← 研踪 PaperTrailarXiv:2611.07537 · v1
Unified Overview of Safety Certificate Functions: Techniques from Hamilton--Jacobi Reachability and Control Barrier Functions
首次提交 2026-11-05 14:47
版本更新 2026-11-05 14:47
雷达观测 2026-11-06 11:06
摘要
Safety is a central concern in modern autonomous systems. Safety certificates---functions whose existence guarantees that a system meets its safety specification---have long been used as a principled tool for rigorously reasoning about safety. Methods for synthesizing such certificates are scattered across research areas, with little guidance on when to use a particular approach. This tutorial provides a holistic treatment of safety certificate synthesis centered on two widely used families: Hamilton--Jacobi (HJ) reachability analysis and control barrier functions (CBFs). For each family of methods, we first introduce its general formulation, along with classical and learning-based tools for certificate synthesis. Next, we introduce two benchmark problems consisting of vehicle systems of differing complexity to assess the certificate quality of different synthesis methods and their effectiveness in safety-critical control. We use these benchmarks to compare various methods and provide practical guidance for selecting an approach.
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v1 · 2026-11-05 14:47 · 最新观测版本
Unified Overview of Safety Certificate Functions: Techniques from Hamilton--Jacobi Reachability and Control Barrier Functions
Safety is a central concern in modern autonomous systems. Safety certificates---functions whose existence guarantees that a system meets its safety specification---have long been used as a principled tool for rigorously reasoning about safety. Methods for synthesizing such certificates are scattered across research areas, with little guidance on when to use a particular approach. This tutorial provides a holistic treatment of safety certificate synthesis centered on two widely used families: Hamilton--Jacobi (HJ) reachability analysis and control barrier functions (CBFs). For each family of methods, we first introduce its general formulation, along with classical and learning-based tools for certificate synthesis. Next, we introduce two benchmark problems consisting of vehicle systems of differing complexity to assess the certificate quality of different synthesis methods and their effectiveness in safety-critical control. We use these benchmarks to compare various methods and provide practical guidance for selecting an approach.
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