Learning Stable Robotic Skills on Riemannian Manifolds

TL;DR

This paper introduces a data-efficient method for learning stable robotic skills on Riemannian manifolds, ensuring geometric consistency and convergence, demonstrated through simulation and real robot experiments.

Contribution

It presents a novel approach leveraging differential geometry to learn diffeomorphic transformations for complex robotic skills on manifolds.

Findings

Successful simulation on benchmark data

Effective real robot bottle stacking

Promising task adaptation and accuracy

Abstract

In this paper, we propose an approach to learn stable dynamical systems evolving on Riemannian manifolds. The approach leverages a data-efficient procedure to learn a diffeomorphic transformation that maps simple stable dynamical systems onto complex robotic skills. By exploiting mathematical tools from differential geometry, the method ensures that the learned skills fulfill the geometric constraints imposed by the underlying manifolds, such as unit quaternion (UQ) for orientation and symmetric positive definite (SPD) matrices for impedance, while preserving the convergence to a given target. The proposed approach is firstly tested in simulation on a public benchmark, obtained by projecting Cartesian data into UQ and SPD manifolds, and compared with existing approaches. Apart from evaluating the approach on a public benchmark, several experiments were performed on a real robot performing bottle stacking in different conditions and a drilling task in cooperation with a human operator. The evaluation shows promising results in terms of learning accuracy and task adaptation capabilities.