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.

Bib

@inproceedings{DBLP:conf/cdc/BreedenP21,
  author       = {Joseph Breeden and
                  Dimitra Panagou},
  title        = {High Relative Degree Control Barrier Functions Under Input Constraints},
  booktitle    = {2021 60th {IEEE} Conference on Decision and Control (CDC), Austin,
                  TX, USA, December 14-17, 2021},
  pages        = {6119--6124},
  publisher    = {{IEEE}},
  year         = {2021},
  url          = {https://doi.org/10.1109/CDC45484.2021.9683705},
  doi          = {10.1109/CDC45484.2021.9683705},
  timestamp    = {Tue, 17 May 2022 15:53:17 +0200},
  biburl       = {https://dblp.org/rec/conf/cdc/BreedenP21.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}