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arXiv · 2503.15014

High-Order Control Barrier Functions: Insights and a Truncated Taylor-Based Formulation

Jianye Xu·Bassam Alrifaee
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Abstract

We examine the complexity of the standard High-Order Control Barrier Function (HOCBF) approach and propose a truncated Taylor-based approach that reduces design parameters. First, we derive the explicit inequality condition for the HOCBF approach and show that the corresponding equality condition sets a lower bound on the barrier function value that regulates its decay rate. Next, we present our Truncated Taylor CBF (TTCBF), which uses a truncated Taylor series to approximate the discrete-time CBF condition. While the standard HOCBF approach requires multiple class K functions, leading to more design parameters as the constraint's relative degree increases, our TTCBF approach requires only one. We support our theoretical findings in numerical collision-avoidance experiments and show that our approach ensures safety while reducing design complexity.

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Jianye Xu, Bassam Alrifaee. 2025-03-19. High-Order Control Barrier Functions: Insights and a Truncated Taylor-Based Formulation. https://arxiv.org/abs/2503.15014

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