From Specification to Certification: TORQ-Ordered Rulebooks and Robust HOCBF Optimization for Safe Autonomous Driving

Autonomous vehicle (AV) planners must satisfy complex, often conflicting, safety constraints, traffic laws, and comfort norms. Conventional methods like formal logics and optimal control may fail under rule conflicts, while learning- based policies lack the necessary formal guarantees for certifica- tion. This paper introduces a unified rulebook framework that encodes heterogeneous driving rules as differentiable violation metrics structured by total order over equivalence classes (TORQ). This removes rule incomparability and enables lexi- cographical optimization of trajectories. The specification inte- grates into real-time control using robust High-Order Control Barrier Functions (HOCBFs) and Control Lyapunov Functions (CLFs) solved via Sequential Quadratic Programming (SQP). A recursive relaxation algorithm maintains the hierarchy of the rules, allowing violations of only the lowest-priority rules neces- sary to resolve conflicts. Extensive simulations, including urban intersections and lane drift scenarios on roads, demonstrate that the system consistently prioritizes high-level safety mandates. By combining formal specification, real-time synthesis, and verification, this framework offers a robust, certifiable, and transparent approach to AV behavior planning.