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

TL;DR

This paper introduces a systematic method to construct uniformly time-varying control barrier functions from time-invariant ones, enabling better handling of time-varying constraints in control systems.

Contribution

It defines {bcla}-shiftable CBFs, provides conditions for deriving time-varying CBFs from time-invariant ones, and relates these to Control Lyapunov Functions, with a practical simulation example.

Findings

{bcla}-shiftable CBFs can be reused for different control tasks.

The systematic construction method ensures satisfaction of time-varying constraints.

Simulation demonstrates the effectiveness of the proposed approach.

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.