Learning Stable Non-Linear Dynamical Systems with Gaussian Mixture Models

This paper presents a method for learning discrete robot motions from a set of demonstrations. We model a motion as a nonlinear 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, called Stable Estimator of Dynamical Systems (SEDS), to learn the parameters of the DS to ensure that all motions follow closely the demonstrations while ultimately reaching in and stopping at the target. Time-invariance and global asymptotic stability at the target ensures that the system can respond immediately and appropriately to perturbations encountered during the motion. The method is evaluated through a set of robot experiments and on a library of human handwriting motions.