PREVISUALIZATION IN ROBOTICS: AN ATOMIC APPROACH

Mauno R

onkk

University of Kuopio, Department of Computer Science

P.O.Box 1627, 70211 Kuopio, Finland

Keywords:

Robotics, previsualization, modelling, emergent dynamics, simulation, formal methods.

Abstract:

In this paper, we discuss use of previsualization in robotics. In previsualization, a computer animates a highly

underspeciﬁed model; thus, helping the designers to detect missing components. When applied to robotics,

previsualization should reveal detailed dynamics that is not explicitly speciﬁed in the model. In particular,

it should reveal interaction dynamics of the physical components. Such a requirement is non-trivial. In this

paper, we investigate an atomic approach that uses emergent dynamics to reveal the interaction dynamics.

The approach is based on use of atoms that obey simple, compositional interaction laws. The laws produce

emergent interaction dynamics for physical components composed of atoms. As the main contribution, we

shall illustrate how the atomic approach, despite its simplicity, captures compactly non-trivial settings, and

reveals effortlessly intricate dynamics that are otherwise considered too laborious for modelling.

1 INTRODUCTION

Previsualization is a design technique used originally

in ﬁlm industry (Ferster, 1998). In previsualization, a

computer animates an underspeciﬁed scene. The an-

imation reveals quickly, if the scene is missing some

key components, or if the dynamics is not as desired.

In this paper, we generalize the idea of previsual-

ization to robotics (Arkin, 1998). In robotics, it is

used as a design tool for improving a model until it is

detailed enough for formal analysis and prototyping.

Unlike simulation (Mosterman, 1999), previsual-

ization does not deal with a detailed model; rather, the

model is highly underspeciﬁed and details appear as

emergent dynamics (Odell, 1998; Arkin, 1998). Con-

sequently, previsualization does not reveal “exact” re-

sults, although the results are rich in realistic details.

When using previsualization in robotics, we wish

to avoid specifying explicit interactions between the

physical components in the model. One reason is that,

during previsualization, the speciﬁcs of the compo-

nents are still unknown. Another reason is that the

number of required interaction equations is quadratic

to the number of components in the system, for in-

stance, 100 components require 10 000 interaction

equations.

One way of avoiding specifying the interaction

equations is to use emergent dynamics to reveal it.

However, this is not trivial in robotics due to inherent

compositional diversity. In robotics, there are many

different kinds and shapes of components interacting

with each other (Arkin, 1998). In addition, the in-

teraction dynamics itself shows various kinds of mo-

tions, rotations, collisions, and other kinematics.

Mere encoding of the text-book equations on dy-

namics, like those found in (Young and Freedman,

2000) and in (Thornton and Marion, 2004), is not

enough, as they describe the dynamics in isolation.

Figuring out the precise interaction equations, on the

other hand, is not reasonable, since the speciﬁcs of

the components are not known ahead of the previsu-

alization. Nevertheless, previsualization must some-

how capture detailed interaction dynamics.

As a solution, we propose in this paper an atomic

approach, where interaction dynamics of the physical

components appear as emergent dynamics. The ap-

proach is based on use of atoms

that are indivisible

particles of constant shape and mass. The atomic ap-

proach is, thus, a speciﬁc variant of a particle system

(Reeves, 1983; Witkin, 1997).

The notion of atoms, here, differs from the notion of

atoms in modern physics (Young and Freedman, 2000), as

well as from the notion of atoms put forth by Greek philoso-

phers Democritus and Leucippus around 400 BC.

110

Rönkkö M. (2004).

PREVISUALIZATION IN ROBOTICS: AN ATOMIC APPROACH.

In Proceedings of the First International Conference on Informatics in Control, Automation and Robotics, pages 110-117

DOI: 10.5220/0001127301100117

 SciTePress

Atoms may move, resist movement, be bound to

each other, and collide with each other. For these

dynamics, there are simple equations that are also

compositional. Moreover, these equations are enough

to produce emergent dynamics capturing interactions

between physical components composed of atoms, re-

gardless of the shape of the components (R

onkk

2003b).

