Characterizing Smooth Safety Filters via the Implicit Function Theorem

Max H. Cohen; Pio Ong; Gilbert Bahati; Aaron D. Ames

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arXiv · 2309.12614

Characterizing Smooth Safety Filters via the Implicit Function Theorem

Max H. Cohen·Pio Ong·Gilbert Bahati·Aaron D. Ames

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Abstract

Optimization-based safety filters, such as control barrier function (CBF) based quadratic programs (QPs), have demonstrated success in controlling autonomous systems to achieve complex goals. These CBF-QPs can be shown to be continuous, but are generally not smooth, let alone continuously differentiable. In this paper, we present a general characterization of smooth safety filters -- smooth controllers that guarantee safety in a minimally invasive fashion -- based on the Implicit Function Theorem. This characterization leads to families of smooth universal formulas for safety-critical controllers that quantify the conservatism of the resulting safety filter, the utility of which is demonstrated through illustrative examples.

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BibTeX RIS

Max H. Cohen, Pio Ong, Gilbert Bahati, Aaron D. Ames. 2023-09-22. Characterizing Smooth Safety Filters via the Implicit Function Theorem. https://arxiv.org/abs/2309.12614

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