Incremental Motion Reshaping of Autonomous Dynamical Systems

This paper presents an approach to incrementally learn a reshaping term that modifies the trajectories of an autonomous dynamical system without affecting its stability properties. The reshaping term is considered as an additive control input and it is incrementally learned from human demonstrations using Gaussian process regression. We propose a novel parametrization of this control input that preserves the time-independence and the stability of the reshaped system, as analytically proved in the performed Lyapunov stability analysis. The effectiveness of the proposed approach is demonstrated with simulations and experiments on a real robot.