Turtle Graphics from computer graphics Evolutionary Robotics Using

Turtle Graphics (from computer graphics) Evolutionary Robotics Using A Formal Grammar To Evolve Robot Bodies and Brains Turtle moves over a 2 D surface. Possesses: 1. Position 2. Orientation 3. Pen, which can be up or down. “Code” for drawing: 1. Move forward 10 paces 2. Turn left 95 degrees 3. Drop pen 4. Move forward 5. Lift pen… Hornby, G. S. , Pollack, J. (2001) Creating high-level components with a generative representation for body-brain evolution. GECCO 2001.

Evolutionary Robotics Using A Formal Grammar To Evolve Robot Bodies and Brains 1. 2. 3. 4. 5. Drop pen For i = 1 to 1000 forward 1 + i/1000 turn 85 degrees left Lift pen 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 contains elements that can be replaced (variables) Evolutionary Robotics Using A Formal Grammar To Evolve Robot Bodies and Brains 2. Define a starting ‘sentence’ composed of elements from V (eg. ‘AB’) 3. Define a set of production rules: rule is composed of two strings: the predecessor and the successor (eg. A AB B 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 sentence only contains constants. Hornby, G. S. , Pollack, J. (2001) Creating high-level components with a generative representation for body-brain evolution. GECCO 2001.

Evolutionary Robotics Using A Formal Grammar To Evolve Robot Bodies and Brains A = algae B = bud (cannot reproduce) A AB is a model of growth: algae ‘spawns’ a bud. B A models maturation: bud becomes adult algae capable of reproduction. Hornby, G. S. , Pollack, J. (2001) Creating high-level components with a generative representation for body-brain evolution. GECCO 2001.

Lindenmayer system = A system in which ‘turtle graphics’ commands serve 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 Robotics Using A Formal Grammar To Evolve Robot Bodies and Brains

Lindenmayer system = Given the right L-system, one can produce structures that look like biological plants: Example: Fractal plant variables : X F constants : + − start : X rules : (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 Evolutionary Robotics Using A Formal Grammar To Evolve Robot Bodies and Brains

Evolutionary Robotics Building bodies with L-systems [ = push state ] = pop state {block}(n) = repeat enclosed block n times. forward: create bar forward backward: move backward Revolute-1: move forward, add joint around Z Revolute-2: move forward, add joint around Y up(n): rotate heading +n*90 o about turtle’s X axis down(n): rotate –n*90 o around X left/right(n): … around Y counter/clockwise(n): … around Z Hornby, G. S. , Pollack, J. (2001) Creating high-level components with a generative representation for body-brain evolution. GECCO 2001.

Building brains with L-systems If turtle’s ‘home’ link connects neuron A to neuron B… Turtle ‘lives’ on synapses. [ = 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; and create a new edge from C to B with weight n.

Connecting Body and Brain 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.

Hornby, G. S. , Pollack, J. (2001) Creating high-level components with a generative representation for body-brain evolution. GECCO 2001.