High Relative Degree Control Barrier Functions Under Input Constraints
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.
Keywords
Cite
@article{arxiv.2106.10345,
title = {High Relative Degree Control Barrier Functions Under Input Constraints},
author = {Joseph Breeden and Dimitra Panagou},
journal= {arXiv preprint arXiv:2106.10345},
year = {2021}
}
Comments
Part of Proceedings of 60th IEEE Conference on Decision and Control (2021), extended to include more information about the simulation computations