Learning Stable Dynamical Systems Using Contraction Theory

This paper discusses the learning of robot point-to-point motions via non-linear dynamical systems and Gaussian Mixture Regression (GMR). The novelty of the proposed approach consists in guaranteeing the stability of a learned dynamical system via Contraction theory. A contraction analysis is performed to derive sufficient conditions for the global stability of a dynamical system represented by GMR. The results of this analysis are exploited to automatically compute a control input which stabilizes the learned system on-line. Simple and effective solutions are proposed to generate motion trajectories close to the demonstrated ones, without affecting the stability of the overall system. The proposed approach is evaluated on a public benchmark of point-to-point motions and compared with state-of-the-art algorithms based on Lyapunov stability theory.