Evolutionary RoboticsUsing A Formal Grammar To

Evolve Robot Bodies and Brains

Hornby, G.S., Pollack, J. (2001)Creating high-level components with a generative representation

for body-brain evolution.GECCO 2001.

Turtle Graphics (from computer graphics)

Turtle moves over a 2D surface.

Possesses:

1. Position2. Orientation3. Pen, which can be up or down.

“Code” for drawing:1. Move forward 10 paces2. Turn left 95 degrees3. Drop pen4. Move forward5. Lift pen…

Evolutionary RoboticsUsing A Formal Grammar To

Evolve Robot Bodies and Brains

Hornby, G.S., Pollack, J. (2001)Creating high-level components with a generative representation

for body-brain evolution.GECCO 2001.

1. Drop pen2. For i = 1 to 10003. forward 1 + i/10004. turn 85 degrees left5. Lift pen

Evolutionary RoboticsUsing A Formal Grammar To

Evolve Robot Bodies and Brains

Hornby, G.S., Pollack, J. (2001)Creating high-level components with a generative representation

for body-brain evolution.GECCO 2001.

Formal grammar:

1. Define an alphabet V that containselements that can be replaced (variables)

2. Define a starting ‘sentence’ composed ofelements from V(eg. ‘AB’)

3. Define a set of production rules:rule is composed of two strings:

the predecessor andthe successor

(eg. A ABB A)

4. If a symbol C in V does not match any predecessor, then C is a constant.

5. Apply the productions rules to the start sentence.

6. Continue to apply the rules until the sentenceonly contains constants.

Using A Formal Grammar To Evolve Robot Bodies and

Brains

Hornby, G.S., Pollack, J. (2001)Creating high-level components with a generative representation

for body-brain evolution.GECCO 2001.

Evolutionary Robotics

A = algaeB = bud (cannot reproduce)

A AB is a model of growth:algae ‘spawns’ a bud.

B A models maturation:bud becomes adult algaecapable of reproduction.

Evolutionary RoboticsUsing A Formal Grammar To

Evolve Robot Bodies and Brains

Lindenmayer system =

A system in which ‘turtle graphics’ commandsserve as the elements in a formal grammar.

Example: “Drawing” Cantor dust.

variables : A B

constants : none

start  : A {starting character string}

rules  : (A → ABA), (B → BBB)

Let A mean "draw forward" and B mean "move forward".

Evolutionary RoboticsUsing A Formal Grammar To

Evolve Robot Bodies and Brains

Lindenmayer system =

Given the right L-system, one can producestructures that look like biological plants:

Example: Fractal plant

variables : X Fconstants : + −start : Xrules : (X → F-[[X]+X]+F[+FX]-X),

(F → FF)

F means "draw forward", - means "turn left 25°", and + means "turn right 25°". X does not correspond to any drawing action.[ = ‘push’ position and angle] = ‘pop’ position and angle

Building bodies with L-systems

Hornby, G.S., Pollack, J. (2001)Creating high-level components with a generative representation

for body-brain evolution.GECCO 2001.

Evolutionary Robotics

[ = push state] = pop state{block}(n) = repeat enclosed

block n times.forward: create bar forwardbackward: move backwardRevolute-1: move forward,

add joint around ZRevolute-2: move forward,

add joint around Yup(n): rotate heading +n*90o

about turtle’s X axisdown(n): rotate –n*90o around Xleft/right(n): … around Ycounter/clockwise(n): … around Z

Turtle ‘lives’ on synapses.

If turtle’s ‘home’ link connects neuron A to neuron B…

[ = push ‘home’ link] = pop new ‘home’ link

decrease-weight(n): subtract n from weight of current link.

duplicate(n): Create new link from A to B with weight n.

loop(n): Create new link from B to itself with weight n.

merge(n): Merge neurons A and B into single neuron, C. new ‘home’ link is nth input link to C.

parent(n): move to nth input link to A.

next(n): move to nth output link from B.

reverse: link changed to point from B to A.

output(n): neuron A sends commands to the closest joint.

split(n): create new neuron C; attach edge from A to C; andcreate a new edge from C to B with weight n.

Building brains with L-systems

In the formal grammar, throw ‘body’ and ‘brain’elements together.

Turtle ‘points’ to both a body part and a synapse.

If a ‘joint’ element is called, output(1) is also called:

connects part of the neural network to the joint.

Connecting Body and Brain

Hornby, G.S., Pollack, J. (2001)Creating high-level components with a generative representation

for body-brain evolution.GECCO 2001.

Hornby, G.S., Pollack, J. (2001)Creating high-level components with a generative representation

for body-brain evolution.GECCO 2001.