Modeling Interactions among Pedestrians and Cars in Shared Spaces [1st ed. 2022] 9783658383442, 9783658383459, 3658383445

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Fatema Tuj Johora

Modeling Interactions among Pedestrians and Cars in Shared Spaces

Modeling Interactions among Pedestrians and Cars in Shared Spaces

Fatema Tuj Johora

Modeling Interactions among Pedestrians and Cars in Shared Spaces

Fatema Tuj Johora Hannover, Germany This thesis was submitted as a dissertation in the Department of Informatics at Technische Universität Clausthal on 21/06/2021, and defended successfully on 30/9/2021. Examiners were Prof. Dr. Jörg P. Müller (first examiner), Prof. Dr.-Ing. habil. Monika Sester (second examiner, Leibniz University Hannover), and Prof. Emeritus Ümit Özgüner (third examiner, The Ohio State University).

ISBN 978-3-658-38344-2 ISBN 978-3-658-38345-9 (eBook) https://doi.org/10.1007/978-3-658-38345-9 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2022 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Responsible Editor: Stefanie Eggert This Springer Vieweg imprint is published by the registered company Springer Fachmedien Wiesbaden GmbH, part of Springer Nature. The registered company address is: Abraham-Lincoln-Str. 46, 65189 Wiesbaden, Germany

Acknowledgements I am very grateful to many people; without their academic and mental support, completing this PhD dissertation would not be possible. First of all, I would like to thank my supervisor, Prof. Jörg Müller, to believe in my potential as a PhD candidate, to support and guide me to be on the right track since 2016. Even with your busy schedule, you are always there whenever I need any academic guidance. I have learned many things from you about the academic world, including how to write a scientific paper. Many thanks for always being so friendly and welcoming. Up next, I would like to thank Prof. Monika Sester for your inspiration, guidance and also to give me a chance for research collaboration. I want to thank all other professors in SocialCars, Prof. Bernhard Friedrich, Prof. Markus Fidler, Prof. Dirk C. Mattfeld, and Prof. Mark Vollrath, for giving valuable feedback and guidance. I would also like to thank Prof. Ümit Özgüner to allow me to collaborate with your research team and guide me during my research stay. I would like to thank all my colleagues from SocialCars and the Institute of Informatics, TU Clausthal, for your support and valuable insights into my research. Especially, I want to thank Awad Mukbil and Hao Cheng for continually reviewing my scientific papers and presentations and giving insightful opinions. Also, I want to thank Jelena Fiosina, Sînziana-Maria Sebe and Rahi Avinash Shet for your insightful advice. I want to thank Jeannette Hermanns for helping me to translate the abstract of my dissertation into German. Thank you, Hao Cheng and Dongfang Yang, for our excellent scientific collaborations. I want to thank Andrea Thiele and Mirko Barthauer and Andrea Selle, Christine Kammann, Stefanie Kehl, and Sandra Karpenstein for guiding me in official tasks during my time in SocialCars and TU Clausthal, respectively. I want to thank my master and bachelor students for being so obedient and focused on your research. Especially, I thank Sakif Hossian and Suhair Ahmed for our fruitful collaboration in two scientific papers. I want to thank my friends for their love and support. Special thanks to Sakif Hossain, Humaun Rashid and Jahid Kabir Himon for proofreading my dissertation and giving valuable suggestions. I want to thank my parents and brothers for their unconditional love and support. Without their support and advice, I would not be able to come abroad for pursuing my higher study and career. I eagerly want to thank my husband for always supporting me, not only mentally but also by helping in household work to make it easy for me to concentrate on my research. Moreover, our fruitful discussion regarding my research gave me ideas and thanks for reading my papers and providing valuable comments.

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Acknowledgements

I want to thank all participants of the DFG research project MODIS (#248905318) and Robert Schönauer for sharing shared space data sets. Last but not least, I want to thank the German Research Foundation (DFG) to fund my research for three years through the Research Training Group SocialCars (GRK 1931). I want to thank TU Clausthal to fund my research currently.

Abstract Sustainable urban traffic and transport is a key to successful future development of our society. Urban traffic is predicted to increase further, and new traffic modalities, such as autonomous vehicles and cargo bikes, will emerge and complement traditional road users like pedestrians, bicycles, cars. The lack of traffic space makes it undesirable to maintain today’s strict separation of different modalities. Shared space design principles promote more flexible use of traffic infrastructure by enabling different traffic modalities to share the same space with few or no explicit regulations. Such traffic design also improves the liveability of urban spaces. Simulation technologies are becoming an essential tool for traffic planners and managers to analyze (1) the safety, efficiency, and human-friendliness of future urban areas and (2) the effects of new traffic modes, before these concepts and technologies are applied on the road. Realistic modeling and simulation of shared spaces are very challenging due to the dynamic nature of the environment and the absence of explicit traffic rules. Moreover, for modeling such mixed-traffic zones, one needs to capture not only different structural and behavioral aspects of heterogeneous road users but also various interactions among them, which further complicate the modeling task. The main contribution of this dissertation is a novel agent-based, realistic and general motion model of pedestrians and (human-driven) vehicles that can capture a large variety of interactions and be utilized to assess the applicability of different shared space schemes and also in the advent of autonomous vehicles. To develop the general model, we propose a novel iterative and continuous design process that includes analyzing, classifying and modeling different motion behaviors and interactions of road users, calibrating and evaluating the model performance. We recognize and classify motion behaviors of pedestrians and vehicles by conducting a literature review and investigating real-world shared space scenarios. The proposed model comprises three interacting modules to capture different levels of motion behaviors and interactions of road users: a module to plan the free-flow paths of road users (i.e., by only considering static obstacles); a force-based modeling module to capture the free-flow motion and simple (e.g., reactive) interactions, and an interactive decision-making module to manage complex situations where road users need to decide between different alternatives. We design a calibration methodology for fine-tuning the model parameters and capturing heterogeneity in pedestrians’ motion patterns. Model performance is evaluated in terms of realistic modeling and generalizability, i.e., its ability to realistically capture road users’ motion behaviors in different environmental settings, using four real-world data sets and several commonly-used metrics. Our results indicate that the proposed model yields significant performance for each considered data set in modeling realistic and safe trajectories of pedestrians and cars. More specifically, the model can suitably replicate the motion behaviors of road users from new environments with incremental integration of new behaviors and calibrating model parameters. From the angle of

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Abstract

computer science, we believe that this work develops a novel and valuable building block for the digital transformation of urban mobility planning. Keywords: Mixed-traffic, shared space, trajectory modeling, different motion patterns and behavior modeling, general motion model, game-theoretic social force model, microscopic model, multi-agent systems

Zusammenfassung Nachhaltiger Stadtverkehr und Transport sind der Schlüssel für eine erfolgreiche zukünftige Entwicklung unserer Gesellschaft. Es wird prognostiziert, dass der städtische Verkehr weiter zunehmen wird; dies ist verbunden mit der Entstehung neuer Verkehrsmodalitäten, wie autonome Fahrzeuge und Lastenfahrräder. Der Mangel an Verkehrsflächen im urbanen Raum wird die Fortführung der heute üblichen strikten Trennung der verschiedenen Modalitäten nicht ermöglichen. Shared-Space-Design-Prinzipien fördern eine flexiblere Nutzung der Verkehrsinfrastruktur, wobei verschiedene Verkehrsmodalitäten den gleichen Raum mit wenigen expliziten Regelungen miteinander teilen können. Eine solche Verkehrsgestaltung verbessert auch die Lebensqualität von Stadträumen. Simulationstechnologien werden zu einem wesentlichen Werkzeug für Verkehrsplaner und -manager, um (1) die Sicherheit, Effizienz und Nutzerfreundlichkeit zukünftiger Stadtgebiete und (2) die Auswirkungen neuer Verkehrsarten zu analysieren, bevor diese Konzepte und Technologien realisiert werden. Die realistische Modellierung und Simulation von Shared Spaces ist aufgrund der dynamischen Natur der Umgebung und des Fehlens expliziter Verkehrsregeln sehr anspruchsvoll. Außerdem muss man für die Modellierung solcher Mischverkehrszonen nicht nur verschiedene strukturelle und verhaltensbezogene Aspekte der heterogenen Verkehrsteilnehmer erfassen, sondern auch verschiedene Interaktionen zwischen ihnen; dies wirkt sich zusätzlich erschwerend auf die Modellierung aus. Der Hauptbeitrag dieser Dissertation ist ein neuartiges, realistisches und allgemeines Bewegungsmodell, das Game-Theoretic Social Force Modell (GSFM), mit Fokus auf Fußgänger, deren Interaktionen untereinander und mit Fahrzeugen. Das Modell kann eine große Vielfalt von Interaktionen erfassen; es kann unterstützen bei der Beurteilung der Anwendbarkeit verschiedener Shared-Space-Modelle sowie bei der Einführung von autonomen Fahrzeugen. Für die Entwicklung des allgemeinen Modells wurde ein neuer iterativer und kontinuierlicher Entwurfsprozess vorgeschlagen und angewendet; er beinhaltet die systematische Analyse, Klassifizierung und Modellierung verschiedener Bewegungsverhalten und der Interaktionen von Verkehrsteilnehmern, sowie die Kalibrierung und Evaluierung der Modellleistung. Wir erkennen und klassifizieren das Bewegungsverhalten von Fußgängern und Fahrzeugen, indem wir eine Literaturrecherche und Untersuchungen von realen Shared-Space-Szenarien einbeziehen. Das vorgeschlagene Modell umfasst drei interagierende Module, um verschiedene Ebenen des Bewegungsverhaltens und der Interaktionen von Verkehrsteilnehmern zu erfassen: ein Modul zur Planung der Wege der Verkehrsteilnehmer im freien Fluss (d. h. unter ausschließlicher Berücksichtigung statischer Hindernisse); ein physikalisches, kräftebasiertes Modellierungsmodul zur Erfassung der Bewegung im freien Fluss und einfacher (z. B. reaktiver) Interaktionen, sowie ein spieltheoretisches Entscheidungsmodul zur Bewältigung komplexer Situationen, in denen Verkehrsteilnehmer zwischen verschiedenen Alternativen entscheiden müssen. Dieses wird ergänzt um eine Kalibrierungsmethodik zur

x

Zusammenfassung

Feinabstimmung der Modell Parametern und zur Erfassung von Heterogenität in den Bewegungsmustern von Fußgängern. Das GFSM-Modell wird im Hinblick auf realistische Modellierung und Generalisierbarkeit bewertet, d.h., die Fähigkeit, das Bewegungsverhalten von Verkehrsteilnehmern in verschiedenen Umgebungen realistisch zu erfassen, wobei vier reale Datensätze und mehrere häufig verwendeten Metriken verwendet wurden. Unsere Ergebnisse zeigen, dass das vorgeschlagene Modell im Vergleich mit State-of-the-Art-Modellen durchweg gute Ergebnisse bei der Modellierung realistischer und sicherer Trajektorien von Fußgängern und Autos aufweist. Insbesondere kann das Modell das Bewegungsverhalten von Verkehrsteilnehmern in neuen Umgebungen mit inkrementeller Integration neuer Verhaltensweisen angemessen nachbilden und die Modellparameter kalibrieren. Wir glauben, dass diese Arbeit aus dem Blickwinkel der Informatik einen neuartigen und wertvollen Baustein für die digitale Transformation der städtischen Mobilitätssteuerung und -planung darstellt. Schlagworte: Modellierung von Mischverkehren, Shared Spaces, Trajektorienmodellierung, Fußgängermodellierung, Agentenbasierte Modellierung, Game-Theoretic Social Force Model, mikroskopisches Modell, Multiagentensysteme

Contents

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix List of Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi 1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Research Problem and Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Research Aim and Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Research Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Dissertation Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 1 3 5 6 8

2

Background and Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Shared Space Design Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Historical background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2 Aims of shared space design . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.3 Impacts of shared spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Interaction Patterns in Shared Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Motion behaviors of pedestrians . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Motion behaviors of vehicles . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 Motion behaviors of cyclists . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.4 Further discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Mixed-Traffic Modeling and Simulation . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Classification of traffic simulation models . . . . . . . . . . . . . . . . 2.3.2 Multiagent-based simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Modeling Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9 9 10 13 14 17 18 19 20 20 22 22 23 26

3

The State of the Art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

xi

xii

Contents

3.1

Path Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 Representation of environment . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2 Shortest path algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conventional Models for Motion Control . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Force-based models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Cellular automata models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3 Models for steering behaviors . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.4 Velocity obstacle models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Decision Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Rule-based constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Logit models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.3 Non-cooperative game theory . . . . . . . . . . . . . . . . . . . . . . . . . . Existing Shared Space Motion Models . . . . . . . . . . . . . . . . . . . . . . . . . Research Gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

29 30 31 32 32 34 35 37 37 37 38 39 40 44

4

GSFM: The Game-Theoretic Social Force Model . . . . . . . . . . . . . . . . . . 4.1 Selection of Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1 Path finding algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.2 Motion control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.3 Decision model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 The Modeling Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Interaction Recognition and Classification . . . . . . . . . . . . . . . . . . . . . . 4.4 Agent Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Path Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Force-based Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6.1 Classical social force model . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6.2 Extended social force model . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7 Interactive Decision-Making . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7.1 Pedestrian-to-car interaction modeling . . . . . . . . . . . . . . . . . . . 4.7.2 Pedestrian groups-to-car modeling . . . . . . . . . . . . . . . . . . . . . . 4.7.3 Car-to-car interaction modeling . . . . . . . . . . . . . . . . . . . . . . . . 4.8 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.8.1 Solving Stackelberg games . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.8.2 Representation of road users in LightJason . . . . . . . . . . . . . . . 4.8.3 Simulation model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

45 45 45 46 47 48 50 57 59 60 61 64 70 72 77 78 79 79 80 83

5

Data Sets and Evaluation Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 5.1 Data Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 5.2 Evaluation Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

6

Calibration Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 6.1 Genetic Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 6.2 Calibration of Model Parameters Universally . . . . . . . . . . . . . . . . . . . . 99 6.2.1 Calibration of SFM parameters . . . . . . . . . . . . . . . . . . . . . . . . . 99 6.2.2 Calibration of game parameters . . . . . . . . . . . . . . . . . . . . . . . . 100

3.2

3.3

3.4 3.5

Contents

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6.3

Identification of Different Movement Patterns of Pedestrians . . . . . . 101 6.3.1 Individual calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 6.3.2 Clustering on individuals’ parameters . . . . . . . . . . . . . . . . . . . 102 6.3.3 Group calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

7

Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 7.1 Goals and Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 7.2 Description of Experiments and Results . . . . . . . . . . . . . . . . . . . . . . . . 110 7.2.1 Realistic trajectory modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 7.2.2 Model generalizability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 7.2.3 Traffic safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 7.2.4 Comparing GSFM with a deep learning model . . . . . . . . . . . . 126 7.3 Interpretation of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

8

Towards Combining Expert- and DL-based Models . . . . . . . . . . . . . . . . 135 8.1 Agent Architecture in GSFM-vs-LSTM . . . . . . . . . . . . . . . . . . . . . . . . 135 8.2 Quantitative Results for Combined Model . . . . . . . . . . . . . . . . . . . . . . 136 8.3 Qualitative Results for Combined Model . . . . . . . . . . . . . . . . . . . . . . . 137

9

Conclusions and Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 9.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 9.2 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 9.3 Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 9.3.1 Model improvements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 9.3.2 Considering new modalities . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

List of Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 10

Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

List of Figures

1.1 1.2

Examples of shared spaces in Europe. . . . . . . . . . . . . . . . . . . . . . . . . . . Interactions among road users, evolving in different shared spaces. . .

2.1 2.2 2.3 2.4

A shared space in Brighton, UK ©Project for Public Spaces . . . . . . . . 9 Example of woonerf and calmed street in the Netherlands. . . . . . . . . . 12 InteRRaP architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 The conceptual structure of a Multiagent System (after Jennings [2000], p. 281) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.1

Different environment representation with valid moves (colored blue) within environment; (a) Grid, (b) Navigation Mesh and (c) Visibility Graph. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The social force model for capturing pedestrian dynamics, combining several simple forces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A set of rules to design boids: (a) Separation, (b) Cohesion and (c) Alignment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Steering behaviors: (a) Seek and Flee, (b) Path following, and (c) Unaligned collision avoidance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.2 3.3 3.4 4.1 4.2 4.3 4.4

4.5 4.6

A systematic process of formulating a general motion model for mixed-traffic environments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Interaction among multiple road users: (a) multiple conflicts (MC) and (b) multiple-user conflict (MUC). . . . . . . . . . . . . . . . . . . . . . . . . . . Types of observed interactions among road users (pedestrians and cars) in shared spaces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . An example of a shared space which combines both road zone (bidirectional motorized traffic) and intersection zone (multi-directional motorized traffic). Here, R indicates the central point of the intersection zone. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Field of View (FOV) of Pedestrians and cars. . . . . . . . . . . . . . . . . . . . . Effective field of view (FOV) compared to the actual FOV . . . . . . . . .

