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Safe Backstepping with Control Barrier Functions

Taylor, Andrew J. and Ong, Pio and Molnár, Tamás G. and Ames, Aaron D. (2022) Safe Backstepping with Control Barrier Functions. . (Unpublished)

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Complex control systems are often described in a layered fashion, represented as higher-order systems where the inputs appear after a chain of integrators. While Control Barrier Functions (CBFs) have proven to be powerful tools for safety-critical controller design of nonlinear systems, their application to higher-order systems adds complexity to the controller synthesis process -- it necessitates dynamically extending the CBF to include higher order terms, which consequently modifies the safe set in complex ways. We propose an alternative approach for addressing safety of higher-order systems through Control Barrier Function Backstepping. Drawing inspiration from the method of Lyapunov backstepping, we provide a constructive framework for synthesizing safety-critical controllers and CBFs for higher-order systems from a top-level dynamics safety specification and controller design. Furthermore, we integrate the proposed method with Lyapunov backstepping, allowing the tasks of stability and safety to be expressed individually but achieved jointly. We demonstrate the efficacy of this approach in simulation.

Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper
Taylor, Andrew J.0000-0002-5990-590X
Ong, Pio0000-0002-9665-1320
Molnár, Tamás G.0000-0002-9379-7121
Ames, Aaron D.0000-0003-0848-3177
Additional Information:This research is supported in part by Ford, the National Science Foundation (CPS Award #1932091, CMMI Award #1923239), Raytheon Technologies, Aerovironment and Dow (#227027AT).
Group:Center for Autonomous Systems and Technologies (CAST)
Funding AgencyGrant Number
Ford Motor CompanyUNSPECIFIED
Raytheon CompanyUNSPECIFIED
Dow Chemical Company227027AT
Record Number:CaltechAUTHORS:20220714-194252464
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:115560
Deposited By: George Porter
Deposited On:15 Jul 2022 22:37
Last Modified:15 Jul 2022 22:37

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