Reproduce “High-Order Control Barrier Functions: Insights and a Truncated Taylor-Based Formulation” on OpenResearch

About this paper

Jianye Xu, Bassam Alrifaee

This research introduces the Truncated Taylor Control Barrier Function (TTCBF) for discrete-time systems, simplifying the design of safety-critical controllers for high relative degree constraints by requiring only a single class K function. The work also provides analytical insights into existing High-Order Control Barrier Functions (HOCBFs), explicitly deriving their safety condition and characterizing an inherent lower bound on the barrier function value.

Key insights

• The safety condition of HOCBFs can be analytically expressed as a single homogeneous linear differential inequality, and its equality form defines a lower bound on the barrier function value that depends on all class K parameters and initial conditions.
• The joint influence of multiple class K parameters in HOCBFs results in complex, non-intuitive tuning behavior for control performance, validating the need for simpler approaches.
• The Truncated Taylor CBF (TTCBF) effectively maintains safety guarantees for high relative degree constraints while drastically reducing design complexity by requiring only one class K function, offering a more straightforward tuning process.

Summary by alphaXiv.