2 4

31 33 35 36 49 52 53

53 54 57 xv

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List of Figures

4.7 4.8

4.9 4.10 4.11 4.12 4.13 4.14 4.15 4.16 4.17 4.18 4.19

4.20 4.21 4.22 4.23 4.24 5.1 5.2 5.3 5.4 5.5 6.1 6.2 6.3 6.4

The conceptual architecture of an agent in the Game-Theoretic Social Force Model (GSFM). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Visibility Graph with the shortest path (colored red) and fine-tuned path (dotted and colored blue). The colored polygons represent static obstacles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Trajectory Planning of (a) Pedestrian and (b) Vehicle, at Intersection zone (the colored and patterned rectangles). . . . . . . . . . . . . . . . . . . . . . Form factor (Eq. 4.5) for anisotropic behavior. . . . . . . . . . . . . . . . . . . . The distance between a pedestrian’s current position and a line as boundary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Coherent group (left) vs. non-coherent group (right). . . . . . . . . . . . . . . The movement states of pedestrian groups. . . . . . . . . . . . . . . . . . . . . . . Modeling the continue and deviate strategies of pedestrian(s) while interacting with car(s) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . An example of a Stackelberg game, i.e., a leader-follower game between a pedestrian (P) and a car (C) with arbitrary utilities. . . . . . The rationale for selecting a car as the leader in any game for handling pedestrian(s)-to-car interaction scenarios. . . . . . . . . . . . . . . . The execution steps of a pedestrian(s)-to-car(s) interaction. . . . . . . . . . Payoff matrix of a game for handling a pedestrian(s)-to-car(s) interaction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Execution steps of a pedestrian group-to-car interaction with strategy 1, 2 and 3 as the decelerate, deviate and accelerate strategy of road users, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The payoff matrix of a game for handling a car-to-car interaction. . . . An example of a Stackelberg game between a pedestrian (P) and a car (C) with arbitrary payoffs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The representation of an agent in LightJason, split into two parts, i.e., agent mind and body. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The workflow of the GSFM simulation model. . . . . . . . . . . . . . . . . . . . Stepwise development of GSFM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A shared street in Hamburg, Germany. . . . . . . . . . . . . . . . . . . . . . . . . . . A shared space in Sonnenfelsplatz, Graz, Austria ©Helke Falk. . . . . . Mixed-traffic areas in a Chinese university campus : (a) an intersection inclus and (b) a roundabout. . . . . . . . . . . . . . . . . . . . . . . . . A car parking area in the Ohio State University campus, the USA. . . . Mixed-traffic data sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

58

59 60 63 64 66 67 69 70 71 72 73

78 79 80 81 84 86 88 88 89 90 91

The workflow of model calibration. Here, Θ denotes a set of parameters, and n can be 2 to 10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 The workflow of parameter calibration using a Genetic Algorithm. . . 99 The elbow method with the k-means clustering algorithm. . . . . . . . . . 103 Different clustered groups of pedestrians from the DUT data set with different motion patterns. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

List of Figures

7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 7.10 7.11 7.12

7.13 7.14

7.15 7.16 7.17 7.18 7.19 8.1 8.2

xvii

Multiple conflicts scenario among pedestrians and cars from the HBS data set. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 A multi-user conflict scenario among pedestrians and cars from the SPG data set. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 A scenario from the HBS data set containing pedestrians-to-cars crossing and car-following interactions. . . . . . . . . . . . . . . . . . . . . . . . . . 113 A interconnected conflict scenario from the HBS data set. . . . . . . . . . . 114 Pedestrians-to-car interaction from the DUT data set. . . . . . . . . . . . . . . 115 Subsequent pedestrians-to-car interactions from the HBS data set. . . . 116 Pedestrians-to-car interaction from the CITR data set. . . . . . . . . . . . . . 117 The difference in trajectory and speed of real and simulated pedestrians and cars of the HBS data set. . . . . . . . . . . . . . . . . . . . . . . . . 119 The difference in trajectory and speed of real and simulated pedestrians and cars of the DUT data set. . . . . . . . . . . . . . . . . . . . . . . . . 119 The difference in trajectory and speed of real and simulated road users of the DUT data set on the adjusted model. . . . . . . . . . . . . . . . . . 121 Surrogate safety measurement of pedestrians on the HBS data set. . . . 124 Surrogate safety measurement of pedestrians on the DUT data set. TTC and PET are measured in seconds. TTC can be classified in terms of severity: TTC ≤ 0.5 is short, 0.5 < TTC ≤ 2 is moderate, and TTC > 2 is long. PET > 4 has no traffic concern. . . . . . . . . . . . . . . 125 Surrogate safety measurement of pedestrians on the CITR data set. . . 125 The structure of the LSTM-DBSCAN model for any target agent i. ⊗ stands for the concatenation of the mapping module’s output and the target agent’s position at each time step. . . . . . . . . . . . . . . . . . . . . . . 127 The performance of GSFM and LSTM-DBSCAN on (a) the HBS data set and (b) the DUT data set. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 HBS scenario one. Here, the real trajectories are in black and the predicted trajectories are color-coded. . . . . . . . . . . . . . . . . . . . . . . . . . . 130 HBS scenario three. Here, the real trajectories are in black and the predicted trajectories are color-coded [Cheng et al., 2020a]. . . . . . . . . 131 HBS scenario three. Here, the real trajectories are in black and the predicted trajectories are color-coded. . . . . . . . . . . . . . . . . . . . . . . . . . . 131 DUT scenario. Here, the real trajectories are in black and the predicted trajectories are color-coded. . . . . . . . . . . . . . . . . . . . . . . . . . . 132 The conceptual architecture of an agent in the combined model, GSFM-w-LSTM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 The performance of the GSFM-w-LSTM model compared to the LSTM-DBSCAN and GSFM models estimated by Euclidean and Hausdorff distance, and heading error (a) on the HBS and (b) DUT data sets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

xviii

8.3

8.4

8.5

10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8

List of Figures

Comparison of the predictions by the GSFM model and the combined model. Ground truth trajectories (GT) shown in black color and predicted trajectories are color-coded. Cars are traveling diagonally. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 Comparison of the predictions by the LSTM-DBSCAN and the combined models. Ground truth trajectories (GT) shown in black color and predicted trajectories are color-coded. Cars are traveling diagonally. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 Comparison of the predictions by the GSFM model and the combined model. Ground truth trajectories (GT) are in black color, predicted trajectories are color-coded. The car is traveling from the right to the left direction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

Model implementation: the complete UML Class diagram. . . . . . . . . . 166 The detailed view of the UML diagram given in Figure 10.1 part one. 167 The detailed view of the UML diagram given in Figure 10.1 part two. 168 The detailed view of the UML diagram given in Figure 10.1 part three.169 The detailed view of the UML diagram given in Figure 10.1 part four.170 The detailed view of the UML diagram given in Figure 10.1 part five. 171 The detailed view of the UML diagram given in Figure 10.1 part six. 172 The detailed view of the UML diagram given in Figure 10.1 part seven. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 10.9 The detailed view of the UML diagram given in Figure 10.1 part eight.174

List of Tables

2.1

Worldwide applications of shared space designs [Anvari, 2013, 2030palette, 2020, Sorenson, 2017] . . . . . . . . . . . . . . . . . . . . . . . . . . . . Space sharing approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Speed and fatality rate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Observed advantages after reconstructing traffic spaces using shared space design principles [Frosch et al., 2019]. . . . . . . . . . . . . . . .

15

4.1 4.2 4.3 4.4

Before backward elimination for Car (Johora and Müller [2021], p .6) After backward elimination for Car (Johora and Müller [2021], p. 6) Before backward elimination (Pedestrian) . . . . . . . . . . . . . . . . . . . . . . After backward elimination (Pedestrian) . . . . . . . . . . . . . . . . . . . . . . . .

75 76 76 76

5.1

Statistics of Datasets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

6.1 6.2

The list of parameters in the GSFM model . . . . . . . . . . . . . . . . . . . . . . . 96 The list of parameters for car-to-car complex interaction and pedestrian group modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 The selection of parameters for performing clustering . . . . . . . . . . . . . 97 Universally calibrated values of the SFM and safety parameters . . . . . 100 The list of game parameters and their calibrated values . . . . . . . . . . . . 101 The calibrated values of model-specific parameters in GSFM-M1. Here, G1, G2, G3 are the clustered groups. . . . . . . . . . . . . . . . . . . . . . . 106 The calibrated values of model-specific parameters in GSFM-M3. Here, G1, G2, G3 are the clustered groups. . . . . . . . . . . . . . . . . . . . . . . 106 The calibrated values of model-specific parameters in GSFM-M2. Here, G1, G2, G3 are the clustered groups. . . . . . . . . . . . . . . . . . . . . . . 107

2.2 2.3 2.4

6.3 6.4 6.5 6.6 6.8 6.7 7.1

11 13 14

Quantitative results i.e., aADE(m) / aFDE(m) / SD(ms–1 ) of the classical SFM and all versions of GSFM in modeling pedestrians trajectories. Here, the bold number denotes the best score. . . . . . . . . . 122

xix

xx

List of Tables

7.2 7.3

Quantitative results of all versions of the GSFM model in modeling the trajectories of cars. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 List of Pros and cons of the GSFM and LSTM-DBSCAN models (Cheng et al. [2020a], p. 10) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

List of Acronyms

ANN AV BDI CITR

Artificial Neural Network Autonomous Vehicle Belief-Desire-Intention Control and Intelligent Transportation Research DUT Dalian University of Technology FOV Field of View GSFM Game-Theoretic Social Force Model HBS Hamburg Bergedorf Station ITS Intelligent Transport Systems MABS Multiagent-based simulation MC Multiple Conflicts NOAI Number of Active Interactions PCA Principal Component Analysis RVO Reciprocal Velocity Obstacle SPA Shortest Path Finding Algorithm SPE Sub-Game Perfect Nash equilibrium SD Speed Deviation VO Velocity Obstacle

ASL ADE CA DL

AgentSpeak Language Average Displacement Error Cellular Automata Deep Learning

DDM Deviation in DecisionMaking FDE Final Displacement Error GT Ground-Truth Trajectory ITE Institute of Traffic Engineers LRCA Long-Range Collision Avoidance Mechanisms MAS Multiagent System MUC Multi-User Conflict PET Post Encroachment Time PDM Probability Density Mapping SFM

Social Force Model

SGN

Social Groups and Navigation model Sonnenfelsplatz, Garz

SPG

TTC Time To Collision WCSS Within Cluster Sum Squares

of

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Chapter 1

Introduction

Urbanization is a global trend; over 50% of the world population lives in urban areas, supposed to increase to 68% by 2050 [UN-DESA, 2018]. Making urban spaces more livable and urban mobility more sustainable is a significant challenge for urban planners and traffic engineers. Computer Science can and must play a vital role to address this challenge by supporting the digital transformation of urban mobility systems and services. Agent-based modeling technologies have been shown to be instrumental for better understanding and evaluating the effects and effectiveness of design and interaction principles in socio-technical systems. In particular, this thesis analyzes the interaction patterns and assesses the safety of a specific and relatively novel urban design: shared space design. A major challenge in doing so is to obtain realistic models of different road user types and their interactions, e.g., guided by social protocols, in such places. The main contribution of this dissertation is that we propose a novel multi-layer, agent-based motion model of pedestrians and vehicles 1 and a novel design process that especially considers the criteria of generalizability of models. We evaluate the quality of our methods and model using different real-world data sets. We believe that this work constitutes - from the point of view of computer science - a novel and useful building block to support the digital transformation of urban mobility planning.

1.1 Motivation Shared space is an umbrella term for street design principles aiming to reduce the dominance of vehicles, vehicle speeds, and accident rates [Schönauer, 2017]. A formal definition of shared spaces is given by Reid (Reid [2009], p. 1) as “a street or place accessible to both pedestrians and vehicles that is designed to enable pedestrians to move more freely by reducing traffic management features that tend to encourage users of vehicles to assume priority”. 1 This dissertation only focuses on human-driven vehicles, not autonomous vehicles.

© The Author(s), under exclusive license to Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2022 F. T. Johora, Modeling Interactions among Pedestrians and Cars in Shared Spaces, https://doi.org/10.1007/978-3-658-38345-9_1

1

2

1 Introduction

Shared space design principles have been drawing considerable attention in recent years to reconstruct conventional streets in many urban areas, including large squares, university campuses, and shopping areas. Two examples are the shared square in Sonnenfelsplatz, Graz, Austria and shared street in Duisburg, Germany, visualized in Figure 1.1.

(a)

(b) Fig. 1.1: Examples of shared spaces in Europe: (a) a shared space in Sonnenfelsplatz, Graz, Austria ©Helke Falk and (b) a shared space in Duisburg, Germany ©Uwe Köppen.

However, the research community still holds split opinions on traffic safety and quality in shared spaces. Some studies suggest that the lack of explicit traffic rules in shared spaces make road users more safety aware, which results in fewer accidents [Hamilton-Baillie, 2008a, Monderman et al., 2006]. Also, pedestrian comfort and their activity seem to be increased in shared spaces, resulting in the enhanced liveliness of the place [Kaparias et al., 2012, Langdon, 2010]. Others argue that road users’ lack of acceptance and knowledge of the shared space concept can endanger their safety [Clayden et al., 2006, Jenks, 1983]. Moreover, disabled people tend to feel uncomfortable in such shared environments [Boampong et al., 2007].

1.2 Research Problem and Challenges

3

Rising demands and the absence of explicit traffic regulations and thereby caused uncertainty makes it crucial to comprehensively investigate and assess the safety and efficiency (e.g., average road user delays and road capacity) concerns in shared spaces during the planning phase, i.e., before risky and expensive field experiments. A realistic model that can reproduce the operations in shared spaces would be beneficial for this purpose. However, for realistic modeling of mixed-traffic situations, it is essential to understand the motion behaviors of individual road user (i.e., at the microscopic level) including how they decide and behave while interacting with others. There have been different methodologies for modeling motion behaviors of road users at the microscopic level; we can broadly distinguish them into two classes: (1) expert-based approaches [Schönauer, 2017, Bandini et al., 2017a], i.e., modeling and simulating road users’ movements with explicit analysis of their decision-making processes; and (2) data-driven approaches [Alahi et al., 2016, Cheng et al., 2020b] for learning and predicting road users’ motion based on (real-world) data. This dissertation is targeted on utilizing expert-based approaches to model and simulate shared space scenarios. Realistic simulation models are beneficial for measuring traffic safety and efficiency of traffic environments [Danaf et al., 2020]. Such models can also form a safe basis for autonomous cars to learn to interact with other road users or can be utilized to generate synthetic data of unusual patterns that are not easy to collect or find to train autonomous cars, e.g., using data-driven methodologies.

1.2 Research Problem and Challenges Mixed-traffic 2 simulation modeling is particularly challenging, because it requires not only to capture different structural and behavioral aspects of different road users, but also their interaction. According to Saunier and Sayed [2008], an interaction is “a situation in which two or more road users are close enough in space and time and their distance is decreasing". Understanding and modeling mixed-traffic interactions are far from trivial. An interaction can be a simple reaction or a result of complex human decision-making processes (i.e., adjusting speed or direction by predicting other’ behaviors or communicating with them [Rasouli and Tsotsos, 2019]); it depends on their transport modes, the situation dynamics and many individual factors (e.g., age, gender, or time pressure [Kaparias et al., 2012]).

2 Mixed-traffic users refers to different types of human road users.

4

1 Introduction

(a)

(b) Fig. 1.2: Interactions among road users, evolving in different shared spaces: (a) road-like environment [Pascucci, 2020] and (b) shared square (adapted from https://youtu.be/qgYzyGvMqjo).

To briefly explain the levels of complexity in interactions among road users, we represent two typical interaction scenarios, captured in two shared spaces with different road structures. In Figure 1.2a, a pedestrian is interacting with approaching vehicles from different directions to decide to cross or not to cross the road. Whereas in figure 1.2b, while making eye-contract with approaching vehicles, a group of pedestrians are walking through a shared space, where the only feasible reaction of both cars is to decelerate to avoid collisions with pedestrians and another car. These scenarios give us two important takeaways: (1) hierarchy (in terms of complexity) in interactions, i.e., reactive interaction and interaction involving complex decision-making processes (Figure 1.2a), and (2) depending on the environment structure, interaction among road users varies, e.g., unlike in Figure 1.2b, cars in Figure 1.2a do not

1.3 Research Aim and Objectives

5

need to interact with each other actively. These are only two example scenarios; shared spaces include many more diverse interaction scenarios (see Section 4.3), and a general motion model should realistically capture all these situations, which makes generating such models very challenging. Moreover, compared to conventional streets, modeling interaction among road users is more complex in shared spaces due to more freedom of movements and unregulated traffic. So far, there are not many works on simulation modeling of shared spaces to the best of our knowledge. We witness mainly two different state-of-the-art approaches: (1) physics-based models, most specifically the social force model (SFM) of pedestrian dynamics [Helbing and Molnar, 1995] with numerous extensions adding, e.g., new forces, decision-theoretic concepts, or rule-based constraints, to model vehicles [Schönauer, 2017, Anvari et al., 2015] or cycles [Rinke et al., 2017]; and (2) Cellular Automata (CA) models for modeling pedestrians [Bandini et al., 2017b], cars [Nagel and Schreckenberg, 1992], and also mixed-traffic flows [Zhang and Duan, 2007, Bandini et al., 2017a], but mainly in settings with explicit traffic regulations– which is not the case in most shared spaces. Although the models mentioned above perform well for modeling single bilateral interactions (i.e., for any point in time, a road user only handles a single explicit interaction with one other user), they do not thoroughly analyze interconnected interactions and multiple interactions (i.e., concurrent interactions with multiple competitive road users) among heterogeneous road users and social groups, and mostly ignore interaction among vehicles – which are very common in shared spaces. Previous works do not adequately reflect the differences in road users’ behaviors induced by differing environmental settings. These models are usually calibrated and validated in specific and limited mixed-traffic settings, which poses the question of whether these models generalize well in other settings. Moreover, these works mostly ignore modeling heterogeneity in motion behaviors of individual types of road users.

1.3 Research Aim and Objectives Our research aims to develop a general motion model that can realistically simulate various interactions among pedestrians and vehicles in shared spaces by addressing limitations in the previous works. We perform a detailed literature review on behavior modeling of road users in both homogeneous and mixed-traffic scenarios, most specifically in shared spaces, to determine the research gap (stated briefly in Section 1.2 and in details in Section 3.5). We define the following objectives to achieve the aim of this dissertation: – To analyze real-world mixed-traffic scenarios to understand and identify different motion patterns of pedestrians and vehicles and the differences in road users’

6

1 Introduction

behaviors in different environmental settings. Moreover, recognize important factors that comprise road users’ behavioral patterns. – To develop a microscopic motion model which is both general and realistic, i.e., can capture realistically both fundamental and environment-specific motion behaviors of pedestrians and cars, including various interaction among them in shared spaces and easily transferable to new environments. – To calibrate and evaluate the proposed model using real-world mixed-traffic scenarios. More specifically, evaluating the model in terms of generalizability and realistic behavior modeling.

1.4 Research Contributions The contributions of this dissertation are in the field of computer science, more specifically in agent-based traffic modeling technologies, which are listed in the following: – Investigate, recognize and classify interactions in shared spaces: We perform a literature review and analyze four real-world shared space data sets (including videos) to interpret motion behaviors of pedestrians and cars and recognize various interactions among them (see Section 2.2). We investigate both (1) fundamental motion behaviors of road users which are similar in shared spaces and traditional streets, e.g., following or stopping actions of cars; and (2) newly observed behaviors in shared spaces like courtesy behaviors of vehicles towards pedestrians, as a prerequisite for reproducing shared space interactions. We classify the observed interactions among road users into several categories based on the complexity of interaction, the numbers and types of participants involved, the interaction angle, and the environment structure. To capture the differences in road users’ behaviors in different environment structures, we broadly classify shared space areas into two classes: intersection (wider/open) zones and road zones (see Section 4.3). – Develop a microscopic motion model for pedestrians and cars: We propose a conceptually systematic and straightforward process of modeling general motion models and output a multi-layer model that can capture a large variety of motion behaviors of pedestrians and cars. Why multi-layer model? As stated in Section 1.2, realistic modeling of heterogeneous road users’ motion is challenging. It requires different levels of modeling, i.e., planning free-flow paths, modeling reactive and short-range evasive behaviors of road users and interactions among road users requiring a sequence of complex decision-making processes (e.g., road crossing example of a pedestrian in Figure 1.2a); a single model might fail to address them all. Thus, we review several methodologies for calculating optimal paths, controlling motion, and capturing decision-making processes of road users to select appropriate methods to

1.4 Research Contributions

7

address our research problem. Our proposed model includes three interacting layers (i.e., modules): path planning, force-based modeling, and interactive decision-making modules. The path planning module plans the free-flow path, the interactive decision-making module captures the complex decision-making processes, and the force-based module handles actual physical movements and reactive and short-range interactions of road users, and executes the decision-making module’s decisions of road users. Our model can capture heterogeneity in pedestrian motion. Different motion patterns of pedestrians are recognized by calibrating motion characteristics (e.g., sensitivity while interacting with others) of individual pedestrians and clustering them into different clustered groups. – Evaluate the motion model in terms of realistic trajectory modeling and generalizability: We qualitatively and quantitatively evaluate our proposed model in terms of realistic behavior modeling and generalizability using four real-world shared space data sets and widely-used evaluation metrics. We define a model as a realistic motion model if it can generate road users’ (1) realistic behavior patterns and (2) trajectories with a minimal error, i.e., less deviation from their real trajectories. We interpret the generalizability of a model as that it can be easily transferable to a new environment and capture various interactions of road users, both fundamental and environment-specific behaviors. It is an essential property of a motion model as it saves time and effort in modeling new behaviors of road users from scratch when capturing new environments; thus, we perform two experiments to analyze and evaluate the generalizability of our model.

