Vibration-Theoretic Approach to Vulnerability Analysis of Nonlinear Vehicle Platoons

This research explores the inherent vulnerability of nonlinear vehicle platoons characterized by the oscillatory behavior triggered by external perturbations. The perturbation exerted on the vehicle platoon is regarded as an external force on an object. Following the mechanical vibration analysis in mechanics, this research proposes a vibration-theoretic approach that advances our understanding of platoon vulnerability from two aspects. First, the proposed approach introduces damping intensity to characterize vehicular platoon vulnerability, which divides platoon oscillations into two types, i.e., underdamped and overdamped. The damping intensity measures the platoon's recovery strength in responding to perturbations. Second, the proposed approach can obtain the resonance frequency of a nonlinear vehicle platoon, where resonance amplifies platoon oscillation magnitude when the external perturbation frequency equals the platoon's damping oscillation frequency. The main contribution of this research lies in the analytical derivation of the closed-form formulas of damping intensity and resonance frequency. In particular, the proposed approach formulates platoon dynamics under perturbation as a second-order non-homogeneous ordinary differential equation, enabling rigorous derivations and analyses for platoons with complicated nonlinear car-following behaviors. Through simulations built on real-world data, this paper demonstrates that an overdamped vehicle platoon is more robust against perturbations, and an underdamped platoon can be destabilized easily by exerting a perturbation at the platoon's resonance frequency. The theoretical derivations and simulation results shed light on the design of reliable platooning control, either for human-driven or automated vehicles, to suppress the adverse effects of oscillations.