An advantage of the atomic approach is that it is

computationally light. A three dimensional model can

be computed and rendered on screen in real-time.

An additional advantage of the atomic approach is

that it supports inclusion of software components to

the model. For instance, we could add a neural net

to the model for controlling some physical compo-

nents. Then, the neural net interacts with the physical

components by manipulating the forces on the corre-

sponding atoms. In this way, we do not need to state

explicit interaction dynamics in the model, and we

can experiment with different software components

to see their effect on the global, behavioral dynam-

ics (Arkin, 1998; Reynolds, 1987).

As the main contribution, we shall illustrate in this

paper how the atomic approach, despite its simplicity,

captures compactly non-trivial settings, and reveals

effortlessly intricate dynamics that are otherwise con-

sidered too laborious for modelling.

Overview. We start by formalizing the atomic ap-

proach in Section 2. In Section 3, we discuss and il-

lustrate modelling with strings of atoms. In Section

4, we discuss and illustrate modelling with planes of

atoms. In Section 5, we discuss and illustrate some

advanced emergent properties, such as friction and ro-

tation. Finally, in Section 6, follows the conclusion.

2 THE ATOMIC APPROACH

In the atomic approach, a model consists of a ﬁxed

number of atoms and forces. An atom is an indepen-

dent and indivisible particle. Based on the deﬁned

forces, the atoms in the model may move, resist move-

ment, be bound to each other, and collide with each

other.

2.1 An Atom

An atom has only four properties: shape, mass, posi-

tion, and velocity. Each atom has the same constant

shape of a unit ball, and the same unit mass. Only the

position and the velocity may vary from atom to atom;

however, even these values are bound by the model of

motion.

As an atom exists in R

-space, we use three dimen-

sional vectors (Adams, 1999) to capture the properties

of an atom. Let ~c denote the position of an atom, i.e.,

the displacement of the center of the atom from the

origin. Then, the magnitude of ~c, i.e., |~c|, gives the

distance of the center of the atom to the origin.

An atom occupies the set P of points in R

, where

|~p −~c| ≤ 1 holds for any ~p in P . Within this space,

the unit mass of an atom is evenly distributed. Con-

sequently, according to (Young and Freedman, 2000),

the center of an atom is also its center of mass.

We do not, however, consider atoms as objects of

dense matter; on the contrary, atoms are objects of

sparse matter. Therefore, several atoms may overlap

in space without any interference, if so desired.

2.2 Model of Motion

Atoms follow a trivial model of motion. A change in

the position of an atom is determined by its velocity.

A change in the velocity of an atom, in turn, is deter-

mined by an impulse on it. The impulse is the sum of

all forces on the atom.

As shown in (R

onkk

o, 2003b), the model of mo-

tion is obtained from the trivial model of motion with

acceleration. First, Euler’s method (Zill and Cullen,

1997) is applied to obtain an approximation equation.

Then, as the approximation equation operates in dis-

crete time on atoms with a unit mass, we may sub-

stitute the acceleration term in the equation with an

impulse term (Young and Freedman, 2000).

Formally, the obtained model of motion is a dif-

ference equation (Zill and Cullen, 1997). Let n and

n + 1 denote two successive iteration rounds, and τ

denote a reasonably small, ﬁxed, time step. Also, let

~c(n), ~v(n), and

j(n) denote the center of an atom, its

velocity, and the impulse on the atom in the iteration

round n. Then, the model of motion is:

~v(n + 1) = ~v(n) +

j(n)

~c(n + 1) = ~c(n) + τ ·~v(n + 1)

Here, the impulse

j(n) is the sum of forces on the

atom in the iteration round n. The forces are com-

puted based on the position and velocity of atoms in

the iteration round n.

The model of motion above is a reﬁnement of

that presented in (R

onkk

o, 2003b). In particular, the

model above provides a more stable motion.

Note that the model of motion for atoms is com-

positional; in particular, it allows us to consider the

position, velocity, and the impulse of an atom inde-

pendently of each other within each iteration round.