8

1 Introduction

1.5 Dissertation Outline The remainder of this dissertation is organized as follows: Chapter 2 presents some fundamental concepts and explanations underlying the overall work of this dissertation, namely, the detailed description of shared space design principles, observed interaction patterns of road users in shared spaces, modeling paradigms and requirements for realistically modeling mixed-traffic trajectories. Chapter 3 discusses existing works on behavior modeling of road users in mixedtraffic environments, most specifically in shared spaces, to determine the research gap. To address the gap, several significant methodologies and also their applications are explained in this chapter. Chapter 4 describes the selection of the appropriate methods for building a general motion model. It also presents the modeling process, the conceptual structure and the implementation of the proposed multi-layer motion model of pedestrians and vehicles. Chapter 5 presents several real-world data sets with different settings (e.g., in terms of traffic volume and environmental structure) and evaluation metrics that are utilized to model, calibrate, and evaluate the proposed model. Chapter 6 describes the calibration methodology including objective functions to calibrate model parameters and clustering approaches to investigate heterogeneity in pedestrian motion. Chapter 7 gives a comprehensive evaluation of the proposed motion model using four real-world shared space data sets and several commonly used evaluation metrics. This chapter compares the proposed model with a deep learning (DL) model to investigate the differences between expert-based and DL-based models. This chapter also discusses the strengths and limitations of the proposed model based on the evaluation results. Based on the results of comparison between our model and the DL-based model in Chapter 7, we propose a combined model of these two approaches to gain their collective advantages in Chapter 8. Chapter 9 summarizes the contribution of this dissertation. It also discusses few aspects where further research is required to improve and extend the proposed model, such as by integrating new traffic modalities (specifically, autonomous car and bicycle) into the model.

Chapter 2

Background and Preliminaries

This chapter presents some basic concepts and explanations, which are necessary for understanding the dissertation work. As stated in Chapter 1, this study focuses on modeling realistic motion behaviors of pedestrians and vehicles in shared spaces; thus, in this chapter, the detailed description of shared space design principles with its historical background, aims and impacts, observed interaction patterns of road users in shared spaces, modeling paradigms and requirements for realistically generating of mixed-traffic scenarios are provided.

2.1 Shared Space Design Principles

Fig. 2.1: A shared space in Brighton, UK ©Project for Public Spaces

Urban streets play an important role in our society not only for facilitating travel from one place to another but also as a public place where people meet, socialize © The Author(s), under exclusive license to Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2022 F. T. Johora, Modeling Interactions among Pedestrians and Cars in Shared Spaces, https://doi.org/10.1007/978-3-658-38345-9_2

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2 Background and Preliminaries

and move around [Department for Transport and Government, 2007]. In the street, motorized vehicles and non-motorized road users such as pedestrians and cyclists often meet, raising concerns regarding safety (mainly for the most vulnerable one, e.g., pedestrians), priority distribution, and traffic congestion. In conventional traffic design, these problems are mostly addressed by separating motorized and nonmotorized road users’ motions through space segregation e.g., using bridges, tunnels, sidewalks, protected lanes, or time segregation (signals) or access restrictions (traffic signs/markings). An alternative approach to regulated traffic designs is shared space design initially introduced by a Dutch traffic engineer Hans Monderman [Monderman et al., 2006]. In shared spaces, road signs, signals, and markings are mostly removed to allow direct interaction among heterogeneous road users, guided by informal rules e.g., speed limitation, social protocols e.g., social courtesy or mutual respect, and negotiation. Uncertainty is deliberately introduced in shared spaces so that road users be more cautious regarding safety, as Monderman said [PPS, 2017]: “The greater the number of prescriptions, the more people’s sense of personal responsibility dwindles. We’re losing our capacity for socially responsible behavior.” Figure 1.1 visualizes a shared space scheme in Brighton, UK. Shared spaces started in the Netherlands, but over the recent years, have been gaining significant attention worldwide, as far afield as the USA and New Zealand. Table 2.1 lists locations where several real-world applications of shared space design principles are applied worldwide.

2.1.1 Historical background The concept of space sharing is not new and can be found in the Dutch woonerfs from the late 1960s [Collarte, 2012]. A woonerf is a residential street, designed with the aim to make a safe and pleasant area for pedestrians (specifically for children) where pedestrians get priority over motorized vehicles [Anvari, 2013]. In a woonerf street, particularly, there is no clear segregation between non-motorized (e.g., pedestrians and bicyclists) and motorized vehicles as for increasing the safety consciousness of all road users while traveling [Appleyard, 1980] and promoting social interactions. Collarte [2012] stated that a woonerf should feature the following properties: (1) an entrance threshold, (2) curve-linear and single surface arrangement, (3) calming traffic measures, e.g., speed bumps or small corner radii, (4) on-street irregular parking facility, and (5) outdoor furnishings like trees and benches. As visualized in Figure 2.2a, the entrance of a woonerf is marked by clear and self-evident sign(s) or mark(s) to make the road users aware that they are entering a woonerf where traffic regulations are different than a conventional street. In the UK, a woonerf is recognized as a home zone [Anvari, 2013]. As stated in [Appleyard and Cox, 2006], there is a slight difference between a woonerf and a home zone: a woonerf promotes a sense of place, while a home zone emphasizes easing traffic and reducing accidents.

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Table 2.1: Worldwide applications of shared space designs [Anvari, 2013, 2030palette, 2020, Sorenson, 2017]

Country Australia Austria

City/Place Bendigo, Cronulla, Kensington, Melbourne, Sydney Feldkirchen bei Graz, Gleinstätten, Graz, Vöcklabruck, Gnas, Velden am Wörther See Argentina Buenos Aires Belgium Ostende Brazil Rio de Janeiro Canada Montreal China Xiamen Denmark Ejby, Copenhagen, Odense, Christiansfeld, Lyngby, Aarhus Spain Madrid, San Sebastian, Barcelona, Bilbao France Paris, Bordeux Germany Blomberg, Bohmte, Calau, Duisburg, Endingen am Kaiserstuhl, Ettenheim, Frankfurt am Main, Hamburg, Haslach im Kinzigtal, Bonn, Luckenwalde, Potsdam, Rudersberg, Wolfach, Hatten OT Kirchhatten Greece Serres Hungary Debrecen Italy Milano Japan Muromachi, Nishiikebukuro Mexico Angela Peralta Netherlands Emmen, Donkerbroek, Drachten, Makkinga, Nijega, Oldeberkoop, Opeinde, Oosterwolde, Olderberkoop, Oudehaske, Wolvega, Haren New Zealand Auckland, Christchurch, Dunedin, Hamilton, Napier, Nelson, Orewa, Papakura, Waitakera, Wellington Portugal Braga Poland Lodz Sweden Norrköping Switzerland Zurich, Bern United King- Ashford, Bath, Brighton, Hove, Caernarfon, Leeds, Londom don, Newbury, Newcastle, Oxford, Shrewsbury, Southampton, Taunton, Woking, Preston United States West Palm Beach, Seattle, New York City, Madison, Eugene, Ipswich, Chicago, Santa Monica, Portland, Batavia, San Francisco

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(a)

(b)

Fig. 2.2: Example of woonerf and calmed street in the Netherlands: (a) a woonerf ©Erauch and (b) a calmed street ©Karl Fjellstrom, Far East Mobility.

Some concepts of woonerf were successfully exported to traffic calming design [Hass-Klau, 1989]. Unlike woonerfs, traffic calming approaches focus on relaxing traffic instead of promoting social interactions and motorized vehicles has priority over non-motorized road users. In traffic calming areas, different design components like speed bumps, chicanes, narrow carriageways, and restricted speed limits are used for reducing vehicles speed [Collarte, 2012]. The Institute of Traffic Engineers (ITE) (Lockwood [1997], p. 22) describes traffic calming as: “The combination of mainly physical measures that reduce the negative effects of motor vehicle use, alter driver behaviour and improve conditions for non-motorized street users.” Figure 2.2b visualizes a traffic calming area in Netherlands. Shared space designs where different types of road users share equal priorities, is the most recent form of space sharing schemes. However, the woonerf experience was necessary to construct shared spaces; firstly, it was the first legally recognized approach for building multi-functional street space and secondly, some concepts of woonerf such as single surface design and the depreciation of road markings/signs are passed on to shared space design. Differences in the woonerf, traffic calming and shared spaces are given in Table 2.2.

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Table 2.2: Space sharing approaches: Woonerf, traffic calming and shared spaces [Shearer, 2011, Anvari, 2013]

Comparison criteria Alternative names

Woonerf

Traffic calming zone Shared space

Home zone, resi- Traffic control, live- Naked intersections, dential yard able streets liveable streets, shared streets/zones Land use Residential Any land use Any land use Consideration Considered Not considered Considered of social interaction Design Flexible Standardized Flexible Objective Slowing down Slowing down traffic Multi-faceted traffic to enable social interaction Priority Pedestrian Motorized vehicles All road users share equal priority Initiated In the 1960s In the 1980s 1991 (first applied in 2004)

2.1.2 Aims of shared space design “The problem that many towns suffer is that, in trying to accommodate traffic, they have allowed streets to become so heavily dominated by vehicles, that those streets have lost their primary purpose, which is as places that attract people, that attract investment, that attract spending." - Ben Hamilton-Baillie 1[PPS, 2017]

Conventional traffic designs promote only the transport/movement function of the road but not the place function. Moreover, traffic control tools exempt drivers from using their intelligence to negotiate with their surroundings, increasing the risk of accidents same as John Adams’s argumentation, i.e., if shielded from hazards, humans read only the risk threshold [Monderman et al., 2006]. Conversely, shared space designs remove excessive traffic restrictions, give individuals equal priority and empower them to take responsibility for their behavior. The foremost aims of shared space designs are to improve traffic environments, road users’ safety, and community vibrancy by reducing the dominance of motor vehicles and utilizing the road space as a place besides to its transport function [Karndacharuk et al., 2014]. Similarly, Kaparias et al. [2012] mentioned that two main objectives of shared space are to increase pedestrians’ confidence and elevate drivers’ attentiveness. As stated in [Reid, 2009], the objectives behind building a successful shared space are as follows: 1 What is shared space? https://www.pps.org/article/what-is-shared-space.

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1. Inspire economic revival, e.g., increased property values or shop occupancy rates. 2. Ease pedestrian movement, e.g., by increasing pedestrian flow, and reducing delay. 3. Increase the sense of place by giving facilities, e.g., seating areas. 4. Reduce vehicle dominance, e.g., by allowing low vehicular speed. 5. Increase pedestrian activity to increase pedestrian comfort. 6. Enhance safety by reducing accident rates, e.g., by allowing a reduced speed for vehicles to around 30 km/h as the risk of severe injuries and death increase at speeds above 32 km/h (see Table 2.3). 7. Promote inclusive design, e.g., by including opinions from end-users. Speed Fatality rate 32 km/h 5% 48 km/h 45% 64 km/h 85% Table 2.3: Speed and fatality rate (Hamilton-Baillie and Jones [2005], p. 44)

2.1.3 Impacts of shared spaces Hans Monderman conducted some analysis of the influences of human factors on traffic accidents. Based on the findings, he performed another experiment in Drachten, a Dutch village by removing all signage and prescribed-traffic control to force motorist and non-motorized road users to interact to avoid or resolve any conflict situation. The results of his experiment were astonishing, not only were traffic speeds and the number of traffic incidents reduced, but the long-lost public space was also attained. Local stores, restaurants and bars (re)opened, not only intersections also an entire village without traffic lights, and signs emerged [Monderman et al., 2006].

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Table 2.4: Observed advantages after reconstructing traffic spaces using shared space design principles [Frosch et al., 2019].

Location Oudehaske and Makkinga, Netherlands [HamiltonBaillie, 2008b,a] Drachten, Netherlands [Gillies, 2009] Bohmte, Germany [Whitlock, 2007] Poynton, England [Kirkup, 2013, Express, 2013]

Advantages Vehicle speed reduced by 40%

In the first year, the number of accidents reduced from eleven accidents per year (on average) to two. On a busy street (12000 vpd), the number of accidents reduced from one per week to none in four weeks. Economic revival (i.e., 80% of retailers report increased turnover) and reduction in traffic speed (20 mph on average), delay, and congestion are observed. The number of traffic conflicts also reduced from 4-7 per year to 1 (minor accident) in the first three years. Exhibition Road, Lon- Reduction in the number and severity of traffic conflicts don, England [Ka- are observed. parias et al., 2013] Graz, Austria [Fis- Reduction in traffic speeds and required travel time of cher, 2011, Schönauer pedestrians and vehicles, improvement of social interacet al., 2012b] tions, awareness, and traffic safety (no reported accidents in the first four months) are observed. Bell Street Park, Seat- Vehicle speeds reduced and traffic safety improved. tle; Davis Street, Portland; Santana Row, Promenade, San Jose, USA [Behrens, 2014] Cambridge, MA Pedestrian activity increased and liveliness of the place [Langdon, 2010] improved. Market Square, Pitts- Social activity and business enhanced. burgh [Snyder, 2014] Fort Street, Auck- Significant reduction in vehicles’ speed, business enland [Nazla and hanced, gradual positive changes in road users perception Williamson, 2012] gradual, improvement in social activity, and raised pervasiveness of tourists are observed.

However, there is still an ongoing debate on traffic safety and quality of shared spaces. Some studies state that due to the lack of explicit traffic regulations, road users become more safety-conscious, which may lead to fewer road accidents [HamiltonBaillie, 2008a, Monderman et al., 2006, Kaparias et al., 2012]. Also, Gaventa [2004] recognized shared spaces as slow and safe environments which promote social negotiation between motorized and non-motorized road users to provide civilized urban

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places. Shared space designs encourage non-motorized modalities by adding more facilities for them and reducing the superiority of the automobile. Thus, traffic volume is expected or even seem to be reduced in shared spaces [Reid, 2009], resulting in a reduction of carbon dioxide (CO2 ) emission. Increasing the number of cyclists and pedestrians in shared spaces can improve these users’ safety based on Jacobsen’s “safety in numbers" effect [Jacobsen, 2015]. Moreover, contrary to the reduced vehicular speed, traffic delay lessens in shared spaces [Wargo and Garrick, 2016], could be due to the reason that traffic signs and signals are installed and programmed mostly without considering real-time situations, e.g., sometimes vehicles have to wait in red signal even if there are no incoming vehicles or pedestrians. On the contrary, some studies [Clayden et al., 2006, Jenks, 1983] argue that the lack of acceptance and understanding of the space sharing concept can compromise safety in shared spaces. The results of a study of British pilot home zones show that residents are worried about safety in shared surfaces, especially for their children’s safety. Some people even reject the space sharing concept completely [Clayden et al., 2006]. Moreover, Boampong et al. [2007] indicated that disabled people who are normally reliant on kerb lines and spatial contexts can feel uncomfortable in such shared environments. Thus, proper physical demarcation should be included in shared space designs for blind and vision-impaired people [Department for Transport and Government, 2007]. Table 2.4 lists the benefits of shared space designs observed in various real-world shared space environments and in most cases, shared space implementation has improved pedestrian safety, reduced traffic speed, and successfully managed both urban and rural areas. There are also some simulation-based studies on the evaluation of shared spaces. For example, in [Frosch et al., 2019], a comparison between conventional traffic design and shared space design in terms of easing traffic congestion is presented. At first, the authors simulated a congested traffic area (not a shared space) in West Virginia University in Morgantown as case study scene and calculated the performance measures of traffic, i.e. required travel time and delay in current traffic configuration. Next, they changed their simulation setting by adding different shared space properties and calculated the performance measures again. Calculated measures in different settings were then compared, and results indicate that in shared space setting, vehicle travel time and delays reduced by up to 43% and 66%, respectively. Shared space was also seen to enhance traffic reliability regarding travel times. In [Pascucci, 2020], the author simulated and evaluated the traffic quality and safety of alternative shared space scenarios in a simulator which has been developed, calibrated and evaluated using a shared space data set (including video data) from Hamburg, Germany. These alternative scenarios were prepared by varying traffic demand and the length of the shared area but not the place’s spatial architecture. The results indicate that pedestrian comfort is decreased when traffic volumes increase or the shared area’s size is reduced. Also, vehicles’ delay does not get affected by the shared road’s length but rises if traffic volumes increase.

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The above discussion about the space sharing concept and its benefits and flaws show that shared space design can be treated as an alternative to conventional traffic separation, but depending on the requirements ( e.g., place or movement or both functions, high or low traffic volumes), vulnerable users and size of the potential space [Gerlach et al., 2009]. Monderman said that even though conventional traffic designs are more appropriate for motorways and busy highways where the sole function of the space is traffic movement, in the public area, e.g., the city center, road signs or signals become unnecessary [Monderman et al., 2006]. Also, analyzing a place’s social, environmental, economical and behavioral factors is crucial before reconstructing it to a shared space [Luca et al., 2012].

2.2 Interaction Patterns in Shared Spaces The motion behavior of road users is led by their conscious and unconscious actions and reactions. A road user’s motion is the combination of her free-flow movement towards a destination and interaction with other road users to avoid and resolve conflicts. Following (Gettman and Head [2003], p. 8), we interpret the notion of conflict as “an observable situation in which two or more road users approach each other in time and space to such an extent that there is a risk of collision if their movements remain unchanged”. The concept of interaction is closely related to conflict [Perkins and Harris, 1968]. In this dissertation, we define interaction as – the negotiation and/or cooperation of road users over the shared space to avoid or resolve possible collision. – the cooperation among group members to maintain social groups. Every interaction is the outcome of complex human decision-making processes, which depends on the current circumstances, types of road users involved, and several individual factors (e.g. age, gender, learned rules and experiences [Zheng et al., 2017]). A new set of social protocols, e.g., seeking eye contact with each other to conduct, appeared in shared spaces, as mentioned by Hamilton-Baillie, a well-known urban designer, in [Monderman et al., 2006]. In shared spaces, road users often seem to concurrently interact with multiple road users to avoid a conflict situation, e.g., to cross a road, pedestrians might need to interact with vehicles coming from both directions. We define such a situation as a multiple conflicts situation, which can be a combination of multiple single conflicts between two road users or a single conflict including multiple road users. Pedestrians, vehicles and cyclists are the most common participants in shared spaces. Thus, the basic movement behavior of pedestrians (including pedestrian groups), vehicles and cyclist and also their interactions in shared spaces are discussed in the following:

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2.2.1 Motion behaviors of pedestrians Although individual pedestrians have unique properties and sometimes behave more or less chaotic [Helbing et al., 2002], many similarities can be observed in their behaviors. In general, the behaviors of pedestrians can be classified into three categories [Crociani et al., 2015]: – Strategic behavioral level: At this level, pedestrians prepare their conceptual plan to stimulate their overall motion before entering into the traffic environment. As an example, a person plans to go shopping in the city center. She would plan in advance things like desired path and the mode of transport, e.g., from home to the city center she will go by bus, then walk to the shop. – Tactical behavioral level: Pedestrians plans, defined on a strategic level, may need modification due to the changes in their local environment. Hence, at this level, they characterize and finalize their activities by re-examining the strategies according to current circumstance. As an example, while walking, a person might need to re-plan her path due to abrupt weather change or consideration of future conflicts in extreme traffic. – Operational behavioral level: At this level, pedestrians’ actual physical movement along their predefined path and the execution of their activities are managed. Their motion is conducted through interacting with their environment (by perceiving and changing its states) and evading other road users and obstacles those come on their way. Pedestrians avoid collision with other pedestrians by longitudinal or lateral evasive maneuvers. While interacting with higher mode of road users e.g., vehicles, for pedestrians, time gap plays an important role for deciding strategy to avoid collision, and their accepted time gap somewhat depend on their age [Kadali and Vedagiri, 2013]. Kadali and Vedagiri [2013] found that the mean values of gap size for elderly, middle-aged and young people are 4.75, 3.35 and 3.5 seconds, respectively. Based on the observation of several shared space schemes in the UK, Shore et al. [2010] mentioned that pedestrians most frequently interact with vehicles than other user modes, and they gave way to vehicles in 69% of the time. However, in some shared space schemes such as Elwick Square in Ashford, New Road in Brighton, and Seven Dials in London, both pedestrians and vehicles gave way equally during interactions. Compared to conventional roads, the motion of pedestrians is more distributed in shared spaces [Shore et al., 2010]. Pedestrians feel more comfortable in shared spaces if their presence is clear to other types of road users. They prefer low vehicular traffic, high pedestrian flow, sufficient lighting and pedestrian-only facilities.

