Learning Stable Nonlinear Dynamical Systems With Gaussian Mixture Models

  • Authors:
  • S. Mohammad Khansari-Zadeh;Aude Billard

  • Affiliations:
  • School of Engineering, Ecole Polytechnique Federale de Lausanne, Lausanne, Switzerland;School of Engineering, Ecole Polytechnique Federale de Lausanne, Lausanne, Switzerland

  • Venue:
  • IEEE Transactions on Robotics
  • Year:
  • 2011

Quantified Score

Hi-index 0.00

Visualization

Abstract

This paper presents a method to learn 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, which is called Stable Estimator of Dynamical Systems (SEDS), to learn the parameters of the DS to ensure that all motions closely follow the demonstrations while ultimately reaching 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 that are encountered during the motion. The method is evaluated through a set of robot experiments and on a library of human handwriting motions.