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

• URL: http://arxiv.org/abs/2401.05629v1
• Date: Thu, 11 Jan 2024 02:51:49 GMT
• Title: Learning Performance-Oriented Control Barrier Functions Under Complex Safety Constraints and Limited Actuation
• Authors: Shaoru Chen, Mahyar Fazlyab
• Abstract summary: Control Barrier Functions (CBFs) provide a framework for designing safety filters for nonlinear control systems. However, finding a CBF that concurrently maximizes the volume of the resulting control invariant set continues to pose a substantial challenge. We propose a novel self-supervised learning framework that holistically addresses these hurdles.
• Score: 8.1585306387285
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Control Barrier Functions (CBFs) provide an elegant framework for designing safety filters for nonlinear control systems by constraining their trajectories to an invariant subset of a prespecified safe set. However, the task of finding a CBF that concurrently maximizes the volume of the resulting control invariant set while accommodating complex safety constraints, particularly in high relative degree systems with actuation constraints, continues to pose a substantial 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 that define the safe set, our approach starts with building a single continuously differentiable function whose 0-superlevel set provides an inner approximation of the safe set. We then use this function together with a smooth neural network to parameterize the CBF candidate. Finally, we design a training loss function based on a Hamilton-Jacobi partial differential equation to train the CBF while enlarging the volume of the induced control invariant set. We demonstrate the effectiveness of our approach via numerical experiments.

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