Decoupled Design of Time-Varying Control Barrier Functions via Equivariances

TL;DR

This paper introduces a systematic, structurally-aware approach for designing time-varying control barrier functions that decouples the time variation design from the core CBF construction, enhancing computational efficiency and applicability in uncertain environments.

Contribution

It presents a novel method leveraging system equivariances to design expressive, decoupled time-varying CBFs, improving flexibility and computational tractability.

Findings

Handles broader class of time-varying constraints

Accounts for input constraints and under-actuation

Requires only qualitative knowledge of constraint variations

Abstract

This article presents a systematic method for designing time-varying Control Barrier Functions (CBF) composed of a time-invariant component and multiple time-dependent components, leveraging structural properties of the system dynamics. The method involves the construction of a specific class of time-invariant CBFs that encode the system's dynamic capabilities with respect to a given constraint, and augments them subsequently with appropriately designed time-dependent transformations. While transformations uniformly varying the time-invariant CBF can be applied to arbitrary systems, transformations exploiting structural properties in the dynamics - equivariances in particular - enable the handling of a broader and more expressive class of time-varying constraints. The article shows how to leverage such properties in the design of time-varying CBFs. The proposed method decouples the design of time variations from the computationally expensive construction of the underlying CBFs, thereby providing a computationally attractive method to the design of time-varying CBFs. The method accounts for input constraints and under-actuation, and requires only qualitative knowledge on the time-variation of the constraints making it suitable to the application in uncertain environments.