🤖 AI Summary
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.
📝 Abstract
Trajectory planning is essential for ensuring safe driving in the face of uncertainties related to communication, sensing, and dynamic factors such as weather, road conditions, policies, and other road users. Existing car-following models often lack rigorous safety proofs and the ability to replicate human-like driving behaviors consistently. This article applies multi-phase dynamical systems analysis to well-known car-following models to highlight the characteristics and limitations of existing approaches. We begin by formulating fundamental principles for safe and human-like car-following behaviors, which include zeroth-order principles for comfort and minimum jam spacings, first-order principles for speeds and time gaps, and second-order principles for comfort acceleration/deceleration bounds as well as braking profiles. From a set of these zeroth- and first-order principles, we derive Newell's simplified car-following model. Subsequently, we analyze phases within the speed-spacing plane for the stationary lead-vehicle problem in Newell's model and its extensions, which incorporate both bounded acceleration and deceleration. We then analyze the performance of the Intelligent Driver Model and the Gipps model. Through this analysis, we highlight the limitations of these models with respect to some of the aforementioned principles. Numerical simulations and empirical observations validate the theoretical insights. Finally, we discuss future research directions to further integrate safety, human-like behaviors, and vehicular automation in car-following models, which are addressed in Part 2 of this study citep{jin2025WA20-02_Part2}, where we develop a novel multi-phase projection-based car-following model that addresses the limitations identified here.