A Physically-Consistent Bayesian Non-Parametric Mixture Model for Dynamical System Learning

Nadia Figueroa, Aude Billard
Proceedings of The 2nd Conference on Robot Learning, PMLR 87:927-946, 2018.

Abstract

We propose a physically-consistent Bayesian non-parametric approach for fitting Gaussian Mixture Models (GMM) to trajectory data. Physical-consistency of the GMM is ensured by imposing a prior on the component assignments biased by a novel similarity metric that leverages locality and directionality. The resulting GMM is then used to learn globally asymptotically stable Dynamical Systems (DS) via a Linear Parameter Varying (LPV) re-formulation. The proposed DS learning scheme accurately encodes challenging nonlinear motions automatically. Finally, a data-efficient incremental learning framework is introduced that encodes a DS from batches of trajectories, while preserving global stability. Our contributions are validated on 2D datasets and a variety of tasks that involve single-target complex motions with a KUKA LWR 4+ robot arm.

Cite this Paper

BibTeX
@InProceedings{pmlr-v87-figueroa18a, title = {A Physically-Consistent Bayesian Non-Parametric Mixture Model for Dynamical System Learning}, author = {Figueroa, Nadia and Billard, Aude}, booktitle = {Proceedings of The 2nd Conference on Robot Learning}, pages = {927--946}, year = {2018}, editor = {Billard, Aude and Dragan, Anca and Peters, Jan and Morimoto, Jun}, volume = {87}, series = {Proceedings of Machine Learning Research}, month = {29--31 Oct}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v87/figueroa18a/figueroa18a.pdf}, url = {https://proceedings.mlr.press/v87/figueroa18a.html}, abstract = {We propose a physically-consistent Bayesian non-parametric approach for fitting Gaussian Mixture Models (GMM) to trajectory data. Physical-consistency of the GMM is ensured by imposing a prior on the component assignments biased by a novel similarity metric that leverages locality and directionality. The resulting GMM is then used to learn globally asymptotically stable Dynamical Systems (DS) via a Linear Parameter Varying (LPV) re-formulation. The proposed DS learning scheme accurately encodes challenging nonlinear motions automatically. Finally, a data-efficient incremental learning framework is introduced that encodes a DS from batches of trajectories, while preserving global stability. Our contributions are validated on 2D datasets and a variety of tasks that involve single-target complex motions with a KUKA LWR 4+ robot arm. } }
Endnote
%0 Conference Paper %T A Physically-Consistent Bayesian Non-Parametric Mixture Model for Dynamical System Learning %A Nadia Figueroa %A Aude Billard %B Proceedings of The 2nd Conference on Robot Learning %C Proceedings of Machine Learning Research %D 2018 %E Aude Billard %E Anca Dragan %E Jan Peters %E Jun Morimoto %F pmlr-v87-figueroa18a %I PMLR %P 927--946 %U https://proceedings.mlr.press/v87/figueroa18a.html %V 87 %X We propose a physically-consistent Bayesian non-parametric approach for fitting Gaussian Mixture Models (GMM) to trajectory data. Physical-consistency of the GMM is ensured by imposing a prior on the component assignments biased by a novel similarity metric that leverages locality and directionality. The resulting GMM is then used to learn globally asymptotically stable Dynamical Systems (DS) via a Linear Parameter Varying (LPV) re-formulation. The proposed DS learning scheme accurately encodes challenging nonlinear motions automatically. Finally, a data-efficient incremental learning framework is introduced that encodes a DS from batches of trajectories, while preserving global stability. Our contributions are validated on 2D datasets and a variety of tasks that involve single-target complex motions with a KUKA LWR 4+ robot arm.
APA
Figueroa, N. & Billard, A.. (2018). A Physically-Consistent Bayesian Non-Parametric Mixture Model for Dynamical System Learning. Proceedings of The 2nd Conference on Robot Learning, in Proceedings of Machine Learning Research 87:927-946 Available from https://proceedings.mlr.press/v87/figueroa18a.html.

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