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arXiv · 2408.12964

From Time-Invariant to Uniformly Time-Varying Control Barrier Functions: A Constructive Approach

Adrian Wiltz·Dimos V. Dimarogonas
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Abstract

In this paper, we define and analyze a subclass of (time-invariant) Control Barrier Functions (CBF) that have favorable properties for the construction of uniformly timevarying CBFs and thereby for the satisfaction of uniformly time-varying constraints. We call them {\Lambda}-shiftable CBFs where {\Lambda} states the extent by which the CBF can be varied by adding a time-varying function. Moreover, we derive sufficient conditions under which a time-varying CBF can be obtained from a time-invariant one, and we propose a systematic construction method. Advantageous about our approach is that a {\Lambda}-shiftable CBF, once constructed, can be reused for various control objectives. In the end, we relate the class of {\Lambda}-shiftable CBFs to Control Lyapunov Functions (CLF), and we illustrate the application of our results with a relevant simulation example.

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Adrian Wiltz, Dimos V. Dimarogonas. 2024-08-23. From Time-Invariant to Uniformly Time-Varying Control Barrier Functions: A Constructive Approach. https://arxiv.org/abs/2408.12964

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