Learning Riemannian Stable Dynamical Systems via Diffeomorphisms

Jiechao Zhang, Hadi Beik Mohammadi, Leonel Rozo
Proceedings of The 6th Conference on Robot Learning, PMLR 205:1211-1221, 2023.

Abstract

Dexterous and autonomous robots should be capable of executing elaborated dynamical motions skillfully. Learning techniques may be leveraged to build models of such dynamic skills. To accomplish this, the learning model needs to encode a stable vector field that resembles the desired motion dynamics. This is challenging as the robot state does not evolve on a Euclidean space, and therefore the stability guarantees and vector field encoding need to account for the geometry arising from, for example, the orientation representation. To tackle this problem, we propose learning Riemannian stable dynamical systems (RSDS) from demonstrations, allowing us to account for different geometric constraints resulting from the dynamical system state representation. Our approach provides Lyapunov-stability guarantees on Riemannian manifolds that are enforced on the desired motion dynamics via diffeomorphisms built on neural manifold ODEs. We show that our Riemannian approach makes it possible to learn stable dynamical systems displaying complicated vector fields on both illustrative examples and real-world manipulation tasks, where Euclidean approximations fail.

Cite this Paper

BibTeX
@InProceedings{pmlr-v205-zhang23b, title = {Learning Riemannian Stable Dynamical Systems via Diffeomorphisms}, author = {Zhang, Jiechao and Mohammadi, Hadi Beik and Rozo, Leonel}, booktitle = {Proceedings of The 6th Conference on Robot Learning}, pages = {1211--1221}, year = {2023}, editor = {Liu, Karen and Kulic, Dana and Ichnowski, Jeff}, volume = {205}, series = {Proceedings of Machine Learning Research}, month = {14--18 Dec}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v205/zhang23b/zhang23b.pdf}, url = {https://proceedings.mlr.press/v205/zhang23b.html}, abstract = {Dexterous and autonomous robots should be capable of executing elaborated dynamical motions skillfully. Learning techniques may be leveraged to build models of such dynamic skills. To accomplish this, the learning model needs to encode a stable vector field that resembles the desired motion dynamics. This is challenging as the robot state does not evolve on a Euclidean space, and therefore the stability guarantees and vector field encoding need to account for the geometry arising from, for example, the orientation representation. To tackle this problem, we propose learning Riemannian stable dynamical systems (RSDS) from demonstrations, allowing us to account for different geometric constraints resulting from the dynamical system state representation. Our approach provides Lyapunov-stability guarantees on Riemannian manifolds that are enforced on the desired motion dynamics via diffeomorphisms built on neural manifold ODEs. We show that our Riemannian approach makes it possible to learn stable dynamical systems displaying complicated vector fields on both illustrative examples and real-world manipulation tasks, where Euclidean approximations fail.} }
Endnote
%0 Conference Paper %T Learning Riemannian Stable Dynamical Systems via Diffeomorphisms %A Jiechao Zhang %A Hadi Beik Mohammadi %A Leonel Rozo %B Proceedings of The 6th Conference on Robot Learning %C Proceedings of Machine Learning Research %D 2023 %E Karen Liu %E Dana Kulic %E Jeff Ichnowski %F pmlr-v205-zhang23b %I PMLR %P 1211--1221 %U https://proceedings.mlr.press/v205/zhang23b.html %V 205 %X Dexterous and autonomous robots should be capable of executing elaborated dynamical motions skillfully. Learning techniques may be leveraged to build models of such dynamic skills. To accomplish this, the learning model needs to encode a stable vector field that resembles the desired motion dynamics. This is challenging as the robot state does not evolve on a Euclidean space, and therefore the stability guarantees and vector field encoding need to account for the geometry arising from, for example, the orientation representation. To tackle this problem, we propose learning Riemannian stable dynamical systems (RSDS) from demonstrations, allowing us to account for different geometric constraints resulting from the dynamical system state representation. Our approach provides Lyapunov-stability guarantees on Riemannian manifolds that are enforced on the desired motion dynamics via diffeomorphisms built on neural manifold ODEs. We show that our Riemannian approach makes it possible to learn stable dynamical systems displaying complicated vector fields on both illustrative examples and real-world manipulation tasks, where Euclidean approximations fail.
APA
Zhang, J., Mohammadi, H.B. & Rozo, L.. (2023). Learning Riemannian Stable Dynamical Systems via Diffeomorphisms. Proceedings of The 6th Conference on Robot Learning, in Proceedings of Machine Learning Research 205:1211-1221 Available from https://proceedings.mlr.press/v205/zhang23b.html.

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