Source-linked AI summary
Are commercially implemented adaptive cruise control systems string stable?
George Gunter, Derek Gloudemans, Raphael E. Stern, Sean McQuade, Rahul Bhadani, Matt Bunting, Maria Laura Delle Monache, Roman Lysecky, Benjamin Seibold, Jonathan Sprinkle, Benedetto Piccoli, Daniel B. Work
TL;DR
The paper asks whether commercially available ACC systems achieve string stability in real vehicles. It fits delay differential equation models to car-following data from seven 2018 vehicle models and assesses their stability. All seven systems were string unstable, and an eight-vehicle test amplified a 6 mph disturbance to 25 mph before the last ACC system disengaged.
Problem
The paper examines whether the traffic-flow benefits predicted for ACC systems are achievable with current commercial vehicles.
Method
The study analyzes more than 1,200 miles of car-following data from seven vehicle models and fits delay differential equation models approximating their ACC behavior.
Results
All seven tested ACC systems were string unstable, and an eight-vehicle platoon amplified an initial 6 mph disturbance by an additional 19 mph before the last vehicle lost ACC control.
Takeaways & Limitations
Commercial ACC systems tested here did not provide string-stable behavior, while the collected driving data enables comparative assessment of their performance variation.
Abstract
from arXiv · showhide
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.
I. INTRODUCTION
This study tests whether commercially available ACC systems dissipate or amplify disturbances through vehicle platoons. Field testing of seven 2018 vehicle models found that all tested systems were string unstable.
- Motivation: Commercial ACC is widely available, but its traffic-flow benefits had not been established for vehicles currently on the market.The unresolved question concerned whether present-day commercial systems could achieve the positive throughput and stability effects reported in theory and simulation.
- Concept: String stability means that small perturbations dissipate through a platoon, whereas string instability allows them to amplify.String-unstable ACC systems can contribute to phantom traffic jams that appear without an obvious external cause.
- Study design: The study field-tested seven commercially available ACC systems across two makes and seven 2018 vehicle models.The experiments required a lead vehicle to follow specified speed profiles while a test vehicle followed with ACC engaged.
- Findings: All tested ACC systems were found to be string unstable, a negative result for phantom traffic jam prevention.The work expanded prior testing of commercial ACC systems and supplied experimental data.
- Validation: In an eight-vehicle platoon, a 6 mph disturbance grew to 25 mph before the last vehicle automatically disengaged ACC.The platoon used one leader followed by seven ACC-equipped vehicles, validating the instability finding with identical real vehicles.
II. ADAPTIVE CRUISE CONTROL DYNAMICS, STABILITY AND DATA FITTING
The paper uses a data-calibrated car-following model as a proxy for analyzing the string stability of black-box ACC software. The model approximates ACC behavior and supports stability analysis after calibration from driving data.
- Model definition: The proposed car-following model approximates ACC driving behavior with parameters calibrated from data.It is designed to represent the vehicle dynamics relevant to the stability analysis.
- Stability analysis: String stability is assessed on the calibrated model as a proxy for the black-box code running on the vehicles.This connects measurable driving behavior to an analysis of the embedded ACC system.
A. Model definition
The paper models ACC platoons with an optimal-velocity model that includes relative velocity and sensing delay, then analyzes plant and string stability using ring-road dynamics.
- Model definition: The ACC platoon dynamics use an optimal-velocity model with a relative velocity term and gains k1 and k2.Acceleration depends on the difference between current and desired velocity and on the speed difference from the vehicle ahead.
- Model definition: The desired effective time gap th specifies the spacing policy, while η denotes the jam space gap when vehicles are stationary.At steady state, vehicles share the same speed and maintain the desired effective time gap.
- Model definition: A time delay τ represents systematic sensor delay, with delayed measurements of space gap and lead-vehicle velocity entering the delay differential equation.The model assumes lead-vehicle measurements have larger delays than measurements of the vehicle’s own velocity.
- Stability analysis: The analysis studies a closed-ring platoon because instability on the ring implies string instability for the equivalent straight-road system.Numerical bifurcation analysis varies k1 and k2 while fixing τ, th, and η.
- Stability analysis: String stability is defined by attenuation of disturbances from the head vehicle to the tail vehicle, whereas plant stability concerns asymptotic equilibrium stability.The analysis uses the head vehicle’s velocity perturbation as input and the following vehicle’s perturbation as output.
- Stability analysis: For th = 1.5 s, τ = 0.1 s, k1 = 0.2 1/s2, k2 = 0.2 1/s, and η = 10 m, the model is string unstable and amplifies disturbances.The corresponding closed-ring system is not asymptotically stable.
