Forced Variational Integrator Networks for Prediction and Control of Mechanical Systems

Aaron Havens, Girish Chowdhary
Proceedings of the 3rd Conference on Learning for Dynamics and Control, PMLR 144:1142-1153, 2021.

Abstract

As deep learning becomes more prevalent for prediction and control of real physical systems, it is important that these models are consistent with physically plausible dynamics. This elicits a problem with how much inductive bias to impose on the model through known physical parameters and principles to reduce complexity of the learning problem to give us more reliable predictions. Recent work employs discrete variational integrators parameterized as a neural network architecture to learn conservative Lagrangian systems. The learned model captures and enforces global energy preserving properties of the system from very few trajectories. However, most real systems are inherently non-conservative and, in practice, we would also like to apply actuation. In this paper we extend this paradigm to account for general forcing (e.g. control input and friction) via discrete D’Alembert’s principle which may ultimately be used for control applications. We show that this forced variational integrator networks (FVIN) architecture allows us to accurately account for energy dissipation and external forcing while still capturing the true underlying energy-based passive dynamics. We show that in application this can result in highly-data efficient model-based control and can predict on real non-conservative systems.

Cite this Paper

BibTeX
@InProceedings{pmlr-v144-havens21a, title = {Forced Variational Integrator Networks for Prediction and Control of Mechanical Systems}, author = {Havens, Aaron and Chowdhary, Girish}, booktitle = {Proceedings of the 3rd Conference on Learning for Dynamics and Control}, pages = {1142--1153}, year = {2021}, editor = {Jadbabaie, Ali and Lygeros, John and Pappas, George J. and A. Parrilo, Pablo and Recht, Benjamin and Tomlin, Claire J. and Zeilinger, Melanie N.}, volume = {144}, series = {Proceedings of Machine Learning Research}, month = {07 -- 08 June}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v144/havens21a/havens21a.pdf}, url = {https://proceedings.mlr.press/v144/havens21a.html}, abstract = {As deep learning becomes more prevalent for prediction and control of real physical systems, it is important that these models are consistent with physically plausible dynamics. This elicits a problem with how much inductive bias to impose on the model through known physical parameters and principles to reduce complexity of the learning problem to give us more reliable predictions. Recent work employs discrete variational integrators parameterized as a neural network architecture to learn conservative Lagrangian systems. The learned model captures and enforces global energy preserving properties of the system from very few trajectories. However, most real systems are inherently non-conservative and, in practice, we would also like to apply actuation. In this paper we extend this paradigm to account for general forcing (e.g. control input and friction) via discrete D’Alembert’s principle which may ultimately be used for control applications. We show that this forced variational integrator networks (FVIN) architecture allows us to accurately account for energy dissipation and external forcing while still capturing the true underlying energy-based passive dynamics. We show that in application this can result in highly-data efficient model-based control and can predict on real non-conservative systems.} }
Endnote
%0 Conference Paper %T Forced Variational Integrator Networks for Prediction and Control of Mechanical Systems %A Aaron Havens %A Girish Chowdhary %B Proceedings of the 3rd Conference on Learning for Dynamics and Control %C Proceedings of Machine Learning Research %D 2021 %E Ali Jadbabaie %E John Lygeros %E George J. Pappas %E Pablo A. Parrilo %E Benjamin Recht %E Claire J. Tomlin %E Melanie N. Zeilinger %F pmlr-v144-havens21a %I PMLR %P 1142--1153 %U https://proceedings.mlr.press/v144/havens21a.html %V 144 %X As deep learning becomes more prevalent for prediction and control of real physical systems, it is important that these models are consistent with physically plausible dynamics. This elicits a problem with how much inductive bias to impose on the model through known physical parameters and principles to reduce complexity of the learning problem to give us more reliable predictions. Recent work employs discrete variational integrators parameterized as a neural network architecture to learn conservative Lagrangian systems. The learned model captures and enforces global energy preserving properties of the system from very few trajectories. However, most real systems are inherently non-conservative and, in practice, we would also like to apply actuation. In this paper we extend this paradigm to account for general forcing (e.g. control input and friction) via discrete D’Alembert’s principle which may ultimately be used for control applications. We show that this forced variational integrator networks (FVIN) architecture allows us to accurately account for energy dissipation and external forcing while still capturing the true underlying energy-based passive dynamics. We show that in application this can result in highly-data efficient model-based control and can predict on real non-conservative systems.
APA
Havens, A. & Chowdhary, G.. (2021). Forced Variational Integrator Networks for Prediction and Control of Mechanical Systems. Proceedings of the 3rd Conference on Learning for Dynamics and Control, in Proceedings of Machine Learning Research 144:1142-1153 Available from https://proceedings.mlr.press/v144/havens21a.html.

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