2.2 Interaction Patterns in Shared Spaces

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Motion Behaviors of Pedestrian Groups According to an empirical analysis of public areas handled by Moussaïd et al. [2010], the proportion of pedestrians travailing in social groups can be as high as 70%. We describe a social group according to [Moussaïd et al., 2010] as, “it is not only referring to several proximate pedestrians that happen to walk close to each other, but to individuals who have social ties and intentionally walk together, such as friends or family members". While interacting with a single pedestrian; naturally, social groups assume that the pedestrian will avoid the conflict; thus, they do not react. If the pedestrian do not take action to avoid the collision, each member of the group responds separately and the group reform afterwards. In case of interaction with other groups or road users with a higher mode, e.g. cyclists or vehicles, the group members typically solve the conflict by utilizing the group leader’s avoidance strategy (s) or breaking into small groups. The leader acts similar to a single person would, but taking into account the group’s spread [Rinke et al., 2017].

2.2.2 Motion behaviors of vehicles Similar to pedestrian motion, the task of driving (human-driven car) can be classified into three levels of control [Michon, 1985]: – Strategic level: At this level, drivers generally plan routes based on required time, cost or other criteria such as involved risk. – Tactical level: At this level, they make maneuver decisions such as a gap or lane selection, overtaking other vehicles and avoiding accidents. – Operational level: This level controls the physical movement of the vehicle. The speed and visibility are drivers’ external ability to interact with the environment, while attentiveness is their inner sense to avoid any possible conflict with other road users [Hobson, 2008]. Even though quantifying attentiveness is hard as it is an internal state, existing research indicates that 65% of near-crashes and almost 80% of crashes linked with driver negligence. The environment can stimulate or suppress the alertness of drivers. Engwicht [2005], an Australian social inventor and road philosopher, has identified intrigue, uncertainty, and humor as drivers’ mental speed bumps to make drivers more attentive about their surroundings; thus, they drive more slowly, increasing road safety. In shared spaces, uncertainty is deliberately introduced; thus, the mean and maximum traffic speeds have declined [Shore et al., 2010, Schönauer et al., 2012a]. Bliek [2010] compared the likelihood of cars stopping to let pedestrians go first at two conventional intersections and two shared spaces in Montreal, with relative size and traffic volume. The results indicate that drivers stop more often in shared spaces

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than in conventional crossings. This response can result from environmental design, speed restrictions, traffic and crowd flow and volume during interaction in shared spaces [Shore et al., 2010]. In a crowded environment, particularly in the presence of children and the elderly, drivers feel more alert and oblige to give way, but also feel uneasy which decreases their willingness to share the space [Kaparias et al., 2012]. Even though the shared space philosophy might clash with public transport’s need for prioritization and barrier-free access at the bus/tram stops as mentioned in [Nickel, 2009], buses or good transport are seen to pass through the shared space.

2.2.3 Motion behaviors of cyclists An empirical study on cyclists’ behavior while changing direction indicates that cyclists develop a visual scanning strategy focusing on recognizing more common and vital hazards, but ignore less frequent threats [Näätänen and Summala, 1974]. To avoid a conflict with others, cyclists often deviate from their trajectory instead of executing a complete stop as it requires a lot of energy. The reaction’s magnitude depends on their speed as maximal centripetal acceleration limits trajectory’s curvature [Rinke et al., 2017]. Duncan [2016] analyzed and found that cyclists rode similarly both in shared and controlled intersections. However, Ben Hamilton Baillie, a well-known urban designer, mentioned that in the Netherlands, cyclists, who rarely use hand signals, started to use unique finger signals. Also, a truck and a cyclist passing each other within meters was considered risky earlier in the UK. However, it now seems normal in shared spaces as road users adopt new behaviors to interact with each other [Monderman et al., 2006].

2.2.4 Further discussion As mentioned earlier, this dissertation focuses on modeling the motion behaviors of pedestrians and vehicles in shared spaces. Thus, how their behavior differs in different environment settings and how they interact with each other are further discussed. The following findings are acquired based on the observation of real-world scenarios and literature review:

Environmental Design Shared spaces are implemented in the environment with different structural designs, e.g., roads and squares of diverse scale and capacity [Schönauer, 2017]. The behavior of pedestrians and vehicles differ regarding their environment structure.

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1. Difference in interaction: At the road-like shared spaces, the main interaction between vehicles is that they follow each other and form an imaginary lane. Whereas, at an intersection or in a more open space, interaction among vehicles might be required to negotiate their priorities over shared spaces explicitly. 2. Difference in trajectory: Pedestrians mostly follow the shortest path to cross the road at a road-like area, whereas in intersections or squares, they tend to go through the safe zone, i.e., pedestrian only area (if any). In open spaces, even vehicles also somewhat deviate from their trajectory due to reactive interaction with pedestrians. 3. Difference in motion: By designing the shared space in totality, i.e., increasing the space sharing between all road users, lowers the speed and stop-and-go behavior of traffic and facilitate the continuous movement of both pedestrian and vehicles [Shore et al., 2010, Schönauer et al., 2012a, Shearer, 2011].

Design Elements Different design elements can influence road users’ motion behavior in several ways [Schönauer et al., 2012a]. For example, kerbs, benches, or regions covered with grass and trees have a separating and guiding impact on traffic behavior and can be utilized as a safe zone for pedestrians. The inclusion of “safe zones", “safe spaces" or “comfort spaces" into shared spaces for pedestrians can increase their comfort and confidence to move around the space [Kaparias et al., 2012, Melis-Dankers et al., 2015]. Points of interests, e.g., shops and seats, attract road users and act as the origin (temporal) destination point.

Traffic Speed and Volume In shared spaces, road users’ behavior and safety are facilitated by speed limits [Shore et al., 2010, Schönauer et al., 2012a]. In areas with a lower speed limit, vehicles favor giving way to pedestrians. If the speed limit exceeded 25 km/h, the willingness of drivers to give way to pedestrians drops drastically [Anvari, 2013]. Traffic volume also has an impact on road users’ motion behavior. When traffic volume is low, the usage of available space changes, both pedestrians and cars use shortcuts that will shorten their commuting time [Schönauer et al., 2012a].

Other Mixed-Traffic Spaces The above-discussed motion behaviors of road users are not only observed in shared spaces, but similar behaviors are also observed in other mixed-traffic scenarios, in particular, uncontrolled crossing or a permissive right or left turn intersection with pedestrians crossing in the right/left-hand traffic [Ni et al., 2016], as in such

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places traffic regulations are weakened. Moreover, some of the discussed properties of road users such as car-following and stopping behaviors of vehicles, pedestrians’ group formation and maintaining, and both modes’ free-flow movements are general behaviors, observed both in conventional and shared traffic spaces.

2.3 Mixed-Traffic Modeling and Simulation Traffic simulation is an essential tool to predict and understand the behavior of road users and also to measure and evaluate performance parameters such as traffic efficiency, safety and environmental issues to develop and optimize road infrastructure, traffic control or advanced Intelligent Transport Systems (ITS) [Archer, 2005]. Compared to conventional traffic designs, road users often interact with each other to coordinate their trajectories and avoid collisions in shared spaces. Increasing demands (see Table 2.1) and the lack of explicit traffic controls and thereby caused uncertainty make it critical to investigate and evaluate shared spaces’ safety issues and efficiency (average delays, road users’ comfort and road capacity) during the planning phase, especially from traffic designers’ perspective. Realistic modeling and simulation of the motion behaviors and interactions of road users can reproduce the shared space operations and be used to estimate and evaluate its performance [Danaf et al., 2020, Pascucci, 2020].

2.3.1 Classification of traffic simulation models Traffic simulation models can be classified into the following four categories with regard to granularity [Hoogendoorn and Bovy, 2001]: 1. Submicroscopic models: These models provide higher-level details of vehicles’ mechanisms (e.g., vehicle physics, steering and perception) and environmental conditions (e.g., weather, road surface, and road lighting). In submicroscopic models, the correlation of friction, gravity, and lateral forces with vehicle components (e.g. engines, brakes) and its environmental system are described using dynamic equations. Thus, these models facilitate the causal understanding of driving behavior, such as analyzing the association between headway and skid resistance of vehicles in rainy circumstances [Samoili et al., 2011]. However, these models might not guarantee enhanced quality for the overall simulation [Schönauer, 2017]. 2. Microscopic models: In microscopic models, individuals are modeled with unique identifiers, associated attributes, operational features, and behaviors, assuming that individuals’ interaction with their surroundings will bring out the overall traffic dynamic. Modeling road users’ behavior using this approach becomes feasible, as their microscopic properties like origins, destinations, current

2.3 Mixed-Traffic Modeling and Simulation

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positions, speeds or velocities are measurable. Microscopic simulations are frequently applied in the field of traffic control and optimization, safety and accident analysis and impact assessment of modern management technologies [Schönauer, 2017]. 3. Macroscopic models: Macroscopic models are only concerned with cumulative traffic behavior, e.g., density or flow rather than with the individual road user. As these models work on the aggregation level, they do not require high computation, but their accuracy is compromised. These models are frequently used to investigate and predict traffic demand of an entire network, e.g., region or country [Schönauer, 2017]. 4. Mesoscopic models: The blending of macroscopic and microscopic models result in mesoscopic models. These models usually define road users in great detail, but describe their motion behavior and interaction in smaller detail. Mesoscopic models are useful in situations when the microscopic simulation elements are desirable but infeasible, e.g., because of extensive network size or restricted resources [Schönauer, 2017]. Microscopic models work at the individual level; they can model individual’s behavior, interaction patterns, and preferences. As the primary focus of this dissertation is to model road users’ motion behavior and interactions to estimate traffic performance rather than modeling road user’s detailed physical mechanisms, microscopic simulation modeling is an appropriate choice.

2.3.2 Multiagent-based simulation Multiagent-based simulation (MABS) is a microscopic modeling paradigm to simulate complex socio-technical systems like transportation system. In a multiagentbased mixed-traffic simulation, each road user can be represented as an autonomous agent with individual characteristics. The concept of autonomous agents and multiagent system are discussed in details in the following for an better understanding of MABS.

2.3.2.1 Autonomous agents An agent is an independent individual, situated in an environment, who is able to perceive its surrounding, make decisions based upon its internal states and the sensed data, and act to change the state of its environment. Normally, this sense-decide-act cycle is a continues process [Wooldridge, 2009, Bordini et al., 2007]. According to Wooldridge and Jennings [1995], an intelligent agent should have these three attributes:

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– Pro-activeness: The ability of an agent to exhibit goal-directed behaviors for satisfying its design purposes. – Reactivity: It means being alert of any changes in the environment and respond to these changes in a timely fashion. – Social ability: It implies to an agent’s capability to being cooperative and coordinate activities with other agents, to achieve common goals. There are three kinds of agent available, namely, human agent, robotic agent and software agent [Stuart et al., 2003]: – Human agents can sense their environment, e.g., using their eyes or ears and act upon their environment, e.g., using their legs, mouth, or different body parts. – Robotic agents perceive their surrounding, e.g., using cameras or laser range finders and perform actions using different actuators. – Software agents are computational objects that both sense and act on their environment using encoded bit strings. An agent has a set of actions and requires to interact with its surroundings regularly. Typically, environments are non-deterministic; thus, the same action may have different effects in different situations. In any specific situation, for an agent, choosing the best action among different alternatives to achieve its goal is a big challenge [Wooldridge, 2009]. Many models enable designing intelligent agents with complex decision processes. One of the best among them is the belief-desire-intention (BDI) model which facilitates modeling human-like behavior [Bordini et al., 2007]. Beliefs are an agent’s knowledge regarding its current state and environment. Desires imply all the states of affairs of an agent that it desires to achieve. Intentions are an agent’s desires that it has chosen to act on. In the BDI model, the process of mapping an agent’s beliefs, desires and intentions to its actions is recognized as practical reasoning. Following is the control cycle of practical reasoning for developing a BDI agent, i.e., a knowledge-based cognitive agent: 1. To perceive the world and update beliefs accordingly; 2. To determine which desire will become intention, i.e., to be fulfilled based on strategic thinking. 3. To use means-ends reasoning for finding an appropriate plan to accomplish the intention. Means-ends reasoning is the process of determining the way i.e., a plan, to accomplish an intention using the available means, i.e. the actions. 4. To execute the plan.

2.3 Mixed-Traffic Modeling and Simulation

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Fig. 2.3: InteRRaP, a hybrid architecture for designing intelligent agent (Müller [1996], p. 53)

A practical application of the BDI concept is InteRRaP architecture, where the agent’s internal state (i.e., knowledge base) and control are organized into a hierarchy of three interacting layers [Müller, 1996]. The principal types of interactions between these layers are, namely, bottom-up activation and top-down execution. The InteRRaP architecture for modeling intelligent agent is visualized in Figure 2.3, and its control layers are described in the following: – Cooperative planning layer: This layer facilitates explicit cooperation and coordination among agents. – Local planning layer: This layer is responsible for planning local tasks, and goal-directed behavior of agents. – Behavior-based layer: This layer handles the reactive behaviors of agents.

Fig. 2.4: The conceptual structure of a Multiagent System (after Jennings [2000], p. 281)

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2.3.2.2 Multiagent system A multiagent system (MAS) is a computerized system comprised of many interacting agents, varying from reactive to cognitive agents, within an environment [Drogoul et al., 2002]. MAS is capable of handling complex operations which are challenging or impossible for an individual agent to perform. In MAS, agents interact with each other to cooperate or coordinate their activities and also negotiate their sphere of influence, as visualized in Figure 2.4. Following are the essential characteristics of a multiagent system [Wooldridge, 2009]: – Autonomy: All agents are partially or fully independent, i.e., able to achieve their goals mostly autonomously. – Local views: Agents have a local view over their environment as normally, their angle of view is limited, and also, the system can be overly complex for an agent to acquire all knowledge. – Decentralization: In MAS, no agent has the exclusive right to control all other agents to avoid being a monolithic system [Panait and Luke, 2005]. Multiagent systems have been increasingly used to simulate the real-world scenarios, for instance, in computer games and traffic simulation [Siebers and Aickelin, 2008]. Other areas where MAS commonly used are electronic commerce, manufacturing, robotics and telecommunications [Leitão et al., 2013]. In this work, the multiagent-based simulation approach is chosen to imitate the motion behaviors of pedestrians and vehicles as this approach can capture both reactive and cognitive behavior of individual road users.

2.4 Modeling Requirements Modeling mixed-traffic is challenging as it requires capturing different structural and behavioral aspects of heterogeneous road users concurrently with interaction among them. Moreover, shared spaces also differ in terms of environment structure (e.g., road, square), design elements, cultures, traffic mixes, and density. As explained in Section 2.2, road users’ motion behaviors vary in different shared space designs, which need to be considered while building a simulation model for realistically capturing shared space scenarios. Based on the discussion in Section 2.1.2 and Section 2.2, the following are the requirements for reproducing operations of shared spaces, at a microscopic level: – Interaction recognition and classification: Based on a literature review (Section 2.2) and analyzing real-world (video) data, recognition of (1) basic motion behaviors of road users such as following, stopping or turning actions of vehicles, which are similar both in shared space and conventional streets; and (2) the overall

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and environment-specific interaction patterns in shared spaces is a prerequisite for reproducing shared space interactions. – Path planning: As mentioned in Section 2.2, road users often plan their desired path to their destination, before actually start moving, which sometimes need to be reevaluated due to changes in their environment. Objects like boundary of building and design elements, e.g., trees, seating or safe zones have a guiding effect on movement behavior of shared space users [Anvari, 2013]. Therefore, these static obstacles should be taken into consideration while planning paths of road users. – Fundamental motion control: The free-flow motion of road users considering their physical constraints, e.g., size, speed and steering properties, need to be generated realistically. The speed profile, physical properties and density of both vehicular and pedestrian traffic should be defined as per shared space traffic rules and observations. – Interaction modeling: Shared spaces are designed to promote shared priority and free movements of motorized and non-motorized users in a two-dimensional space. Road users more frequently interact with each other to avoid conflicts and coordinate their trajectories. Interaction among road users depends on personal factors, e.g., age, gender or time-pressure, and various traffic factors involved in the current circumstance, e.g., road users speed, traffic density, or inter distance among road users. These interactions can vary from a simple evasive action to complex interaction [Helbing and Molnar, 1995] where road users need to modify their speed or direction by predicting others’ behavior, or communicating with them [Rasouli and Tsotsos, 2019]. The requirements to model reactive behavior and short-range evasive behavior are different from modeling long-range interaction that requires a sequence of complex decision-making processes (e.g., road crossing example of pedestrians); thus, a single model might fail to address them all. The first type mostly depends on the observed and measured properties, and commonly reproduced using physicsbased, or Cellular Automata approaches. Whereas, the latter one also involves road users (unobservable) mental state and requires greater foresight. Hence, decisiontheoretic models, e.g., probabilistic and game-theoretic models, are more capable of modeling these complex behaviors [Helbing and Molnar, 1995], more details are given in Chapter 3. State-of-the-models for modeling mixed-traffic situations, and notably used models for path planning, motion and interaction modeling are discussed in the next chapter 3.

Chapter 3

The State of the Art

In this chapter, existing works on mixed-traffic behavior modeling in shared spaces and their limitations are discussed. As discussed in Section 2.4, realistic modeling of heterogeneous road users’ motion including various interactions to avoid collisions, is very challenging and requires combining features from different modules: path planning, motion control, and decision-theoretic models. Several significant models for path planning, motion, and interaction handling, also their applications, are explained in this chapter to find the appropriate ones for this research.

3.1 Path Planning Path planning, i.e., planning the best path from one node to another in a graph, is one of the core elements of many essential domains, such as GPS, robotics, video games, and crowd or traffic simulation [Koefoed-Hansen and Brodal, 2012, Abd Algfoor et al., 2015]. The best route could mean the most comfortable one or the shortest path or the fastest path, or the combination of two strategies for adaptive path planning [Anvari, 2013]. In this dissertation, we considered the shortest route of road users as their best way at the planning level. The path of a road user between her start position and final destination comprises a set of goal positions that she should reach sequentially to reach her final destination. These intermediate goals enable the road user to move around obstacles by avoiding collisions. There are several existing algorithms to find the optimal shortest path. However, representing the path searching environment as a graph structure is a prerequisite for executing those algorithms [Millington and Funge, 2009]. In the following, several representations of the environment and several path planning algorithms are reviewed.

