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Backup Control Barrier Functions: Formulation and Comparative Study

Chen, Yuxiao and Jankovic, Mrdjan and Santillo, Mario and Ames, Aaron D. (2021) Backup Control Barrier Functions: Formulation and Comparative Study. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20210510-141404463

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Abstract

The backup control barrier function (CBF) was recently proposed as a tractable formulation that guarantees the feasibility of the CBF quadratic programming (QP) via an implicitly defined control invariant set. The control invariant set is based on a fixed backup policy and evaluated online by forward integrating the dynamics under the backup policy. This paper is intended as a tutorial of the backup CBF approach and a comparative study to some benchmarks. First, the backup CBF approach is presented step by step with the underlying math explained in detail. Second, we prove that the backup CBF always has a relative degree 1 under mild assumptions. Third, the backup CBF approach is compared with benchmarks such as Hamilton Jacobi PDE and Sum-of-Squares on the computation of control invariant sets, which shows that one can obtain a control invariant set close to the maximum control invariant set under a good backup policy for many practical problems.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/2104.11332arXivDiscussion Paper
ORCID:
AuthorORCID
Chen, Yuxiao0000-0001-5276-7156
Jankovic, Mrdjan0000-0002-4591-9462
Santillo, Mario0000-0001-9152-4747
Ames, Aaron D.0000-0003-0848-3177
Additional Information:Attribution 4.0 International (CC BY 4.0).
Record Number:CaltechAUTHORS:20210510-141404463
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210510-141404463
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:109061
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:10 May 2021 21:20
Last Modified:10 May 2021 21:20

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