Keywords

1 Introduction

Adaptive Cruise Control (ACC) is a driving assistance feature that provides the driver with additional comfort when traveling on highways by adjusting the speed while following a leader vehicle. ACC is commonly classified as an SAE J3016 Level 1 system (or Level 2 when coupled with lane-centering assistance) meaning that the driver will always have to be ready to take control at any time and the same will remain legally liable. ACCs have been investigated for a long time both via theoretical simulation studies [7] and, more recently, via real-world experiments [1, 5]. Frequently, the two types of assessment have led to contrasting outcomes: on one side theoretical studies have envisaged a beneficial effect of ACC introduction based on the adopted assumptions, on the other side, the actual mass-market ACCs did not prove to deliver increased stability performance with respect to human driving [1].

Albeit higher-level automation systems, i.e., systems where the feature provides proper driving automation thus transferring the legal liability to the manufacturer in contrast to driving assistance, are gradually approaching the market [2], driving assistance still has the largest market penetration share.

To the end of monitoring the evolution of driving assistance technologies, the authors have organized a testing campaign in Germany involving three vehicles featuring advanced Level 2 systems. During the testing, it became apparent to the driver sitting in one specific vehicle that the same was never able to achieve a constant speed while following a leader. The present contribution characterizes the specific instability phenomenon. The paper reports on the effect and the potential implications of a similar ACC design on the transportation network if left uncorrected by the car manufacturer. The effort leverages a mixture of experimental characterization together with a simulation-based approach to enlarge the scope.

2 Methodology

2.1 Perturbation Identification

The experimental campaign took place in November 2023, about 3000 km were driven in Germany using 3 vehicles equipped with state-of-the-art SAE J3016 Level 2 systems while trying to maximize the use of the driving assistance features. The vehicles were instrumented with external GNSS antennas to record the positions and velocities. To isolate the oscillation effect, the testers drove for long sections of the motorway while the leader kept a constant speed with no disturbance upfront. By repeating the procedure multiple times, 40 intervals were identified covering a range of different target speeds. The oscillations were analyzed by removing the mean component of the speed and fitting a sine wave to the residual speed profile. The sine functions calibration procedure returned the wave’s frequency, amplitude, and phase. The latter signal was disregarded as it did not provide useful information. On the contrary, two distributions could be obtained for the oscillation frequency and amplitude, respectively, by repeating the sine function fitting procedure to all the 40 intervals produced.

Additionally, the extra fuel consumption associated with the oscillation behavior was characterized using the CO\(_2\)MPAS software tool (https://code.europa.eu/jrc-ldv/co2mpas) developed by the Joint Research Centre for European Commission to establish the fuel/energy consumption of passenger cars and light duty vehicles. The CO\(_2\)MPAS microsimulation tool has been executed on the trajectory exhibiting the oscillation and on the same trajectory subject to a non-causal low-pass filter removing the oscillatory component while maintaining the same average speed to match the distance traveled. The procedure was repeated for the whole set of identified perturbations to identify the average additional energy expenditure.

2.2 Traffic Flow Implications

Following the characterization of the oscillation abnormality, a stochastic simulation study was put in place to assess the foreseen implications on longer and heterogeneous platoons which were not possible to accomplish during the public road testing. A thorough validation effort for the simple simulation model to match the behavior of the vehicle under test goes beyond the article’s aim. Instead, the simulation uses a stochastic approach to enlarge the scope to embrace vehicles with different controllers’ tuning but similar undamped follow behavior.

The simulation setup was derived from earlier authors’ work [3, 4] and leveraged a simple car-following model where the well-known linear controller model gives the car-following control law [6]:

$$\begin{aligned} u_{\text {ACC}}(t)=k_d(v_L(t-T)-v(t)) +k_p(s(t-T)-t_g v(t)-\eta ). \end{aligned}$$
(1)

In Eq. (1), \(s(\cdot )\) represents the ego-leader distance, \(v_L(\cdot )\) the leader’s speed, \(v(\cdot )\) the ego’s speed and \(u(\cdot )\) the control action. \(k_d\) and \(k_p\) are the controller’s gains, \(t_g\) the desired time-gap, T is the estimation delay, and \(\eta \) is the standstill spacing. The target acceleration \(u_{\text {ACC}}\) is saturated in the interval \([-5.0, \,2.0]~\mathrm {m/s^2}\). Each virtual vehicle is calibrated by randomly sampling its parameters from the intervals reported Table 1 assuming uniform distribution assumptions. The intervals are derived from real-world characterizations of ACC behavior as of [5].

