Body symmetry. Studies in the Framsticks simulator · Framsticks Symmetry itself Static symmetry...

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Body symmetry.Studies in the Framsticks simulator

Wojciech Jaśkowski, Maciej Komosiński

Poznan University of Technology

May 29, 2007

FramsticksSymmetry itself

Static symmetryMotion symmetry

Further research

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. .1 Framsticks

Reminder of the creature modelWhat’s new?

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2 Symmetry itself

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3 Static symmetryMotivationsApproachExperiments

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4 Motion symmetryMotivationsApproach

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5 Further research



Further research


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.Model components

BodyParts (3D location & orientation)Joints

BrainNeurons (embodied or not)Connections

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Properties

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Physical and biological: lengths, sizes, masses, etc.



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.Model constraints

at most one Joint can directly connect two Parts

each Joint must be connected with two distinct Parts

all Parts must be directly or indirectly connected with eachother



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.Native simulation engine – MechaStick

physics-based: create real-world feeling to intuitivelyunderstand behaviors

not necessarily very accurate but fast – performancematters

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demo

Parts: atomic physical objects

Joints: description of internal forces and constraints,visualized as sticks

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rigid bodies: no

volume bodies: no

collision detection within creatures: no



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.New features of the simulator

v3.0 on the way (recent official release was v2.11, May 2006)

new genetic encodings (biological, self-assembling, messy,Lindenmayer-generative)new simulation engine – LGPL’ed ODE (Open DynamicsEngine, ode.org)

rigid body dynamics, “real” volume bodies, accurate collisiondetection, articulated joints

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demo

lots of extensionsbody disturbance (imperfection)communication sensors and effectorsnumerous additions to FramScriptnew graphics and GUIs (Framsticks Theater

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demo ),enhanced network protocol (server)

ode.org



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.Symmetry

Figure: Vitruvian Man



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.Symmetry. What’s that?

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Definition

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Symmetry is an intrinsic property of a mathematical object whichcauses it to remain invariant under certain classes oftransformations (such as rotation, reflection, inversion, or moreabstract operations).



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.Symmetry in various disciplines

Figure: The Taj Mahal, Agra,India, 1648 r.

Physics

Math

Music

Poetry

Architecture

Moral symmetry(tit for tat)



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.Symmetry

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Herman Weyl, “Symmetry”

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Symmetry is an idea which has guided man through the centuriesto the understanding and the creation of order, beauty andperfection.



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.Symmetry in biology

Figure: Symmetry – a popularevolutionary concept.

Popular evolutionaryconcept

Usually bilateralsymmetry (the bilateria)

Oldest known symmetricalorganism: Vernanimalcula(600 mln years ago)

Notable asymmetricalexceptions: sponges.



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.Sponges

Figure: Sponges



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.Symmetry everywhere?

Animals are symmetrical only superficially and only in a macroscale

Asymmetry in chemistry

Alice’s cat

DNA is clockwise



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.What is on the other side of looking glass?

Figure: On the other side

Is the reflected worldpossible?

Let us reflect the wholeuniverse... from stars tillatoms...

A reflection of neutrino isimpossible → reflectedworld is impossible...

unless we also reflect thetimearrow...



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MotivationsApproachExperiments

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.Why symmetry is such a popular evolutionary concept?

An open problem.

Females of some species prefer males with the mostsymmetrical sexual ornaments.

For humans, there are proved positive correlations betweenfacial symmetry and health and

between facial symmetry and perception of beauty

Intuition: bilateral symmetry resulted from the direction ofmovement of living creatures

Proof: positive correlations between locomotive efficiency andmorphological symmetry

If so, why in the world of flowers symmetry (usually radical) isso common? Certainly not for locomotion.



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.Numerical measure of symmetry – motivations

Common language is capable to express various degrees ofsymmetry, but no general numerical symmetry definition exists

Natural, binary notion of symmetry is insufficient for research

Numerical measure of symmetry could allow determining theextent to what an object is symmetrical, but also...

if one object is more symmetrical than another.

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Symmetry is not such a popular concept in artificial worlds, so inorder to study the phenomenon of symmetry and its implications,there is a need for defining a numerical, fully automated andobjective measure of symmetry for creatures living in artificialenvironments



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.More motivations

A tool for researcher (earlier: “similarity” measure)Possible research applications:

Do symmetrical creatures move faster/further/more reliably?Do symmetrical creatures perform better in environments theywere not evolved in?Does evolution produce more symmetrical creatures in worldswith difficult terrain/bigger/smaller gravitation?... and more



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.Creature’s model (framsticks)

Only skeleton is taken into account.



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.Solid 3D objects



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.Symmetry measure design (1)

The Symmetry Condition. If c is perfectly bilaterallysymmetrical, then sym(c) = 1.0.

