Evolution of Legged Locomotion

Thc realistic animation of human and animal figures has long been a prime goal in computer graphics. A recent, physically-based approach to the problem suggests ~nodr l ing creatures as act,~latcd articulated bodies equipped with a "virtual brain" which generates the control signals required by the a;tuators to produce t,lle desired motion. The animation of such a creature is simply a forward sin~ulation of the resulting motion under the laws of physics in time. While using tmllis approach ensures physically realistic rnotion, there is no obvious ~ o l u t ~ i o n to the problem of devising a control syst,enl that leads t,o the desired motion. Even though good results have been achieved by carefully handcrafting control systems on the basis of biolnechanical knowledge and physical intuition, it is desirable to produce control system autmornat,ically. Evolut'ionary algorithms n-hich it,eratively improve randomly generated initial cont.rol systems have shown to he a promising approach to this problem. This thesis introduces spectral synthesis as a tool for generating control syst,erns to be opt,i~rlizetl in an evolutionary process and demonstrat,es the viahilit,y of t,he approaclt by evolving creatures for the t,ask of legged locomotion. Other than represer~t~atior~s of control systems t,hat have previously been used for evolving useful behavior, spectral synthesis guarantees evolvability, improving the cllances of the evolutionary search t,o succeed. Virt,ual creatures esl~ibit,iug a great variet>y of niodes of locomotion, including hopping, crawling, jumping, and walking, have been evolved as part of t,his work. The incorporat,ion of more goal-direct,etl components remains as a future goal. A second accorriplishrnent of this t,hesis is t8he derivation of t,he equat,ions describing t8he effect of applying a contact force t,o an a r t i~u la t~ed body on its accelerat,ion, making it possible t,o gmcralize the common algorithms for handling contacts in systems of rigid bodies t,o articulated bodies. The physical simulation algorithm described in this thesis allows for real t#irne simulation of articulated creatures of up to about twenty degrces of freedom. Efficient simulation algor~thmb are espec~ally irnportant as evolutionary optinuzation requires the exaluation and therefore sirnulat~on of the behawor of a great number of creatures. I'd like to thank Dave for encouragement, support, and helpful advice, and the other members of my examining committee for useful input which helped shaping the final version of this thesis.