Euclideanizing Flows: Diffeomorphic Reduction for Learning Stable Dynamical Systems

Muhammad Asif Rana, Anqi Li, Dieter Fox, Byron Boots, Fabio Ramos, Nathan Ratliff
Proceedings of the 2nd Conference on Learning for Dynamics and Control, PMLR 120:630-639, 2020.

Abstract

Execution of complex tasks in robotics requires motions that have complex geometric structure. We present an approach which allows robots to learn such motions from a few human demonstrations. The motions are encoded as rollouts of a dynamical system on a Riemannian manifold. Additional structure is imposed which guarantees smooth convergent motions to a goal location. The aforementioned structure involves viewing motions on an observed Riemannian manifold as deformations of straight lines on a latent Euclidean space. The observed and latent spaces are related through a diffeomorphism. Thus, this paper presents an approach for learning flexible diffeomorphisms, resulting in a stable dynamical system. The efficacy of this approach is demonstrated through validation on an established benchmark as well demonstrations collected on a real-world robotic system.

Cite this Paper

BibTeX
@InProceedings{pmlr-v120-rana20a, title = {Euclideanizing Flows: Diffeomorphic Reduction for Learning Stable Dynamical Systems}, author = {Rana, Muhammad Asif and Li, Anqi and Fox, Dieter and Boots, Byron and Ramos, Fabio and Ratliff, Nathan}, booktitle = {Proceedings of the 2nd Conference on Learning for Dynamics and Control}, pages = {630--639}, year = {2020}, editor = {Bayen, Alexandre M. and Jadbabaie, Ali and Pappas, George and Parrilo, Pablo A. and Recht, Benjamin and Tomlin, Claire and Zeilinger, Melanie}, volume = {120}, series = {Proceedings of Machine Learning Research}, month = {10--11 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v120/rana20a/rana20a.pdf}, url = {https://proceedings.mlr.press/v120/rana20a.html}, abstract = {Execution of complex tasks in robotics requires motions that have complex geometric structure. We present an approach which allows robots to learn such motions from a few human demonstrations. The motions are encoded as rollouts of a dynamical system on a Riemannian manifold. Additional structure is imposed which guarantees smooth convergent motions to a goal location. The aforementioned structure involves viewing motions on an observed Riemannian manifold as deformations of straight lines on a latent Euclidean space. The observed and latent spaces are related through a diffeomorphism. Thus, this paper presents an approach for learning flexible diffeomorphisms, resulting in a stable dynamical system. The efficacy of this approach is demonstrated through validation on an established benchmark as well demonstrations collected on a real-world robotic system.} }
Endnote
%0 Conference Paper %T Euclideanizing Flows: Diffeomorphic Reduction for Learning Stable Dynamical Systems %A Muhammad Asif Rana %A Anqi Li %A Dieter Fox %A Byron Boots %A Fabio Ramos %A Nathan Ratliff %B Proceedings of the 2nd Conference on Learning for Dynamics and Control %C Proceedings of Machine Learning Research %D 2020 %E Alexandre M. Bayen %E Ali Jadbabaie %E George Pappas %E Pablo A. Parrilo %E Benjamin Recht %E Claire Tomlin %E Melanie Zeilinger %F pmlr-v120-rana20a %I PMLR %P 630--639 %U https://proceedings.mlr.press/v120/rana20a.html %V 120 %X Execution of complex tasks in robotics requires motions that have complex geometric structure. We present an approach which allows robots to learn such motions from a few human demonstrations. The motions are encoded as rollouts of a dynamical system on a Riemannian manifold. Additional structure is imposed which guarantees smooth convergent motions to a goal location. The aforementioned structure involves viewing motions on an observed Riemannian manifold as deformations of straight lines on a latent Euclidean space. The observed and latent spaces are related through a diffeomorphism. Thus, this paper presents an approach for learning flexible diffeomorphisms, resulting in a stable dynamical system. The efficacy of this approach is demonstrated through validation on an established benchmark as well demonstrations collected on a real-world robotic system.
APA
Rana, M.A., Li, A., Fox, D., Boots, B., Ramos, F. & Ratliff, N.. (2020). Euclideanizing Flows: Diffeomorphic Reduction for Learning Stable Dynamical Systems. Proceedings of the 2nd Conference on Learning for Dynamics and Control, in Proceedings of Machine Learning Research 120:630-639 Available from https://proceedings.mlr.press/v120/rana20a.html.

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