C. Model calibration
The study calibrates model parameters to reproduce experimental ACC behavior by minimizing velocity prediction error subject to parameter bounds.
- Model calibration: The parameters k1, k2, th, τ, and η are calibrated to reproduce experimental data, with lower and upper bounds imposed.The calibrated parameters are decision variables in the fitting problem.
- Model calibration: Mean square error on velocity compares measured follower velocity with the model’s simulated velocity over the experiment duration.The measured velocity is vm(t), the simulated velocity is v, and T denotes experiment duration.
- Model calibration: The calibration optimization uses measured follower space gap and velocity together with measured leader velocity.The objective determines parameter values for the delay differential equation model.
III. EXPERIMENTAL METHODS
The experiments combine two-vehicle car-following tests for model fitting and an eight-vehicle platoon test to validate string-stability findings for the most common vehicle.
- III. EXPERIMENTAL METHODS: Two-vehicle tests use a lead vehicle with a prescribed speed profile and an ACC-equipped follower vehicle.These tests provide data for calibrating the assumed ACC model and evaluating its fit.
- III. EXPERIMENTAL METHODS: An eight-vehicle experiment places seven identical ACC vehicles behind a lead vehicle that generates a velocity slowdown event.The setup validates the string-stability finding for the most common tested vehicle.
- III. EXPERIMENTAL METHODS: Across all experiments, follower vehicles form a single-lane platoon with longitudinal control supplied by ACC.The lead vehicle follows a pre-specified speed profile.
- III. EXPERIMENTAL METHODS: More than 1,200 miles of driving were recorded, and all collected data were made openly available for public use.The dataset supports comparative analysis of ACC-equipped vehicles.
A. Vehicle fleet
The study tests seven widely available 2018 vehicles from two manufacturers using controlled speed-following experiments that include steady-state and transient conditions.
- A. Vehicle fleet: The fleet contains seven widely available 2018 model-year vehicles from two manufacturers.Six vehicles use traditional internal combustion engines and one is a hybrid electric vehicle.
- A. Vehicle fleet: Testing is conducted above Make 1’s 25 mph minimum ACC operating speed for consistency across manufacturers.Make 2 vehicles can come to a complete stop under ACC.
- A. Vehicle fleet: High-accuracy GPS receivers collect vehicle position and speed, with reported mean position accuracy of 0.24 m and speed error of 0.002 m/s.Antenna locations are recorded to calculate space gaps accurately.
- A. Vehicle fleet: The tests use flat or nearly flat 16 km (10 mile) road sections, including straight highway for high-speed trials.The same lead vehicle is used in each two-vehicle test.
- A. Vehicle fleet: The two-vehicle tests target steady-state following behavior and transient responses to changing lead-vehicle speeds and space gaps.The design includes oscillatory, step, and speed-dip profiles.
- A. Vehicle fleet: Speed-dip tests apply 2.7 m/s (6 mph), 4.5 m/s (10 mph), 6.7 m/s (15 mph), and 8.9 m/s (20 mph) reductions.Each dip is held for 5 seconds before the lead vehicle returns to 24.5 m/s (55 mph).
D. Autonomous test lead vehicle
The CAT Vehicle provides controlled autonomous lead-vehicle operation for the platoon experiments. Its drive-by-wire platform supports commanded acceleration, speed, and steering.
- The CAT Vehicle is a modified Ford Hybrid Escape capable of autonomous or human-controlled operation.
- Its drive-by-wire platform uses multiple control subsystems, a central embedded controller, and a wireless emergency-stop system.
- Closed-loop drive-by-wire control allows users to command the CAT Vehicle’s acceleration, speed, or steering.
- Lower-level commands to the CAT Vehicle use the JAUS communications protocol.
E. Eight vehicle platoon test
The eight-vehicle test uses a controlled lead vehicle and seven identical ACC followers to examine platoon behavior after a speed reduction. The experiment supports assessment of string-stability consequences and comparison with simulations.
- The aggregate-level test uses a platoon experiment to evaluate emergent traffic-flow behavior of ACC vehicles.
- The lead vehicle follows a prespecified speed profile while seven followers drive in one lane to form a large platoon.
- The CAT Vehicle enables consistent velocity commands and greater control over the lead vehicle’s deceleration rate.
- The test begins at 22.4 m/s (50 mph), with seven Vehicle A followers using ACC at the minimum following setting.
- After steady state, the lead vehicle decelerates to 19.7 m/s (44 mph), and follower behavior is observed with a safety chase vehicle following the platoon.
- The results section uses platoon simulations to assess disturbance-growth variability and a platoon experiment to validate those simulations.
A. ACC model calibration results
The study calibrates car-following models against collected ACC data, evaluates their fit and parameter ranges, and determines string stability. All tested vehicles are string unstable under both following settings.
