Learning robot reaching motions by demonstration using nonlinear autoregressive models

This paper presents NAR-RM, a method for learning robot reaching motions from a set of demonstrations using Nonlinear AutoRegressive (NAR) polynomial models. Reaching motions are modeled as solutions to autonomous discrete-time nonlinear dynamical systems, so that the movements started near the data of the demonstrations follow the trained trajectories and always reach and stop at the target. Since NAR models obtained using standard system identification techniques do not always adequately model the reaching motions, in this paper we present a method that uses a least-squares estimator with constraints to impose the location of fixed points in the model. With the imposition of new fixed points it is possible to change the location of the original fixed points of the model, thus allowing the learning of stable reaching motions. We evaluate our method using a library of human handwriting motions, a mobile robot and an industrial manipulator.