2.3 An Impulse

An impulse is, by deﬁnition (Young and Freedman,

2000), the sum of forces affecting the velocity. In our

model, there are only four kind of forces: damping

PREVISUALIZATION IN ROBOTICS: AN ATOMIC APPROACH

111

forces, bond forces, collision forces, and other case-

speciﬁc external forces.

For simplicity, all the impulses considered in this

paper depend only on the properties of atoms; in par-

ticular, we do not consider here any impulses that de-

pend on the number of the iteration round.

In the sequel, we shall refer to a speciﬁc atom in the

model using subscripts. For instance, we shall denote

the center of the i’th atom in the model by ~c

, and its

velocity by ~v

A damping force. A damping force resists the mo-

tion of an atom. Its direction is opposite to the direc-

tion of the velocity, and the magnitude is always less

or equal to the magnitude of the velocity.

Assuming a coefﬁcient m ∈ [0, 1], we deﬁne a

damping force

fd(i, m) with a magnitude of m·100%

on the i’th atom in the model (R

onkk

o, 2003b):

fd(i, m) = −m ·~v

A bond force. A bond force maintains a prede-

ﬁned distance between two speciﬁc atoms. Gener-

ally speaking, a bond force is modelled as a function

over the desired distance

and the current distance

between the two atoms.

We model a bond force with a non-linear function,

because it has better approximation properties than a

linear function (R

onkk

o, 2003b). Assuming a desired

distance r ∈ [0, ∞), we deﬁne a bond force

fb(i, r, k)

on the i’th atom in the model with respect to the k’th

atom in the model (R

onkk

o, 2003b):

fb(i, r, k) = (~c

−~c

) · (1 − r

|~c

−~c

−2

)

Note that a bond force is symmetric, i.e.,

fb(i, r, k) = −

fb(k, r, i). Thus, a pair of bond forces

preserves Newton’s third law

(Young and Freedman,

2000).

A bond force, as deﬁned above, results in acceler-

ating motion. Consequently, an additional force, such

as a damping force, may be needed for the motion to

converge.

Note that an atom may well be bound to many

atoms at the same time. Then, we may consider each

bond independently, and the sum of the bond forces is

the total bond force on the atom. Due to the model of

motion, the bond forces can be evaluated in any order

without affecting the result.

We consider only the distance between the centers of

the atoms, as the center of an atom is also its center of mass.

The signiﬁcance of Newton’s third law is that it pre-

serves symmetry in the model. Then, from the model, we

may freely choose one atom, and use it as the center of

events. Due to symmetry, the result is independent of our

choice.

A collision force A collision force affects only

overlapping atoms by pushing them apart. Atoms are

considered to be apart, when their distance exceeds

the sum of their radii, 2.

We model a collision force as a semi-bond force.

Thus, we deﬁne a collision force

fc(i, k) on the i’th

atom in the model with respect to the k’th atom in the

model (R

onkk

o, 2003b):

fc(i, k) = (~c

−~c

) · min{0, (1 − 4 · |~c

−~c

−2

)}

The collision force is also symmetric; hence, a pair

of collision forces preserves Newton’s third law.

Note that an atom has no materialistic properties,

such as elasticity. Consequently, the collision force

above deﬁnes exhaustively a collision between two

atoms. More speciﬁcally, it captures an elastic col-

lision (R

onkk

o, 2003b). An inelastic collision can,

thus, never occur between two atoms without any ad-

ditional forces. This does not, however, preclude an

inelastic collision between components composed of

atoms, as we shall see later in the examples.

Similarly to the bond forces, there can be many col-

lision forces on an atom at the same time. Then, we

may consider each collision independently, and the

sum of the collision forces is the total collision force

on the atom. Due to the model of motion, the collision

forces can be evaluated in any order without affecting

the result.

Case-speciﬁc external forces. We do not attempt

to formalize other case-speciﬁc external forces. The

reason for this is simply the overwhelming variety of

such forces. Examples of case-speciﬁc external forces

are, among others, gravity, impulses originating from

various power sources, and impulses used for visual-

ization purposes, i.e., forcing the atoms to move into

desired direction to reveal the emergent dynamics of

that motion.