- The calibration problem is solved numerically using constrained optimization, with parameter bounds selected to exclude unrealistic car-following behavior.
- Training uses the first quarter of the 2.7 m/s (6 mph) low-speed oscillatory data, with remaining data reserved for testing.
- The calibrated model closely matches Vehicle A’s recorded follower speed and spacing, including speed overshoot and undershoot, with similar test-data fit.
- The calibrated gains span 0.012 1/s2 to 0.071 1/s2 for k1 and 0.110 1/s to 0.338 1/s for k2, while effective time gaps range from 0.544 s to 2.054 s.
- For Vehicles A through D, theoretical jam space gaps are not physically attainable because ACC disengages below 25 mph.
- Test speed errors are generally low, but spacing errors are larger and increase as vehicle speeds increase.
- All tested vehicles are string unstable under both the minimum and maximum following settings.
B. Platoon simulations under calibrated ACC models
Calibrated ACC models show string-unstable platoon behavior, with disturbance amplification varying across vehicles and following settings. Simulations also identify cases where vehicles disengage ACC or violate spacing constraints as platoon length increases.
- The calibrated models exhibit different string-unstable behaviors across the tested ACC vehicles.The simulations characterize variability in disturbance amplification and minimum spacing across vehicle models.
- 6 mph (2.7 m/s) initial disturbance amplifies to 21 mph (9.4 m/s) in the eight-vehicle Vehicle A simulation under the minimum following setting.The simulated follower vehicles use the calibrated Vehicle A model and the lead trajectory from the platoon experiment.
- Vehicle A remains string unstable under the maximum following setting, although the perturbation growth rate is much smaller than under the minimum setting.The same lead-vehicle speed profile is used for both following settings.
- For almost all vehicles, disturbances amplify faster under minimum than maximum following, whereas Vehicles E and C show nearly identical rates across settings.Vehicle C does not disengage for simulated platoons up to 15 vehicles, but longer platoons cause disengagement for all vehicle models.
- Vehicle F at the minimum following setting disengages for the shortest simulated platoon length, with disengagement occurring for platoons longer than four vehicles.Simulations terminate when vehicle speed falls below the minimum ACC operating speed or inter-vehicle spacing becomes negative.
C. Validation via a platoon experiment
An eight-vehicle experiment with one lead vehicle and seven identical ACC followers confirms the simulated string instability. Each follower brakes more severely than its predecessor, and the last vehicle hands control back to the human driver after dropping below the ACC operating-speed threshold.
- The experiment confirms string instability in an eight-vehicle platoon with identical vehicles.The confirmation is based on the progressively amplified braking response and ACC disengagement of the last vehicle.
- A 2.7 m/s (6 mph) lead-vehicle slowdown produces progressively more extreme braking responses through the seven ACC followers.The experiment uses identical Vehicle A followers with ACC engaged at following setting 1.
- 11.2 m/s (25 mph) is the last follower’s minimum ACC operating-speed threshold, below which control returns to the human driver.The last vehicle’s response is large enough to cross this threshold.
- The experiment produces a larger final speed drop than simulation: below 11.2 m/s (25 mph) experimentally versus slightly below 15 m/s (33.6 mph) in simulation.This comparison indicates that the calibrated simulation underestimates the observed extent of string instability.
V. CONCLUSION
The study tests commercial ACC string stability across seven vehicle models from two makes using calibrated delay-differential models and an identical-vehicle platoon experiment. All tested ACC systems are string unstable, while the authors identify modeling and scope boundaries for interpreting the results.
- Seven vehicle models from two makes are tested for ACC string stability using more than 1,200 miles of car-following data.The study aims to quantify system stability and capture performance variation across commercial systems.
- Linear second-order delay differential equation models are calibrated under minimum and maximum following settings for the tested vehicles.The models approximate the driving behavior of ACC-controlled vehicles and are then analyzed for stability.
- All vehicles under all following settings are found to be string unstable.An eight-vehicle platoon test with identical vehicles confirms this finding experimentally.
- 6 mph disturbance is amplified by an additional 19 mph before the last vehicle falls below the ACC operating-speed threshold and returns control to the human driver.This result comes from the identical-vehicle eight-vehicle platoon test.
- Commercial ACC is assessed because it may affect traffic-flow stability and the occurrence of phantom jams.The paper focuses on systems available on commercial cars, including ACC offered as a standard feature.
- Higher-fidelity ACC models may be needed for vehicle classes with distinct acceleration and deceleration behaviors, such as hybrid vehicles.The authors also caution that commercial ACC may outperform human drivers in perturbation-growth rates, but comparisons with human drivers remain future work.