Task Generalization with Stability Guarantees via Elastic Dynamical System Motion Policies

Tianyu Li, Nadia Figueroa
Proceedings of The 7th Conference on Robot Learning, PMLR 229:3485-3517, 2023.

Abstract

Dynamical System (DS) based Learning from Demonstration (LfD) allows learning of reactive motion policies with stability and convergence guarantees from a few trajectories. Yet, current DS learning techniques lack the flexibility to generalize to new task instances as they overlook explicit task parameters that inherently change the underlying demonstrated trajectories. In this work, we propose Elastic-DS, a novel DS learning and generalization approach that embeds task parameters into the Gaussian Mixture Model (GMM) based Linear Parameter Varying (LPV) DS formulation. Central to our approach is the Elastic-GMM, a GMM constrained to SE(3) task-relevant frames. Given a new task instance/context, the Elastic-GMM is transformed with Laplacian Editing and used to re-estimate the LPV-DS policy. Elastic-DS is compositional in nature and can be used to construct flexible multi-step tasks. We showcase its strength on a myriad of simulated and real-robot experiments while preserving desirable control-theoretic guarantees.

Cite this Paper

BibTeX
@InProceedings{pmlr-v229-li23b, title = {Task Generalization with Stability Guarantees via Elastic Dynamical System Motion Policies}, author = {Li, Tianyu and Figueroa, Nadia}, booktitle = {Proceedings of The 7th Conference on Robot Learning}, pages = {3485--3517}, 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/li23b/li23b.pdf}, url = {https://proceedings.mlr.press/v229/li23b.html}, abstract = {Dynamical System (DS) based Learning from Demonstration (LfD) allows learning of reactive motion policies with stability and convergence guarantees from a few trajectories. Yet, current DS learning techniques lack the flexibility to generalize to new task instances as they overlook explicit task parameters that inherently change the underlying demonstrated trajectories. In this work, we propose Elastic-DS, a novel DS learning and generalization approach that embeds task parameters into the Gaussian Mixture Model (GMM) based Linear Parameter Varying (LPV) DS formulation. Central to our approach is the Elastic-GMM, a GMM constrained to SE(3) task-relevant frames. Given a new task instance/context, the Elastic-GMM is transformed with Laplacian Editing and used to re-estimate the LPV-DS policy. Elastic-DS is compositional in nature and can be used to construct flexible multi-step tasks. We showcase its strength on a myriad of simulated and real-robot experiments while preserving desirable control-theoretic guarantees.} }
Endnote
%0 Conference Paper %T Task Generalization with Stability Guarantees via Elastic Dynamical System Motion Policies %A Tianyu Li %A Nadia Figueroa %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-li23b %I PMLR %P 3485--3517 %U https://proceedings.mlr.press/v229/li23b.html %V 229 %X Dynamical System (DS) based Learning from Demonstration (LfD) allows learning of reactive motion policies with stability and convergence guarantees from a few trajectories. Yet, current DS learning techniques lack the flexibility to generalize to new task instances as they overlook explicit task parameters that inherently change the underlying demonstrated trajectories. In this work, we propose Elastic-DS, a novel DS learning and generalization approach that embeds task parameters into the Gaussian Mixture Model (GMM) based Linear Parameter Varying (LPV) DS formulation. Central to our approach is the Elastic-GMM, a GMM constrained to SE(3) task-relevant frames. Given a new task instance/context, the Elastic-GMM is transformed with Laplacian Editing and used to re-estimate the LPV-DS policy. Elastic-DS is compositional in nature and can be used to construct flexible multi-step tasks. We showcase its strength on a myriad of simulated and real-robot experiments while preserving desirable control-theoretic guarantees.
APA
Li, T. & Figueroa, N.. (2023). Task Generalization with Stability Guarantees via Elastic Dynamical System Motion Policies. Proceedings of The 7th Conference on Robot Learning, in Proceedings of Machine Learning Research 229:3485-3517 Available from https://proceedings.mlr.press/v229/li23b.html.

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