2.4 Modelling with Atoms

Modelling with atoms is simple. In a model, we de-

ﬁne for each atom

1. its initial position and velocity

2. the forces on it

The model of motion is then used to compute the po-

sition and the velocity of the atom in the next iteration

round.

In a model, bond forces are used to compose com-

ponents from atoms. The number of bond forces

per atom deﬁnes also the rigidness of the component

onkk

o, 2003b). Collision forces, in turn, are used

for deﬁning which atoms (of the components) may

collide with each other.

ICINCO 2004 - ROBOTICS AND AUTOMATION

112

Figure 1: Visualization of colliding rods and threads. The top row shows a collision of two rods, the middle row shows a

collision of a rod and a thread, and the bottom row shows a collision of two threads. The computed iteration rounds are

indicated in each image. The initial conﬁguration, shown in the leftmost image in the top row, is the same for each collision.

3 MODELLING WITH STRINGS

OF ATOMS

For modelling components like rods, threads, tri-

angles, and rings, we use strings of atoms. In a

string, bond forces are used for deﬁning the shape

of the component and the rigidness of the component

onkk

o, 2003b). For brevity, we shall consider only

threads and rods in this section.

We exemplify use of strings of atoms by visualizing

non-trivial collisions of rods and threads. In these ex-

amples, we do not consider any damping forces; thus,

the rods and threads behave as if they were in space.

For clarity, we limit the investigation to collisions of

two components at a time.

Both a rod and a thread are modelled using a string

of 70 atoms. The colliding strings are aligned diago-

nally with respect to the y and z-axes. Also, the align-

ment of the strings with respect to each other is di-

agonal and non-symmetric, as shown in the leftmost

image in the top row in Figure 1.

The atoms in a string are initially positioned so that

ﬁve neighboring atoms overlap, to give an impression

of dense material (R

onkk

o, 2003b). The two strings

are then set to collide by giving them an opposite ini-

tial velocity along the x-axis.

The impulse on an atom in a string is the sum of

bond forces and collision forces. In a rod, each atom

is bound to every other atom, whereas, in a thread,

an atom is bound only to its neighboring atoms. For-

mally, in a rod, the total bond force on the i’th atom

j=0

fb(i,

√

0.125, j) for all j 6= i. Correspond-

ingly, the total bond force on the i’th atom in a thread

j=0

fb(i,

√

0.125, j) for all |j − i| = 1.

The total collision forces prevent the atoms in the

colliding strings from slipping through each other.

Thus, there is a collision force on the i’th atom in

a string is

j=0

fc(i, j), where j refers to atoms in

the other string. In addition, we also wish to prevent

the non-overlapping atoms within a string from slip-

ping through themselves. Therefore, there is an ad-

ditional collision force on the i’th atom in a string:

k=0

fc(i, k) for all |k − i| ≥ 8, where k refers to

atoms in the same string. The total collision force on

an atom in a string is then the sum of these two colli-

sion forces.

Figure 1 visualizes three different non-trivial colli-

sions involving rods and threads. The top row shows

a collision of two rods, the middle row shows a colli-

PREVISUALIZATION IN ROBOTICS: AN ATOMIC APPROACH

113

Figure 2: Visualization of two bouncing balls on an elastic surface. Initially both balls are in the air, falling down. The

computed iteration rounds are indicated in each image.

sion of a rod and a thread, and the bottom row shows

a collision of two threads. The initial conﬁguration is

the same in each case, shown in the leftmost image in

the top row.

It is important to notice that we do not explicitly

specify in the model how rods or threads collide. We

only state which atoms of the two strings may collide

with each other. Still, the collision dynamics seem

very natural in each case, although they are entirely

emergent.

