Compact One-Shot Modeling of High-Dimensional Demonstrations Using Laplacian Eigenmaps

Learning control policies from high-dimensional robot demonstrations remains challenging due to the need for large datasets, limited generalization, and high model complexity. These limitations hinder data-efficient learning and reactive deployment from limited demonstrations. This paper introduces LEMON-DS, a compact and data-efficient framework for one shot learning of stable control policies from high-dimensional demonstrations. LEMON-DS proceeds in three stages: (i) a graph Laplacian–based spectral embedding that reveals a quasi linear latent structure from a single trajectory, (ii) defining a globally asymptotically stable dynamical system (DS) in the latent space, and (iii) learning a diffeomorphic mapping that reconstructs the demonstrated behaviour. Collectively, this pipeline yields a lightweight reactive control policy in the form of a dynamical system that is parameter-efficient, globally asymptotically stable, and faithfully reproduces the demonstrated behaviour generalizing across initial conditions. We show empirical performance across diverse robot tasks up to 23 dimensions, outperforming prior approaches in accuracy and model compactness.