TTCBF: A Truncated Taylor Control Barrier Function for High-Order Safety Constraints

arXiv (Cornell University)

Abstract

Control Barrier Functions (CBFs) enforce safety by rendering a prescribed safe set forward invariant. However, standard CBFs are limited to safety constraints with relative degree one, while High-Order CBF (HOCBF) methods address higher relative degree at the cost of introducing a chain of auxiliary functions and multiple class K functions whose tuning scales with the relative degree. In this paper, we introduce a Truncated Taylor Control Barrier Function (TTCBF), which generalizes standard discrete-time CBFs to consider high-order safety constraints and requires only one class K function, independent of the relative degree. We also propose an adaptive variant, adaptive TTCBF (aTTCBF), that optimizes an online gain on the class K function to improve adaptability, while requiring fewer control design parameters than existing adaptive HOCBF variants. Numerical experiments in a relative-degree-six spring-mass system and a cluttered corridor navigation validate the above theoretical findings.

Authors 2

1. Jianye Xu Aachen Chair of Embedded Software

   RWTH Aachen University

   Affiliation as printed

   Chair of Embedded Software , RWTH Aachen University , Aachen 52072 , Germany

2. Bassam Alrifaee

   Universität der Bundeswehr München

   Affiliation as printed

   Department of Aerospace Engineering , University of the Bundeswehr Munich , Munich 85579 , Germany