[Paper Review] Are commercially implemented adaptive cruise control systems string stable?

George Gunter, Derek Gloudemans+10 more|arXiv (Cornell University)|May 6, 2019

Traffic control and management48 references268 citations

TL;DR

The study tests seven 2018 ACC-equipped vehicles and finds all are string unstable; it calibrates a data-driven delay differential equation model from over 1,200 miles of driving and validates instability with an eight-vehicle platoon.

ABSTRACT

In this article, we assess the string stability of seven 2018 model year adaptive cruise control (ACC) equipped vehicles that are widely available in the US market. Seven distinct vehicle models from two different vehicle makes are analyzed using data collected from more than 1,200 miles of driving in car-following experiments with ACC engaged by the follower vehicle. The resulting dataset is used to identify the parameters of a linear second order delay differential equation model that approximates the behavior of the black box ACC systems. The string stability of the data-fitted model associated with each vehicle is assessed, and the main finding is that all seven vehicle models have string unstable ACC systems. For one commonly available vehicle model that offers ACC as a standard feature on all trim levels, we validate the string stability finding with a multi-vehicle platoon experiment in which all vehicles are the same year, make, and model. In this test, an initial disturbance of 6 mph is amplified to a 25 mph disturbance, at which point the last vehicle in the platoon is observed to disengage the ACC. The data collected in the driving experiments is made available, representing the largest publicly available comparative driving dataset on ACC equipped vehicles.

Motivation & Objective

• Assess whether current commercial ACC systems are string stable in real-world driving.
• Develop a data-driven, delay-based car-following model that approximates ACC behavior from field data.
• Quantify string stability of each tested ACC system and understand how disturbances propagate in platoons.
• Validate stability findings with multi-vehicle platoon experiments using identical vehicles.

Proposed method

• Model ACC dynamics with a delay differential equation similar to an optimal velocity with relative-velocity term (OVRV) and a time delay: ˙s_i(t)=v_{i-1}(t)−v_i(t), ˙v_i(t)=k1[s_i(t−τ)−η−t_h v_i(t)]+k2[v_{i−1}(t−τ)−v_i(t)].
• Calibrate parameters (k1, k2, t_h, τ, η) by minimizing mean squared error between simulated and measured follower velocity using NOMAD on training data.
• Analyze string stability via the head-to-tail transfer function Γ(z) from the delayed system and use DDE-BIFTOOL to explore parameter regions for stability.
• Collect data from 1,200+ miles of driving across two makes and seven models, and perform two-vehicle tests plus an eight-vehicle platoon test for validation.
• Utilize open-field data and publish datasets for public use.

Experimental results

Research questions

• RQ1 Are seven commercially available 2018 ACC systems string stable in real-world driving?
• RQ2 Can a data-driven delayed car-following model accurately reproduce ACC behavior across different vehicle models?
• RQ3 Do calibrated ACC models exhibit string instability in simulated platoons?
• RQ4 Does a large platoon validate the instability observed in two-vehicle tests and lead to ACC disengagement in practice?

Key findings

• All seven tested ACC models are string unstable under both minimum and maximum following settings.
• Calibrated model parameters vary across vehicles but yield unstable stability classifications (k1, k2, t_h, τ, η differ per vehicle).
• In an eight-vehicle platoon, a 6 mph disturbance amplified to 25 mph before the last vehicle disengaged ACC, demonstrating practical instability.
• Two-vehicle tests and simulations show disturbance growth across the platoon for all vehicles studied.
• The publicly released driving data represent the largest open dataset for ACC-equipped vehicle testing to date.