Learning rhythmic movements by demonstration using nonlinear oscillators

ATR Human Information Science Laboratories, Kyoto, JapanEmail: ijspeert@usc.edu, jun@his.atr.co.jp, sschaal@usc.eduAbstractThis paper presents a new approach to the generationof rhythmic movement patterns with nonlinear dy-namical systems. Starting from a canonical limit cy-cle oscillator with well-de ned stability properties, wemodify the attractor landscape of the canonical sys-temby meansof statisticallearning methods toembedarbitrary smooth target patterns, however, withoutlosing the stability properties of the canonical sys-tem. In contrast to non-autonomous movement rep-resentations like splines, the learned pattern gener-ators remain autonomous dynamical systems whichrobustly cope with external perturbations that disruptthe time ow of the original pattern, and which canalso be modi ed on-line by additional perceptual vari-ables. A simple extension allows to cope with mul-tiple degrees-of-freedom (DOF) patterns, where allDOFs share the same fundamental frequency but,otherwise, can move in arbitrary phase and ampli-tude o sets to each other. We evaluate our meth-ods in learning from demonstration with an actual30 DOF humanoid robot. Figure-8 and drummingmovements are demonstrated by a human, recordedin joint angle space with an exoskeleton, and em-bedded in multi-dimensional rhythmic pattern gener-ators. The learned patterns can be used by the robotin various workspace locations and from arbitraryinitial conditions. Spatial and temporal invarianceof the pattern generators allow easy amplitude andspeed scaling without losing the qualitative signatureof a movement. This novel way of creating rhyth-mic patterns could tremendously facilitate rhythmicmovement generation, in particular in locomotion ofrobots and neural prosthetics in clinical applications.

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