High Relative Degree Control Barrier Functions Under Input Constraints

TL;DR

This paper develops methods to ensure safety constraints with high-relative-degree functions in systems with input limits, using Zeroing Control Barrier Functions to guarantee states stay within safe sets.

Contribution

It introduces a novel approach to convert high-relative-degree constraints into ZCBFs under input constraints, including a general form and a special case for certain systems.

Findings

Proposed ZCBF formulations ensure forward invariance under input constraints.

Comparison shows improved safety guarantees over prior methods.

Case study demonstrates effectiveness in asteroid observation control.

Abstract

This paper presents methodologies for ensuring forward invariance of sublevel sets of constraint functions with high-relative-degree with respect to the system dynamics and in the presence of input constraints. We show that such constraint functions can be converted into special Zeroing Control Barrier Functions (ZCBFs), which, by construction, generate sufficient conditions for rendering the state always inside a sublevel set of the constraint function in the presence of input constraints. We present a general form for one such ZCBF, as well as a special case applicable to a specific class of systems. We conclude with a comparison of system trajectories under the two ZCBFs developed and prior literature, and a case study for an asteroid observation problem using quadratic-program based controllers to enforce the ZCBF condition.