Learning Certified Control Using Contraction Metric

Dawei Sun, Susmit Jha, Chuchu Fan
Proceedings of the 2020 Conference on Robot Learning, PMLR 155:1519-1539, 2021.

Abstract

In this paper, we solve the problem of finding a certified control policy that drives a robot from any given initial state and under any bounded disturbance to the desired reference trajectory, with guarantees on the convergence or bounds on the tracking error. Such a controller is crucial in safe motion planning. We leverage the advanced theory in Control Contraction Metric and design a learning framework based on neural networks to co-synthesize the contraction metric and the controller for control-affine systems. We further provide methods to validate the convergence and bounded error guarantees. We demonstrate the performance of our method using a suite of challenging robotic models, including models with learned dynamics as neural networks. We compare our approach with leading methods using sum-of-squares programming, reinforcement learning, and model predictive control. Results show that our methods indeed can handle a broader class of systems with less tracking error and faster execution speed. Code is available at https://github.com/sundw2014/C3M.

Cite this Paper

BibTeX
@InProceedings{pmlr-v155-sun21b, title = {Learning Certified Control Using Contraction Metric}, author = {Sun, Dawei and Jha, Susmit and Fan, Chuchu}, booktitle = {Proceedings of the 2020 Conference on Robot Learning}, pages = {1519--1539}, year = {2021}, editor = {Kober, Jens and Ramos, Fabio and Tomlin, Claire}, volume = {155}, series = {Proceedings of Machine Learning Research}, month = {16--18 Nov}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v155/sun21b/sun21b.pdf}, url = {https://proceedings.mlr.press/v155/sun21b.html}, abstract = {In this paper, we solve the problem of finding a certified control policy that drives a robot from any given initial state and under any bounded disturbance to the desired reference trajectory, with guarantees on the convergence or bounds on the tracking error. Such a controller is crucial in safe motion planning. We leverage the advanced theory in Control Contraction Metric and design a learning framework based on neural networks to co-synthesize the contraction metric and the controller for control-affine systems. We further provide methods to validate the convergence and bounded error guarantees. We demonstrate the performance of our method using a suite of challenging robotic models, including models with learned dynamics as neural networks. We compare our approach with leading methods using sum-of-squares programming, reinforcement learning, and model predictive control. Results show that our methods indeed can handle a broader class of systems with less tracking error and faster execution speed. Code is available at https://github.com/sundw2014/C3M.} }
Endnote
%0 Conference Paper %T Learning Certified Control Using Contraction Metric %A Dawei Sun %A Susmit Jha %A Chuchu Fan %B Proceedings of the 2020 Conference on Robot Learning %C Proceedings of Machine Learning Research %D 2021 %E Jens Kober %E Fabio Ramos %E Claire Tomlin %F pmlr-v155-sun21b %I PMLR %P 1519--1539 %U https://proceedings.mlr.press/v155/sun21b.html %V 155 %X In this paper, we solve the problem of finding a certified control policy that drives a robot from any given initial state and under any bounded disturbance to the desired reference trajectory, with guarantees on the convergence or bounds on the tracking error. Such a controller is crucial in safe motion planning. We leverage the advanced theory in Control Contraction Metric and design a learning framework based on neural networks to co-synthesize the contraction metric and the controller for control-affine systems. We further provide methods to validate the convergence and bounded error guarantees. We demonstrate the performance of our method using a suite of challenging robotic models, including models with learned dynamics as neural networks. We compare our approach with leading methods using sum-of-squares programming, reinforcement learning, and model predictive control. Results show that our methods indeed can handle a broader class of systems with less tracking error and faster execution speed. Code is available at https://github.com/sundw2014/C3M.
APA
Sun, D., Jha, S. & Fan, C.. (2021). Learning Certified Control Using Contraction Metric. Proceedings of the 2020 Conference on Robot Learning, in Proceedings of Machine Learning Research 155:1519-1539 Available from https://proceedings.mlr.press/v155/sun21b.html.

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