Animals: Form & Function

References & Reading Material: Sims, K. "Evolving Virtual Creatures", proc. SIGGRAPH 1994, ACM Press, pp15-22 Todd, S, Latham, W. "Evolutionary Art & Computers", Academic Press 1992 Reynolds, C.W, "Competition, Co-evolution and the Game of Tag" Artificial Life IV, Brooks & Maes (eds), MIT Press 1994 van de Panne, M., Fiume, E. "Sensor-Actuator Networks" proc. SIGGRAPH 1993, ACM Press, pp335-342 Koza, J. "Genetic Programming: On the Programming of Computers by Means of Natural Selection", MIT Press 1992

1. Creating Virtual Creatures

A simple model organism can be constructed from three sub-systems:

• A model of organism perception (for input)
  
  
• A model of organism computation (for generating behaviour)
  
  
• A physical model (for output)

*Note the philosophical standpoint from which such a model stems: that an organism may be understood as receiving input from the environment, processing it in some way and then altering/acting on the environment accordingly.

The way an organism behaves is intimately tied to its physical structure.

Eg.

• If you have only one leg you can't run
• If you have no wings you can't fly
• If you have no teeth you can't chew
• If you have eyes you can avoid predators from afar
• If you are tall you can eat leaves from tree-tops etc.

How might it be possible to specify:

• a particular physical model of an organism and
  
  
• some high level behaviour...

...and have the computer automatically calculate how the organism might go about achieving the specified behaviour?

Sample behaviours:

• Interesting organism design can lead to interesting methods of locomotion.
  
  
• Typically, the more complex a model's structure, the more difficult it is to successfully animate.
  
  
• Artificial evolutionary techniques can be used to design a structure and its method of locomotion simultaneously and automatically.
  
  
• Just as in Dawkin's biomorphs, a genotype may be created which may develop into a phenotype with (virtual) physical structure.
  

A hierarchy of simple, articulated, rigid primitives may be built from a directed graph or tree.

The directed graph may be considered to be the genotype of the creature whose phenotype consists of:

1. A physical / visual representation / rendered primitives
   
   
2. The behaviour of the structure in some environment

The directed graph encodes instructions for growing the creature. Recursion in the graph provides a means of re-using graph sections to construct organisms with recursive structure.

Genotype: directed graph	Phenotype: hierarchy of 3D parts	Node data in the graph may describe: type of primitive the node represents type of joint which connects it to its parent number of connections to child nodes location, orientation, reflection and scale relative to the parent node force which may be applied at the joint component's mass and other physical properties recursive limit which dictates to what depth the node may recurse 'terminal only' flag: causes a connection to be applied at the recursive limit set of neurons (explained shortly)
From Sims, "Evolving Virtual Creatures", SIGGRAPH 1994

Creature Behaviour

Each creature has a simple brain which:

• accepts input from the sensors
  
  
• does some computation
  
  
• applies forces and torques at the structure's joints

Internal signals, sensory data and effector data are represented as (positive or negative) continuous scalar values.

Body-part specific sensors may measure:

• joint angles (continuous)
  
  
• contact (binary)
  
  
• light source direction (relative vector)
  

Creature Brain-Power

Neurons are implemented as a set of complex functions rather than the typical threshold/fire model. Sample neural functions: sum product divide sum_threshold greater_than sign-of min max abs sin cos atan interpolate log integrate differentiate smooth memory osciallate_wave oscillate_saw etc. Neuronal functions have parameters which may be constant or may be received from the outputs of sensors or other neurons. The genotype, as well as encoding physical topology, encodes the connections between blocks of neurons. Here is one of Sims' creatures: On the right is this virtual creature's brain / controller.

From Sims, "Evolving Virtual Creatures", SIGGRAPH 1994

Effectors, Actuators & Creature Control

• The input of an effector is the output of a single neuron or sensor
  
  
• Effectors scale their input and convert it to a (strength-limited) joint-force
  
  
• Blocks of neurons, sensors and effectors are repeated as determined by a creature's genotype
  
  
• Centralized control or synchronization may arise from a single block of neurons which is not specific to any body part of the creature. These neurons may communicate with other parts of the creature's neural network or amongst themselves.

