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.
2017
2017 14th International Conference on Ubiquitous Robots and Ambient Intelligence, URAI 2017
Piscataway, New Jersey, USA
Institute of Electrical and Electronics Engineers Inc.
978-1-5090-3056-9
Blocher, C.; Saveriano, M.; Lee, D.
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].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/331037
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