On the Utility of Koopman Operator Theory in Learning Dexterous Manipulation Skills

Yunhai Han, Mandy Xie, Ye Zhao, Harish Ravichandar
Proceedings of The 7th Conference on Robot Learning, PMLR 229:106-126, 2023.

Abstract

Despite impressive dexterous manipulation capabilities enabled by learning-based approaches, we are yet to witness widespread adoption beyond well-resourced laboratories. This is likely due to practical limitations, such as significant computational burden, inscrutable learned behaviors, sensitivity to initialization, and the considerable technical expertise required for implementation. In this work, we investigate the utility of Koopman operator theory in alleviating these limitations. Koopman operators are simple yet powerful control-theoretic structures to represent complex nonlinear dynamics as linear systems in higher dimensions. Motivated by the fact that complex nonlinear dynamics underlie dexterous manipulation, we develop a Koopman operator-based imitation learning framework to learn the desired motions of both the robotic hand and the object simultaneously. We show that Koopman operators are surprisingly effective for dexterous manipulation and offer a number of unique benefits. Notably, policies can be learned analytically, drastically reducing computation burden and eliminating sensitivity to initialization and the need for painstaking hyperparameter optimization. Our experiments reveal that a Koopman operator-based approach can perform comparably to state-of-the-art imitation learning algorithms in terms of success rate and sample efficiency, while being an order of magnitude faster. Policy videos can be viewed at https://sites.google.com/view/kodex-corl.

Cite this Paper

BibTeX
@InProceedings{pmlr-v229-han23a, title = {On the Utility of Koopman Operator Theory in Learning Dexterous Manipulation Skills}, author = {Han, Yunhai and Xie, Mandy and Zhao, Ye and Ravichandar, Harish}, booktitle = {Proceedings of The 7th Conference on Robot Learning}, pages = {106--126}, year = {2023}, editor = {Tan, Jie and Toussaint, Marc and Darvish, Kourosh}, volume = {229}, series = {Proceedings of Machine Learning Research}, month = {06--09 Nov}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v229/han23a/han23a.pdf}, url = {https://proceedings.mlr.press/v229/han23a.html}, abstract = {Despite impressive dexterous manipulation capabilities enabled by learning-based approaches, we are yet to witness widespread adoption beyond well-resourced laboratories. This is likely due to practical limitations, such as significant computational burden, inscrutable learned behaviors, sensitivity to initialization, and the considerable technical expertise required for implementation. In this work, we investigate the utility of Koopman operator theory in alleviating these limitations. Koopman operators are simple yet powerful control-theoretic structures to represent complex nonlinear dynamics as linear systems in higher dimensions. Motivated by the fact that complex nonlinear dynamics underlie dexterous manipulation, we develop a Koopman operator-based imitation learning framework to learn the desired motions of both the robotic hand and the object simultaneously. We show that Koopman operators are surprisingly effective for dexterous manipulation and offer a number of unique benefits. Notably, policies can be learned analytically, drastically reducing computation burden and eliminating sensitivity to initialization and the need for painstaking hyperparameter optimization. Our experiments reveal that a Koopman operator-based approach can perform comparably to state-of-the-art imitation learning algorithms in terms of success rate and sample efficiency, while being an order of magnitude faster. Policy videos can be viewed at https://sites.google.com/view/kodex-corl.} }
Endnote
%0 Conference Paper %T On the Utility of Koopman Operator Theory in Learning Dexterous Manipulation Skills %A Yunhai Han %A Mandy Xie %A Ye Zhao %A Harish Ravichandar %B Proceedings of The 7th Conference on Robot Learning %C Proceedings of Machine Learning Research %D 2023 %E Jie Tan %E Marc Toussaint %E Kourosh Darvish %F pmlr-v229-han23a %I PMLR %P 106--126 %U https://proceedings.mlr.press/v229/han23a.html %V 229 %X Despite impressive dexterous manipulation capabilities enabled by learning-based approaches, we are yet to witness widespread adoption beyond well-resourced laboratories. This is likely due to practical limitations, such as significant computational burden, inscrutable learned behaviors, sensitivity to initialization, and the considerable technical expertise required for implementation. In this work, we investigate the utility of Koopman operator theory in alleviating these limitations. Koopman operators are simple yet powerful control-theoretic structures to represent complex nonlinear dynamics as linear systems in higher dimensions. Motivated by the fact that complex nonlinear dynamics underlie dexterous manipulation, we develop a Koopman operator-based imitation learning framework to learn the desired motions of both the robotic hand and the object simultaneously. We show that Koopman operators are surprisingly effective for dexterous manipulation and offer a number of unique benefits. Notably, policies can be learned analytically, drastically reducing computation burden and eliminating sensitivity to initialization and the need for painstaking hyperparameter optimization. Our experiments reveal that a Koopman operator-based approach can perform comparably to state-of-the-art imitation learning algorithms in terms of success rate and sample efficiency, while being an order of magnitude faster. Policy videos can be viewed at https://sites.google.com/view/kodex-corl.
APA
Han, Y., Xie, M., Zhao, Y. & Ravichandar, H.. (2023). On the Utility of Koopman Operator Theory in Learning Dexterous Manipulation Skills. Proceedings of The 7th Conference on Robot Learning, in Proceedings of Machine Learning Research 229:106-126 Available from https://proceedings.mlr.press/v229/han23a.html.

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