Control Barrier Function Synthesis for Nonlinear Systems with Dual Relative Degree

Fuente: arXiv
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Main Authors: Bahati, Gilbert, Cosner, Ryan K., Cohen, Max H., Bena, Ryan M., Ames, Aaron D.
Format: Preprint
Published: 2025
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author Bahati, Gilbert
Cosner, Ryan K.
Cohen, Max H.
Bena, Ryan M.
Ames, Aaron D.
author_facet Bahati, Gilbert
Cosner, Ryan K.
Cohen, Max H.
Bena, Ryan M.
Ames, Aaron D.
contents Control barrier functions (CBFs) are a powerful tool for synthesizing safe control actions; however, constructing CBFs remains difficult for general nonlinear systems. In this work, we provide a constructive framework for synthesizing CBFs for systems with dual relative degree -- where different inputs influence the outputs at two different orders of differentiation; this is common in systems with orientation-based actuation, such as unicycles and quadrotors. In particular, we propose dual relative degree CBFs (DRD-CBFs) and show that these DRD-CBFs can be constructively synthesized and used to guarantee system safety. Our method constructs DRD-CBFs by leveraging the dual relative degree property -- combining a CBF for an integrator chain with a Lyapunov function certifying the tracking of safe inputs generated for this linear system. We apply these results to dual relative degree systems, both in simulation and experimentally on hardware using quadruped and quadrotor robotic platforms.
format Preprint
id arxiv_https___arxiv_org_abs_2504_00397
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Control Barrier Function Synthesis for Nonlinear Systems with Dual Relative Degree
Bahati, Gilbert
Cosner, Ryan K.
Cohen, Max H.
Bena, Ryan M.
Ames, Aaron D.
Systems and Control
Control barrier functions (CBFs) are a powerful tool for synthesizing safe control actions; however, constructing CBFs remains difficult for general nonlinear systems. In this work, we provide a constructive framework for synthesizing CBFs for systems with dual relative degree -- where different inputs influence the outputs at two different orders of differentiation; this is common in systems with orientation-based actuation, such as unicycles and quadrotors. In particular, we propose dual relative degree CBFs (DRD-CBFs) and show that these DRD-CBFs can be constructively synthesized and used to guarantee system safety. Our method constructs DRD-CBFs by leveraging the dual relative degree property -- combining a CBF for an integrator chain with a Lyapunov function certifying the tracking of safe inputs generated for this linear system. We apply these results to dual relative degree systems, both in simulation and experimentally on hardware using quadruped and quadrotor robotic platforms.
title Control Barrier Function Synthesis for Nonlinear Systems with Dual Relative Degree
topic Systems and Control
url https://arxiv.org/abs/2504.00397