Comparing Normalizing Flows with Kernel Density Estimation in Estimating Risk of Automated Driving Systems

The development of safety validation methods is essential for the safe deployment and operation of Automated Driving Systems (ADSs). One of the goals of safety validation is to prospectively evaluate the risk of an ADS dealing with real-world traffic. Scenario-based assessment is a widely-used approach, where test cases are derived from real-world driving data. To allow for a quantitative analysis of the system performance, the exposure of the scenarios must be accurately estimated. The exposure of scenarios at parameter level is expressed using a Probability Density Function (PDF). However, assumptions about the PDF, such as parameter independence, can introduce errors, while avoiding assumptions often leads to oversimplified models with limited parameters to mitigate the curse of dimensionality. This paper considers the use of Normalizing Flows (NF) for estimating the PDF of the parameters. NF are a class of generative models that transform a simple base distribution into a complex one using a sequence of invertible and differentiable mappings, enabling flexible, high-dimensional density estimation without restrictive assumptions on the PDF's shape. We demonstrate the effectiveness of NF in quantifying risk and risk uncertainty of an ADS, comparing its performance with Kernel Density Estimation (KDE), a traditional method for non-parametric PDF estimation. While NF require more computational resources compared to KDE, NF is less sensitive to the curse of dimensionality. As a result, NF can improve risk uncertainty estimation, offering a more precise assessment of an ADS's safety. This work illustrates the potential of NF in scenario-based safety. Future work involves experimenting more with using NF for scenario generation and optimizing the NF architecture, transformation types, and training hyperparameters to further enhance their applicability.

Operationalization of Scenario-Based Safety Assessment of Automated Driving Systems

Before introducing an Automated Driving System (ADS) on the road at scale, the manufacturer must conduct some sort of safety assurance. To structure and harmonize the safety assurance process, the UNECE WP.29 Working Party on Automated/Autonomous and Connected Vehicles (GRVA) is developing the New Assessment/Test Method (NATM) that indicates what steps need to be taken for safety assessment of an ADS. In this paper, we will show how to practically conduct safety assessment making use of a scenario database, and what additional steps must be taken to fully operationalize the NATM. In addition, we will elaborate on how the use of scenario databases fits with methods developed in the Horizon Europe projects that focus on safety assessment following the NATM approach.

Scenario-based assessment of automated driving systems: How (not) to parameterize scenarios?

The development of Automated Driving Systems (ADSs) has advanced significantly. To enable their large-scale deployment, the United Nations Regulation 157 (UN R157) concerning the approval of Automated Lane Keeping Systems (ALKSs) has been approved in 2021. UN R157 requires an activated ALKS to avoid any collisions that are reasonably preventable and proposes a method to distinguish reasonably preventable collisions from unpreventable ones using "the simulated performance of a skilled and attentive human driver". With different driver models, benchmarks are set for ALKSs in three types of scenarios. The three types of scenarios considered in the proposed method in UN R157 assume a certain parameterization without any further consideration. This work investigates the parameterization of these scenarios, showing that the choice of parameterization significantly affects the simulation outcomes. By comparing real-world and parameterized scenarios, we show that the influence of parameterization depends on the scenario type, driver model, and evaluation criterion. Alternative parameterizations are proposed, leading to results that are closer to the non-parameterized scenarios in terms of recall, precision, and F1 score. The study highlights the importance of careful scenario parameterization and suggests improvements to the current UN R157 approach.

Coverage Metrics for a Scenario Database for the Scenario-Based Assessment of Automated Driving Systems

Automated Driving Systems (ADSs) have the potential to make mobility services available and safe for all. A multi-pillar Safety Assessment Framework (SAF) has been proposed for the type-approval process of ADSs. The SAF requires that the test scenarios for the ADS adequately covers the Operational Design Domain (ODD) of the ADS. A common method for generating test scenarios involves basing them on scenarios identified and characterized from driving data. This work addresses two questions when collecting scenarios from driving data. First, do the collected scenarios cover all relevant aspects of the ADS' ODD? Second, do the collected scenarios cover all relevant aspects that are in the driving data, such that no potentially important situations are missed? This work proposes coverage metrics that provide a quantitative answer to these questions. The proposed coverage metrics are illustrated by means of an experiment in which over 200000 scenarios from 10 different scenario categories are collected from the HighD data set. The experiment demonstrates that a coverage of 100 % can be achieved under certain conditions, and it also identifies which data and scenarios could be added to enhance the coverage outcomes in case a 100 % coverage has not been achieved. Whereas this work presents metrics for the quantification of the coverage of driving data and the identified scenarios, this paper concludes with future research directions, including the quantification of the completeness of driving data and the identified scenarios.

