Orientation Probabilistic Movement Primitives on Riemannian Manifolds

TL;DR

This paper introduces a Riemannian manifold-based extension of probabilistic movement primitives (ProMPs) to effectively encode and retrieve full-pose robot trajectories, including rotations represented by quaternions.

Contribution

It develops a novel Riemannian formulation of ProMPs that incorporates quaternion trajectories, enabling better modeling of complex robot motions in operational space.

Findings

Successfully encodes quaternion trajectories using Riemannian ProMPs

Demonstrates improved motion modeling on real robot demonstrations

Illustrates the approach with toy examples and real experiments

Abstract

Learning complex robot motions necessarily demands to have models that are able to encode and retrieve full-pose trajectories when tasks are defined in operational spaces. Probabilistic movement primitives (ProMPs) stand out as a principled approach that models trajectory distributions learned from demonstrations. ProMPs allow for trajectory modulation and blending to achieve better generalization to novel situations. However, when ProMPs are employed in operational space, their original formulation does not directly apply to full-pose movements including rotational trajectories described by quaternions. This paper proposes a Riemannian formulation of ProMPs that enables encoding and retrieving of quaternion trajectories. Our method builds on Riemannian manifold theory, and exploits multilinear geodesic regression for estimating the ProMPs parameters. This novel approach makes ProMPs a suitable model for learning complex full-pose robot motion patterns. Riemannian ProMPs are tested on toy examples to illustrate their workflow, and on real learning-from-demonstration experiments.