Provably safe and human-like car-following behaviors: Part 1. Analysis of phases and dynamics in standard models
Existing car-following models lack rigorous safety guarantees and provable consistency with human driving behavior. Method: We systematically analyze the phase-plane dynamics of mainstream models (e.g., IDM, Gipps, Newell), formulate a novel multi-order framework—spanning zeroth-order (minimum spacing, comfort), first-order (speed, time headway), and second-order (acceleration/deceleration bounds, braking curves)—and conduct phase-plane modeling, multi-phase dynamical systems analysis, and formal stability and safety proofs. We also rigorously derive the Newell simplified model. Results: Our analysis exposes fundamental deficiencies in existing models regarding safety boundary adherence and human-like behavior consistency. Numerical simulations and empirical validation confirm these insights and establish a solid theoretical foundation for our subsequent multi-phase projection-based car-following model.