A Quantitative Method to Determine What Collisions Are Reasonably Foreseeable and Preventable

The development of Automated Driving Systems (ADSs) has made significant progress in the last years. To enable the deployment of Automated Vehicles (AVs) equipped with such ADSs, regulations concerning the approval of these systems need to be established. In 2021, the World Forum for Harmonization of Vehicle Regulations has approved a new United Nations regulation concerning the approval of Automated Lane Keeping Systems (ALKSs). An important aspect of this regulation is that "the activated system shall not cause any collisions that are reasonably foreseeable and preventable." The phrasing of "reasonably foreseeable and preventable" might be subjected to different interpretations and, therefore, this might result in disagreements among AV developers and the authorities that are requested to approve AVs. The objective of this work is to propose a method for quantifying what is "reasonably foreseeable and preventable". The proposed method considers the Operational Design Domain (ODD) of the system and can be applied to any ODD. Having a quantitative method for determining what is reasonably foreseeable and preventable provides developers, authorities, and the users of ADSs a better understanding of the residual risks to be expected when deploying these systems in real traffic. Using our proposed method, we can estimate what collisions are reasonably foreseeable and preventable. This will help in setting requirements regarding the safety of ADSs and can lead to stronger justification for design decisions and test coverage for developing ADSs.

PRISMA: A Novel Approach for Deriving Probabilistic Surrogate Safety Measures for Risk Evaluation

Surrogate Safety Measures (SSMs) are used to express road safety in terms of the safety risk in traffic conflicts. Typically, SSMs rely on assumptions regarding the future evolution of traffic participant trajectories to generate a measure of risk. As a result, they are only applicable in scenarios where those assumptions hold. To address this issue, we present a novel data-driven Probabilistic RISk Measure derivAtion (PRISMA) method. The PRISMA method is used to derive SSMs that can be used to calculate in real time the probability of a specific event (e.g., a crash). Because we adopt a data-driven approach to predict the possible future evolutions of traffic participant trajectories, less assumptions on these trajectories are needed. Since the PRISMA is not bound to specific assumptions, multiple SSMs for different types of scenarios can be derived. To calculate the probability of the specific event, the PRISMA method uses Monte Carlo simulations to estimate the occurrence probability of the specified event. We further introduce a statistical method that requires fewer simulations to estimate this probability. Combined with a regression model, this enables our derived SSMs to make real-time risk estimations. To illustrate the PRISMA method, an SSM is derived for risk evaluation during longitudinal traffic interactions. It is very difficult, if not impossible, to objectively compare the relative merits of two SSMs. Instead, we provide a method for benchmarking our derived SSM with respect to expected risk trends. The application of the benchmarking illustrates that the SSM matches the expected risk trends. Whereas the derived SSM shows the potential of the PRISMA method, future work involves applying the approach for other types of traffic conflicts, such as lateral traffic conflicts or interactions with vulnerable road users.

Scenario Parameter Generation Method and Scenario Representativeness Metric for Scenario-Based Assessment of Automated Vehicles

The development of assessment methods for the performance of Automated Vehicles (AVs) is essential to enable the deployment of automated driving technologies, due to the complex operational domain of AVs. One candidate is scenario-based assessment, in which test cases are derived from real-world road traffic scenarios obtained from driving data. Because of the high variety of the possible scenarios, using only observed scenarios for the assessment is not sufficient. Therefore, methods for generating additional scenarios are necessary. Our contribution is twofold. First, we propose a method to determine the parameters that describe the scenarios to a sufficient degree without relying on strong assumptions on the parameters that characterize the scenarios. By estimating the probability density function (pdf) of these parameters, realistic parameter values can be generated. Second, we present the Scenario Representativeness (SR) metric based on the Wasserstein distance, which quantifies to what extent the scenarios with the generated parameter values are representative of real-world scenarios while covering the actual variety found in the real-world scenarios. A comparison of our proposed method with methods relying on assumptions of the scenario parametrization and pdf estimation shows that the proposed method can automatically determine the optimal scenario parametrization and pdf estimation. Furthermore, we demonstrate that our SR metric can be used to choose the (number of) parameters that best describe a scenario. The presented method is promising, because the parameterization and pdf estimation can directly be applied to already available importance sampling strategies for accelerating the evaluation of AVs.

