Gaussian Mixture Models

Abstract

This paper presents a method to learn discrete robot motions froma set of demonstrations.We model a motion as a non- linear autonomous (i.e., time-invariant) dynamical system (DS) and define sufficient conditions to ensure global asymptotic stability at the target. We propose a learning method, which is called Stable Estimator of Dynamical Systems (SEDS), to learn the parameters of the DS to ensure that all motions closely follow the demonstra- tions while ultimately reaching and stopping at the target. Time- invariance and global asymptotic stability at the target ensures that the system can respond immediately and appropriately to pertur- bations that are encountered during the motion. The method is evaluated through a set of robot experiments and on a library of human handwriting motions.