© The Author(s), under exclusive license to Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2022 F. T. Johora, Modeling Interactions among Pedestrians and Cars in Shared Spaces, https://doi.org/10.1007/978-3-658-38345-9_3

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3.1.1 Representation of environment A path searching environment can be divided into regions to represent the environment as a graph, where each part is a node, and connections between regions are the graph’s edges [Millington and Funge, 2009]. There are mainly two classes of methods to represent an environment into a graph [Souissi et al., 2013]; (1) the cell decomposition methods, e.g., regular and irregular grids or navigation meshes and (2) the precalculation of paths between points (like outline vertices of any obstacle) in the modeled environment, e.g., Visibility Graphs. These representations are described in the following [Koefoed-Hansen and Brodal, 2012]: – Grid representation: In this approach, a modeled environment is divided into numerous cells. These cells can be in square, rectangular, or any other convex polygon shape that fits a grid cell. Each cell has an associated cost to specify if the cell is passable or blocked and to define the required cost to move through it, if passable. As visualized in Figure 3.1a, in a grid-based environment, movements in four or eight neighboring cells are possible from each cell unless any adjacent cell is blocked. – Navigation mesh: In navigation mesh-based representation, the unobstructed areas within an environment are divided into a mesh of convex polygons. Each polygon is linked to its adjacent polygons to create a navigable graph. These polygons can be in any shapes as long as they are convex; in Figure 3.1b, a mesh of triangle polygons are visualized. – Visibility graph: A visibility graph consists of a set of outline vertices of obstacles and a set of edges where each edge connects two visible vertices and does not collide with any line segment that outlines any obstacle. Before searching the shortest path between two positions, these two positions need to be added to the visibility graph unless those positions are from existing vertices. For the same environment, these three representations most likely results in a different number of vertices and edges in the connectivity graph. In the grid representation, the number of nodes and edges will always be the same, disregarding the number of obstacles that exist in the environment. However, in both the visibility graph and navigation mesh representations, the quantity of vertices and edges solely depends on the number of obstacles in the environment [Souissi et al., 2013].

3.1 Path Planning

(a)

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(b)

(c)

Fig. 3.1: Different environment representation with valid moves (colored blue) within environment; (a) Grid, (b) Navigation Mesh and (c) Visibility Graph.

3.1.2 Shortest path algorithms There are many existing optimal shortest path finding algorithms (SPAs); some can only search in eight directions (as shown in Figure 3.1a), e.g., grid-based A*, JumpPoint Search (JPS) algorithm [Harabor and Grastien, 2011], or Subgoal Graphs algorithm [Uras et al., 2013]. In contrast, some SPAs can find paths in any-angle, e.g., Theta* [Nash et al., 2007], Block A* [Yap et al., 2011], and A* on Visibility Graphs [Lozano-Pérez and Wesley, 1979]. Pascucci et al. [2017] implemented Dijkstra’s Algorithm on a Visibility Graph to find free-flow paths (i.e., only considering static obstacles) of road users in shared spaces. Dijkstra’s algorithm is a well-known SPA that works on a weighted, directed or undirected graph with non-negative edge [Cormen et al., 2009] and finds optimal paths from a source to all many goal positions. Hart et al. [1968] proposed A* algorithm, an extension of Dijkstra’s algorithm, for reducing the number of the graph vertices searched by Dijkstra’s algorithm utilizing a heuristic that leads to the goal node. Kneidl et al. [2012] applied three algorithms for planning paths for pedestrians with varying levels of local knowledge; for pedestrians with complete knowledge about their location, a modified version of the Dijkstra algorithm was used, the paths of pedestrians with partial knowledge were planned using the heuristic A* algorithm and the ways of pedestrians with no local information were planned using the Probabilistic Choice Algorithm. The authors extended the Dijkstra algorithm by considering dynamic edge weights, and each edge’s weight represents traveling time instead of the distance between nodes. In [Schönauer, 2017, Bandini et al., 2017b], road users’ free-flow paths are planned using flood fill Methods. The activity environment needs to be divided into grids of cells to utilize a flood fill algorithm, where each cell has an assigned value. Such an environment is called a distance map, calculated by finding the nearest

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neighborhood cells of each cell and calculating the distance value to its nearest cell using metrics such as the Manhattan, Euclidean, or Chessboard. The shortest path’s direction can be determined in a distance map by following the negative gradient direction [Johansson and Kretz, 2012].

3.2 Conventional Models for Motion Control Modeling motion behavior of road users is challenging. However, many existing models attempt to handle the motion of road users. The most commonly-used motion models, namely, force-based, cellular automata, steering behavioral, and velocity obstacle models and their application, are discussed in this section.

3.2.1 Force-based models In the classical social force model (SFM), which originated in Helbing and Molnar [1995], pedestrians’ movement at a specific place and time is illustrated by differential equations containing a set of simple attractive and repulsive forces that they experience from their surroundings. These forces are not directly applied to pedestrians but work as environmental influences to motivate them to perform particular actions. SFM was initially proposed and has been utilized for modeling pedestrian dynamics. Johora et al. [2017] integrated a path planner with SFM for realistically modeling pedestrians’ motion. In Huang et al. [2018], SFM was extended to represent both intra-group and inter-group interactions of pedestrian groups. Kremyzas et al. [2016] extended SFM to model small pedestrian groups’ behaviors, i.e., group coherence, splitting into smaller groups (e.g. in the crowded area) and reformation to re-establish its coherence. Helbing et al. [2002] proposed a generalized SFM that can be transformed from simulating the pedestrian motion in ordinary to that of in evacuation situations. Kamphuis and Overmars [2004] combined a path planning approach with SFM to model flock movement inside corridors, maintaining their coherence.

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Fig. 3.2: The social force model for capturing pedestrian dynamics, combining several simple forces.

SFM has also been used and extended to capture motion behavior of heterogeneous road users. Valero et al. [2020] extended SFM to simulate e-scooters’ motion including the interaction between e-scooters and pedestrians. Zeng et al. [2014] integrated several new forces (from the traffic signal, crosswalk boundary and left-turning vehicles) to SFM to represent pedestrians’ behavior in signalized crosswalks in Japan. Unlike the classical SFM, Zeng et al. [2014] considered both relative distance and relative time to conflict point for calculating the repulsive force between pedestrians. Yang et al. [2020] improved SFM for modeling pedestrians’ motion by adding vehicle influences on pedestrians as a separate force. Anvari et al. [2015] modeled the motion of pedestrians and cars by extending the repulsive force term of SFM and using rule-based constraints for the short-range interactions and long-range conflicts among road users, respectively. Chao et al. [2015] combined a decision model and SFM to handle pedestrian-to-car interactions. Rinke et al. [2017] extended SFM with long-range collision avoidance mechanisms (LRCA) to model motion behaviors of pedestrians (groups), vehicles, and bicycles. LRCA mechanisms are the followings: change the direction of road users’ motion in pedestrian(group)-to-pedestrian(group) interactions, decrease or increase the speed in case of pedestrian-to-vehicle interactions and utilize both strategies in pedestrian(group)-to-cyclist, and cyclist-to-cyclist interactions. Antonucci et al. [2020] merged SFM and learning-based model (feed-forward neural network) where the neural network structure (neurons, hidden layers, and activation) was designed as such that it estimates the parameters of SFM. This model requires a smaller number of input samples and exhibits explainability.

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3.2.2 Cellular automata models In Cellular Automata (CA), the environment is divided into identical discrete cells and time is also considered discrete. In CA-based traffic models, each road user has a finite number of discrete states, and they change their state (e.g., move) by using a set of predefined rules [Schadschneider et al., 2011]. CA models are utilized to model motion behaviors of both homogeneous road users e.g. pedestrians [Bandini et al., 2017b], cars [Chai and Wong, 2015] and mixed traffic [Zhang and Duan, 2007, Bandini et al., 2017a]. Bandini et al. [2017b] designed the motion of pedestrians and pedestrian groups with heterogeneous speed profiles and varying cohesion intensity among group members using CA. In [Burstedde et al., 2001], a CA-based model is proposed to illustrate both repulsive (in short distances, to avoid colliding) and attractive (in longer distances, as predecessor following behaviors) interactions among pedestrians. Nagel and Schreckenberg [1992] designed a simplistic car-following model using four simple rules for modeling acceleration, deceleration, and random behavior of cars and updating positions. Lan and Chang [2005] proposed a motion model for cars and motorcycles, where a set of deterministic CA rules handle their interactions. In this model, cars and motorcycles have non-identical sizes (i.e., occupy a different number of cells) and heterogeneous speed profiles are designed using stochastic CA rules. Bandini et al. [2017a] designed road crossing behavior of pedestrians in three distinctive phases with specific CA rules: pedestrians approach crosswalk with an average speed, cross the road at high speed, and at the middle phase, they slow down to interact with vehicles to decide on stopping or continuing based on their accepted time gap and the type of vehicle drivers (i.e. compliant or non-compliant). Zhang and Duan [2007] also proposed a CA-based model to address pedestrian crossing behaviors for analyzing the influence of various factors, e.g., pedestrian volume or traffic light timing on mixed traffic flows. In [Chen et al., 2018a], a cellular automaton model for studying bicycle-to-vehicle interactions and its influence on traffic delay is introduced. Dailisan and Lim [2020] reconstructed the Nagel–Schreckenberg model for generating the movement of buses, including their stopping criterion for picking passengers. This model also considers the motion behaviors of cars. CA models are also combined with other approaches to provide a richer model. For examples, in [Chai and Wong, 2015], the complex decision-making of vehicle driver are designed by integrating CA (for movement modeling) and Fuzzy Logic (for decision process). Also, Kim and Kim [2020] combined a deep artificial neural network (ANN) with a cellular automaton to predict traffic congestion in crowded environments. The ANN supports the CA-based simulation model by predicting its parameters and functions. As seen above, CA models are used to model motion behavior of different types of road users in case there are clear rules for traffic management – which is not the case in most shared spaces.

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3.2.3 Models for steering behaviors Reynolds [1987] proposed a set of simple local rules to design boids (e.g., flocks of birds and schools of fish) in a way that they steer themselves by avoiding collisions but still, stay aligned and adjacent with nearby flock members, as visualized in Figure 3.3. Neighborhood of a flock member is specified by a distance range and its field of view. – Separation: Each flock member steers from their neighboring members to avoid getting very close. – Cohesion: Each unit steers to the average position of adjacent flock members. – Alignment: They steer toward the average velocity of nearby flock members. Reynolds [1988] extended his model by adding rules to avoid with both static and dynamic obstacles. Several studies extended Reynolds’ flocking model. For example, Lai et al. [2005] trained a model to generate realistic group behavior of discrete agents by extending this flocking model. As the boid’s movement depends only on local information in Reynolds’ flocking model, in cluttered environments, they can get stuck. To address this problem, Bayazit et al. [2003] combined this flocking concept with probabilistic road-maps to lead the herd members to their goals.

(a)

(b)

(c) Fig. 3.3: A set of rules to design boids: (a) Separation, (b) Cohesion and (c) Alignment, from (Reynolds [1999], p. 15).

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Reynolds [1999] further extended the flocking model to include additional steering behaviors for autonomous units, e.g., vehicle; some of these behaviors are visualized in Figure 3.4 and briefly discussed in the following: Seek behavior directs an autonomous unit toward a target within their world. As a solution to the seek behavior’s problem, i.e., an actor moves back and forth to its target if it fails to reach, Reynolds introduced arrival behavior. This behavior makes the actor slowing down when it comes near its target, i.e., entering within a slowing radius. Flee behavior is the opposite of the seek behavior; it steers a character away from a designated point. Unaligned collision avoidance actions prevent an actor from colliding with others while moving. Path following behavior forces a character to move along a preset path (i.e., a spine with a radius). Based on the situation, an actor can switch from one behavior to another or combine several behaviors to result in complex behavior.

(a)

(b)

(c) Fig. 3.4: Steering behaviors: (a) Seek and Flee, (b) Path following, and (c) Unaligned collision avoidance, from ([Reynolds, 1999], p. 8 - p. 14).

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3.2.4 Velocity obstacle models Velocity Obstacle (VO) based models are another group of approaches for reproducing agents’ collision-free trajectory in complicated environments and commonly used in computational geometry and robotics [Lämmel and Plaue, 2014]. A velocity obstacle is the set of all velocities of an agent, which will shortly result in a conflict with another agent if the other agent continues moving with its current velocity [Fiorini and Shiller, 1998]. In the VO based model, agents try to navigate (passively) through moving obstacles without conflicting. An enhancement of the VO concept is Reciprocal Velocity Obstacle (RVO). In RVO [Van den Berg et al., 2008], agents move with the belief that the other agents will make similar collisionavoidance reasoning and unlike VO, in any conflict situation among two agents, both indeed take equal responsibility to avoid the accident. Lämmel and Plaue [2014] model crowd behavior using reciprocal velocity obstacle. Many studies extended VO approaches for modeling movement behaviors of various agent and robot types, for example, to model holonomic crowd motion [Rowan Hughes and Dingliana, 2014], the non-holonomic motion of robot [Wang et al., 2018a, Huang et al., 2019], and mixed-traffic motion [Charlton et al., 2020]. Charlton et al. [2020] modeled the movement of pedestrian and autonomous vehicles, including pedestrian-to-pedestrian and pedestrian-to-vehicle interactions using an extended version of VO which is known as optimal reciprocal collision avoidance.

3.3 Decision Models As explained in Section 2.4, a motion model like SFM or CA model cannot solely handle the complex decision-making processes of road users. Also, decision-theoretic models are more capable of handling complex situations where road users need to choose an action among different alternatives. In this section, several decisiontheoretic methods are reviewed.

3.3.1 Rule-based constraints To handle complex conflict situations, many studies utilized rule-based constraints as decision model of road users. For examples, Fujii et al. [2017] applied a discrete choice model to capture pedestrian’s decision making during pedestrian-topedestrian interaction. In this paper, pedestrians choose appropriate behavior among free-walk, mandatory stopping, overtaking, collision avoidance, and following behaviors, based on predefined rules for surmising their surroundings.

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Prédhumeau et al. [2021] proposed a hybrid model, combining SFM with a decision model for pedestrians, to model the interaction among pedestrians and pedestrian(s)to-single autonomous vehicle (AV) interaction. To understand the current situation and suggest specific rule(s) to handle the particular situation, the decision model uses three essential concepts: time-to-collision, interaction angle and expected crossing order at the conflict point. An example of such rules is that pedestrians will sharply turn if the interaction with AV is frontal and conflict is apparent. In [Chao et al., 2015], the social force model is combined with a rule-based decision model for pedestrians to decide whether to cross the road or wait based on their preferred gap to the immediate states of incoming cars. Anvari [2013] used rule-based constraints to model pedestrian-to-car interactions and car-to-car interactions while driving in the opposite direction. Possible conflicts between agents are estimated based on their current states, and conflict avoidance rules to solve these conflicts are the combination of speed and direction change. For example, in the case of pedestrian-to-car interaction, the agent with a higher speed requires to accelerate and deviate and the other agent decelerates and deviates correspondingly.

3.3.2 Logit models Multinomial logit model, also recognized as multinomial logistic regression, is a classification method for predicting the likelihood of different potential outcomes of a (categorically distributed) dependent variable based on a set of independent variables. The option that has the highest probability (μ) can be regarded as the outcome. Independent variables (X) can be real-valued, binary-valued, or categorical-valued. Considering one possible outcome as the baseline (J), the multinomial logit presumes that the log-odds of each alternatives j (j = 1,...,J-1) is linearly distributed with intercept αj and a vector of regression coefficients βj , as shown in Equation 3.1 [Pascucci et al., 2017]. (3.1) ln(μj /μJ ) = αj + Xβj Pascucci et al. [2017] employed a multinomial logit model for managing complex conflict scenarios between pedestrians and motorized vehicles, detected from realworld shared space data set. Conventional action choices of both user types and a set of potential parameters like inter-distance or time-to-collision that may influence the action choice are identified to build the logit model. Each road users utilize this model to choose their response among different alternatives in any specific conflict situation. Zhou et al. [2013] used a logit model to predict pedestrians’ type while crossing at signalized intersections using explanatory attributes like gender, age, arrival time, accompanied, oncoming car or road length, extracted from a survey. Here, pedestrians are categorized into four types based on how much they obey traffic signal: (1) regular

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users, who cross while the signal is green, (2) late starters, who start but not finish crossing during the green signal, (3) sneakers, who cross while the signal is red, and (4) partial sneakers, who begin crossing during the red signal but finish in the green signal. Logit models are also used to identify influential factors or analyze the reasons for road accidents. For example, Bham et al. [2012] performed a post-analysis on various crashes in highways using a multinomial logit model to investigate the differences in influential factors in different collision types. The results suggest that the significance of collision-related factors varies in terms of crash severity and collision types. Moreover, drivers’ actions significantly influence the risks associated with crashes; plus, accident types are also heavily related to driver behavioral parameters than environmental aspects.

3.3.3 Non-cooperative game theory Game theory is the mathematical research of interaction among autonomous agents. A good description about game theory was given by Osborne and Rubinstein [1994]: “The basic assumptions that underlie the theory are that decision-makers pursue well-defined exogenous objectives (they are rational) and take into account their knowledge or expectations of other decision-makers’ behavior (they reason strategically)." Game-theoretic models are broadly categorized into two branches, namely, non-cooperative and cooperative game theory. In a non-cooperative game, the basic modeling unit is individual players who can decide by deliberating others’ actions. Alternatively, in a cooperative game, the basic modeling unit is groups of agents (or coalitions) who can agree and benefit from cooperating following some binding agreements [Chalkiadakis et al., 2011]. Game-theoretic models, most specifically non-cooperative games, have often been applied to analyze and predict behaviors of both homogeneous and heterogeneous traffic by interpreting road users’ complex decision-making processes. In [Kita, 1999, Yoo and Langari, 2013], non-cooperative games are utilized to model merging-give way interaction between vehicles. Li et al. [2017] combined gametheoretic and reinforcement learning approaches to train an autonomous vehicle to interact with its environment, i.e., other vehicles. Yoo and Langari [2012] modeled interaction of an individual vehicle with two other vehicles in adjacent lanes using a 3person game. In [Asano et al., 2010], a game model is used to illustrate pedestrians’ negotiation process while interacting with another pedestrian to avoid a possible collision. Using game theory, Rahmati et al. [2020] modeled pedestrian’s decision-making process in scenarios where the pedestrian has to interact with another pedestrian and a vehicle. Here, a pedestrian handles such a situation by playing two concurrent games with her two competitors (i.e., another pedestrian and a vehicle). In [Schönauer,

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2017], the author modeled pedestrian-to-car interactions in shared spaces using game theory. Amini et al. [2021] introduced a game-theoretic approach to model pedestrian-to-vehicle interactions at uncontrolled crossing areas considering various vehicle types, namely, two-wheeler, three-wheeler, small car, and heavy commercial vehicles. Michieli and Badia [2018] analyzed the difference in cyclist/pedestrian behavior while interacting with human-driven and autonomous vehicles. Bjørnskau [2017] illustrated the cyclist-to-car driver interaction at Zebra Crossing using game theory and showed that the chosen strategies of both players by game playing (Cyclist: cycle over the zebra crossing and Car driver: give way to the cyclist) are different from the solution which is suggested by the traffic rules, and road users’ behaviors are aligned with the solution generated by the game. Elvik [2014] reviewed different game-theoretic models to illustrate different traffic situations such as the interaction between police and driver for speed enforcement or cyclist-to-vehicle driver interaction to avoid any collision.