Figure 1 reveals also other intricacies that we do not

explicitly address in the model. Namely, the top row

shows how the impact causes minute vibrations to the

colliding rigid bodies. Also, the middle row shows

how a non-rigid body wraps around a rigid body in

a collision. The collision is, thus, inelastic. Still, as

explained earlier, a collision force between two atoms

as such captures only an elastic collision. An extreme

of an inelastic collision is shown in the bottom row of

the ﬁgure, where the collision of two non-rigid bodies

lead to a severe entanglement.

The model of colliding threads and rods is com-

putationally light; it can be computed and rendered

in real-time. For instance, a modest 500MHz Pow-

erPC G3-processor computes 4000 iteration rounds in

about 3.2 seconds.

When considering robotics, this example shows

that the atomic approach supports modelling and pre-

visualization of materialistic properties. For instance,

we could model and previsualize a robot lifting non-

rigid components and then transporting them to some

other location. Such a previsualization would reveal

in real-time how gravity affects the non-rigid compo-

nents during the process.

4 MODELLING WITH PLANES

OF ATOMS

For modelling surfaces we use planes of atoms. In a

plane, bond forces are used for deﬁning the shape and

the rigidness of the surface.

We exemplify use of planes of atoms by visualizing

a non-trivial model, where two balls fall and bounce

on an elastic surface. The gravitational force affects

only the balls; thus, the surface acts as if it was a cloth

ﬂoating on water.

The balls are modelled using single atoms. The

surface is modelled using a square with a side of 25

atoms; thus, the index n(x, y) of an atom at coordi-

nate (x, y) in the surface is 25y + x.

The two balls reside initially above the surface as

indicated in Figure 2. The impulse on a falling ball

is the sum of a constant gravity force, and collision

forces. The collision forces cover collisions between

the two balls, and between all the atoms in the surface.

For instance, the total collision force on one of the

falling balls is

fc(i, j) +

x=0

y=0

fc(i, n(x, y)),

where i refers to the falling ball, j refers to the other

falling ball, and n(x, y) refers to an atom in the sur-

face.

The atoms in the surface are initially overlapping

and aligned along x and y-axes around the origin as

shown in Figure 2. The initial distance, d(i, j, x, y),

between two atoms at coordinates (i, j) and (x, y) in

the surface is given by

(i−x)

+(j−y)

. We con-

sider this also the desired distance between the two

atoms.

The impulse on an atom in the surface is the sum

of bond forces and collision forces. Since the sur-

ICINCO 2004 - ROBOTICS AND AUTOMATION

114

face is considered elastic, an atom is bound only to

its neighboring atoms. Hence, the total bond force

on an atom at coordinate (i, j) in the surface is

x=0

y=0

fb(n(i, j), d(i, j, x, y), n(x, y)) for all

0 < d(i, j, x, y) < 2. Since we do not consider colli-

sions between the atoms in the surface, the total col-

lision force on an atom at coordinate (i, j) in the sur-

face is simply

fc(n(i, j), k) +

fc(n(i, j), l), where k

and l refer to the falling balls.

Figure 2 visualizes the bouncing of the balls on

the elastic surface. The images in the ﬁgure clearly

show how the emergent dynamics reveals realistic de-

tails that we do not explicitly state in the model. For

instance, both of the balls bounce from the surface;

yet, we only deﬁne which atoms may collide in the

model. Also, when the balls bounce from the surface,

they generate ripples that gradually progress through-

out the entire surface. This is clearly visible in im-

ages after 250 and 350 iterations. Also, once a ball is

at rest on the surface, the surface caves in due to the

gravity force on the ball. This can be observed from

the images after 450 and 700 iterations. Lastly, as the

surface becomes partially tilted, the balls start sliding

on it. As there is nothing to stop the surface from tilt-

ing, the balls eventually fall out of the surface. This

can be observed from the last image in the ﬁgure.

This model is also computationally light; it can be

computed in and rendered in real-time. For instance,

a modest 500MHz PowerPC G3-processor computes

4000 iteration rounds in about 8.3 seconds.

When considering robotics, this example shows

that the atomic approach supports modelling of soft

and elastic surfaces. For instance, we could model

and previsualize a robot moving on an elastic surface.

