Communicating with two vehicles immediately ahead boosts traffic capacity sixfold in connected autonomous vehicle platoons

Abstract

Addressing urban congestion through enhanced traffic capacity has emerged as a critical objective for connected autonomous driving technologies. An irredundant communication connectivity topology is essential for ensuring the high efficiency and stability of the traffic system, which has not been fully validated due to the scarcity of real-world tests. Motivated by this fact, this paper deploys a connected autonomous vehicle platoon without relying on the information of a platoon leader to preserve the possibility of extending the platoon in future practical applications. The study is supported by both real-world experiments and simulations, where the following vehicles communicate with the two vehicles immediately ahead. The simulation extends the experimental results to several typical scenarios. The results demonstrate that such a communication structure largely enhances traffic capacity and stability, highlighting the effectiveness of connected autonomous vehicles in managing complex traffic environments. This work gains valuable insights into the sixfold traffic capacity improvement through connected autonomous driving.

Introduction

In the midst of rapid urbanization, where urban populations swell and economic activities intensify, the challenge of traffic congestion has emerged as a formidable issue confronting cities worldwide¹. Several interrelated factors contribute to the pervasive issue from the traffic demand side². Firstly, the rapid growth of urban populations in recent decades has resulted in a surge in the number of vehicles on roads. Secondly, this demographic shift, coupled with rising disposable incomes and urban sprawl, has substantially heightened the demand for private vehicles as a primary travel mode.

The impacts of urban traffic congestion extend far beyond mere inconvenience. Congestion leads to productivity losses due to time wasted in traffic jams, increased traffic instability and accident risks, and elevated transportation costs for daily commutes³. Moreover, prolonged idling and slow-/stop-and-go traffic contribute to massive energy consumption and environmental pollution, leading to more carbon emissions and harmful particulate matter⁴. These nuisances collectively deteriorate the quality of urban life and hinder sustainable development of cities, emphasizing the urgent necessity for sustainable transportation solutions⁵. In response to these challenges, governments have to allocate substantial resources to expand road networks and address the environmental and social issues exacerbated by congestion, often at the expense of other critical urban development projects. Despite many cities have struggled extensively with outdated road systems over the past few decades, they still fail to efficiently handle the influx of vehicles during peak hours⁶.

Autonomous driving is widely regarded as one of the most effective solutions for alleviating traffic congestion and enhancing traffic efficiency. Over the past decade, autonomous vehicle (AV) has been testing and evaluating its performance^7,8,9, and has developed from a concept to a marketed product. The AV technology is designed not only to mitigate human errors¹⁰ and enhance driving safety^11,12, but also to reduce travel time and improve traffic capacity¹³. Due to their potential to revolutionize traffic safety and mobility, an increasing number of productive AVs are released on the road, paving the way for large-scale autonomous driving in future transportation.

The primary scenario in the large-scale deployment of AVs is vehicle platooning, in which time gap setting is one of the decisive factors affecting traffic performance. However, experimental results utilizing typical sensors and actuators indicate that it is challenging to achieve a satisfactory traffic performance with AV following at a time gap of less than 1 s in practice^14,15,16. Motivated by the high-speed low-latency wireless communication technology, it has been demonstrated that connected autonomous vehicle (CAV) can gather information about surrounding vehicles and reduce the inter-vehicle spacing in car following much closer than that in a non-connected environment¹⁷. This benefit would pave the way for implementing sizeable vehicle platooning, with trailing vehicles following closely with a heading vehicle. A simultaneous decrease in air resistance and greenhouse gas emissions can also be accompanied by a long vehicle platoon¹⁸. Nevertheless, due to the scarcity of real-world tests, ensuring the long-tight platoon operation in a safe and stable manner remains a challenging issue.

Indeed, truck platooning within a connected environment has attracted the interest of many governments and research institutions over the past decades. Consequently, several projects on field experiments^19,20,21 have been launched to explore this idea, including the California PATH project on automated highway systems^22,23, European Commission SARTRE project^24,25, Japan Energy ITS project²⁶, etc. These studies discover that truck platooning can enhance driving safety, traffic capacity, and environmentally friendly metrics such as fuel consumption and emissions. However, the experiments gain limited insights into traffic flow stability around the large-scale platoon deployment.

Moreover, given the relatively recent advances in connected autonomous driving technology on light-duty vehicles, field experimental studies have also been conducted in car platooning tasks^{17,27,28,29,30}. Apart from the aforementioned benefits, these studies also emphasize evaluating traffic flow stability, which is crucial for ensuring the reliability and safety of car-platoon operations.

The configurations of these featured field studies are summarized in Table 1. The leader-involved platoon communication connectivity topology is used in all of those experiments. However, two disadvantages accompanied by such centralized topologies can be foreseen, as shown in Fig. 1a, and outlined as follows:

• (i) Reduced the practicability of communication connectivity. There tends to be a considerable spacing gap between the platoon leader and the rear of the former platoon. Specifically, the inter-platoon gap is usually large. In situations with small platoon sizes, there will be numerous inter-platoon gaps, largely reducing traffic capacity. The increase in platoon size could mitigate the negative effects of inter-platoon gaps on traffic capacity. However, it is worth mentioning that when pursuing to reduce the loss of traffic capacity, the communication distance in a platoon would increase as the platoon size increases. Due to the fact²¹ that vehicle-to-everything communication typically operates at high frequencies and has limited diffraction capabilities against obstacles like buildings, implementation methods like repeated broadcasting and/or redundant roadside units are usually necessary to strengthen communication signals. However, it is important to note that these solutions can elevate the complexity of the communication connectivity system and might even compromise the system’s ability to resist interference.

• (ii) Diminished robustness. In centralized topologies with a designated platoon leader, the traffic performance of a car platoon heavily relies on connected information from the platoon leader, particularly in terms of traffic stability. If communication from the platoon leader fails, the following vehicles must be degraded to the cooperative adaptive cruise control mode or even the adaptive cruise control mode. As a result, the platoon might lose its original string stability¹³ and become susceptible to the risk of vehicle collisions. In contrast, in communication topologies with the nearest multiple vehicles, each following vehicle only depends on the connected information of its preceding ones. Hence, despite the communication failure of some vehicles, other vehicles can operate normally, reducing the impact of communication failure on the overall platoon.

Table 1 Summary of field experiment studies on CAV platoon formation

Fig. 1: The simulation-to-reality (Sim-to-Real) solution to achieve a long, tight, and stable platoon.

a Centralized topologies may reduce practicability and diminish the robustness of long vehicle platoons compared to decentralized topologies. b Underlying exogenous/endogenous stochasticity may introduce a gap between simulation and real-world operation. c Based on the simulation-based optimization method, the upper-level controller of CAVs can be further optimized within a realistic simulation environment that incorporates the Sim-to-Real gap.

Therefore, decentralization can be regarded as a promising solution to solve these inefficiency issues. Our work is dedicated to demonstrating that there is no necessity to communicate with a platoon leader, and a two-predecessor following (TPF) topology could yield these benefits while extending platoon length. Moreover, it should be noted that due to the impact of underlying exogenous and endogenous stochasticity in the real-world operation of CAVs, there inevitably exists a gap between simulation and real-world performance, known as the Simulation-to-Reality (Sim-to-Real) gap. An illustration is shown in Fig. 1b. Therefore, quantifying and modeling the Sim-to-Real gap is another crucial contribution of this work, providing a technological route to generate a realistic simulation environment and further optimize CAV control performance, as shown in Fig. 1c. Firstly, we carry out a field experiment utilizing five programmable CAVs. The real-world data are collected, including the communication data and trajectory data of all vehicles. Then, we assess the real-world performance of field vehicle platoons. Secondly, we analyze the gap and further model it to account for the inherent errors of sensors and components in CAV operations. Next, we extend the experimental results of limited real-vehicle platoons to longer platoons and various scenarios to improve the traffic impact of the large-scale deployment of CAV platoons in a realistic simulation environment that bridges the Sim-to-Real gap. The results of our research suggest the potential for achieving an exceptionally high traffic throughput and reliable traffic stability. In such scenarios, vehicles could be platooned in a long, tight, and stable manner with relatively small desired spacing (no longer than 4 m under the common free-flow speed of 120 km·h⁻¹), in which each vehicle only needs to communicate with its two immediate neighbors ahead but the capacity increases by sixfold theoretically compared to the conventional traffic flow.

Results

Experiment setting and dataset

Conducting controlled real-world vehicle experiments is crucial to acquiring field data within a connected environment before its implementation. To this end, we conducted a field experiment with five programmable CAVs operating in platoon formation on May 31, 2023, on an approximately 1.5-km straight track. All vehicles moved straightforwardly and did not perform overtaking maneuvers. Detailed information on position, speed, spacing, command acceleration, and actual acceleration (achieved by the vehicle in real motion) of the ego vehicle and surrounding vehicles was recorded.

To design the experiment scenarios, the leading CAV in the platoon was programmed to follow a specific speed profile, carefully designed with multiple target speeds and various perturbances. The speed profile included a consistent acceleration or deceleration of 1 m·s⁻² during the start and stop stages. Between the two transition stages, two distinct types of perturbances were tested, i.e., deceleration-to-acceleration (Dec.-to-Acc.) and acceleration-to-deceleration (Acc.-to-Dec.). In these perturbances, the leading CAV initially decelerates/accelerates with a target deceleration/acceleration from the target speed until it reaches a predefined lower/higher speed. It then reverses its acceleration/deceleration, working towards the target speed again. The on-site snapshot and the setting of experiment scenarios are reported in Fig. 2a. More details on the experimental settings can be found in Supplementary Section S.1.

Fig. 2: The real-world experiment and its results.

a On-site snapshot of the experiment and its setting of perturbance scenarios. b The relationship between traffic speed and flow rate is almost linear. Each scatter in the speed-flow diagram denotes the average result throughout each experimental run. For details on the scatter calculation, see Supplementary Section S.2.2. c An example under the target speed of 60 km·h⁻¹, the perturbance magnitude of 30 km·h⁻¹, and the target acceleration of 1 m·s⁻².

Vehicle platooning leverages traffic throughput

Traffic throughput has been analyzed to assess the extent to which traffic capacity can be improved with such a formation of vehicle platooning in the experimental campaigns. Speed, flow rate, and density of vehicles are the three fundamental parameters of traffic flow. In the context of the experimental CAVs, a fixed car-following spacing strategy is implemented through a pre-specific upper-level control algorithm (refer to the “Methods” section for a description of the control algorithm of these following CAVs). Throughout the run, the spacing between vehicles typically remains constant, except during the adjustments for acceleration or deceleration. In this way, speed becomes a pivotal factor influencing traffic throughput. The relationship between traffic speed and flow rate is shown in Fig. 2b. It is evident that traffic throughput increases remarkably. Even at 20 km·h⁻¹ in our experiment, a throughput of 2000 veh·h⁻¹ can be achieved. At 60 km·h⁻¹, vehicles are separated by about 5 m, and the traffic flow rate in a steady state reaches 5800 veh·h⁻¹. Figure 2c shows the experimental data profiles from one run. It can be seen that the following CAVs can closely track the speed of the leading CAV, maintaining spacing fluctuations within a safety range. We have assessed the spacing error in each run, and it falls within the range of −1.23–2.47 m (the details can be found in Supplementary Section S.2.1). This suggests that there may be potential to reduce the standstill spacing ${G}_{\min }$ (from the front bumper of the rear car to the rear bumper of the front car at standstill) in the future, further enhancing traffic flow efficiency.

Analysis of the Sim-to-Real gap

In the real world, various exogenous and endogenous stochastic factors can affect the performance of CAV operations. These factors can mainly originate from (i) vehicle and system dynamics (e.g., transmission, brake, and engine performance), (ii) perception and detection capabilities of equipment (e.g., sensor errors, localization errors, and communication latency), etc.³¹. The stochasticity resulting from these confounding factors consequently affects traffic flow status. We have compared the results of two repeated experimental runs, as shown in Fig. 3a. Although the speed profiles between each other are similar, the spacing profiles show remarkable differences. Moreover, we have conducted the car-following test within a deterministic simulation environment with the input of initial conditions of the experimental run. It is evident that under the influence of these inevitably stochastic factors, the actual operation of CAVs in the real world mismatches the performance tested in simulation environments, leading to a remarkable gap between each other. The statistical results for the Sim-to-Real gap shown in the right sub-figure of Fig. 3a indicate that (i) the field speed/spacing of CAVs is larger/smaller than the estimated one in simulation, which may lead to collisions and conflicts; (ii) the field speed/spacing of CAVs is smaller/larger than the estimated one in simulation, which can lead to underestimation of traffic capacity.

Fig. 3: Overall architecture of bridging the Sim-to-Real gap and its validation result in a realistic simulation environment.

a Comparison of two repeated experimental runs and their simulation results shows nearly identical speed profiles but remarkable differences in the spacing profiles. The values in the boxplot represent the maximum and minimum speed and spacing profiles using the experiment data minus the deterministic simulation data. The central point within each box represents the median of the dataset. The lower and upper boundaries of the box correspond to the first (Q1) and third quartiles (Q3), respectively, such that the box height reflects the interquartile range (IQR = Q3−Q1; the middle 50% of the data). The whiskers extend to the most extreme data points within 1.5 × IQR from the lower and upper quartiles. Data outside this range are plotted individually as outliers and are shown as unfilled points. b The Sim-to-Real gap is captured and quantified. c The comparison output based on the modeled Sim-to-Real gap using a mean-reversion process. Upon this, the speed and spacing profiles between the experiment and realistic simulations are compared. The 95% confidence interval (CI) is calculated based on the results of multiple realizations. Note that 95% is widely used in the literature, e.g., Xu et al.⁴⁶. The stochasticity parameters in Eq. (5b), i.e., the speed of reversion (denoted as κ) and the amplitude of randomness (denoted as σ), are 0.8556 s⁻¹ and 0.0123 m·s⁻², respectively.

Test of domain randomization in CAV operations using the Sim-to-Real approach

Sim-to-Real is a comprehensive concept applied in various fields, including robotics and classic machine vision tasks^32,33. Enhancing the Sim-to-Real transfer process requires further attention to understanding and modeling the Sim-to-Real gap. Domain randomization has been validated as one of the effective approaches for addressing this gap. Researchers typically empirically examine which randomizations to add to improve the transferability of simulations to real-world scenarios. During our field experiment, we first empirically capture the Sim-to-Real gap of CAV operation between real-world and deterministic simulation tests. Then, we model the gap using a stochastic process and incorporate it into the resulting actual acceleration as an aggregated effect. The overall architecture for capturing and quantifying the Sim-to-Real gap is illustrated in Fig. 3b. Please refer to the “Methods” section for a more detailed description of the modeling and estimation of the aggregated stochasticity. The comparison of speed and spacing profiles between the experiment and realistic simulations can be found in Fig. 3c. We find that (i) the bandwidth of the 95% confidence interval for simulated speeds is remarkably narrow and closely resembles the experimental speed profiles, while the one for simulated spacing is noticeably wider. This is due to the fact that vehicle speed is based on the cumulative sum of acceleration, while vehicle position is based on the cumulative sum of speed. In this process, real-world stochasticity experiences second-order accumulation and is transmitted from acceleration noise to random spacing, leading to notable fluctuation intervals in spacing³⁴. (ii) The experimental spacing profiles align closely with the 95% confidence interval for simulated spacings. The result also underscores the importance of repeated scenario tests when assessing the driving safety of CAVs.

Test of large-scale CAV deployments

In the near future, the vehicle-to-vehicle with extremely close spacing may become a reality on expressways and highways. Large-scale CAV platoons are expected to emerge, improving road usage efficiency. Since the actual motion of CAVs is finally determined by the lower-level control system of individual vehicles to execute commands from the upper-level control algorithm, each CAV has specific lower-level control parameters, potentially leading to different control performance (refer to the “Methods” section for a description of the lower-level controller of CAVs). Large-scale CAV systems exhibit heterogeneity even if they are from the same manufacturer (please refer to Supplementary Section S.3 for more details). However, this raises a new issue: how does the aforementioned stochasticity and heterogeneity in vehicle operation impact traffic flow? Before answering this question, we optimize the solution of the upper-level control algorithm by employing a stochastic simulator to ensure as much realism as possible in the Sim-to-Real transfer (please refer to the “Methods” section for more details). The primary goal is to achieve traffic stability and high traffic capacity with minimal performance degradation.

Given the lower-level controller, the optimized stable parameters of the upper-level control algorithm are as follows: ${k}_{a1}=0.2889,\,{k}_{a2}=0.6676,{k}_{v1}=0.6265\,{{{\rm{s}}}}^{-1},\,{k}_{v2}=0.3703\,{{{\rm{s}}}}^{-1},{k}_{g}=0.4437\,{{{\rm{s}}}}^{-2},\,{T}_{g}=0.0736\,{{\rm{s}}},{G}_{\min }=1.0$ ${{\rm{m}}}$. In the subsequent simulation tests, we extend the analysis to explore the impact of communication delay, stochasticity, and heterogeneous CAV lower-level dynamics on large-scale CAV deployments across four specific scenarios: long platoon formation, merging, two-lane highway with four consecutive on-/off-ramps, and four-lane urban road with three consecutive signalized intersections.

Traffic safety, stability, and throughput

To assess the impact of stochasticity and heterogeneity on traffic flow, various simulation scenarios are examined for long vehicle platooning, incorporating perturbances of varying strengths, including different amplitudes and variations in acceleration aggressiveness. The simulated speed and spacing profiles of 100-CAV-platoon and the measurement of traffic stability using the ∞-norm (denoted as ${L}_{\infty }$) can be found in Supplementary Section S.4.2. The statistical results reported in Fig. 4a indicate that even in the presence of stochasticity and heterogeneity resembling real-world conditions, the ratios of ${L}_{\infty ,n}/{L}_{\infty ,2}$ consistently decrease from 1 along the vehicle platoon without any vehicle collisions. In such cases, traffic exhibits string stability. Therefore, the optimized stable solution remains effective in long vehicle platoons under the TPF topology. Next, traffic throughput in simulated long platoons is quantitatively measured. The relationship between traffic speed and flow rate reports that the maximum theoretical traffic capacity at 120 km·h⁻¹ can reach over 14,000 veh·h⁻¹ with an average vehicle density of 115.704 veh·km⁻¹.

Fig. 4: Simulation results in a realistic simulation environment.

a Results regarding spacing, traffic stability, and the relationship between traffic speed and flow rate. The perturbance is aggressive: Acceleration rate = 3 m·s⁻² and deceleration rate = 7 m·s⁻². V_s denotes the target speed, V_d denotes the magnitude of perturbance. b Sketch of the on-ramp scenario and the results regarding the speed heatmap, sample trajectories, and speeds of specific mergers, and their surrounding mainline CAVs. More details of the merging setting and more results under different traffic demands can be found in Supplementary Section S.4.3. c Sketch of a two-lane highway with four consecutive on-/off-ramps and the results regarding the speed heatmap, speed, and flow rate. There are three typical types of lane-changing cooperation behavior: CP.I-Preemptive lane-changing; CP.II-Cooperation and merging from the on-ramp; CP.III-Cooperation and exit into the off-ramp. CZ cooperation control zone for on-ramp vehicles, MZ merging zone, EZ exiting zone. More details of the simulation setting can be found in Supplementary Section S.4.4. See Supplementary Movies 1 and 2 for a local visualization of the simulation. d Sketch of a four-lane urban road with three consecutive signalized intersections and the results regarding the speed heatmap, speed, and flow rate. More details of the simulation setting can be found in Supplementary Section S.4.5. See Supplementary Movies 3 and 4 for a local visualization of the simulation.

Cooperation and merging

In real-world traffic operations, vehicle merging is a typical traffic behavior that often leads to the formation of traffic bottlenecks, causing traffic congestion to propagate upstream from the merging point. To showcase the effectiveness of CAVs in managing merging in high-density traffic flow, we conduct a numerical test for a typical on-ramp scenario. Our simulation implements a cooperation control zone (CZ) upstream of the on-ramp bottleneck. As CAVs enter this zone, their merging sequence is determined by a simple “first-in-first-out” principle. The results of the speed heatmap, sample trajectories, and speeds are presented in Fig. 4b. In high-density CAV flow, smooth cooperation and merging can be achieved despite real-world traffic stochasticity and heterogeneity. As measured by a virtual loop detector, the traffic throughput downstream of the merging point reaches approximately 13,600 veh·h⁻¹, nearly 95% of the maximum theoretical traffic capacity. Additionally, we observe that (i) the average travel delay of 0.24 s, (ii) the on-ramp CAV merges into the mainline immediately upon entering the merging zone (MZ) without any delay, and (iii) an average speed in the CZ and MZ of 117.11 km·h⁻¹, nearly 98% of the free-flow speed. These results indicate that TPF-enabled CAVs can effectively manage merging in high-density traffic, leading to low travel delay, prompt merging once entering the MZ, and only a minimal reduction in traffic efficiency compared to scenarios without bottlenecks.

Simulation of a two-lane highway with four consecutive on-/off-ramps

Next, to demonstrate the effectiveness of CAVs in managing more complex traffic environments, we consider a scenario involving four consecutive on-/off-ramps on a two-lane highway. The scenario encompasses critical maneuvers, such as lane-changing, merging, exiting, and multiple types of cooperative maneuvers to support these actions. It serves to extend our findings to conditions more representative of real-world highways or expressways, and to explore whether TPF-enabled CAVs with cooperative behavior can facilitate smooth traffic operations in critical situations, such as (i) preemptive lane changes to create space for on-ramp flows (CP.I), (ii) on-ramp vehicles merging into the main lane (CP.II), and (iii) vehicles exiting the off-ramp from the main lane 1 (CP.III). The speed heatmap of the main lanes and the corresponding speed and flow rate across different sites are illustrated in Fig. 4c. Even under this complex environment, traffic flow remains smooth at a demand level of 12,000 veh·h⁻¹·lane⁻¹. It is noteworthy that, in this two-lane, four consecutive on-/off-ramp scenario, the mainline flow does not sustain its maximum theoretical capacity. This limitation arises because the main lane 2 must accommodate lane changes from the main lane 1, reserving capacity to ensure seamless traffic transitions. Despite this, downstream traffic throughput still achieves 80% of the maximum theoretical capacity. Additionally, simulation results also reveal that (i) the average travel delay is 0.76 s, (ii) the on-ramp CAV merges into the mainline immediately upon entering the MZ without any delay, (iii) the off-ramp CAV exits the mainline immediately upon entering exiting zone (EZ) without any delay, and (iv) the average speed is 118.77 km·h⁻¹ in the CZ and MZ, representing approximately 99% of the free-flow speed. These findings highlight the ability of TPF-enabled CAVs to effectively manage vehicle lane-changing, merging, and exiting in high-density traffic, even within a realistic and challenging traffic environment.

Simulation of a four-lane urban road with three consecutive signalized intersections

Furthermore, to generalize our findings to interrupted traffic flow conditions, we examine a signalized urban road scenario featuring a four-lane main road with three consecutive signalized intersections. This setup encompasses critical situations to explore whether TPF-enabled CAVs integrated with the vehicle-to-infrastructure system can facilitate high-efficiency traffic operations. The speed heatmap of main lanes, along with corresponding speed and flow rates across different sites is illustrated in Fig. 4d. Even in this urban enviroment, traffic flow maintains satisfactory performance at a demand level of approximately 10,000 veh·h⁻¹ from the main road and 1000 veh·h⁻¹·lane⁻¹ from byroads with a desired speed of 60 km·h⁻¹. Intersection throughput of through traffic achieves above 80% of its theoretical capacity. Additionally, simulation results further indicate that (i) the average travel delay is 13.89 s, (ii) the time taken by CAVs for lane changes from the initial lane to the target lane is 7.55 s, and (iii) the average speed is 59.95 km·h⁻¹, representing approximately 99% of the desired speed. These findings underscore the effectiveness of TPF-enabled CAVs in enhancing intersection throughput and overall traffic efficiency in urban environments.

Discussion

We conducted a real-world experiment with a platoon of five programmable CAVs in a communication environment. The experiment employed the TPF topology, where each following vehicle communicates with two immediately preceding vehicles. Our study gains insights into traffic stability and throughput. The findings indicate that stable traffic flow can be achieved by optimizing upper-level control parameters with no more than a 4-meter separation between each pair of consecutive vehicles at the free-flow speed of 120 km·h⁻¹. As a result, traffic throughput can be largely enhanced sixfold compared to the typical ideal light-duty vehicle saturation, i.e., 2400 veh·h⁻¹·lane⁻¹ suggested by Highway Capacity Manual³⁵. Our study indicates that even in the presence of empirically examined stochastic factors resembling real-world conditions, achieving extremely high traffic throughput, dependable traffic stability, smooth cooperation, and merging remains a viable possibility.

Due to budget, time, and safety constraints, our experiments were limited to one specific platoon communication connectivity topology (namely, TPF topology). However, we conducted simulation-based CAV platooning tests for the one-predecessor and multi-predecessor following topologies (please refer to Supplementary Section S.5 for detailed simulation results). The relationship between the optimal time gap and the number of connected predecessors is studied, see Fig. 5a. We use the log-log scale plot and find that the two quantities exhibit an approximate inverse linear relationship. It is suggested that a multiple-predecessor communication scheme provides a benefit with respect to the minimum time gap²⁹; however, the marginal effect of communication with more vehicles is unremarkable. It also indicates that if a zero-time gap is pursued to achieve a stable traffic situation, the cost of communication connectivity may be enormous under the constant time gap policy, which can complicate the communication connectivity topology and introduce redundancy in the connected data. Furthermore, the optimal T_g for traffic stability is 0.1235 s under the one-predecessor following topology. This value is much greater than the one under the TPF topology, resulting in a notable wastage of traffic capacity, as shown in Fig. 5b. Although previous experimental results³⁰ have demonstrated that achieving stable traffic flow with a small time gap is also quite challenging, it highly depends on the performance of the lower-level controller of the employed CAVs^36,37,38. It is conjectured that due to the gear-free in electric vehicles, they generally outperform conventional fuel vehicles in terms of execution accuracy and delay.

Fig. 5: Comparison of the optimal time gap and the simulation result among multi-predecessor following topologies.

a The number of communication vehicles and optimal time gap exhibit a log-log scale relationship. b The increase in platoon size could mitigate the negative effects of inter-platoon gaps on traffic capacity. The traffic speed is 120 km·h⁻¹. The inter-platoon time gap is 2 s, and the intra-platoon time gap is optimal. The spatial gap at zero speed is 1.0 m, and the vehicle length is 4.835 m.

Furthermore, our analysis has limitations that highlight important avenues for future research. (i) In our study, we utilized only one type of upper-level control algorithm. The effectiveness of the TPF topology may be associated with the constant time gap policy. It is worth investigating whether the one-predecessor following topology can achieve similar or superior control outcomes when combined with other advanced upper-level control algorithms. (ii) Our study is conducted within a fully CAV environment. The use of the TPF communication topology in mixed traffic, consisting of both CAVs and conventional vehicles, is also a critical topic that warrants further exploration through real-world experiments. (iii) In vehicle-to-vehicle communication, only the communication delay is introduced, without addressing factors such as communication channel, data transmission rate, and communication distance, as highlighted by Uno et al.³⁹. Extending the work to integrate testing for both CAV control algorithms and data transmission algorithms represents a purposeful advancement of the paper. (iv) Real-world traffic systems will comprise AVs from different manufacturers with differing capabilities⁴⁰. Our study identifies and examines the impact of weak heterogeneity in CAV dynamics arising from specific lower-level controllers. However, the effects of strong heterogeneity stemming from different CAV manufacturers on traffic systems remain unclear. (v) For abnormal events, such as emergency braking or communication losses, it is crucial to establish robust emergency response protocols⁴¹. Furthermore, additional field tests or simulations are necessary to assess the resilience of the CAV system. This is critical for ensuring string stability, allowing the system to handle disturbances or failures effectively.

Methods

Setting of the upper-level controller of CAVs

In our experiment, the control of all following CAVs is realized through two controllers: the upper-level controller and the lower-level controller. In the upper-level control, the Autoware platform calculates the command acceleration based on the collected status information. The command acceleration is subsequently transmitted to the lower-level controller. In our study, the constant time gap car-following policy with TPF topology is implemented in the upper-level longitudinal controller to generate the command acceleration, which integrates spacing data measured by lidar as well as command acceleration and speed obtained from communication for the two vehicles immediately ahead. The upper-level control model is given by

$${a}_{{cmd},n}\left(t\right) = {k}_{a1}{a}_{{cmd},n-1}\left(t-\eta \right)+{k}_{a2}{a}_{{cmd},n-2}\left(t-\eta \right)\\ +{k}_{v1}\left({v}_{n-1}\left(t-\eta \right)-{v}_{n}\left(t\right)\right)+{k}_{v2}\left({v}_{n-2}\left(t-\eta \right)-{v}_{n}\left(t\right)\right)\\ +{k}_{g}\left({\Delta x}_{n}\left(t\right)-{G}_{\min }-{T}_{g}{v}_{n}\left(t\right)\right)$$

(1)

where ${a}_{{cmd},n}\left(t\right)$ is the command acceleration of vehicle $n$ at time $t$; ${v}_{n}\left(t\right)$ is the speed of vehicle $n$ at time $t$; ${\Delta x}_{n}\left(t\right)$ is the measured spacing from the front of vehicle $n$ to the rear of preceding vehicle $n-1$; ${k}_{a1}$, ${k}_{a2}$, ${k}_{v1}$, ${k}_{v2}$, and ${k}_{g}$ are the control gains; ${T}_{g}$ is the target time gap; ${G}_{\min }$ is the standstill spacing; $\eta$ is the communication delay.

The corresponding CAV configuration of longitudinal car-following is presented in Fig. 6a. The parameter values of the upper-level control algorithm are pre-specified: ${k}_{a1}=0.5,\,{k}_{a2}=0.4,{k}_{v1}=0.4\,{{{\rm{s}}}}^{-1},\,{k}_{v2}=0.5\,{{{\rm{s}}}}^{-1},{k}_{g}=0.1\,{{{\rm{s}}}}^{-2},\,{T}_{g}=0\,{{\rm{s}}},\,{G}_{\min }=5\,{{\rm{m}}}$. Note that for the secondary leader in the platoon, there are not two vehicles ahead. As a result, the parameter values for Car 2 are set as follows: ${k}_{a1}=0.9,\,{k}_{v1}=0.9\,{{{\rm{s}}}}^{-1},\,{k}_{g}=0.1\,{{{\rm{s}}}}^{-2},{T}_{g}=0\,{{\rm{s}}},\,{G}_{\min }=5\,{{\rm{m}}}$, while ${k}_{a2}$ and ${k}_{v2}$ are not applicable in this case. As measured from the experimental data, the communication delay is 0.05 s.

Fig. 6: CAV configuration of longitudinal car-following.

a Control structure of the ego CAV. b Sketch of car-following operation.

Calibration and validation of the lower-level controller of CAVs

The lower-level controller of CAVs plays a critical role in converting commands from the upper-level control algorithm into actual vehicle motion. The car-following operation of the ego CAV is depicted in Fig. 6b.

Since the lower-level controller of CAV for users is a black box, it is necessary to model and calibrate it. The lower-level controller can be mathematically represented as a transfer function between the command and actual accelerations in the frequency domain as follows:

$$A\left(s\right)=G\left(s\right){A}_{{cmd}}\left(s\right)$$

(2)

where ${A}_{{cmd}}\left(s\right)$ and $A\left(s\right)$ denote the command acceleration and the actual one in the frequency domain, respectively. $G\left(s\right)$ denotes the transfer function, which is described using a commonly used second-order response model^17,42, as shown below.

$$G\left(s\right)=\frac{K}{{s}^{2}+2\theta \omega s+{\omega }^{2}}{e}^{-\tau s}$$

(3)

where $K$ denotes the static gain; $\theta$ and $\omega$ denote the damping factor and natural frequency, respectively; $\tau$ denotes the time delay.

The calibration problem for the lower-level control system is formulated as an optimization problem to minimize the mean square error between the time series of actual accelerations between experiment and simulation as follows:

$${{\rm{m}}}{{\rm{in}}}\mathop{\sum }\limits_{r{{\mathscr{\in }}}{{\mathcal{R}}}}\frac{1}{T}{\sum }_{t=1}^{T}{\left({a}_{t,r}^{{sim}}-{a}_{t,r}^{\exp }\right)}^{2}$$

(4)

where ${a}_{t,r}^{{sim}}$ and ${a}_{t,r}^{\exp }$ denote the actual accelerations in the simulation and experiment at time $t$ in experimental run $r$, respectively; $T$ denotes the duration; ${{\mathcal{R}}}$ denotes the run set of the same vehicle.

The calibrated model parameters and a comparison of the time series of actual acceleration between simulation and experiment can be found in Supplementary Section S.3.

Modeling and estimation of the Sim-to-Real gap in CAV operations

In the context of real-world CAV operations, the trajectory of CAVs often exhibits variations from deterministic simulations. These variations can result from errors in state measurement, information communication, vehicle control, and other factors. We consider these errors as an aggregated stochasticity that affects the resulting actual acceleration, and model it using a mean-reversion process⁴³. The mathematical representation of this process is as follows:

$${a}_{n}\left(t\right)={\widetilde{a}}_{n}\left(t\right)+{\xi }_{n}\left(t\right)$$

(5a)

$${\xi }_{n}\left(t\right)=\left(1-\kappa {dt}\right){\xi }_{n}\left(t-{dt}\right)+\sigma d{W}_{n}$$

(5b)

where ${\widetilde{a}}_{n}$ denotes the ideal actual acceleration; ${\xi }_{n}$ denotes the aggregated stochasticity. κ and σ denote the speed of reversion and the amplitude of randomness, respectively; ${W}_{n}$ is a Wiener process, and its increments are normally distributed with zero mean and variance ${dt}$.

To capture the Sim-to-Real gap, we propose a framework to calibrate the stochastic process $\xi$ and construct a realistic simulation environment. This framework presents a procedure in which both data streams are studied to provide an understanding of the correlation between the CAV states in the Sim-to-Real and the Deterministic Sim-to-Stochastic Sim, so that one can have an accurate expectation of how the realistic simulation will perform similarly to the real counterpart.

Specifically, we first take into account deviations between the experimental CAV states (i.e., spacing and speed) and the simulation results in the absence of the stochastic process. The resulting deviations can be considered as the probability distribution of errors in spacing and speed, and be denoted as ${{{\mathcal{P}}}}_{\Delta x}^{{Exp}\leftrightarrow {Sim\backslash }\xi }$ and ${{{\mathcal{P}}}}_{v}^{{Exp}\leftrightarrow {Sim\backslash }\xi }$ for spacing and speed, respectively. When the stochastic process is introduced into the CAV model, there may be deviations between the simulation results in the presence and absence of the stochastic process, and be denoted as ${{{\mathcal{P}}}}_{\Delta x}^{{Sim}\cup \xi \leftrightarrow {Sim\backslash }\xi }$ and ${{{\mathcal{P}}}}_{v}^{{Sim}\cup \xi \leftrightarrow {Sim\backslash }\xi }$ for spacing and speed, respectively. Next, the modeled stochastic process is considered to be similar to the actual errors in real-world operations if the distributions of ${{{\mathcal{P}}}}_{\Delta x}^{{Sim}\cup \xi \leftrightarrow {Sim\backslash }\xi }$ and ${{{\mathcal{P}}}}_{v}^{{Sim}\cup \xi \leftrightarrow {Sim\backslash }\xi }$ closely match the ones of ${{{\mathcal{P}}}}_{\Delta x}^{{Exp}\leftrightarrow {Sim\backslash }\xi }$ and ${{{\mathcal{P}}}}_{v}^{{Exp}\leftrightarrow {Sim\backslash }\xi }$ Upon this, we formulate an optimization problem to calibrate the parameters of $\xi$. This optimization approach aims to minimize the differences between the two distributions (i.e., ${{{\mathcal{P}}}}_{\cdot}^{{Sim}\cup \xi \leftrightarrow {Sim\backslash }\xi }{{\rm{vs}}}{{{\mathcal{P}}}}_{\cdot}^{{Exp}\leftrightarrow {Sim\backslash }\xi }$) by adjusting the parameters of ξ. The calibration formulation can be described as follows.

$$\min \mathop{\sum }\limits_{r{{\mathscr{\in }}}{{\mathcal{R}}}}\mathop{\sum }\limits_{n{{\mathscr{\in }}}{{\mathscr{N}}}}{\min }_{j\le J}\left({{{\mathcal{D}}}}_{{{{\mathcal{P}}}}_{v},n,r,j}+{{{\mathcal{D}}}}_{{{{\mathcal{P}}}}_{\Delta x},n,r,j}\right)$$

(6)

where ${{{\mathcal{D}}}}_{{{{\mathcal{P}}}}_{v},n,r,j}$ and ${{{\mathcal{D}}}}_{{{{\mathcal{P}}}}_{\Delta x},n,r,j}$ denote the distribution deviations of ${{{\mathcal{P}}}}_{v}$ and ${{{\mathcal{P}}}}_{\Delta x}$ for Car $n$ in the $j$ th simulation of the experimental run $r$, respectively. ${{\mathcal{D}}}$ is the two-sample Kolmogorov-Smirnov test statistic, i.e., ${{\mathcal{D}}}={\max }_{x}|{{{\mathcal{F}}}}_{\cdot}^{{Exp}\leftrightarrow {Sim\backslash }\xi }\left(x\right)-{{{\mathcal{F}}}}_{\cdot}^{{Sim}\cup \xi \leftrightarrow {Sim\backslash }\xi }\left(x\right)|$. ${{\mathcal{F}}}$ is the sample cumulative distribution function of ${{\mathcal{P}}}$. ${\min }_{j\le J}\left(\cdot\right)$ is adopted to find the minimum value in $J$-time stochastic realizations.

We split the platoon into multiple leader(s)-follower car-following pairs to facilitate the simulation-based optimization. The simulated scenario is then built by emulating the experiment scenario, focusing on the follower in each pair. This simulation involves the input of all trajectories, speeds, and command accelerations of leader(s), as well as the initial speed, command acceleration, actual acceleration of the follower, and the initial spacing between each two consecutive vehicles.

Search for a stable solution of CAVs in realistic simulation environments

It is important to note that, given the vehicle, the lower-level controller parameters are typically not changeable, as they are closely tied to the physical characteristics and capabilities of the vehicle. However, the upper-level control algorithm, along with its associated parameters, can be customized and set by the auto manufacturer. The choices made in designing this upper-level control algorithm can impact the performance of CAVs and, by extension, the overall traffic flow.

Existing studies have developed ${H}_{\infty }$-norm optimal platoon controllers in the frequency domain to identify a controller for ensuring traffic stability²⁹. However, synthesizing traffic safety and efficiency alongside traffic stability in the frequency domain proves to be complex. To this end, an alternative optimization problem is formulated in the time domain. This approach aims to search for a solution to the upper-level control algorithm of CAVs that ensures string stability while balancing traffic throughput and safety. The optimization problem is structured to address this by generating scenarios involving different types of perturbances with varying amplitudes and accelerations in constructed realistic simulation environments. The goal is to identify an upper-level control algorithm that meets the string stability criteria for a range of perturbance scenarios. More details about perturbance scenarios can be found in Supplementary Section S.4.1. The optimization formulation is designed to minimize the combination of overshooting/undershooting amplitudes in speed and desired spacing, ensuring positive and safe spacing. The formulation is described as follows.

$$\min \mathop{\sum }\limits_{s\in S}\left({{\mathcal{P}}}{{\cdot}}\max \left\{0,{L}_{\infty ,N}^{s}-{L}_{\infty ,2}^{s}\right\}{{\mathscr{-}}}{{\mathcal{P}}}{{\cdot}}\min \left\{0,\Delta {x}_{\min }^{s}\right\}\right)+\Delta {x}_{d}$$

(7)

where $S$ denotes the set of scenarios. ${L}_{\infty ,n}^{s}$ denotes the $\infty$-norm of the difference between the actual speed and the stable speed of vehicle n in scenario s. $\Delta {x}_{\min }^{s}$ denotes the minimum spacing of all vehicles in scenario s; $\Delta {x}_{d}$ denotes the sum of desired spacings at speeds of 10, 20, …, 120 km·h⁻¹, expressed as $\Delta {x}_{d}={\sum }_{v=0}^{120}\left[{T}_{g}\cdot\frac{v}{3.6}+\left({G}_{\min }-{\min }_{s}\Delta {x}_{\min }^{s}\right)\right]$. ${G}_{\min }$ is a preset value. ${{\mathcal{P}}}$ denotes a penalty factor, which is set to be a positive real number and largely outweighs $\Delta {x}_{d}$.