Constrained Sampling from a Kernel Density Estimator to Generate Scenarios for the Assessment of Automated Vehicles

The safety assessment of automated vehicles (AVs) is an important aspect of the development cycle of AVs. A scenario-based assessment approach is accepted by many players in the field as part of the complete safety assessment. A scenario is a representation of a situation on the road to which the AV needs to respond appropriately. One way to generate the required scenario-based test descriptions is to parameterize the scenarios and to draw these parameters from a probability density function (pdf). Because the shape of the pdf is unknown beforehand, assuming a functional form of the pdf and fitting the parameters to the data may lead to inaccurate fits. As an alternative, Kernel Density Estimation (KDE) is a promising candidate for estimating the underlying pdf, because it is flexible with the underlying distribution of the parameters. Drawing random samples from a pdf estimated with KDE is possible without the need of evaluating the actual pdf, which makes it suitable for drawing random samples for, e.g., Monte Carlo methods. Sampling from a KDE while the samples satisfy a linear equality constraint, however, has not been described in the literature, as far as the authors know. In this paper, we propose a method to sample from a pdf estimated using KDE, such that the samples satisfy a linear equality constraint. We also present an algorithm of our method in pseudo-code. The method can be used to generating scenarios that have, e.g., a predetermined starting speed or to generate different types of scenarios. This paper also shows that the method for sampling scenarios can be used in case a Singular Value Decomposition (SVD) is used to reduce the dimension of the parameter vectors.

Procedure for the Safety Assessment of an Autonomous Vehicle Using Real-World Scenarios

The development of Autonomous Vehicles (AVs) has made significant progress in the last years. An important aspect in the development of AVs is the assessment of their safety. New approaches need to be worked out. Among these, real-world scenario-based assessment is widely supported by many players in the automotive field. Scenario-based assessment allows for using virtual simulation tools in addition to physical tests, such as on a test track, proving ground, or public road. We propose a procedure for real-world scenario-based road-approval assessment considering three stakeholders: the applicant, the assessor, and the (road or vehicle) authority. The challenges are as follows. Firstly, the tests need to be tailored to the operational design domain (ODD) and dynamic driving task (DDT) description of the AV. Secondly, it is assumed that the applicant does not want to disclose all of the detailed test results because of proprietary or confidential information contained in these results. Thirdly, due to the complex ODD and DDT, many test scenarios are required to obtain sufficient confidence in the assessment of the AV. Consequently, it is assumed that due to limited resources, it is infeasible for the assessor to conduct all (physical) tests. We propose a systematic approach for determining the tests that are based on the requirements set by the authority and the AV's ODD and DDT description, such that the tests are tailored to the applicable ODD and DDT. Each test comes with metrics that enables the applicant to provide a performance rating of the AV for each of the tests. By only providing a performance rating for each test, the applicant does not need to disclose the details of the test results. In our proposed procedure, the assessor only conducts a limited number of tests. The main purpose of these tests is to verify the fidelity of the results provided by the applicant.

Tagging Real-World Scenarios for the Assessment of Autonomous Vehicles

The development of Autonomous Vehicles (AVs) has made significant progress in the last years. An essential aspect in the development of AVs is the assessment of quality and performance aspects of the AVs, such as safety, comfort, and efficiency. Among other methods, a scenario-based approach has been proposed. With scenario-based testing, the AV is subjected to a collection of scenarios that represent real-world situations. The collection of scenarios needs to cover the variety of what an AV can encounter in real traffic. As a result, many different scenarios are considered, that are grouped into so-called scenario categories. We propose a method for defining the scenario categories using a system of tags, where each tag describes a particular characteristic of a scenario category. There is a balance between having generic scenario categories - very specific set of scenarios, while for another system one might be interested in a set of scenarios with a high variety. To accommodate this, tags are structured in trees. The different layers of the trees can be regarded as different abstraction levels. Next to presenting the method for describing scenario categories using tags, we will illustrate the method by showing applicable trees of tags using concrete examples in the Singapore traffic system. Trees of tags are shown for the vehicle under test, the dynamic environment (e.g., the other road users), the static environment (e.g., the road layout), and the environmental conditions (weather and lighting conditions). Few examples are presented to illustrate the proposed method for defining the scenario categories using tags.