Such a model could be used for analysing how vari-

ous cruising algorithms function, when the landscape

is no longer even, and when the landscape caves in

underneath the robot.

5 EMERGENT PROPERTIES:

FRICTION AND ROTATION

The advantage of using emergent dynamics in pre-

visualization is that it captures many physical phe-

nomena on its own. Thus, we may omit them in the

model entirely. Some of such phenomena are vibra-

tion, bouncing, friction, and rotation.

We exemplify emergent friction and rotation by vi-

sualizing a non-trivial model, where a ring is dropped

on a surface. The surface is slightly tilted, so that

when the ring bounces on the surface, it gains mo-

mentum and starts rolling. Rolling is due to emerging

friction between the ring and the surface. We show

also two other variants of this example; one, where

the ring is elastic, and another, where the surface soft

like a wet ground.

The ring is modelled as a speciﬁc string of atoms,

whereas the surface is modelled as a plane of atoms.

Initially the ring is above the surface and falls down

due to gravity. The initial conﬁguration is shown in

the leftmost image in the top row in Figure 3.

The ring consists of 20 atoms. The atoms are par-

tially overlapping, and form a perfectly aligned ring.

More speciﬁcally, the i’th atom of the ring resides at

(4 cos(

iπ

)−4.3, 6+4 sin(

iπ

), 0). In such a ring, the

distance, d(i, j), between the i’th and j’th atom is

given by

(4 − 4 cos(

|i−j|π

))

+ (4 sin(

|i−j|π

))

We consider this also the desired distance between the

two atoms.

The impulse on an atom in the ring is the sum of a

constant gravity force, and a number of bond forces

and collision forces. The number of the bond forces

in the ring depends on the elasticity of the ring. For

an elastic ring, one atom is bound only to 8 neighbor-

ing atoms in the ring. Let n(i) denote the index of the

i’th atom in the ring, i.e., n(i) = (20 + i) mod 20.

Then, the total bond force on the i’th atom in the

ring is

i+4

j=i−4

fb(i, d(i, n(j)), n(j)) for all i 6= j.

For an inelastic ring, the total bond force is simply

i+9

j=i−9

fb(i, d(i, n(j)), n(j)) for all i 6= j. The col-

lision forces, on the other hand, capture the collision

of an atom in the ring with an atom in the surface.

Thus, the total collision force on the i’th atom in the

ring is

288

j=0

fc(i, j), where j refers to atoms in the

surface.

The tilted surface is modelled using a square with a

side of 17 atoms; thus, the index n(x, y) of an atom at

coordinate (x, y) is 17y+x. The atoms are positioned

sparsely, so the initial distance d(i, j, x, y) between

two atoms at coordinates (i, j) and (x, y) is given

6.76(x−i)

+0.01(x−i)

+4(y−j)

. We con-

sider this also the desired distance between the two

atoms.

The impulse on an atom in the surface is the

sum of bond forces, collision forces, and a damping

force. The total bond force on an atom at coordinate

(i, j) is

x=0

y=0

fb(n(i, j), d(i, j, x, y), n(x, y))

for all 0 < d(i, j, x, y) < 2. The collision forces

capture the collision between an atom in the ring

and an atom in the surface. Thus, the total collision

force on an atom at coordinate (i, j) in the surface is

k=0

fc(n(i, j), k), where k refers to atoms in the

ring. The damping force makes the surface to ap-

pear soft. The damping force on an atom at coordi-

nate (i, j) in the surface is

fd(n(i, j), 0.04). However,

when the surface is considered totally inelastic, there

is no damping force. Instead, we use a case speciﬁc

external force. It is precisely opposite to the current

impulse at each iteration round; thus, preventing the

PREVISUALIZATION IN ROBOTICS: AN ATOMIC APPROACH

115

Figure 3: Visualization of what happens when a ring is dropped on a tilted surface. The top row shows an inelastic ring

rolling on an inelastic surface. The middle row shows an elastic ring rolling on an inelastic surface. The bottom row shows

an inelastic ring falling sideways on an soft surface. The computed iteration rounds are indicated in each image. The initial

conﬁguration, shown in the leftmost image in the top row, is the same for each of the three cases.

atoms in the surface from moving altogether.