3.4 Existing Shared Space Motion Models In Section 3.1–3.3, several studies on modeling homogeneous and heterogeneous traffic are reviewed with a focus on their applied methodological approaches. The purpose of that literature review is to analyze alternative methodologies of modeling different motion behaviors of road users to select the appropriate methods for this research. The selection process is discussed in Section 4.1. This section elaborates more on the existing works for modeling mixed-traffic situations, mainly from shared spaces, with the aim to identify the research gap. To the best of our knowledge, not many works have been done to model and simulate shared spaces so far. State-of-the-art models are mostly formulated based on physicsbased approaches, most prominently the social force model (SFM) of pedestrian dynamics [Helbing and Molnar, 1995] and also it’s various extensions by adding, e.g., new forces, decision-theoretic models, or rule-based constraints, to illustrate the motion of other types of actors like cars in [Yang et al., 2020, Schönauer, 2017, Anvari et al., 2015] or bicycles in [Rinke et al., 2017, Schönauer, 2017]. Cellular Automata models are also commonly applied to model motion of heterogeneous road users but in settings including explicit traffic regulations, unlike most shared spaces [Lan and Chang, 2005, Zhang and Duan, 2007, Bandini et al., 2017a]. Prédhumeau et al. [2021] combined SFM with a decision model to capture pedestrian groups, pedestrian-to-pedestrian and pedestrian(s)-to-single autonomous vehicle interactions and evaluate the model with two open-source shared space data sets from [Yang et al., 2019]. Yang et al. [2020] modified the classical SFM to incorporate interactions between a pedestrian and a car. Kabtoul et al. [2020] modeled pedestrians trajectory (motion) in shared spaces considering cars’ existence. In this model, while interacting with a vehicle, a pedestrian’s willingness to give way to a car is

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calculated using a quantitative time-varying function. The trajectories of pedestrians are predicted based on their willingness and surroundings using a linear regression model. These models can capture lateral, front and back (not included in [Kabtoul et al., 2020]) interactions among pedestrians and a vehicle in open spaces, i.e., not restricted only for crosswalks, but only from pedestrians perspective, i.e., the decision-making of the car is not considered. Unlike the models mentioned above, the following models captured both vehicles and pedestrians motion behaviors (some also considers bicyclists). Anvari [2013] integrated new forces and rule-based constraints into SFM to capture pedestrians and cars motion behaviors and validated the model using two shared-street data sets from England. Pascucci [2020] proposed an SFM-based model to the motion behaviors of pedestrians and vehicles and validated the model using scenarios from a shared-street data set. Schönauer [2017] modeled pedestrians and vehicles motion by combining SFM with a game-theoretic model. Even though the evaluation of this model was performed using one street-like and one intersection (or Square) data sets, the differences in road users’ behaviors in different settings are not analyzed and considered explicitly. Only a few works on modeling motion behaviors of road users (not specifically in shared spaces) considered heterogeneous movement patterns for individual road user types [Kabtoul et al., 2020, Alahi et al., 2017, Yu et al., 2014]. In [Kabtoul et al., 2020], manual annotation of some predefined pedestrian types is performed based on pedestrians’ willingness to give way to a car. Alahi et al. [2017] determined various motion styles of pedestrians by learning individual’s collision avoidance parameters and clustering them into groups. This model can only capture pedestrianonly scenarios. Yu et al. [2014] categorized pedestrians into groups depending on their age range and gender to set individual speed profiles for each group. Instead of analyzing real-world scenarios, the authors collected these speed profiles from literature. All the above-mentioned models considered only single conflicts between two road users (i.e., at a time, a road user can only deal with a single explicit conflict with one other user). These works overlooked interconnected and multiple conflicts (i.e., concurrent conflicts of a road user with multiple competitive road users), which is a common scenario in shared spaces. Schiermeyer et al. [2017] took an attempt to model multiple conflicts, precisely, lateral interactions of a car to multiple pedestrians and pedestrian-to-multiple cars conflicts, by following the steps below: (1) The probabilities of all possible reactions of the target road user (e.g., the pedestrian in pedestrian-to-multiple cars conflict) are calculated using a logit model to avoid conflict with each competitive user individually as if they were in a bilateral conflict situation. (2) For each possible action of the target user, the probabilities of choosing that action over all single conflicts are aggregated to get the global probability. (3) Then the target user chooses the action with the highest global probability to avoid conflict with all competitive users unless the target user is a pedestrian. (4) For a pedestrian as target user, the probability of the prudent (i.e., giving way) action is

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compared to a threshold value (T), and if the probability is higher than T, the prudent action is selected; else, the action with the highest global probability is chosen. Schiermeyer et al. [2017] did not thoroughly analyze multiple conflicts among road users, like the dynamic of such conflicts in different configurations (number and type of involved road users) and classification of multiple conflicts into various kinds based on the situation dynamics. Moreover, this work considered only limited multiple conflict situations. Existing models have mostly ignored social group phenomena. In [Rinke et al., 2017], the movement behavior of pedestrian groups is somewhat captured. Here, the authors modeled the single pedestrian-to-pedestrian group and group-to-group interactions. Modeling interaction among pedestrian group and vehicles is very challenging due to, e.g., the heterogeneity in different groups, and none of these works has analyzed group-to-vehicle interactions. In this research, the previously-discussed models are defined as expert-based models since these require human experts to form explicit decision rules and reasoning mechanisms of road users to model their motion behaviors. Recently, data-driven models, most specifically deep learning (DL) models, are widely used to predict road users’ trajectories, for examples, to predict pedestrian’s motion [Alahi et al., 2016], car-following behavior [Wang et al., 2017], or trajectories of heterogeneous road users [Cheng et al., 2020b]. A DL model, i.e., a complex neural network structure with optimized parameters or weights, can be trained and derived by processing the data, extracted mostly from real-world circumstances [LeCun et al., 2015]. These models are usually black boxes that make it challenging for the human modeler to understand and govern the models to achieve particular desired behaviors [Hu et al., 2016]. The lack of explainability and reliable control of the model may lead to incorrect or contradictory behavior. Also, the computational cost of DL models can be a bottleneck [Schmidhuber, 2015]. Studies considering the performance of DL-based microscopic motion models in comparison with expert-based models for modeling complex socio-technical systems like shared spaces are still missing, to our knowledge. This dissertation is dedicated to developing an expert-based model, i.e., modeling and simulating road users’ motion behaviors with explicit analysis of their decisionmaking processes. A detailed analysis and comparison between expert-based and data-driven approaches are given in Chapter 7.

Microscopic traffic simulators Existing frameworks for traffic flow simulation are to some degree capable of modeling and simulating mixed-traffic flows at a microscopic level. Some of them emphasize on the behavior of individual entities like ARCHISIM [Bonte et al., 2006], some like AIMSUN, can support both mesoscopic and microscopic approaches to some extent [Casas et al., 2010]. Another class of simulators such as MassMotion [Mor-

3.4 Existing Shared Space Motion Models

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row, 2011] or PedSim1 focus on crowd/pedestrian simulation and do not support modeling realistic mixed-traffic scenarios. In respect of this dissertation, closed-source commercial simulators e.g., AIMSUN or VISSIM are not that useful, as they cannot be extended, for instance, to integrate new behaviors of road users into the model or improve the performance of the model. On the other hand, SUMO [Lopez et al., 2018] is open source, but has only bounded means for modeling interaction between heterogeneous road users. To overcome this issue, several works attempted to combine SUMO with agent frameworks like JADE [Soares et al., 2013] or JASON [M. Fiosins et al., 2016]. However, these approaches experience major scalability problems, see [Aschermann et al., 2017a]; also it is difficult to add new environmental features or describe new kinds of road users in SUMO. Also, SUMO lacks flexibility regarding lane width and vehicle width, which is restrictive for many mixed-traffic situations. Hence, for the sake of clean software architecture, reduction of the integration and maintenance effort, and generating realistic behavior, developing a new model to simulate mixed-traffic scenarios is vital.

1 https://www.pedsim.net/pedsim/

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3 The State of the Art

3.5 Research Gap Based on the literature survey in Section 3.4, we can conclude that previous studies on modeling and simulation of shared space scenarios have several limitations and developing a new mixed-traffic simulation model is essential. The limitations of prior research are outlined below: – Previous research did not consider analyzing multiple conflicts among heterogeneous road users and groups. Modeling conflict scenarios among multiple decision-makers with heterogeneous profiles is very challenging, and a single conflict scenario might constitute several conflicts among sub-groups of road users. – Even though pedestrian groups comprise a large part (70%) of the crowd [Moussaïd et al., 2010], previous works have not paid considerable attention to model groups’ motion behavior, and wholly ignored group-to-vehicle interaction. – Most of the previous works ignored interactions among vehicles. Although Alahi et al. [2016] considered car-following behavior among vehicles, and Schönauer [2017] modeled the strategic interaction among vehicles, none of them considered both types of behaviors together. – Previous studies did not satisfactorily analyze the differences in road users’ behaviors caused by differing environmental settings. In most works, the motion model was calibrated and evaluated using extracted mixed-traffic scenarios from a single data set. Even if the model’s evaluation was performed using multiple data sets in some studies, the differences in road users’ behaviors in different circumstances are not investigated and recognized explicitly. More specifically, these studies did not analyze and evaluate the generalizability of their motion models. – Previous works mostly ignored modeling heterogeneity in motion behaviors of individual road user types. – Expert-based and data-driven motion modeling approaches are two distinct methodologies to address a somewhat similar problem. However, the input, output, even evaluation criteria of these approaches are different. Both methodologies can have their respective weaknesses and strengths. A fair comparison among these approaches is challenging but essential to move towards a hybrid approach for collective advantages, which is currently missing in the related works. In this thesis, we investigate and attempt to address the above-mentioned research gaps to realistically model the movement behaviors of pedestrians (including pedestrian groups) and vehicles. Most specifically, we propose and develop a general motion model of pedestrians and cars that is transferable to different environment settings with limited effort and can model a large variety of motion behaviors, including zone or environment-specific behaviors.

Chapter 4

GSFM: The Game-Theoretic Social Force Model

This chapter presents the developing process and architecture of a mathematical model to capture the motion behaviors of pedestrians and cars in shared spaces. Starting from finding the appropriate methods for planning paths, modeling physical movements, and decision-making processes of road users in Section 4.1, we propose the modeling process of a general model to reproduce motion behaviors of heterogeneous road users in Section 4.2. We analyze the typical interactions among shared space users in Section 4.3. We illustrate the architecture, sub-models and implementation of our proposed model, which we name as Game-Theoretic Social Force Model (GSFM), in Section 4.4, Section 4.5–4.7, and Section 4.8, respectively.

4.1 Selection of Methods Based on the literature review in 3, in this section, we discuss the process of selecting suitable methods of path finding, motion planning and decision-making of pedestrians and vehicles in shared spaces.

4.1.1 Path finding algorithm In this dissertation, the A* algorithm on visibility graphs is chosen for planning the shortest paths of road users. The basis of this decision, inferring from Section 3.1.2, is noted below: – The primary reason is that the A* algorithm on visibility graphs is a well-known optimal (shortest) any-angle path finding algorithm. – As stated in [Zeng and Church, 2009], A* algorithm notably outperforms the best implementations of the Dijkstra algorithm.

© The Author(s), under exclusive license to Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2022 F. T. Johora, Modeling Interactions among Pedestrians and Cars in Shared Spaces, https://doi.org/10.1007/978-3-658-38345-9_4

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4 GSFM: The Game-Theoretic Social Force Model

– A* algorithm has a vast scope for optimization in terms of its time and space complexity [Millington and Funge, 2009]. – A* algorithm can search shortest paths both in visibility graphs and grid-based environments. Advantages of visibility graphs over grids are that the paths found in a visibility graph are guaranteed to be optimal, and a visibility graph has a significantly reduced number of nodes. Moreover, the grid-based approach restricts branching in the search trees [Shah and Gupta, 2016]. – In a visibility graph, an environment can be easily modified during run time, e.g., closing a door or making a position unreachable can be achieved by only deleting the corresponding edge [Kneidl et al., 2012]. Although A* algorithm on a visibility graph always guarantee optimal paths at any angle, A* slows down in complex environments due to high average vertex degree. However, this problem can be addressed using efficient data-structure like quadtree [Shah and Gupta, 2016], or pruning unnecessary edges or taut paths [Oh and Leong, 2017]. In [Oh and Leong, 2016], a taut path is defined as “a path where every heading change in the path “wraps" tightly around some obstacle".

4.1.2 Motion control Reproducing all crowd phenomena (e.g., self-organization) is challenging for a single model; unlike other models, the social-force model can capture a larger sets of crowd behaviors realistically [Anvari, 2013]. As discussed in Section 3.2, SFM is not restricted to modeling pedestrians, but also suitable for representing the motion behaviors of other types of road users such as vehicles or cyclists. Moreover, the previous research on road users’ behavior modeling in shared spaces is mostly built on the SFM and results in realistic simulations. One of the main strengths of SFM is that its variables have physical interpretations which can be calibrated for specific requirements, e.g., for evacuation scenarios [Anvari, 2013]. Therefore, in this dissertation, the social force model is selected for controlling the motion of road users in shared spaces. In the following, we outline the strengths of the SFM model compared to other approaches reviewed in Section 3.2: – Cellular Automata Model(s) vs Social Force Model: Compared to the SFM, CA models simulate mixed-traffic efficiently in terms of computation as the same set of rules is utilized over multiple time steps rather than finding solutions of differential equations. However, CA models are discrete in nature; thus, these models might fail to explain precisely the cause of surprising macroscopic behavior that emerged from the local interactions. Moreover, a road user’s position is more of a continuous variable than a discrete variable [Anvari et al., 2015]. – Velocity Obstacle based Models vs Social Force Model: Compared to the SFM, VO models are more computational and memory intensive [Charlton et al.,

4.1 Selection of Methods

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2020]. Reciprocal Velocity Obstacle does not explicitly differentiate between pedestrians moving in the same direction and those who might collide in the near future [Lämmel and Plaue, 2014]. – Steering Behavioral Model vs Social Force Model: Steering behavioral models of Reynolds [Reynolds, 1999] focused more on modeling flocking behaviors of boids than road users’ motion behaviors. However, Reynolds’s concept of switching from one behavior to another based on the current situation can be beneficial for modeling mixed-traffic. Specific behavioral models, e.g., path following or leader following, can be combined with the SFM.

4.1.3 Decision model As stated in Section 2.4, decision-theoretic models can capture complex interaction among road users more accurately than motion models which focus more on physical movements and reactive behaviors of road users. In Section 3.3, we discuss state-ofthe-art models, i.e., rule-based constraints, logit model and game-theoretic model, for capturing road users’ complex decision-making processes. From our perspective, among these models, game-theoretic models can handle complex scenarios more precisely, as: – Game-theoretic models are frequently used to illustrate interaction among road users. As in the real world, in a game model, a decision maker decides on actions based on the prediction of others’ intentions [Gindele et al., 2010]. – In rule-based models, a fixed set of rules built on a few factors, e.g., timeto-collision, are utilized to handle any complicated situation. For example, in [Anvari, 2013], in any conflict situation between any two agents, the faster agent accelerates and deviates, whereas the other agent decelerates and deviates to handle the situation. However, a human’s mind is much more complex; each decision results from complex decision-making depending on their levels of control and many factors, both personal and environmental. The same agent may behave differently in different situations, or two individual agents may react distinctively in the same situation. – In a logit model, each individual decision-maker determines an action depending on present data, disregarding what others might do. Before illustrating any conflict or interaction scenario as a game, selecting a proper game model is necessary. Similar to [Schönauer, 2017], we choose a non-cooperative leader-follower game, i.e., the Stackelberg game, with perfect information and no repetition as the decision model for road users, as: – Non-cooperative games: In a traffic situation, usually, the basic modeling unit is an individual agent (unless in a group), and there is no possibility of exchanging information or strategies among players. Moreover, there is no binding agreement

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among players (i.e., road users) to cooperate; thus, a non-cooperative game is more suitable for modeling traffic situation. However, a non-cooperative game does not indicate that there is no cooperation among players; cooperative and courtesy behaviors of agents can be reflected in the payoff matrices. Modeling interaction among pedestrian groups and other road users as a non-cooperative game is discussed in Section 4.7. – Leader-follower games: In conflict situations, it can often be seen that one road user initializes the interaction and the others follow [Schönauer, 2017]. Thus, to handle traffic scenarios, sequential leader-follower games can be useful. In most traffic scenarios, it is not apparent who might interact first (i.e., the leader). The leader selection process in a leader-follower game is given in Section 4.7. – Perfect Information games: The next step is to define the transparency of pay-off matrices of games. Assuming that each road user has a similar perception of the current situation, the same mutual interest to resolve the conflict, and knows the set of other users’ possible strategies, we design the game as a game of perfect information. – Number of repetitions: A game can be played once or repetitively to solve a given situation. From our perspective, a one-shot game is more appropriate to handle a traffic situation as the amount of time a road user has to decide action is often not so long to make multiple decisions. A possible number of players in a single game, leader selection, and payoff estimation are discussed in Section 4.7 and the game solving process is discussed in Section 4.8. Now though, we have decided which methods to utilize for modeling motion behaviors of road users, we move forward to the actual modeling task. In the next section, we propose the formulation of a general motion model of heterogeneous road users.

4.2 The Modeling Process A general motion model should be capable of (1) modeling realistic movements of heterogeneous road users in various settings regarding environment structures, culture or social norms, traffic modes, and types of interaction and (2) adapting to new environments with limited time and work; thus, developing general models is very challenging.

4.2 The Modeling Process

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«input» Origin-Destination Matrix, Speed profiles, Road user type

M1

A1: Model free-flow movement

«input»

M2

Real-world data set(s)

A2: Check data set (s)

Yes

A3: Identify and extract conflict scenarios A4: Interaction recognition and classification

D2: New type of interaction(s)?

No

Yes

Add a new user type

Evaluate model on a new data set

D1: New?

No

A5: Add New Interaction(s) into Model M3 A6: Calibrate Model on Real-World Interaction Scenarios A7: Evaluate model

D3: Stop Criterion Fulfilled?

Yes

Fig. 4.1: A systematic process of formulating a general motion model for mixed-traffic environments.

To formulate a general model for reproducing motion behaviors of road users, we propose a systematic process, visualized in Figure 4.1. Here, D, A, and M denotes the decision, action and merge nodes, respectively. The process begins with modeling the free-flow motions of road users (A1), taking the type and origin, destination, and speed profiles of road users as input. Investigating and modeling different interactions among road users is the next step. For that, one can examine a real-world traffic environment (A2) to recognize and extract conflict scenarios among two or

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more road users (A3). Extracted scenarios (and also literature) then can be used to identify and classify the interactions among the road users (A4) to model these interactions (A5). For modeling both free-flow movement and interaction, selecting the appropriate method(s) is a prerequisite. The final steps are to calibrate (A6) and evaluate (A7) the model. To build a realistic model, both quantitative (minimize the deviation between real and generated trajectories) and qualitative (realistic behaviors modeling) evaluation of the model using real-world scenarios is vital. However, building a general motion model is a continuing process that demands evaluating the model with new data set(s) from new environments and also integrating new modalities. As shown in Figure 4.1, to evaluate the performance of the model using a new (D1) data set, checking (D2) for new kind of interaction(s) is essential and if new interaction type(s) exists, then this needs to be added (A5) to the model. For identifying new interaction types, one needs to check if the current model can reproduce these new scenarios. If it fails to capture these scenarios, then examine the new scenarios, i.e., how do they differ from the existing interaction scenarios (e.g., in terms of angle, or the types of participants involved, see Section 4.3). For each data set, calibrating all parameters (including the new ones) and evaluating the model are required. In case of adding a new user type (M1), e.g., adding cars’ motion behavior into the pedestrian-only motion model, one requires to complete all the steps in Figure 4.1. This iterative modeling process stops once a predefined stopping criterion, e.g., a certain level of accuracy in realistic motion modeling, has been fulfilled. The stopping criterion depends on the application. The proposed process is different than others Anvari [2013], Pascucci [2020] in terms of generalizability. For example, even though the first steps are similar, when it comes to evaluating the motion model with a new data set, consideration of new interaction types is missing. In this dissertation, this process is utilized to output the Game-Theoretic Social Force Model for realistically modeling various motion behaviors and interactions of pedestrians and cars from different shared spaces. Interaction recognition and classification (A4), developing the model including these interactions (A1 and A5), the calibration (A6) and evaluation (A7) of the model are discussed in Section 4.3, Section 4.4, Chapter 6 and Chapter 7, respectively.