The Asymmetry Condition. If c is completely asymmetricalthen sym(c) = 0.0.

The Common Sense Condition. If c1 is more symmetricalthan c2, then sym(c1) > sym(c2).

The Proportional Difference Condition. The differencebetween sym(c1) and sym(c2) should correspond to thedifference in anatomical symmetry between c1 and c2.

The Scalability Condition. The proposed measure should berobust against scaling: for creature c2 that is a scaled versionof c1 (body enlarged or diminished), we expectsym(c2) = sym(c1).



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.Symmetry measure design (2)

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Let us denote symmetry of a creature c about plane p as sym(c , p).We say that “a creature is symmetrical” if it is symmetrical aboutany plane, therefore we are looking for a plane that yields thehighest symmetry:

sym(c) = maxp

(sym(c , p)) (1)



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.Creature’s model

Looking for matching sticks...



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.How to compute sym(c , p)? (1)

s1

s2

s3

p

(a)

SL SR

s1

s2

s4

s3

s5

p

(b)



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s1

s2

s3

p

(a)

s1

s2

img(s1,p)

p

(b)

s3

img(s2,p)

img(s3,p)

S img(S,p)



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sym(c , p) = maxΠ

(∑(s1,s2)∈Π ws1s2sim(s1, s2)∑

(s1,s2)∈Π ws1s2

)(2)

where

ws1s2 =

{len(s1) + len(s2) if s1 6= s2

len(s1) if s1 = s2(3)

sim(s1, s2) = exp−dist2(s1, s2)

(α · sf )2 (4)

where α is a constant, and sf is a creature scale factor.



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.Sample landscape

sym

1

0.8

0.6

0.4

0.2

0

β

32.5

21.5

10.5

0α

32.5

21.5

10.5

0

1

0.8

0.6

0.4

0.2

0

Figure: In order to find the plane of the highest symmetry, we samplethe 3-dimensional (α, β, t) space for each creature stick and then performa local search to further improve the best found plane.



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.Illustration of symmetry planes (1)

Figure: Exemplary creatures, estimation of their symmetry planes andsymmetry values. Values of symmetry are: 1.0, 1.0, 0.99



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Figure: Values of symmetry are: 0.97, 0.82



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Figure: Values of symmetry are: 0.70, 0.39



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Figure: Top row: Chair (1.0), Pink Panther (0.84), Chair crooked (0.92).Bottom row: Scorpion (1.0), Scorpion moving (0.82).



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.A random set of individuals

Figure: 30 diverse creatures arranged horizontally according to theirvalues of symmetry (the most symmetrical on the right).



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.Symmetry in human design and evolution

0%

20%

40%

60%

80%

100%

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Per

cent

of c

reat

ures

Symmetry

EvolvedDesigned

Figure: Distribution of symmetry values among 84 creatures (38designed, 46 evolved).



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.Evolved creatures

Figure: Evolved creatures. Constructs with the highest symmetry areusually simple.



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.Designed creatures

Figure: Designed creatures with symmetry of 1.0.



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.Reviewers’ opinion

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Anonymous reviewer 1

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(...) this work is important in that it could motivate interestingstudies (...)”

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Anonymous reviewer 2

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OK, there are many symmetry measures, authors took some ofthem, and selected some creatures from the database... So what?



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MotivationsApproach

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.Motivations

Operates on the phenotype in motion (opposed to: symmetryof genotype)

Characterizes motion (a feature of the motion pattern).

Other: whether (to what degree) the movement is periodic orchaotic, how dynamic, effective it isImplications:

understanding the evolution on Earthmethods of locomotion both in living animals and designedrobots



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MotivationsApproach

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.Static symmetries

(a) Basic Quadruped(1.000)

(b) Bulldog (1.000)

(c) Rototiller (0.850) (d) Imunus Katehe (0.956)

Figure: Symmetry planes of the four considered creatures. Symmetryvalues are given in brackets.



Further research

MotivationsApproach

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.3D paths

-30 -25 -20 -15 -10 -5 0 5 10 6 7

8 9

10 11

0

0.05

0.1

0.15

0.2

0.25

z

x

y

z

(a) Basic Quadruped

0 20 40 60 80 100 120 140 160 180 200 0 20

40 60

80 100

120 140

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

z

x

y

z

(b) Bulldog

-4 -2 0 2 4 6 8 10 12 4 6

8 10

12 14

16 18

0

0.1

0.2

0.3

0.4

0.5

0.6

z

x

y

z

(c) Rototiller

5 10 15 20 25 30 35 40 45 0 20

40 60

80 100

0

0.5

1

1.5

2

z

x

y

z

(d) Imunus Katehe

Figure: Exemplary 3D paths for four creatures.