Figure 3 visualizes three different variants of the

example, where the ring is dropped on the surface.

The top row shows the case with an inelastic ring and

an inelastic surface. The middle row shows the case

with an elastic ring and an inelastic surface. The bot-

tom row shows the case with an elastic ring and a soft

surface. The initial conﬁguration is the same in each

case, as shown in the leftmost image in the top row.

The dynamics is different in each case; however, in

the ﬁrst two cases, as the gravity pulls the ring along

the tilted inelastic surface, the dropped ring gains

slowly momentum and starts rolling on the surface.

The rolling is due to emergent friction between the

ring and the surface. Despite the emergent friction,

in the second case, the ring preserves its elasticity, as

shown by the images in the middle row in Figure 3.

In the last case, the dynamics differs considerably

from the ﬁrst two cases. Then, the soft surface caves

in underneath the ring. This, in turn, causes the ring

to fall sideways.

It is important to notice that, in all three cases,

bouncing, friction, rolling, and falling are emergent

dynamics. We do not explicitly specify them in the

model; yet, the visualization clearly displays all these

dynamics.

Again, the model is computationally light; and can

be computed and rendered in real-time. For instance,

a modest 500MHz PowerPC G3-processor computes

4000 iteration rounds in about 2.7 seconds.

When considering robotics, this examples shows

that the atomic approach supports modelling of com-

ponents with varying rigidness. For instance, we

could model and previsualize what happens to a robot,

when it suddenly has a ﬂat tire.

6 CONCLUSION

In this paper, we discussed use of previsualization in

robotics. In previsualization, a computer animates a

highly underspeciﬁed model, to reveal if the model

misses some key components, or if the dynamics is

not as desired.

We investigated in this paper an atomic approach

to previsualization. Its main advantage is that it uses

emergent dynamics to reveal detailed interaction dy-

namics from a model. Thus, in the model, we only

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need to specify the shape of the interacting compo-

nents using atoms, and determine which of the atoms

may collide with each other. In the atomic approach,

this information is enough for computing the interac-

tion dynamics between the components.

The interaction dynamics revealed by emergent dy-

namics is rich in realistic details. We illustrated how

effortlessly the emergent dynamics captures vibra-

tion, entanglement, bouncing, caving in, friction, and

rotation. All of these dynamics are usually considered

too laborious when modelling free-form objects.

The atomic approach supports experimentation. In

a model, we can replace one component with another

without having to consider the changes in the interac-

tion dynamics. The interaction dynamics is emergent.

Also, we can easily attach software components, such

as neural nets, to the model. They can be used, for

instance, for controlling the dynamics on the physical

components. This is done by inﬂicting desired forces

on some speciﬁc atoms in the physical components.

Another advantage of the atomic approach is that

the forces on the atoms are captured by simple and

compositional mathematical formulae. Consequently,

models become computationally light, and they can

be computed and rendered in real-time. An object-

oriented implementation of the atomic approach can

be found, for instance, in (R

onkk

o, 2003a).

Clearly, the use of the atomic approach is not limit

to previsualization of solid objects in robotics. It can

also be applied to other ﬁelds, such as study of ﬂuid

dynamics. Then, ﬂuid as material is modelled as a

collection of individual atoms. The denseness of the

ﬂuid depends on the number of atoms, whereas the

stiffness of the ﬂuid depends on the damping forces on

the atoms. The granularity of the ﬂuid is controlled

by introducing pairs, or triples, of atoms with bond

forces in to the ﬂuid.

The atomic approach is our ﬁrst attempt to harness

emergent dynamics to help design and development

in robotics. In our future studies, we wish to ﬁnd

out how far we can push this technology. In partic-

ular, our near future goal is to polish the approach so

that it is easily applicable by scientists and researchers

studying complex interaction dynamics.

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