Evolving L-systems to generate virtual creatures
Introduction
As computers become more powerful it is increasingly our design ability, rather than computing power, that limits the richness of virtual worlds. Evolutionary algorithms (EAs), a technique inspired by biological evolution, have shown much promise in automating the process of producing creatures for virtual environments, yet the most recent work in this area [1], [2] has produced ungainly creatures with less than 50 components. The asymmetries of these creatures is a result of using a direct encoding, an explicit encoding with a one-to-one mapping from genotypic encoding to creature-part. As direct encodings have no re-use, symmetries and regularities do not occur, except by chance, and evolved structures tend to be unnatural looking.
In this we return to the spirit of [3], in which a graph structure was used as a generative encoding for the creatures. A generative encoding is a developmental method for producing a structure using a set of grammatical re-writing rules or a procedural process, not unlike a computer program with re-usable sub-procedures. Designs produced by a generative encoding have fractal-like self-similarities, giving them an organic look, and have been shown to have better scaling properties than direct encodings [4], [5]. Here we use Lindenmayer systems (L-systems) [6] as a more powerful, and general purpose, generative encoding than that of [3] to achieve moving creatures with hundreds of parts whose structure is more natural looking than [1], [2].
More common than co-evolving morphology and controller has been work evolving controllers for pre-specified morphologies. Control systems for these works has included stimulus-response rules [7], [8], neural controllers [9], and genetic programs [10]. The controllers of the creatures in this work are oscillator circuits; each actuated joint is controlled by an oscillator with its own frequency and relative phase offset. To achieve controllers that are reactive to the environment joints can be controlled by recurrent neural networks, as with [1], [2], [3], by including neural-network construction commands into the encoding language [11].
In the following sections, we first outline the design space and describe the components of our generative design system, then we present our results and finally close with a discussion and conclusion of our work.
Section snippets
Methods
The system for producing moving creatures consists of an algorithm for optimizing creature designs, an encoding to represent the creatures for the optimization algorithm, and a method of constructing creatures from their encoding.
Evolutionary algorithms are used as the optimization algorithm for producing the virtual creatures. EAs are a class of stochastic search and optimization techniques inspired by natural evolution, these include genetic algorithms [12], evolutionary strategies [13],
Discussion
For this work, we used parametric L-systems as a way to increase complexity over basic L-systems. Using parameters also has the advantage of allowing one production rule to be used to generate a class of objects, such as by using the parameter to specify the size of an attribute generated by the production rule or number of times to perform a loop. In this way, parameters are analogous to the arguments of a function in a computer program and the evolution of an L-system becomes like the
Conclusion
A system for creating virtual creatures was achieved by using evolutionary techniques to evolve parametric Lindenmayer systems. Using this system, morphologies and controllers were evolved for moving creatures. The evolved creatures consist of an order of magnitude more parts and a higher degree of regularity than [1], [2], [3]. Already our creatures are capable of playing background characters with insect-level behaviors for animations. As we move from simple oscillator circuits to
Acknowledgements
This research was supported in part by the Defense Advanced Research Projects Administration (DARPA) Grant, DASG60-99-1-0004. The authors would like to thank the members of the DEMO Lab: A. Bucci, E. DeJong, S. Ficici, P. Funes, S. Levy, H. Lipson, O. Melnik, E. Sklar, S. Viswanathan and R. Watson.
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