theory and Applications - AS/IE, pages 75-78

DOI: 10.5220/0002084900750078

 SciTePress

coordinates. A designer may wish to use regions

instead of coordinates as execution parameters, e.g.

‘on the table’, ‘in the room’, etc., and in some cases

it may also be needed to represent locations in terms

of vague regions such as ‘near the wall’, ‘in front of

the table’, etc.

We define a Vague Location L as a binary fuzzy

relation in the Cartesian plane:

}),(|)),(),,{((

ℜ∈= yxyxyxL

The degree of membership μ

of each pair (x,y)

in the vague location represents the plausibility of a

point at (x,y) belonging to the location represented

by L.

We define affine transformations (i.e. translation,

rotation and scale) on vague locations as follows:

Let L be a vague location with membership function

. Let also M be a 2x2 affine transformation matrix.

Then L’ is the transformation of L by M iff:

]''[][|),()','(|)','(

−

==∀ Myxyxyxyxyx

μμ

Vague Locations can be further combined in

more complex linguistic expressions using fuzzy

operators and quantifiers, such as AND, OR, NOT

and VERY. We propose plausible representations

for distance and direction relations (Vazirgiannis,

2000) as vague locations. As stated in (Gapp, 1994),

the interpretation of spatial relations depends

strongly on the reference object’s size. Furthermore,

people do not account for every detail of the

reference object when applying spatial relations

(Landau and Jackendoff, 1993), and therefore, an

oriented bounding rectangle approximation can be

used. Based on the above, the definition of vague

locations from spatial relations can take place on a

prototype object, which will then be scaled,

translated and rotated according to the geometric

properties of the reference object. We use an object

with a bounding rectangle of size 1 x 1 located at the

origin and oriented towards the positive Y-axis as

the prototype on which all spatial relations are

defined.

Concerning the spatial relation ‘near’, we define

N as the near value, a distance below which a

coordinate is assumed to be near the reference

object, and F as the far value, a distance beyond

which a coordinate is assumed to be far from that

object. The prototype NEAR membership function

for that object is defined as follows:

⎪

⎩

⎪

⎨

⎧

≥

−

−<<

≤

),(

FdN

NEAR

where d is the Euclidean distance of the point (x,y)

from the origin, thus:

yxd +=

. Fig. 1 shows a

possible vague location ‘near object A’.

A plausible interpretation of the spatial relation

‘far’ is to define its membership function as the

equivalent to the NOT NEAR function, so μ

FAR

(x,y)

= 1-μ

NEAR

(x,y).

Figure 1: Vague Locations of ‘near A’ and ‘between A

and B’.

Concerning direction relations ‘front of’,

‘behind’, ‘left of’ and ‘right of’, we propose the

membership function FRONT, which is a plausible

interpretation of the ‘front of’ spatial relation of the

prototype reference object. It is defined as follows:

⎪

⎩

⎪

⎨

⎧

+−

≤≤−>

−<>

≤

)5.0(

,5.0;0

1,5.05.0;0

)5.0(

,5.0;0

0,0

),(

FRONT

Spatial relations can be interpreted in various ways

(Olivier and Tsujii, 1994), according to the frame of

reference. We use the intrinsic and deictic

interpretation of direction relations. In the intrinsic

interpretation the reference frame is centered at the

reference object and adopts its intrinsic orientation,

whilst in the deictic interpretation, it is centered at

the observer and adopts his orientation. The vague

location of a directional relation for an actual

reference object in the environment is calculated by

scaling the prototype FRONT location by the

reference object’s size, by translating it to the

reference object’s position and by rotating it to the

appropriate direction denoted by the type of the

directional relation.

Concerning the vague location ‘between objects

A and B’ (Fig. 1), we adopt the following approach:

the Vague Location D_FRONT_OF_A is calculated,

which is the deictic ‘front of’ using object A as

reference object and B as observer. Then, the

respective location D_FRONT_OF_B is calculated

by swapping reference object and observer. The

final Vague Location BETWEEN_A_AND_B is the

combination of these two locations using the AND

connective:

GRAPP 2007 - International Conference on Computer Graphics Theory and Applications

BETWEEN_A_AND_B

(x,y) = min(μ

D_FRONT_OF_A

(x,y),

D_FRONT_OF_B

(x,y)).

3 A FUZZY RULE-BASED

CONTROLLER

An agent is usually equipped with a visual sensor

that updates its internal model of the environment

based on the objects that are in its field of view, and

with a number of effectors that can execute actions

sequentially or in parallel. Some of these effectors

may utilize spatial behaviors, e.g. in the case of

anthropomorphic agents there can be effectors such

as gaze direction, body orientation, pointing, target-

based navigation, etc. Spatial vagueness exists at

both the perception the action levels. We propose a

fuzzy rule-based mechanism for the low-level

decision process of virtual agents in dynamic

environments that operates using vague locations.

The proposed architecture is presented in Fig. 2.

