  This article proposes a novel methodology to learn a stable robot control law
driven by dynamical systems. The methodology requires a single demonstration
and can deduce a stable dynamics in arbitrary high dimensions. The method
relies on the idea that there exists a latent space in which the nonlinear
dynamics appears quasi linear. The original nonlinear dynamics is mapped into a
stable linear DS, by leveraging on the properties of graph embeddings. We show
that the eigendecomposition of the Graph Laplacian results in linear embeddings
in two dimensions and quasi-linear in higher dimensions. The nonlinear terms
vanish, exponentially as the number of datapoints increase, and for large
density of points, the embedding appears linear. We show that this new
embedding enables to model highly nonlinear dynamics in high dimension and
overcomes alternative techniques in both precision of reconstruction and number
of parameters required for the embedding. We demonstrate its applicability to
control real robot tasked to perform complex free motion in space.
