BM: An iterative algorithm to learn stable non-linear dynamical systems with Gaussian mixture models

We model the dynamics of non-linear point-to-point robot motions as a time-independent system described by an autonomous dynamical system (DS). We propose an iterative algorithm to estimate the form of the DS through a mixture of Gaussian distributions. We prove that the resulting model is asymptotically stable at the target. We validate the accuracy of the model on a library of 2D human motions and to learn a control policy through human demonstrations for two multi-degrees of freedom robots. We show the real-time adaptation to perturbations of the learned model when controlling the two kinematically-driven robots.