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MotivationsApproach

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.2D paths

-30

-20

-10

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10

20

30

40

50

-30 -20 -10 0 10 20 30 40 50

y

x

(a) Basic Quadruped

-250

-200

-150

-100

-50

0

50

100

150

-250 -200 -150 -100 -50 0 50 100 150 200 250

y

x

(b) Bulldog

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0

5

10

15

20

25

-5 0 5 10 15 20 25

y

x

(c) Rototiller

-80

-60

-40

-20

0

20

40

60

80

100

-60 -40 -20 0 20 40 60 80 100

y

x

(d) Imunus Katehe

Figure: 10 paths for four considered creatures.



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MotivationsApproach

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.Symmetry (3df) over time

0

0.2

0.4

0.6

0.8

1

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

sym

met

ry

time

(a) Basic Quadruped

0

0.2

0.4

0.6

0.8

1

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

sym

met

ry

time

(b) Bulldog

0

0.2

0.4

0.6

0.8

1

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

sym

met

ry

time

(c) Rototiller

0

0.2

0.4

0.6

0.8

1

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

sym

met

ry

time

(d) Imunus Katehe

Figure: The values of symmetry over time



Further research

MotivationsApproach

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.2D paths with symmetries

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6.5

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7.5

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8.5

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9.5

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10.5

-30 -25 -20 -15 -10 -5 0 5 10 15

y

x

(a) Basic Quadruped

0

20

40

60

80

100

120

140

0 20 40 60 80 100 120 140 160 180 200

y

x

(b) Bulldog

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6

8

10

12

14

16

18

-4 -2 0 2 4 6 8 10 12

y

x

(c) Rototiller

0

10

20

30

40

50

60

70

80

-2 0 2 4 6 8 10 12 14 16

y

x

(d) Imunus Katehe

Figure: The creature 2D paths (red) with vertical planes shown (green).



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MotivationsApproach

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.Smoothed paths

6

6.5

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7.5

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8.5

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9.5

10

10.5

-30 -25 -20 -15 -10 -5 0 5 10

y

x

(a) Basic Quadruped

0

20

40

60

80

100

120

140

0 20 40 60 80 100 120 140 160 180 200

y

x

(b) Bulldog

4

6

8

10

12

14

16

18

-4 -2 0 2 4 6 8 10 12

y

x

(c) Rototiller

0

10

20

30

40

50

60

70

80

-2 0 2 4 6 8 10 12 14 16

y

x

(d) Imunus Katehe

Figure: The original paths (red) and the ones smoothed using a low passfilter (blue) .



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MotivationsApproach

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.Movement directions

-1.5

-1

-0.5

0

0.5

1

1.5

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

rz

time

(a) Basic Quadruped

-1.5

-1

-0.5

0

0.5

1

1.5

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

rz

time

(b) Bulldog

-1.5

-1

-0.5

0

0.5

1

1.5

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

rz

time

(c) Rototiller

-1.5

-1

-0.5

0

0.5

1

1.5

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

rz

time

(d) Imunus Katehe

Figure: Movement directions based on the smoothed paths over time



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MotivationsApproach

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.Vertical (1df) symmetry over time

0

0.2

0.4

0.6

0.8

1

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

sym

met

ry

time

(a) Basic Quadruped

0

0.2

0.4

0.6

0.8

1

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

sym

met

ry

time

(b) Bulldog

0

0.2

0.4

0.6

0.8

1

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

sym

met

ry

time

(c) Rototiller

0

0.2

0.4

0.6

0.8

1

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

sym

met

ry

time

(d) Imunus Katehe

Figure: The values of vertical (1df) symmetry over time



Further research

MotivationsApproach

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.Static symmetries

(a) Basic Quadruped(1.000)

(b) Bulldog (1.000)

(c) Rototiller (0.850) (d) Imunus Katehe (0.956)

Figure: Symmetry planes of the four considered creatures. Symmetryvalues are given in brackets.



Further research

MotivationsApproach

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.Finals symmetry values (soft 1df symmetry)

Table: Soft dynamic 1df symmetries (soft 1df), their standard deviationsand maximal and minimal values.

creature soft 1df std.dev. min max

Basic Quadruped 0.777 0.063 0.588 0.950Bulldog 0.475 0.062 0.162 0.768

Rototiller 0.688 0.109 0.154 0.932Imunus Katehe 0.327 0.119 0.090 0.737



Further research

MotivationsApproach

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.Evolving movement

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MechaStickexperiments in 2001: diverse ways of movement evolved

were they really diverse?mostly simple creatures (a few sticks... large constructs are inefficient)most interesting ones were designed by hand and NNs were evolvednew discovery: unexpected numerical instability

ODEhigh expectations (accuracy, volume bodies, self-collisions)

evolving movement turned out to be even more difficult! :oelasticity of MechaStick was so important!sticks as cylinders: rolling (“passive”)... and stability phase does not helpsticks as cuboids: instability of simulation, oscillations, and... rolling (“active”)many simulation parameters, each of them is importantinterdependence between mass, gravity, collision parameters,muscle strength and speedrolling is a local optimum (so far)

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demo

lots of lessons learned... and weeks of simulation.



