Learning robot motions with stable dynamical systems under diffeomorphic transformations

Accuracy and stability have in recent studies been emphasized as the two major ingredients to learn robot motions from demonstrations with dynamical systems. Several approaches yield stable dynamical systems but are also limited to specific dynamics that can potentially result in a poor reproduction performance. The current work addresses this accuracy-stability dilemma through a new diffeomorphic transformation approach that serves as a framework generalizing the class of demonstrations that are learnable by means of provably stable dynamical systems. We apply the proposed framework to extend the application domain of the stable estimator of dynamical systems (SEDS) by generalizing the class of learnable demonstrations by means of diffeomorphic transformations τ. The resulting approach is named τ-SEDS and analyzed with rigorous theoretical investigations and robot experiments.