4.3 Interaction Recognition and Classification Based on analyzing real-world shared space scenarios (details on the data sets are given in Section 5.1) and literature review [Helbing and Molnar, 1995], we classify the interactions among shared space users broadly into the following two categories, depending on the complexity of interaction:

4.3 Interaction Recognition and Classification

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1. A simple interaction among road users indicates the direct mapping of percepts to actions, i.e., percept → act, which can be sub-categorized into: – Reactive interaction: When road users do not have time for complex decisionmaking or planning their actions, they behave re-actively. For example, if a pedestrian abruptly jumps in front of a car, then to avoid a serious accident, the car driver will either heavily break or steer away quickly. – Following behavior: Following behavior refers to following the road user in front, most specifically, car-following behavior or pedestrians in a group following their group members. There is no marked lane for vehicles in shared spaces, but empirical observation shows that vehicles merge into assumed lanes and follow the vehicle in front of them [Anvari, 2013]. 2. In case of complex interaction, road users require to decide their actions from different alternatives, i.e., percept → decide → act. Complex interactions can be sub-categorized into the followings: – Implicit interaction between two or more road users: In any conflict situation, road users often choose their best actions by predicting others’ actions. For example, when interacting with a car approaching at a low speed, a pedestrian may presume that the car driver will decelerate to let her pass first. However, in most scenarios, this prediction depends on many factors, e.g., traffic situation, speed and the current behavior of both road users. Often, a road user might require to concurrently interact with multiple road users to handle the conflict situation. – Explicit interaction: Road users also interact with each other through signaling, e.g., hand signals or horns. Note: these types of interactions are out of the scope of this dissertation. We further categorize the interactions that include several road users into two classes: – Multiple conflicts: We call any conflict situation that combines multiple single conflicts between two road users as multiple conflicts (MC). Such a situation includes several road users, but not all users are “co-dependent”. For example, in Figure 4.2a, to resolve a conflict situation, pedestrian P1 needs to interact with car C1 and C2, but the cars do not need to interact with each other. – Multi-user conflict: A single conflict scenario can involve multiple road users where all users in the conflict are “co-dependent", as shown in Figure 4.2b; we call this multiple-users conflict (MUC). Interaction can be categorized depending on the types of participants involved: – Pedestrian-to-pedestrian interaction. – Pedestrian-to-car interaction. – Single or multiple pedestrian-to-cars interaction.

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– Multiple pedestrian-to-car interaction. – Car-to-car interaction.

(a)

(b)

Fig. 4.2: Interaction among multiple road users: (a) multiple conflicts (MC) and (b) multiple-user conflict (MUC).

Road users’ interaction can also be categorized in terms of the angle of interaction, namely, lateral, front and back interaction. – Lateral interaction implies the scenarios where one (or more) road user cross another from in front or behind. – Front interaction indicates face-to-face interaction. – In a back interaction, one (or more) road user approaches the other(s) from behind. All these interaction types fall into the simple and complex interaction category. The summary of the observed types of interaction among road users in mixed-traffic scenarios is visualized in Figure 4.3.

4.3 Interaction Recognition and Classification

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Fig. 4.3: Types of observed interactions among road users (pedestrians and cars) in shared spaces.

We also observe significant differences in road users’ behaviors in different environment structures by investigating shared road-like (contain bidirectional motorized traffic) and intersection areas (contain multi-directional motorized traffic), visualized in Figure 4.4.

Fig. 4.4: An example of a shared space which combines both road zone (bidirectional motorized traffic) and intersection zone (multi-directional motorized traffic). Here, R indicates the central point of the intersection zone.

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– Difference in terms of interaction among road users. For example, in the roadlike area, the interaction between vehicles is mostly the car-following interaction, whereas cars frequently need to interact with other cars to negotiate their priorities over shared spaces at an intersection. Subsequently, in the case of pedestrian(s)to-vehicles interaction in a road-like environment, cars only need to consider the pedestrian(s), i.e., MC. However, in an intersection, pedestrian(s)-to-vehicles interaction is a MUC as the cars might require to interact with all participants, including other vehicles, like C1 in Figure 4.4, who has to interact concurrently with both C3 and P1 to handle the conflict situation. – Conflict recognition and classification in road-like and intersection zones are also different, deduced from the previous point. – There is also diversity in trajectories of road users in different zones, for example, in a road-like environment, pedestrians often cross the road taking the shortest route (straight or diagonal), whereas, at intersections, they seem to go through the safe zones like the central point (R) in Figure 4.4. Based on our observation, we classify shared space environments into two classes, namely, intersection zones and road zones, for investigating and realistically modeling zone-specific motion behaviors of pedestrians and vehicles.

Fig. 4.5: Field of View (FOV) of Pedestrians and cars (Ahmed et al. [2019], p. 7).

We design the detection of simple and complex interactions differently and separately as, unlike complex conflicts, simple interactions are more general and mostly not zone-specific. Recognition of simple conflicts among road users is performed by calculating the inter-distance and angle among them, as stated below: – Pedestrian-to-pedestrian interaction: Pedestrians re-actively interact with other pedestrians who falls into their field of view (FOV). Normally, FOV of pedestrians varies from 120° to 180° [Psotka et al., 1998]. In this dissertation, we consider that the FOV of pedestrians is 180°, i.e., a pedestrian can view any object within her view range (i.e., a specific distance) if it falls within 0° to 90° or 270° to 360° angle with respects to her walking direction (see Figure 4.5). We consider varying FOV of cars concerning the competitive road users, as shown in Figure 4.5.

4.3 Interaction Recognition and Classification

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– Car-following: When two vehicles move in the same direction, the one behind follows the car in front. Let assume that α and β are the leader and the follower cars, respectively, β will follow α, only if: θeα nˆ βα ≤ 10° θeα nˆ βα ≥ 350°and the movement direction of β (eβ ) is ∼ equal to eα : eα .eβ ≤ 0.95. Here, nˆ βα is the normalized vector from β to α and θeβ nˆ βα is the angle between vectors eα and nˆ βα . – Car to pedestrian reactive interaction: If pedestrian β already start crossing in front of the vehicle α: θeα nˆ βα ≤ 8° θeα nˆ βα ≥ 352°, to avoid serious collision α requires to react quickly. – Front and back interaction between pedestrian (α) and car (β): This type of long interaction is detected if distance dαβ (t) < Dmin and (C1 or (C2 and C3 ) ), where C1 , C2 , and C3 are denoted in Eq. (4.1) with g = eα · eβ , i.e., the dot product of long

the direction vectors of α and β. Here, Dmin symbolizes a critical spatial distance. C1 = θeβ nˆ βα < 2° or θeβ nˆ βα > 358° C2 = g ≥ 0.99 or g ≤ –0.99 C3 = θeβ nˆ βα ≥ 348° or θeβ nˆ βα ≤ 12°

(4.1)

We propose Algorithm 1 to detect and classify complex interactions among pedestrians and cars in shared spaces based on our observation and classification of the typical interaction types and shared zones. At any specific time, Algorithm 1 takes the sets of all pedestrians and cars in the environment as input and outputs all potential complex conflicts with the corresponding conflict types by considering FOV and view range (VR ) of road users. Algorithm 1 has two parts, particularly, Conflict Recognition for detecting current conflicts in the environment and Conflict Classification to assign a specific type (Figure 4.3) to the recognized conflict. Both conflict recognition and classification functions consider the differences in intersection and road zones. All these coefficients, e.g., angle values, that we utilize in the above equations, in Figure 4.5, and the Algorithm 1 are decided by observing real scenarios and performing simulation-based evaluation. For example, an object that falls within 0° to 10° or 350° to 360° angle with respects to the direction of movement of an agent (see Figure 4.6) is actually in front of that agent; thus, these values are used in modeling car-following behavior. Moreover, the dot product of the direction vectors of the following and leader cars is less than or equal to 0.95 indicates that both cars are traveling in the same direction. The practicality of all these angle values is validated by using many synthetic scenarios and real-world interaction scenarios extracted from different data sets.

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Algorithm 1 Conflict Recognition Algorithm (Johora and Müller [2020], p. 4) 1: function Conflict Recognition(setofCars,setofPedestrians) 2: conflictSet ← {} ⊲ VR ← View Range, SC ← Scaling Factor, Dmin ← Critical Distance 3: setofAll ← setofCars ∪ setofPedestrians ⊲ x(t) ← Current Position, G ← Goal 4: for each i ∈ setofCars do ⊲ i.pastConflict() ← get competitive users of i from previously detected but active conflicts of i 5: otherCars ← {}, otherPeds ← {} ⊲ otherPeds ← surrounding pedestrians of i 6: if i.inIntersectionZone() then 7: for each j ∈ setofAll and j ≠ i and  j ∈ i.pastConflict() and  i ∈ j.conflict() do 8: if dist(i,j) ≤ VR and ((∃ j ∈ setofCars and (θei nˆ ji ≤ 90° or θei nˆ ji ≥ 270°) ) or (∃ j ∈ setofPedestrians and (θei nˆ ji ≤ 113° or θei nˆ ji ≥ 247°) ) ) then 9: predictedPositioni ← xi (t) + SC * i.maxSpeed() * ei 10: predictedPositionj ← xj (t) + SC * j.maxSpeed() * ej 11: if distance(predictedPositioni , predictedPositionj ) ≤ Dmin then 12: if ∃ j ∈ setofCars then otherCars ∪ {j} 13: else otherPeds ∪ {j} 14: end if 15: end if 16: end if 17: end for 18: else 19: for each j ∈ setofPedestrians and  j ∈ i.pastConflict() do 20: if dist(i,j) ≤ VR and (θei nˆ ji ≤ 113° or θei nˆ ji ≥ 247°) then 21: backPositionj ← xj (t) - j.diameter() * ej 22: if segmentIntersect(backPositionj , Gj , xi (t), xdes ) then otherPeds ∪ {j} i 23: end if 24: end if 25: end for 26: end if 27: conflictSet ∪ Conflict Classification(i,otherPeds,otherCars,setofCars) 28: end for 29: return conflictSet 30: end function 31: function Conflict Classification(u,p,c,cars) 32: otherUsers ← {}, mC ← {} 33: if u.inIntersectionZone() and (p ≠ ∅ or c ≠ ∅) then 34: if p ≠ ∅ and c ≠ ∅ then return {u, otherUsers ∪ p ∪ c, Pedestrian(s)-toCars} 35: else if p == ∅ and c ≠ ∅ then return {u, otherUsers ∪ c, Car-to-Car} 36: else return {u, otherUsers ∪ p, Pedestrian(s)-to-Car} 37: end if 38: else if p ≠ ∅ then ⊲ If in road zone 39: ∀x ∈ cars: if (x.nearestOne() == u.nearestOne()) then mC ∪ {x}, x.conflict() ← {} 40: if mC ≠ ∅ then return {u, otherUsers ∪ p ∪ mC, Pedestrian(s)-to-Cars} 41: else return {u, otherUsers ∪ p, Pedestrian(s)-to-Car} 42: end if 43: else return {u, otherUsers, No New Conflict} 44: end if 45: end function

4.4 Agent Architecture

57

Fig. 4.6: Effective field of view (FOV) compared to the actual FOV

4.4 Agent Architecture As discussed earlier, realistic modeling of the motion behaviors of heterogeneous road users requires different levels of modeling, i.e., planning free-flow paths, modeling simple and short-range evasive behaviors and also complex interactions, which demands a series of complex decision-making processes; a single model might be unable to address them all. Thus, we develop a novel multi-layer, agent-based motion model for pedestrians and cars. We name our proposed motion model as Game-Theoretic Social Force Model (GSFM). The agent architecture in the GSFM model is inspired by InteRRaP, a well-known hybrid agent architecture (see Figure 2.3). The conceptual architecture of an agent in the GSFM model is represented in Figure 4.7. All three layers or modules of our proposed agent architecture instantiated from the three layers in the InteRRaP architecture, but the control flow among the modules in GSFM is different than the one in InteRRaP.

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4 GSFM: The Game-Theoretic Social Force Model

Fig. 4.7: The conceptual architecture of an agent in the Game-Theoretic Social Force Model (GSFM).

In GSFM, each road users is illustrated as an individual agent and their motion behaviors are handled by three interacting modules, specifically, path planning, forcebased modeling, and interactive decision-making modules. As visualized in Figure 4.7, each module has individual roles. The path planning module plans the free-flow path of road users. The interactive decision-making module handles the complex decision-making processes of road users. The force-based module conducts actual physical movements, including the execution of the interactive decision-making module’s decisions, and simple interactions of road users. The BDI (Belief, Desire, Intention) controller facilitates the control flow among these modules. Depending on the present circumstance, the BDI controller activates a suitable module, which then notifies the controller on completing its task. In GSFM, these three modules take control alternatively without maintaining any particular sequence. However, at the beginning of the simulation, GSFM maintains a hierarchy. It begins with the path planning module with the assumption that agents plan their routes before they actually start moving. Once paths are planned, the BDI controller activates the force-based modeling module to conduct agents’ physical movement. Conflict detection and classification are performed at regular intervals as discussed in Section 4.3, and if any complex conflict is detected, the controller activates the interactive decision-making module. When road users’ conflict handling decisions are made, the BDI controller activates again the force-based modeling

4.5 Path Planning

59

module to execute these decisions. In GSFM, interactions depending on their seriousness get prioritized; for example, for cars, pedestrian-to-car interaction takes precedence over car-following behavior. As discussed in Section 4.2, generating a general motion model is a repetitive process; we go through the process shown in Figure 4.7 several times to develop the current version of GSFM, which is described in this chapter. All three modules of GSFM are presented in details in the following sections.

4.5 Path Planning At this level, we only consider planning the free-flow paths (i.e., considering only static obstacles like walls or trees) of road users in two-dimensional environments. Representing the respective environment as a graph is a prerequisite to calculate the free-flow paths of road users. Transformation of a path-searching environment into a visibility graph is performed by connecting outline vertices of each obstacle in the environment. As visualized in Figure 4.8, in a visibility graph, two vertices are connected only if their connecting edge does not collide with outlines of any obstacle.

Fig. 4.8: Visibility Graph with the shortest path (colored red) and fine-tuned path (dotted and colored blue). The colored polygons represent static obstacles.

In addition, for considering intersection zone(s), based on environment structure, we add extra nodes to the graph: – As visualized in Figure 4.9b, to find the free-flow paths of cars, for each intersection zone, we add two nodes for each connecting roads (i.e., the orange circles) to the graph. The arrows in Figure 4.9b indicate possible movement directions of vehicles in a intersection.

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4 GSFM: The Game-Theoretic Social Force Model

– To plan a pedestrian’s trajectory in an intersection zone, we consider two hypothetical rectangles A and B, as shown in Figure 4.9a. Rectangle A is outlined around the (predicted) central point (R). Rectangle B is formulated using the vector from the pedestrian’s current position to her goal and a radius P. If these two rectangles intersect, then the intersected point will be counted as an intermediate goal of that pedestrian. Before performing a path-finding algorithm, the final step is to add the start and destination positions of each agent to the visibility graph.

(a)

(b)

Fig. 4.9: Trajectory Planning of (a) Pedestrian and (b) Vehicle, at Intersection zone (the colored and patterned rectangles).

As stated in 3.1, we consider the shortest paths of the road users as their best routes at this planning level. Thus, we apply the shortest path-finding algorithm A* on the visibility graph to plan free-flow paths of road users. A* starts searching from a specific node, expanding that node to get its all immediate neighbor nodes and then expanding the neighbor nodes and so on until it finds the destination node and returns a set of positions as the shortest path from start node to the destination node. To model humans’ behavior to keep some distance from obstacles, we fine-tune the inner path vertices’ placement regarding their distance to obstacles as visualized in Figure 4.8.

4.6 Force-based Modeling The force-based module directs the actual execution of road users’ physical motion through their planned path (calculated in the path planning module). This module

4.6 Force-based Modeling

61

also captures the simple interactions between road users which might make them deviate from their desired path. The execution of road users’ decisions made in the interactive decision-making module (see Section 4.7) is performed here. In this module, the Social Force Model (SFM) is applied and extended to conduct road users’ movement behaviors.

4.6.1 Classical social force model In classical SFM [Helbing and Molnar, 1995], a pedestrian’s movement, more specifically the temporal change of her desired velocity, is formulated by combining a set of simple attracting and repulsive forces that pedestrian faces at any specific time. These forces represent different motivations and interactions of a pedestrian and known as social forces, signifying the environmental impacts on a pedestrian’s behavior. The environment does not directly apply forces on the pedestrian to act something, but the circumstance influences them to perform their respective actions. We utilize the classical SFM to model the driving force of both pedestrians and cars towards their destinations, the repulsive interaction of pedestrians with static obstacles and other road users, and the repulsive interaction of cars with pedestrians. These forces are discussed in details below.

Driving Force Pedestrians usually prefer to reach their (final or intermediate) destination in the shortest possible way. Thus, the desired velocity v∗ i (t) of a pedestrian i at any specific time t is formulated by the following equation: v∗ i (t) = v∗ i ei (t). Here, v∗ i and ei (t) denote the desired speed and direction of i, respectively. The desired direction of i is calculated by: xdes – xi (t)  ei (t) =  i  des  xi – xi (t) and xi (t) are the desired destination and current position of i, respectively. Here, xdes i The road user i reaches her destination with velocity v∗ i (t) and if she needs to modify her velocity (vi (t)) due to any distraction, she tries to achieve her desired velocity again within a relaxation time τ. Hence, the driving force of a road user towards her destination (Doi ) can be computed using the following formula: Doi =

v∗ i (t) – vi (t) , τ

(4.2)

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4 GSFM: The Game-Theoretic Social Force Model

The relaxation time (τ) determines how quickly a road user changes from her current velocity vi (t) to the desired velocity v∗ i (t).