All sensor data are stored in the agent’s memory,

which contains the known objects and their property

values. The agent’s effectors operate using crisp

positions. They have an equal number of fuzzy rule

sets assigned to them, and they receive crisp input

after a complete fuzzyfication - evaluation -

defuzzification loop. Fuzzy rule sets contain

condition – action rules that are defined by the

designer using vague locations. The condition part

of a rule may be a simple or a compound condition.

The fuzzification process is executed in two

steps. Initially, all vague locations are recalculated

using the actual geometric properties of the objects

they refer to, as described in section 2. Then, the

condition of each rule is examined and a truth value

is assigned to it.

During the rule evaluation process, a fuzzy

inference takes place. The truth value of each

condition defines the proportion of the respective

rule taking part in the final output. We adopt the

PRODUCT inference method, according to which,

the vague location defined in the action part of each

rule will be scaled down by the truth value of the

respective condition. Thus, if t

∈[0,1] is the truth

value of the condition of a rule and L is the vague

location of the action part, the output location L’ of

this rule will be defined as: μ

L’

(x,y) = μ

(x,y)⋅t

The next step in the evaluation process is the

composition of the rules into the resulting vague

location. We use the MAX composition method: the

membership value of each coordinate in the vague

location L is the maximum value of all respective

membership values of the same coordinate in the

output locations of the rules. Thus, if L

, L

, …, L

the output locations of the rules, the resulting

location L will be defined as:

(x,y) = max(μ

(x,y), μ

(x,y), …, μ

(x,y))

The final step is the defuzzification process, in

which a crisp result is produced from the resulting

vague location. Using the CENTROID

defuziffication method on a vague location L, a crisp

position (x,y) can be calculated as follows:

∫∫

⋅

dydxyx

dydxyxx

),(

∫∫

⋅

dydxyx

dydxyxy

),(

The crisp output position is used by the effector

as argument to execute the agent’s actions.

4 CASE STUDY

We have created a prototype implementation of the

control mechanism described in the previous section

and connected it to the locomotion process of a

virtual agent in a 3D environment. Additionally, we

have designed and implemented a scripting language

for defining the fuzzy rule set of the agent using

vague locations. The representation of spatial

relations as vague locations is processed after

projecting the 3D model of the reference object(s)

on the ground plane and calculating their oriented

bounding rectangle. The complete system has been

implemented in Java and Java3D.

The implemented system has been used to set

up a case study, in order to assess the functionality

of the proposed framework. We have designed an

agent to operate as a guide in a virtual exhibition.

The 3D environment contains the static geometry

(walls, doors, etc.), a number of exhibits represented

Memory

Sensor

Fuzzy

Rules

Fuzzification

Rule

Evaluation

Defuzzification

Effector 1

RULE SET 1

AGENT

RULE

SET 2

crisp position

Effector 2

Effector N

RULE

SET N

…

object

properties

vague location

Figure 2: Architecture of the fuzzy rule-based controller.

HANDLING SPATIAL VAGUENESS IN VIRTUAL AGENT CONTROL

as 3D objects, the agent and the user’s avatar. The

goals of the agent are:

• To avoid collision with static objects or the

user

• To stand besides the exhibit that the user is

currently looking at, and present it to him.

The first test was the collision avoidance using

the vague location framework. We used the

following set of rules:

1: if nearest in front_of *me

and left_of *me

and near *me

then move_to right_of *me

2: if nearest in front_of *me

and right_of *me

and near *me

then move_to left_of *me

According to these rules, if the object that is nearest

to the agent is in front of the agent and at a close

distance, then it is probably going to obstruct its

navigation. In this case the agent is ordered to move

to the left if the obstacle is located to its right, and

the vice versa.

The second goal involved dynamic positioning of

the agent. It had to move itself to a place near the

exhibit, in order to present it to the user, but not in a

position that blocks the user’s view. Therefore, the

agent should not be in front of the exhibit as seen by

the user. Based on these requirements, the final rule

was defined as follows:

3: if “exhibit” in front_of “avatar”

and near “avatar”

then move_to very near “exhibit”

and not d_front_of “exhibit”

asb “avatar”

The condition of this rule tests whether an

exhibit is located in front of the user (“avatar”) and

near him. In that case, the user is probably studying

the exhibit. If this rule fires, the agent is ordered to

move to a place that is close to the exhibit (using the

spatial relation ‘near’ and the fuzzy quantifier

‘very’), but not in the region defined by the deictic

relation ‘d_front_of’ with the exhibit as a reference

object and the user as an observer.

5 CONCLUSIONS

We have presented a framework for handling spatial

vagueness in virtual agent control using binary fuzzy

relations in the Cartesian plane to represent vague

locations. We have proposed plausible

interpretations of spatial relations using vague

locations and presented a fuzzy rule-based control

mechanism that operates in dynamic environments

with linguistic descriptions of locations. The main

advantages of the proposed approach are the

functionality it offers a designer to define complex

locations at both the perception and action level of

an agent, and the ability of the control process to

demonstrate adaptive behavior in dynamic

environments.

ACKNOWLEDGEMENTS

This research is partially supported by the

Pythagoras EPEAEK II Programme of the Greek

Ministry of National Education and Religious

Affairs, co-funded by the European Union.

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