Olaf Op den Camp

Erwin de Gelder, Maren Buermann, Olaf Op den Camp

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.

Erwin de Gelder, Jasper Hof, Eric Cator et al.

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.

Erwin de Gelder, Eric Cator, Jan-Pieter Paardekooper et al.

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.

Erwin de Gelder, Olaf Op den Camp

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.

Erwin de Gelder, Olaf Op den Camp

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.

Erwin de Gelder, Jeroen Manders, Corrado Grappiolo et al.

Scenario-based methods for the assessment of Automated Vehicles (AVs) are widely supported by many players in the automotive field. Scenarios captured from real-world data can be used to define the scenarios for the assessment and to estimate their relevance. Therefore, different techniques are proposed for capturing scenarios from real-world data. In this paper, we propose a new method to capture scenarios from real-world data using a two-step approach. The first step consists in automatically labeling the data with tags. Second, we mine the scenarios, represented by a combination of tags, based on the labeled tags. One of the benefits of our approach is that the tags can be used to identify characteristics of a scenario that are shared among different type of scenarios. In this way, these characteristics need to be identified only once. Furthermore, the method is not specific for one type of scenario and, therefore, it can be applied to a large variety of scenarios. We provide two examples to illustrate the method. This paper is concluded with some promising future possibilities for our approach, such as automatic generation of scenarios for the assessment of automated vehicles.