Alternate Methods for Virtual Creature Control

• Look up table for stimulus/response
  
  
• Finite State Automata
  
  
• Conventional Neural Networks
  
  
• Machine Code (or other language)
  
  
• Any method for describing algorithms

Obtaining Working Creatures

Constructing complex creatures is not a task suitable for mortals.

The power of genetic algorithmscan be utilized to search the space of possible organisms for creatures which meet predetermined criteria.

Begin with a random population of organisms Run a dynamic simulation of the organisms Select the fittest organisms (fastest swimmers, highest jumpers etc.) Breed the fittest organisms to produce a new generation Return to step 2 until a virtual creature has evolved to meet the requirements Some creatures evolved by Sims for swimming appear on the right

Mating Directed Graphs

In producing a child genotype from two parents: Crossover: copy the genes of one parent into the child's genotype. One or more crossover points cause a switch to copying the genes from the other parent. Grafting: Two graphs may be grafted together to form a child. The connections of a node are copied with the node. Any connections left floating are randomly assigned new terminating nodes in the child. A small amount of mutation may occur in the copying of genes from a parent to a child. This is implemented as a random change in a parameter or the re-connection of a link in the graph.

2. Introduction to Physically-Based Modelling

Realistic animation of animal behaviour is (sometimes) achievable through physical simulation.

Here are four stepping-stones towards physical models of vertebrates.

1. Differential Equations
   
   
2. Particle Dynamics
   
   
3. Rigid-Body Dynamics
   
   
4. Articulated-Body Dynamics

Kinematics concerns itself directly with the acceleration, velocity and position of a body, without reference to the body's mass or the forces required to move it.

Dynamics concerns itself with the effects of forces applied to a massive body and the resultant changes in acceleration, velocity and position of that body.

Euler's Method

This is a nasty hack (which just about everyone uses anyway)...

The value of x in the future is given by the sum of the current value of x, and the step size multiplied by the derivative of the function.

(This is just what you are used to doing when you employ the formula: v'=v+at and s'=s+vt)

Curves and Euler's Method

When approximating a curve using Euler's method... the smaller the step size, the more accurate the approximation of the curve the accumulation of error in Euler's method may be slowed by reducing the step size, but never eliminated

Euler's method may be unstable under some circumstances. It may oscillate about (or even diverge from) the correct value. The figure shows the inaccuracy of Euler's method: Computing a circular orbit as a spiral!

Integration using the Runge-Kutta Method

More accurate methods of numerical integration exist. The 4th order Runge-Kutta scheme is one example:

A measure of the error in such methods can be seen by examining the Taylor's series expansion:

Consult your nearest Numerical Methods textbook for further details.

• When the function is changing rapidly, small step sizes are needed to approximate it accurately.
  
  
• When the function is changing slowly, large step sizes will save evaluations and maintain accuracy.
  
  
• It is therefore beneficial to have an adaptive step size!
  
  
• The step size may be reduced or increased according to an estimate of the error in approximating the function.

• A particle system is a simple example of a physically-based model.
  
  
• A particle's important characteristics for dynamical simulation (a particle may be simulated kinematically without all this) are:
  
  
  • Mass (M)
  • Acceleration (A)
  • Velocity (V)
  • Position (X)

Using Euler's method gives...

• A = Force / M
• V1 = V0 + A * TimeStep
• P1 = P0 + V1 * TimeStep
  

A simple dynamical model of worm locomotion may be created using two particles connected by a spring (or more such systems linked together).

• Directional friction between the ground and a point mass may be simply simulated by fixing a mass if the force arising from the spring is negative.
  
  
• The force applied by the spring to the non-fixed mass is given:
  
  
  Force = k(L-l) - D(dl/dt)
  
  
  
  • k is the spring constant
  • L is the spring resting length
  • l is the current spring length
  • D is the damping factor (scaled by the rate of change of the spring length, i.e. the spring length velocity)
  
  
• The model may be animated by varying the resting length L of the spring.

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