Learning Performance-oriented Control Barrier Functions Under Complex Safety Constraints and Limited Actuation

Lakshmideepakreddy Manda, Shaoru Chen, Mahyar Fazlyab
Proceedings of The 8th Conference on Robot Learning, PMLR 270:4793-4804, 2025.

Abstract

Control Barrier Functions (CBFs) offer an elegant framework for constraining nonlinear control system dynamics to an invariant subset of a pre-specified safe set. However, finding a CBF that simultaneously promotes performance by maximizing the resulting control invariant set while accommodating complex safety constraints, especially in high relative degree systems with actuation constraints, remains a significant challenge. In this work, we propose a novel self-supervised learning framework that holistically addresses these hurdles. Given a Boolean composition of multiple state constraints defining the safe set, our approach begins by constructing a smooth function whose zero superlevel set provides an inner approximation of the safe set. This function is then used with a smooth neural network to parameterize the CBF candidate. Finally, we design a physics-informed training loss function based on a Hamilton-Jacobi Partial Differential Equation (PDE) to train the PINN-CBF and enlarge the volume of the induced control invariant set. We demonstrate the effectiveness of our approach on a 2D double integrator (DI) system and a 7D fixed-wing aircraft system (F16).

Cite this Paper

BibTeX
@InProceedings{pmlr-v270-manda25a, title = {Learning Performance-oriented Control Barrier Functions Under Complex Safety Constraints and Limited Actuation}, author = {Manda, Lakshmideepakreddy and Chen, Shaoru and Fazlyab, Mahyar}, booktitle = {Proceedings of The 8th Conference on Robot Learning}, pages = {4793--4804}, year = {2025}, editor = {Agrawal, Pulkit and Kroemer, Oliver and Burgard, Wolfram}, volume = {270}, series = {Proceedings of Machine Learning Research}, month = {06--09 Nov}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v270/main/assets/manda25a/manda25a.pdf}, url = {https://proceedings.mlr.press/v270/manda25a.html}, abstract = {Control Barrier Functions (CBFs) offer an elegant framework for constraining nonlinear control system dynamics to an invariant subset of a pre-specified safe set. However, finding a CBF that simultaneously promotes performance by maximizing the resulting control invariant set while accommodating complex safety constraints, especially in high relative degree systems with actuation constraints, remains a significant challenge. In this work, we propose a novel self-supervised learning framework that holistically addresses these hurdles. Given a Boolean composition of multiple state constraints defining the safe set, our approach begins by constructing a smooth function whose zero superlevel set provides an inner approximation of the safe set. This function is then used with a smooth neural network to parameterize the CBF candidate. Finally, we design a physics-informed training loss function based on a Hamilton-Jacobi Partial Differential Equation (PDE) to train the PINN-CBF and enlarge the volume of the induced control invariant set. We demonstrate the effectiveness of our approach on a 2D double integrator (DI) system and a 7D fixed-wing aircraft system (F16).} }
Endnote
%0 Conference Paper %T Learning Performance-oriented Control Barrier Functions Under Complex Safety Constraints and Limited Actuation %A Lakshmideepakreddy Manda %A Shaoru Chen %A Mahyar Fazlyab %B Proceedings of The 8th Conference on Robot Learning %C Proceedings of Machine Learning Research %D 2025 %E Pulkit Agrawal %E Oliver Kroemer %E Wolfram Burgard %F pmlr-v270-manda25a %I PMLR %P 4793--4804 %U https://proceedings.mlr.press/v270/manda25a.html %V 270 %X Control Barrier Functions (CBFs) offer an elegant framework for constraining nonlinear control system dynamics to an invariant subset of a pre-specified safe set. However, finding a CBF that simultaneously promotes performance by maximizing the resulting control invariant set while accommodating complex safety constraints, especially in high relative degree systems with actuation constraints, remains a significant challenge. In this work, we propose a novel self-supervised learning framework that holistically addresses these hurdles. Given a Boolean composition of multiple state constraints defining the safe set, our approach begins by constructing a smooth function whose zero superlevel set provides an inner approximation of the safe set. This function is then used with a smooth neural network to parameterize the CBF candidate. Finally, we design a physics-informed training loss function based on a Hamilton-Jacobi Partial Differential Equation (PDE) to train the PINN-CBF and enlarge the volume of the induced control invariant set. We demonstrate the effectiveness of our approach on a 2D double integrator (DI) system and a 7D fixed-wing aircraft system (F16).
APA
Manda, L., Chen, S. & Fazlyab, M.. (2025). Learning Performance-oriented Control Barrier Functions Under Complex Safety Constraints and Limited Actuation. Proceedings of The 8th Conference on Robot Learning, in Proceedings of Machine Learning Research 270:4793-4804 Available from https://proceedings.mlr.press/v270/manda25a.html.

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