Table 1. Vehicle platoon simulation parameters.
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The simulation setup is such that a platoon of ACC-equipped vehicles, starting from a steady-state condition, is subject to a perturbation induced by the leader vehicle. In particular, a set of 15 mild perturbations derived from the “highD” dataset [8] were adopted for the purpose. To replicate the effect of the leader vehicle experiencing the oscillatory behavior observed during the testing campaign, which is not present in the highD dataset, a sinusoidal wave speed profile has been superimposed on top of the original leader’s trajectory. Each simulation is repeated 20 times by randomizing over the vehicle parameters in Table 1 and over the calibrated oscillation parameters frequency and amplitude as described in Sect. 2.1. The analysis was repeated twice for two platoon reference lengths: 5 vehicles and 20 vehicles (including the leader). Thus, the impact of the oscillation propagation can be better grasped. The assessment is carried out via computing the average root mean square (RMS) platoon longitudinal acceleration \(a_{x,\text {RMS}}\) and the number of rear-end collisions as a proxy for comfort and safety degradation metrics.

3 Results

3.1 Oscillations Characterization

Figure 1 shows a recorded oscillation (blue dots) together with the calibrated sine wave (red line) and leader’s speed (black dots). Albeit the leader is traveling at constant velocity the follower is exhibiting a clearly undamped oscillation which can be effectively fitted with a sine function.

Fig. 1.
figure 1

Example of recorded oscillation and fitted sine wave.

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The computation of the Pearson correlation between the amplitude of the oscillatory component and the mean speed component returns a negative statistic (–0.0108) and a p-value equal to 0.947 suggesting that the quantities are uncorrelated.

The median oscillation corresponds to a low-frequency \(0.225~\mathrm {rad/s}\) (\(T=27.3~\textrm{s}\)) wave having a mean \(0.873~\mathrm {m/s}\) amplitude as shown in Fig. 2. The standard deviations are \(0.00248~\mathrm {(rad/s)}\) and \(0.0955~\mathrm {(m/s)}\) respectively. The statistical test assessing the normality of the distributions returns a value higher than 0.05, suggesting that the null hypothesis of the distributions being normal cannot be rejected.

Concerning the fuel consumption analysis, for the particular vehicle model considered, an average reduction of 3.30% could be accomplished by filtering the oscillatory component of speed while maintaining the same traveled distance. Overall, the oscillation only contributes to a marginal increase in fuel consumption that would be barely noticeable in a real-world scenario considering an individual vehicle only.

3.2 Traffic Simulation Results

The simulation assessment of longer platoons provides insightful findings.

Figure 3 displays the 5-vehicles long platoon aggregated results in terms of \(a_{x,\text {RMS}}\) and virtual crashes. Similarly, Fig. 4 shows the outcome associated with the longer 20 vehicles platoon.

Fig. 2.
figure 2

Histogram of oscillation frequencies (left) and amplitude (right).

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Fig. 3.
figure 3

Bar charts: acceleration RMS (left) and collision (right). 5 vehicles platoon.

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Fig. 4.
figure 4

Bar charts: acceleration RMS (left) and collision flow (right). 20 vehicles platoon.

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The introduction of the oscillatory components marks a clear surge in the acceleration RMS value which is increased by approximately 50% in the 5 vehicles long platoon suggesting that comfort and energy consumption are sensibly affected. On the contrary, safety is marginally reduced. The situation gets substantially worse when the longer platoon is considered. In this case, the RMS acceleration more than doubles and the platoon is hardly capable of maintaining a stable car-follow with a substantial increase in rear-end collisions.

4 Conclusion

The study summarized the testing results of SAE J3016 Level 2 assisted driving vehicles, highlighting concerns about poor stability in one vehicle’s ACC mode. Firstly, the phenomenon has been characterized in terms of its frequency and amplitude showing that the oscillation has a relatively slow period of \(T\approx 27~\textrm{s}\) and a mean amplitude slightly inferior to \(1~\mathrm {m/s}\). The energy consumption analysis demonstrated how, for one vehicle only, the phenomenon yields only a slight increase in fuel consumption which could be hardly measurable. However, once the phenomenon is enlarged via simulation to multiple vehicles exhibiting a string unstable behavior significant safety and comfort/energy worsening effects were reported, in particular in longer platoons. The results support the need for a regulation framework for lower automation systems to prevent potentially harmful impacts on traffic networks.