Orientation Probabilistic Movement Primitives on Riemannian Manifolds

Leonel Rozo, Vedant Dave
Proceedings of the 5th Conference on Robot Learning, PMLR 164:373-383, 2022.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v164-rozo22a, title = {Orientation Probabilistic Movement Primitives on Riemannian Manifolds}, author = {Rozo, Leonel and Dave, Vedant}, booktitle = {Proceedings of the 5th Conference on Robot Learning}, pages = {373--383}, year = {2022}, editor = {Faust, Aleksandra and Hsu, David and Neumann, Gerhard}, volume = {164}, series = {Proceedings of Machine Learning Research}, month = {08--11 Nov}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v164/rozo22a/rozo22a.pdf}, url = {https://proceedings.mlr.press/v164/rozo22a.html}, 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. } }
Endnote
%0 Conference Paper %T Orientation Probabilistic Movement Primitives on Riemannian Manifolds %A Leonel Rozo %A Vedant Dave %B Proceedings of the 5th Conference on Robot Learning %C Proceedings of Machine Learning Research %D 2022 %E Aleksandra Faust %E David Hsu %E Gerhard Neumann %F pmlr-v164-rozo22a %I PMLR %P 373--383 %U https://proceedings.mlr.press/v164/rozo22a.html %V 164 %X 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.
APA
Rozo, L. & Dave, V.. (2022). Orientation Probabilistic Movement Primitives on Riemannian Manifolds. Proceedings of the 5th Conference on Robot Learning, in Proceedings of Machine Learning Research 164:373-383 Available from https://proceedings.mlr.press/v164/rozo22a.html.

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