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. Timeinvariance 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. Index Terms—Dynamical systems (DS), Gaussian mixture model, imitation learning, point-to-point motions, stability analysis. I.

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This work considers our approach to robot motion control learning from the standpoint of multiple data sources. Our paradigm derives data from human teachers providing task demonstrations and tactile corrections for policy refinement and reuse. We contribute a novel formalization for this data, and identify future directions for the algorithm to reason explicitly about differences in data source. 1

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