Verified Path Following Using Neural Control Lyapunov Functions

Alec Reed, Guillaume O Berger, Sriram Sankaranarayanan, Chris Heckman
Proceedings of The 6th Conference on Robot Learning, PMLR 205:1949-1958, 2023.

Abstract

We present a framework that uses control Lyapunov functions (CLFs) to implement provably stable path-following controllers for autonomous mobile platforms. Our approach is based on learning a guaranteed CLF for path following by using recent approaches — combining machine learning with automated theorem proving — to train a neural network feedback law along with a CLF that guarantees stabilization for driving along low-curvature reference paths. We discuss how key properties of the CLF can be exploited to extend the range of the curvatures for which the stability guarantees remain valid. We then demonstrate that our approach yields a controller that obeys theoretical guarantees in simulation, but also performs well in practice. We show our method is both a verified method of control and better than a common MPC implementation in computation time. Additionally, we implement the controller on-board on a $\frac18$-scale autonomous vehicle testing platform and present results for various robust path following scenarios.

Cite this Paper

BibTeX
@InProceedings{pmlr-v205-reed23a, title = {Verified Path Following Using Neural Control Lyapunov Functions}, author = {Reed, Alec and Berger, Guillaume O and Sankaranarayanan, Sriram and Heckman, Chris}, booktitle = {Proceedings of The 6th Conference on Robot Learning}, pages = {1949--1958}, year = {2023}, editor = {Liu, Karen and Kulic, Dana and Ichnowski, Jeff}, volume = {205}, series = {Proceedings of Machine Learning Research}, month = {14--18 Dec}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v205/reed23a/reed23a.pdf}, url = {https://proceedings.mlr.press/v205/reed23a.html}, abstract = {We present a framework that uses control Lyapunov functions (CLFs) to implement provably stable path-following controllers for autonomous mobile platforms. Our approach is based on learning a guaranteed CLF for path following by using recent approaches — combining machine learning with automated theorem proving — to train a neural network feedback law along with a CLF that guarantees stabilization for driving along low-curvature reference paths. We discuss how key properties of the CLF can be exploited to extend the range of the curvatures for which the stability guarantees remain valid. We then demonstrate that our approach yields a controller that obeys theoretical guarantees in simulation, but also performs well in practice. We show our method is both a verified method of control and better than a common MPC implementation in computation time. Additionally, we implement the controller on-board on a $\frac18$-scale autonomous vehicle testing platform and present results for various robust path following scenarios.} }
Endnote
%0 Conference Paper %T Verified Path Following Using Neural Control Lyapunov Functions %A Alec Reed %A Guillaume O Berger %A Sriram Sankaranarayanan %A Chris Heckman %B Proceedings of The 6th Conference on Robot Learning %C Proceedings of Machine Learning Research %D 2023 %E Karen Liu %E Dana Kulic %E Jeff Ichnowski %F pmlr-v205-reed23a %I PMLR %P 1949--1958 %U https://proceedings.mlr.press/v205/reed23a.html %V 205 %X We present a framework that uses control Lyapunov functions (CLFs) to implement provably stable path-following controllers for autonomous mobile platforms. Our approach is based on learning a guaranteed CLF for path following by using recent approaches — combining machine learning with automated theorem proving — to train a neural network feedback law along with a CLF that guarantees stabilization for driving along low-curvature reference paths. We discuss how key properties of the CLF can be exploited to extend the range of the curvatures for which the stability guarantees remain valid. We then demonstrate that our approach yields a controller that obeys theoretical guarantees in simulation, but also performs well in practice. We show our method is both a verified method of control and better than a common MPC implementation in computation time. Additionally, we implement the controller on-board on a $\frac18$-scale autonomous vehicle testing platform and present results for various robust path following scenarios.
APA
Reed, A., Berger, G.O., Sankaranarayanan, S. & Heckman, C.. (2023). Verified Path Following Using Neural Control Lyapunov Functions. Proceedings of The 6th Conference on Robot Learning, in Proceedings of Machine Learning Research 205:1949-1958 Available from https://proceedings.mlr.press/v205/reed23a.html.

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