A Quantum-Statistical Approach Towards Robot Learning by Demonstration

Abstract

Abstract—Statistical machine learning approaches have been in the epicenter of the ongoing research work in the field of robot learning by demonstration in the last years. One of the most successful methodologies used for this purpose is Gaussian mixture regression (GMR). In this paper, we propose an extension of GMR-based learning by demonstration models, to incorporate concepts from the field of quantum mechanics. Indeed, conventional GMR models are formulated under the notion that all the observed data points can be assigned to a distinct number of model states (mixture components). In this work, we reformulate GMR models, introducing some quantum states constructed by superposing conventional GMR states by means of linear combinations. The so-obtained quantum statistics-inspired mixture regression algorithm is subsequently applied to obtain a novel robot learning by demonstration methodology, offering a significantly increased quality of regenerated trajectories for computational costs comparable to currently state-of-the-art trajectory-based robot learning by demonstration approaches. We experimentally demonstrate the efficacy of the proposed approach. I