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.
Learning stable dynamical systems using contraction theory / Blocher, C.; Saveriano, M.; Lee, D.. - (2017), pp. 124-129. (Intervento presentato al convegno 14th International Conference on Ubiquitous Robots and Ambient Intelligence, URAI 2017 tenutosi a Maison Glad Jeju, kor nel 2017) [10.1109/URAI.2017.7992901].
Learning stable dynamical systems using contraction theory
Saveriano M.;
2017-01-01
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione