Simeon C. Calvert

Frederik Baymler Mathiesen, Simeon Calvert, Luca Laurenti

Providing non-trivial certificates of safety for non-linear stochastic systems is an important open problem that limits the wider adoption of autonomous systems in safety-critical applications. One promising solution to address this problem is barrier functions. The composition of a barrier function with a stochastic system forms a supermartingale, thus enabling the computation of the probability that the system stays in a safe set over a finite time horizon via martingale inequalities. However, existing approaches to find barrier functions for stochastic systems generally rely on convex optimization programs that restrict the search of a barrier to a small class of functions such as low degree SoS polynomials and can be computationally expensive. In this paper, we parameterize a barrier function as a neural network and show that techniques for robust training of neural networks can be successfully employed to find neural barrier functions. Specifically, we leverage bound propagation techniques to certify that a neural network satisfies the conditions to be a barrier function via linear programming and then employ the resulting bounds at training time to enforce the satisfaction of these conditions. We also present a branch-and-bound scheme that makes the certification framework scalable. We show that our approach outperforms existing methods in several case studies and often returns certificates of safety that are orders of magnitude larger.

Saeed Rahmani, Gözde Körpe, Zhenlin et al.

Automated driving at unsignalized intersections is challenging due to complex multi-vehicle interactions and the need to balance safety and efficiency. Model Predictive Control (MPC) offers structured constraint handling through optimization but relies on hand-crafted rules that often produce overly conservative behavior. Deep Reinforcement Learning (RL) learns adaptive behaviors from experience but often struggles with safety assurance and generalization to unseen environments. In this study, we present an integrated MPC-RL framework to improve navigation performance in multi-agent scenarios. Experiments show that MPC-RL outperforms standalone MPC and end-to-end RL across three traffic-density levels. Collectively, MPC-RL reduces the collision rate by 21% and improves the success rate by 6.5% compared to pure MPC. We further evaluate zero-shot transfer to a highway merging scenario without retraining. Both MPC-based methods transfer substantially better than end-to-end PPO, which highlights the role of the MPC backbone in cross-scenario robustness. The framework also shows faster loss stabilization than end-to-end RL during training, which indicates a reduced learning burden. These results suggest that the integrated approach can improve the balance between safety performance and efficiency in multi-agent intersection scenarios, while the MPC component provides a strong foundation for generalization across driving environments. The implementation code is available open-source.

Xue Yao, Simeon C. Calvert, Serge P. Hoogendoorn

Current approaches to identifying driving heterogeneity face challenges in capturing the diversity of driving characteristics and understanding the fundamental patterns from a driving behaviour mechanism standpoint. This study introduces a comprehensive framework for identifying driving heterogeneity from an Action-chain perspective. First, a rule-based segmentation technique that considers the physical meanings of driving behaviour is proposed. Next, an Action phase Library including descriptions of various driving behaviour patterns is created based on the segmentation findings. The Action-chain concept is then introduced by implementing Action phase transition probability, followed by a method for evaluating driving heterogeneity. Employing real-world datasets for evaluation, our approach effectively identifies driving heterogeneity for both individual drivers and traffic flow while providing clear interpretations. These insights can aid the development of accurate driving behaviour theory and traffic flow models, ultimately benefiting traffic performance, and potentially leading to aspects such as improved road capacity and safety.

Ashwin George, Lucas Elbert Suryana, Lorenzo Flipse et al.

Partial driving automation creates a tension: drivers remain legally responsible for vehicle behaviour, yet their active control is significantly reduced. This reduction undermines the engagement and sense of agency needed to intervene safely. Meaningful human control (MHC) has been proposed as a normative framework to address this tension. However, empirical methods for evaluating whether existing systems actually provide MHC remain underdeveloped. In this study, we investigated the extent to which drivers experience MHC when interacting with partially automated driving systems. Twenty-four drivers completed a simulator study involving silent automation failures under two modes - haptic shared control (HSC) and traded control (TC). We derived behavioural metrics from telemetry data, subjective perception scores from post-trial surveys and used them to test hypothesised relations between them derived from the properties of systems under MHC. The confirmatory analysis showed a significant negative correlation between the perception of the automated vehicle (AV) understanding the driver and conflict in steering torques. An exploratory analysis also revealed a surprising positive correlation between reaction times and the perception of sufficient control. Qualitative feedback from open-ended post-experiment questionnaires revealed that mismatches in intentions between the driver and automation, lack of safety, and resistance to driver inputs contribute to the reduction of perceived MHC, while subtle haptic guidance aligned with driver intent had a positive effect. These findings suggest that future designs should prioritise effortless driver interventions, transparent communication of automation intent, and context-sensitive authority allocation to strengthen meaningful human control in partially automated driving.

Tin T. Nguyen, Simeon C. Calvert, Guopeng Li et al.

The fast-growing amount of traffic data brings many opportunities for revealing more insightful information about traffic dynamics. However, it also demands an effective database management system in which information retrieval is arguably an important feature. The ability to locate similar patterns in big datasets potentially paves the way for further valuable analyses in traffic management. This paper proposes a content-based retrieval system for spatiotemporal patterns of highway traffic congestion. There are two main components in our framework, namely pattern representation and similarity measurement. To effectively interpret retrieval outcomes, the paper proposes a graph-based approach (relation-graph) for the former component, in which fundamental traffic phenomena are encoded as nodes and their spatiotemporal relationships as edges. In the latter component, the similarities between congestion patterns are customizable with various aspects according to user expectations. We evaluated the proposed framework by applying it to a dataset of hundreds of patterns with various complexities (temporally and spatially). The example queries indicate the effectiveness of the proposed method, i.e. the obtained patterns present similar traffic phenomena as in the given examples. In addition, the success of the proposed approach directly derives a new opportunity for semantic retrieval, in which expected patterns are described by adopting the relation-graph notion to associate fundamental traffic phenomena.

Yiru Jiao, Simeon C. Calvert, Sander van Cranenburgh et al.

Accurately and proactively alerting drivers or automated systems to emerging collisions is crucial for road safety, particularly in highly interactive and complex urban environments. However, existing approaches to identifying potential collisions either require labour-intensive annotation of sparse risk, struggle to consider varying contextual factors, or are only useful in specific scenarios. To address these limits, this study introduces the Generalised Surrogate Safety Measure (GSSM), a new data-driven approach that learns collision risk exclusively from naturalistic driving without the need for crash or risk labels. GSSM captures the patterns of normal driving and estimates the extent to which a traffic interaction deviates from the norm towards an unsafe state. Diverse data from naturalistic driving, including motion kinematics, weather, lighting, etc., are used to train multiple GSSMs, which are tested with 2,591 reconstructed real-world crashes and near-crashes. These test events are also released here as the largest dataset of its kind to date. A basic GSSM using only instantaneous motion kinematics achieves an area under the precision-recall curve of 0.9 and secures a median time advance of 2.6 seconds to prevent potential collisions. Additional interaction patterns and contextual factors provide further performance gains. Across various types of collision risk scenarios (such as rear-end, merging, and turning interactions), the accuracy and timeliness of GSSM consistently outperforms existing baselines. GSSM therefore establishes a scalable, context-aware, and generalisable foundation for proactively quantifying collision risk in traffic interactions. This can support and facilitate autonomous driving systems, traffic safety assessment, and road emergency management. Code and experiment data are openly accessible at https://github.com/Yiru-Jiao/GSSM.

Yiru Jiao, Sander van Cranenburgh, Simeon Calvert et al.

The effectiveness of neural network models largely relies on learning meaningful latent patterns from data, where self-supervised learning of informative representations can enhance model performance and generalisability. However, self-supervised representation learning for spatially characterised time series, which are ubiquitous in transportation domain, poses unique challenges due to the necessity of maintaining fine-grained spatio-temporal similarities in the latent space. In this study, we introduce two structure-preserving regularisers for the contrastive learning of spatial time series: one regulariser preserves the topology of similarities between instances, and the other preserves the graph geometry of similarities across spatial and temporal dimensions. To balance the contrastive learning objective and the need for structure preservation, we propose a dynamic weighting mechanism that adaptively manages this trade-off and stabilises training. We validate the proposed method through extensive experiments, including multivariate time series classification to demonstrate its general applicability, as well as macroscopic and microscopic traffic prediction to highlight its particular usefulness in encoding traffic interactions. Across all tasks, our method preserves the similarity structures more effectively and improves state-of-the-art task performances. This method can be integrated with an arbitrary neural network model and is particularly beneficial for time series data with spatial or geographical features. Furthermore, our findings suggest that well-preserved similarity structures in the latent space indicate more informative and useful representations. This provides insights to design more effective neural networks for data-driven transportation research. Our code is made openly accessible with all resulting data at https://github.com/yiru-jiao/spclt

Xue Yao, Simeon C. Calvert, Serge P. Hoogendoorn

Current approaches to identifying driving heterogeneity face challenges in comprehending fundamental patterns from the perspective of underlying driving behavior mechanisms. The concept of Action phases was proposed in our previous work, capturing the diversity of driving characteristics with physical meanings. This study presents a novel framework to further interpret driving patterns by classifying Action phases in an unsupervised manner. In this framework, a Resampling and Downsampling Method (RDM) is first applied to standardize the length of Action phases. Then the clustering calibration procedure including ''Feature Selection'', ''Clustering Analysis'', ''Difference/Similarity Evaluation'', and ''Action phases Re-extraction'' is iteratively applied until all differences among clusters and similarities within clusters reach the pre-determined criteria. Application of the framework using real-world datasets revealed six driving patterns in the I80 dataset, labeled as ''Catch up'', ''Keep away'', and ''Maintain distance'', with both ''Stable'' and ''Unstable'' states. Notably, Unstable patterns are more numerous than Stable ones. ''Maintain distance'' is the most common among Stable patterns. These observations align with the dynamic nature of driving. Two patterns ''Stable keep away'' and ''Unstable catch up'' are missing in the US101 dataset, which is in line with our expectations as this dataset was previously shown to have less heterogeneity. This demonstrates the potential of driving patterns in describing driving heterogeneity. The proposed framework promises advantages in addressing label scarcity in supervised learning and enhancing tasks such as driving behavior modeling and driving trajectory prediction.

Saeed Rahmani, Sabine Rieder, Erwin de Gelder et al.

The rapid development of automated vehicles (AVs) promises to revolutionize transportation by enhancing safety and efficiency. However, ensuring their reliability in diverse real-world conditions remains a significant challenge, particularly due to rare and unexpected situations known as edge cases. Although numerous approaches exist for detecting edge cases, there is a notable lack of a comprehensive survey that systematically reviews these techniques. This paper fills this gap by presenting a practical, hierarchical review and systematic classification of edge case detection and assessment methodologies. Our classification is structured on two levels: first, categorizing detection approaches according to AV modules, including perception-related and trajectory-related edge cases; and second, based on underlying methodologies and theories guiding these techniques. We extend this taxonomy by introducing a new class called "knowledge-driven" approaches, which is largely overlooked in the literature. Additionally, we review the techniques and metrics for the evaluation of edge case detection methods and identified edge cases. To our knowledge, this is the first survey to comprehensively cover edge case detection methods across all AV subsystems, discuss knowledge-driven edge cases, and explore evaluation techniques for detection methods. This structured and multi-faceted analysis aims to facilitate targeted research and modular testing of AVs. Moreover, by identifying the strengths and weaknesses of various approaches and discussing the challenges and future directions, this survey intends to assist AV developers, researchers, and policymakers in enhancing the safety and reliability of automated driving (AD) systems through effective edge case detection.

Saeed Rahmani, Zhenlin Xu, Simeon C. Calvert et al.

The integration of automated vehicles (AVs) into transportation systems presents an unprecedented opportunity to enhance road safety and efficiency. However, understanding the interactions between AVs and human-driven vehicles (HVs) at intersections remains an open research question. This study aims to bridge this gap by examining behavioral differences and adaptations of AVs and HVs at unsignalized intersections by utilizing two large-scale AV datasets from Waymo and Lyft. By using a systematic methodology, the research identifies and analyzes merging and crossing conflicts by calculating key safety and efficiency metrics, including time to collision (TTC), post-encroachment time (PET), maximum required deceleration (MRD), time advantage (TA), and speed and acceleration profiles. Through this approach, the study assesses the safety and efficiency implications of these behavioral differences and adaptations for mixed-autonomy traffic. The findings reveal a paradox: while AVs maintain larger safety margins, their conservative behavior can lead to unexpected situations for human drivers, potentially causing unsafe conditions. From a performance point of view, human drivers tend to exhibit more consistent behavior when interacting with AVs versus other HVs, suggesting AVs may contribute to harmonizing traffic flow patterns. Moreover, notable differences were observed between Waymo and Lyft vehicles, which highlights the importance of considering manufacturer-specific AV behaviors in traffic modeling and management strategies for the safe integration of AVs. The processed dataset, as well as the developed algorithms and scripts, are openly published to foster research on AV-HV interactions.

Xue Yao, Shengren Hou, Serge P. Hoogendoorn et al.

Lane-changing (LC) is a challenging scenario for connected and automated vehicles (CAVs) because of the complex dynamics and high uncertainty of the traffic environment. This challenge can be handled by deep reinforcement learning (DRL) approaches, leveraging their data-driven and model-free nature. Our previous work proposed a cooperative lane-changing in mixed traffic (CLCMT) mechanism based on TD3 to facilitate an optimal lane-changing strategy. This study enhances the current CLCMT mechanism by considering both the uncertainty of the human-driven vehicles (HVs) and the microscopic interactions between HVs and CAVs. The state-of-the-art (SOTA) DRL algorithms including DDPG, TD3, SAC, and PPO are utilized to deal with the formulated MDP with continuous actions. Performance comparison among the four DRL algorithms demonstrates that DDPG, TD3, and PPO algorithms can deal with uncertainty in traffic environments and learn well-performed LC strategies in terms of safety, efficiency, comfort, and ecology. The PPO algorithm outperforms the other three algorithms, regarding a higher reward, fewer exploration mistakes and crashes, and a more comfortable and ecology LC strategy. The improvements promise CLCMT mechanism greater advantages in the LC motion planning of CAVs.