Further research

MotivationsApproach

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.Evolving movement

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MechaStickexperiments in 2001: diverse ways of movement evolvedwere they really diverse?mostly simple creatures (a few sticks... large constructs are inefficient)

most interesting ones were designed by hand and NNs were evolvednew discovery: unexpected numerical instability



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demo




Further research

MotivationsApproach

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.Evolving movement

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MechaStickexperiments in 2001: diverse ways of movement evolvedwere they really diverse?mostly simple creatures (a few sticks... large constructs are inefficient)most interesting ones were designed by hand and NNs were evolved

new discovery: unexpected numerical instabilityODE

high expectations (accuracy, volume bodies, self-collisions)


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demo




Further research

MotivationsApproach

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.Evolving movement

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MechaStickexperiments in 2001: diverse ways of movement evolvedwere they really diverse?mostly simple creatures (a few sticks... large constructs are inefficient)most interesting ones were designed by hand and NNs were evolvednew discovery: unexpected numerical instability



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demo




Further research

MotivationsApproach

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.Evolving movement

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ODEhigh expectations (accuracy, volume bodies, self-collisions)evolving movement turned out to be even more difficult! :oelasticity of MechaStick was so important!

sticks as cylinders: rolling (“passive”)... and stability phase does not helpsticks as cuboids: instability of simulation, oscillations, and... rolling (“active”)many simulation parameters, each of them is importantinterdependence between mass, gravity, collision parameters,muscle strength and speedrolling is a local optimum (so far)

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demo




Further research

MotivationsApproach

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.Evolving movement

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ODEhigh expectations (accuracy, volume bodies, self-collisions)evolving movement turned out to be even more difficult! :oelasticity of MechaStick was so important!sticks as cylinders: rolling (“passive”)... and stability phase does not help

sticks as cuboids: instability of simulation, oscillations, and... rolling (“active”)many simulation parameters, each of them is importantinterdependence between mass, gravity, collision parameters,muscle strength and speedrolling is a local optimum (so far)

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demo




Further research

MotivationsApproach

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.Evolving movement

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ODEhigh expectations (accuracy, volume bodies, self-collisions)evolving movement turned out to be even more difficult! :oelasticity of MechaStick was so important!sticks as cylinders: rolling (“passive”)... and stability phase does not helpsticks as cuboids: instability of simulation, oscillations, and... rolling (“active”)

many simulation parameters, each of them is importantinterdependence between mass, gravity, collision parameters,muscle strength and speedrolling is a local optimum (so far)

.

demo




Further research

MotivationsApproach

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.Evolving movement

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.


ODEhigh expectations (accuracy, volume bodies, self-collisions)evolving movement turned out to be even more difficult! :oelasticity of MechaStick was so important!sticks as cylinders: rolling (“passive”)... and stability phase does not helpsticks as cuboids: instability of simulation, oscillations, and... rolling (“active”)many simulation parameters, each of them is importantinterdependence between mass, gravity, collision parameters,muscle strength and speed

rolling is a local optimum (so far)

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demo




Further research

MotivationsApproach

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.Evolving movement

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ODEhigh expectations (accuracy, volume bodies, self-collisions)evolving movement turned out to be even more difficult! :oelasticity of MechaStick was so important!sticks as cylinders: rolling (“passive”)... and stability phase does not helpsticks as cuboids: instability of simulation, oscillations, and... rolling (“active”)many simulation parameters, each of them is importantinterdependence between mass, gravity, collision parameters,muscle strength and speedrolling is a local optimum (so far)

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demo




Further research

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.Further research

For which objectives (speed and locomotion, predation,height, etc.) evolution promotes symmetrical creatures?

Is symmetry beneficial for creatures evolved spontaneously?

Does symmetry emerge for creatures evolved spontaneously?(Evolve, observe, surprise!)

Which genetical encodings promote symmetry?

Symmetry as a component of fitness formula.

Encoding that preserves symmetry. Comparison with others.

Body symmetry. Studies in the Framsticks simulator · Framsticks Symmetry itself Static symmetry...

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Transcript of Body symmetry. Studies in the Framsticks simulator · Framsticks Symmetry itself Static symmetry...