Imitation learning of globally stable non-linear point-to-point robot motions using nonlinear programming

This paper presents a methodology for learning arbitrary discrete motions from a set of demonstrations. We model a motion as a nonlinear autonomous (i.e. time-invariant) dynamical system, and define the sufficient conditions to make such a system globally asymptotically stable at the target. The convergence of all trajectories is ensured starting from any point in the operational space. We propose a learning method, called Stable Estimator of Dynamical Systems (SEDS), that estimates parameters of a Gaussian Mixture Model via an optimization problem under non-linear constraints. Being time-invariant and globally stable, the system is able to handle both temporal and spatial perturbations, while performing the motion as close to the demonstrations as possible. The method is evaluated through a set of robotic experiments.