Repulsive Force from Another Road User A pedestrian’s motion can be affected by other pedestrians. Typically, a pedestrian feels uncomfortable when she gets closer to any unknown person; thus, she keeps some distance from unknown pedestrians. In SFM, the following force vector represents the repulsive behavior of a pedestrian towards other pedestrians:   ri + rj – dij (t) o (4.3) Iij = Vij exp nˆ ij Fij σ Here, Voij and σ are SFM parameters and symbolize the interaction strength and the range of this repulsive interaction, respectively. dij (t) is the distances from i to j, at a specific time and nˆ ij symbolizes a normalized vectors pointing from pedestrian j to i. nˆ ij is calculated by using the following equation: xi (t) – xj (t)  nˆ ij =    xi (t) – xj (t)

(4.4)

Fij represents the anisotropic behavior of humans, which indicates that humans are affected mainly by the objects that fall within their field of view [Johansson et al., 2008]. Subsequently, the influence of others who are out of their field of view is less. The following equation formulates this behavior: Fij = λ + (1 – λ)

1 + cos 𝜑ij 2

(4.5)

Here, λ is a SFM parameter and stands for the strength of interactions from behind and 𝜑ij symbolizes the angle between i and j. The value of λ needs to be less than 1 to consider a human’s anisotropic character. The form factor for anisotropic behavior of a human with different values is visualized in Figure 4.10. Equation 4.3 can also be used for modeling pedestrian-to-car and car-to-pedestrian repulsive interactions by adapting the interaction strength and range parameters.

Repulsive Force from Static Obstacle Pedestrians maintain some distance from boundaries or any static obstacles to avoid any risk of being injured [Manual, 1985]. In SFM, this behavior is designed as a repulsive force and formulated using the following equation:

4.6 Force-based Modeling

63

Fig. 4.10: Form factor (Eq. 4.5) for anisotropic behavior, after (Apel [2004], p. 12).

 IiW =

UoiW exp

 ri – diW (t) nˆ iW γ

(4.6)

Here, UoiW and γ are SFM parameters and denote the interaction strength and the range of this repulsive interaction, respectively. diW (t) indicates the distance from pedestrian i and static obstacle W at a specific time t, and nˆ iW denotes a normalized vector pointing from W to i, which can be calculated similarly as Eq. 4.4. We consider each static obstacle as a polygon, i.e., a closed plane shape formed by straight lines and diW (t) as the distance between pedestrian i and the polygon outline with the shortest distance from i. The distance diW (t) can be calculated using two different methods. The first method (shown in Figure 4.11a) calculates diW (t) as the perpendicular distance between i and W (a line). The second one (shown in Figure 4.11b) considers the distance between i and the obstacle’s closest endpoints as diW (t). As visualized in Figure 4.11, the first method calculates the shortest distance between the pedestrian and obstacle. Thus, we calculate diW (t) using the first approach, which is formulated in the following equation:   (4.7) s = p + eqp · (xi (t) – p) eqp Here, s denotes the perpendicular base point on the obstacle, p and q are endpoints of W, and eqp is the normalized vector pointing from p to q. Finally, the following condition verifies if s is on or outside the examined line segment. If it results true for any polygon line, this line is used for further force calculation; otherwise, that line is left out.

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4 GSFM: The Game-Theoretic Social Force Model

(a)

(b)

Fig. 4.11: The distance between a pedestrian’s current position and a line as boundary: (a) Perpendicular distance and (b) Distance to closest point.

 C=

true,

      s – p + s – q = p – q

false,

otherwise

(4.8)

4.6.2 Extended social force model We extend the classical social force model to represent the car-following behavior (Ifollow ), pedestrian-to-car reactive interaction (Istop ), and the front and back interaction (Ilong ) between pedestrian and car.

Car-following Behavior We formulate the car-following behavior of a car i in Eq. (4.9) and describe as follows: if dij (t) ≥ Dmin , Ifollow = nˆ pi xi (t) , i.e., i continues moving towards a position pi = xi (t) + vˆ j (t) ∗ Dmin , otherwise, i decelerates to maintain safe distance from j (the leader car). Here, Dmin is the minimum vehicle distance, vˆ j (t) is the normalized velocity of j, and dij (t) denotes the distance between i and j.  Ifollow =

nˆ pi xi (t) , if dij (t) ≥ Dmin , Decelerate, otherwise.

(4.9)

Pedestrian-to-Car Reactive Interaction Istop presents the reactive behavior of a car towards pedestrian(s) to avoid serious conflict. Istop emerges only if pedestrian(s) have already begun walking in front of the car. Then the vehicle decelerates, if necessary, completely stops, to let the pedestrian(s) proceed.

4.6 Force-based Modeling

65

The Front and Back Interaction We incorporate the front and back interaction between pedestrian i and vehicle j to our model as a single type, that is, the longitudinal interaction Ilong . We formulate the longitudinal interaction between i and j, as follows: Ilong = nˆ pi xi (t), which indicates that i continues moving towards pi to avoid possible conflict. Here, pi is a temporary goal and pi = xi (t) + Rf for the respective pedestrian i with Rf as the rotation of f = ej ∗ c using rotation theory in Eq. (4.10) [Weisstein, 2003] and the calculation of c and θ are given in Eq. (4.12) and Eq. (4.11) respectively. f x2 = cos θf x – sin θf y f y2 = sin θf x + cos θf y  90°, if θej nˆ ji ≥ 348° θ= 180°, otherwise 

1, b= 1.5,

 3 ∗ b, if g ≤ –0.99 c= otherwise 2.2 ∗ b,

if θej nˆ ji ≥ 348° otherwise

(4.10)

(4.11)

(4.12)

In Eq.(4.12), g = ei · ej , i.e., the dot product of the direction vectors of i and j. All coefficients utilized in this dissertation are set by observing real scenarios and performing sensitivity analysis and validated by various interaction scenarios as stated in Section 4.3.

Modeling Pedestrian Groups We extend1 two extensions of SFM, namely, the Social Groups and Navigation model (SGN) of Kremyzas et al. [2016] and the model of Moussaïd et al. [2011], to model → − pedestrian group structure and their intra-group interaction I group .

1 Modeling pedestrian groups and their interactions with other road users are performed in collaboration with my master student, Suhair Ahmed. We both equally contributed in this work.

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4 GSFM: The Game-Theoretic Social Force Model

Fig. 4.12: Coherent group (left) vs. non-coherent group (right), adapted from (Ahmed et al. [2019], p. 10).

Similar to [Kremyzas et al., 2016], we utilize the leader-follower structure to form pedestrian groups. As visualized in Figure 4.12, each group has a group leader L and last member Lm, i.e., the farthest member from the leader. Both leader and last member roles are changeable during simulation. A group is coherent if the distance between Lm and leader L does not exceed a specific threshold dsocial [Kremyzas et al., 2016]. Our model chooses L in four different methods: the nearest member to the competitive vehicle, the nearest member to the group destination, the nearest member to the road borders, or randomly (at the beginning of the simulation). Figure 4.12 shows an example of coherent and non-coherent group structure. → − Intra-group interaction I group combines two forces for maintaining the group struc→ − → − → − ture, particularly, visibility force f vis and attraction force f att . f vis denotes a → − pedestrian’s desire to keep her group members within her FOV, and f att attracts any group member (Gm ) except L, to the centroid (C) of the group (G) if Gm exceeds a calculated threshold value d. Unless Gm already reaches her destination in that case her desired velocity v∗ (t) becomes zero. → − → − → − I group = f vis + f att

(4.13)

→ − → − f vis = Svis ∗ θ ∗ v∗ (t)

(4.14)

⎧ ⎪ −n (d ⎪S ∗ → ⎨ → − Gm C ), f att = att ⎪ ⎪ 0, ⎩

→ − → − if d Gm C (t) ≥ d and v∗ (t) ≠ 0 otherwise.

(4.15)

4.6 Force-based Modeling

67

Here, Svis and Satt denote global strength parameters, θ signifies the minimum angle between every two members of G that they should maintain to stay within each other’s −n (d FOV, → Gm C ) denotes the distance between Gm and the centroid C, normalized in unit length. The C is formulated as follows: 1 x(t) |G| |G|

C=

(4.16)

1

Here, |G| denotes the total number of members in G and x(t) is the current position of any member Gm of G. We model the motion behaviors of pedestrian group members in three states, i.e. walking, waiting and coordination states, visualized in Figure 4.13. At the beginning

Fig. 4.13: The movement states of pedestrian groups, adapted from (Ahmed et al. [2019], p. 11).

of the simulation, all group members are in the walking state, walking together using equation 4.18. If the group lost its coherence, the group leader L shifts to the waiting state and waits for other group members. In contrast, the other members switch to the coordination state and set xL (t), the current position of L as a temporary goal, and stay in this state until they reach xL (t). The coherence of G is reestablished when every member reaches L, and therefore all group members return to the walking state. However, group members can stay at the waiting or coordination states if and only if they are in a safe zone, i.e., a safe place to wait or coordinate, like pedestrian zones or mixed-traffic areas with no vehicles within any member’s FOV. In comparison, overcrowded pedestrian zones or mixed-traffic zone in the existence of cars are considered as danger zones. Thus, the intra-group behavior of pedestrian is reformulated as follows:

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4 GSFM: The Game-Theoretic Social Force Model



f vis + f att , → − I group = 0,

if Safe zone and not in waiting state if Danger zone.

(4.17)

Execution of Interactive Decision-Making module’s Decisions As stated earlier, the execution of game decisions is performed in the force-based module. However, the process of determining which actions to perform are handled in the interactive decision-making module which is discussed in Section 4.7. During playing a game to handle any complex situation, Continue, Decelerate and Deviate are the viable actions for road users, but Deviate is only considered for pedestrians. −e – Continue: Any pedestrian i crosses a car j from the point pi = xj (t) + SAD ∗ → j → − → − des if line(xi (t), xi ) intersects line(xj (t) + SAD ∗ e j , xj (t) – SB ∗ e j ), otherwise −e is the direction vector, continues her free-flow motion (see Figure 4.14). Here, → are the current and (final or SB = 5 meter (m), SAD is a scaling factor, x(t) and xdes i intermediate) destination positions respectively. Cars continue by following their free-flow motion. – Decelerate: Road users decelerate and in the end stop, if required. For pedestrians, Speedi (t) newSpeedi = , unless the car is very near (i.e., dij (t) ≤ ri + rj + 1 m), in 2 that case pedestrian will stop and in case of cars, newSpeedj = Speedj (t)–decRate.

Here, decRate =

⎧ Speed (t) ⎪ ⎪ ⎨ 2 j , if dij (t) ≤ Dmin , ⎪ 2

Speedj ⎪ ⎪ ⎪ dij (t)–Dmin , otherwise. ⎩ Dmin is the critical spatial distance.

– Deviate: A pedestrian i passes a car j from behind from a position pi = xj (t) – −e (up till j is within the range of view of i) and then i proceeds moving SAD ∗ → j towards her original destination (see Figure 4.14). Fig 4.14 Summing up the process of modeling the motion behavior of road users in GSFM, at any time step t, the executions of the motion of a pedestrian and a car are performed using Eq. (4.18) and (4.19), respectively. Here, i and j indicate the target and competitive road users. Pedestrian:

Car:

→ −  → d vt i → − → − → − → − → − − = D oi + Σ I iW + Σ I ij + wp · I long + I group or I game (4.18) dt

→ −

→  → → d vt i → − − − −  → − = D oi + wc · I ij or I follow and/or I game or I stop , dt

(4.19)

j≠car

Pedestrian-to-car longitudinal interaction and a car’s slight deviation from their path are environment-specific behaviors; that is why we use the weights wp and wc , both are valued either 0 or 1 — more details about these weights is given in Section 5.1.

4.6 Force-based Modeling

69

→ − → − In Eq. (4.19), I follow and/or I game indicates that if the (game) decision of the car → − i in a complex situation is to decelerate than only I game will be active; otherwise → − → − both I follow and I game will be active. To sum up our contribution in this section, among all forces in Eq. (4.18) and Eq. → − → − → − (4.19), the driving force D oi and interaction forces I iW and I ij are components of the classical SFM for modeling pedestrians that we also adapt for vehicles and other → − → − → − → − → − forces, i.e., I long , I group , I follow , I game , and I stop are introduced and developed in this dissertation.

(a) A pedestrian goes through a temporary inter- (b) A pedestrian continues free-flow trajectory mediate goal point to avoid going very nearer to the car

(c) A pedestrian deviates the car from behind Fig. 4.14: Modeling the continue and deviate strategies of pedestrian(s) while interacting with car(s)

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4 GSFM: The Game-Theoretic Social Force Model

4.7 Interactive Decision-Making The interactive decision-making module manages the complex interactions among agents, such as multiple conflicts among pedestrians and cars. As discussed in 4.1.3, we select a non-cooperative leader-follower game, i.e., the Stackelberg game, with perfect information and no repetition as the decision model for road users, similar to the work in [Schönauer, 2017]. In a Stackelberg game, first, the leader player selects a strategy that maximizes its utility by predicting all feasible reactions of follower player(s). Next, the follower(s) reacts to the leader’s decision by determining its best response [Schönauer, 2017]. In Figure 4.15, a Stackelberg game is represented in an extensive game form to visualize sequential moves of players at different points in time. In this example game instance,

Fig. 4.15: An example of a Stackelberg game, i.e., a leader-follower game between a pedestrian (P) and a car (C) with arbitrary utilities. Here, Con, Dec, and Dev denote continue, decelerate, and deviate as road users’ strategy.

a car driver as the leader can see that if he continues driving, then the pedestrian’s best response as the follower will be to deviate. However, if the leader decelerates, then the pedestrian’s best reaction will be to continue walking. Among these two strategy sets, the first one, i.e., the car driver continues, and the pedestrian deviates, gives the leader the highest utility. Thus, in this example, the leader will decide to continue, and the follower will react with the strategy (deviate), which gives her the highest payoff as to the leader decision. We perform separate experiments with (1) the pedestrian as a leader, (2) the faster agent as a leader (i.e., the car), and (3) a randomly chosen leader, using real-world interaction scenarios. The result visualized in Figure 4.16 suggests that the speedier agent as a leader is the best choice compared to considering the pedestrian as a leader, as it predicts a larger number of accurate strategies. The produced result with a randomly chosen leader is unpredictable, sometimes it produces a more accurate result, but sometimes more errors. Thus, the faster agent is considered as the leader

4.7 Interactive Decision-Making

71

in any game playing. However, if the scenario includes more than one car, such as pedestrian-to-cars interaction or car-to-car interaction, the one who detects the conflict first is regarded as the leader.

(a) The decision matrix for cars with considering the car as a leader

(b) The decision matrix for pedestrians, considering the car as a leader

(c) The decision matrix for cars with considering the pedestrian as a leader

(d) The decision matrix for pedestrians, considering the pedestrian as a leader Fig. 4.16: The rationale for selecting a car as the leader in any game for handling pedestrian(s)to-car interaction scenarios.

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4 GSFM: The Game-Theoretic Social Force Model

4.7.1 Pedestrian-to-car interaction modeling

Start a game

Leader (a car)

Nearest competitive user of leader (a pedestrian)

Solve the game and select strategy pair (Ls, Fs)

Both players execute selected stategies

No Multiple followers? Yes Follower is a pedestrian?

No Leader car and follower car execute Ls

Yes All pedestrian followers execute Fs

Fig. 4.17: The execution steps of a pedestrian(s)-to-car(s) interaction.

An individual game manages each complex interaction between two or more road users, and the games are independent of each other. In each game, the number of leaders is set to one, but the followers can be more. In the case of interaction between two road users, the process is simplistic, one road user is the leader, and the other is the follower. However, for handling interaction among multiple road users, still, only one game is played between the leader and its nearest competitor, but considering all other road users involved in the situation when calculating the payoff matrix. The process of handling a pedestrian(s)-to-car(s) interaction is shown in Figure 4.17 and described below.

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73

– Pedestrians-to-car interaction: The car is the leader, and all pedestrians are the followers, even though the game is played only with the nearest follower. All followers follow the same strategy. For example, if the car decides to decelerate, then all pedestrians will continue or all deviate. – Pedestrian(s)-to-cars interaction: One car is the leader, and the pedestrian(s) and the other car are considered as the followers. The leader car plays a game with the nearest pedestrian follower. The follower2 car mirrors the leader car’s strategy, and all pedestrian followers execute the same strategy. As an example, if the leader car decides to continue, all pedestrian(s) decelerates, and the follower car also continues driving. To handle a single complex conflict situation, one may need to consider all possible subsets of that conflict as one game (worst-case scenario), making the situation more complicated. Thus, the influence of follower-to-follower interaction and follower-toother-agent interaction is not considered in the scope of a single game.

Fig. 4.18: Payoff matrix of a game for handling a pedestrian(s)-to-car(s) interaction.

As visualized in Figure 4.18, to estimate the payoff matrix of each game, firstly, all actions of the players are ordinally valued, considering that road users prefer to reach their destination safely and soon. Secondly, several observable features are selected by analyzing real-world situations to capture situation dynamics. Let i be a road user which interacts with another road user j; then the relevant features to calculate variable Cc , Cd , Pd , Pcdev , and Pddev are given below: – NOAI: the number of active interactions of i as a car. – CarStopped: has value 1 if i as a car already decelerating to give way to another road user j’, otherwise 0. min – MinDist: has value Smin dis - dij (t), if dij (t) < Sdis ; its difficult to stop for car i, min otherwise 0. Sdis is a distance parameter of GSFM.

, otherwise 0. – CompetitorSp: has value 1, if current speed of j, vj (t) < vmean j 2 Here, the terms leader and follower are different from what these mean in the case of a car-following or group following scenario.

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4 GSFM: The Game-Theoretic Social Force Model

– OwnSp:

⎧ ⎪ vj (t), ⎪ ⎪ ⎪ ⎨ ⎪ 1, ⎪ ⎪ ⎪ ⎪ ⎪ 0, ⎩

if i is a car high

if i is a pedestrian and vj (t) > vj otherwise

– Angle: These angle values are set considering the anisotropic behavior of agents (see Figure 4.6 and Figure 4.10). Moreover, these angles and their corresponding values (i.e., 8 to 1) are validated through simulation-based evaluation. ⎧ ⎪ 8, ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ 7, ⎪ ⎪ ⎨ ⎪ 6, ⎪ ⎪ ⎪ ⎪ 5, ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ 1, ⎩

if(θej nˆ ij < 16° and ≥ 0°) or θej nˆ ij > 344 if (θej nˆ ij ≤ 42° and ≥ 16°) or (θej nˆ ij ≤ 344° and ≥ 318°) if (θej nˆ ij ≤ 65° and > 42°) or (θej nˆ ij < 318° and ≥ 295°) if (θej nˆ ij ≤ 90° and > 65°)or(θej nˆ ij < 295° and ≥ 270°) otherwise

– CarFollowed: has value 1 if i is a car driver followed by another car j’, otherwise 0. – CarFollowing: has value 1 if i is a car driver following another car j , otherwise 0. – GivewayNr: number of give way of i as a car. To reduce the complexity and improve the model’s performance, we select the most relevant features among these features from the perspective of both pedestrian and car. We perform the backward elimination process, a simple but widely used feature selection methods [García de Soto et al., 2014]. The steps of this method are given in the following: 1. Pick a significance level (p-value, e.g. for this research: 0.05 [Nuzzo, 2014]). A p-value is a statistical measure, i.e., the probability of an observed difference occurring by a random chance. This measure is applied to determine whether the null hypothesis is true or not. Our null hypothesis is that the chosen features of the model do not impact the results. 2. Fit the model with all features. 3. Pick the feature with the highest p-value. If its p-value is higher than the predefined value, go to step 4; otherwise, the null hypothesis will be rejected, i.e., the remaining set of features are important to the model; thus, the method will terminate. 4. Drop this feature. 5. Fit the model with the rest of the features, and go back to step 3.

4.7 Interactive Decision-Making

75

For calculating the p-value of each feature, we employ a multinomial logit model (which utilizes maximum likelihood estimation) due to its categorical structure of the response; three discrete outcomes for pedestrians and two for cars. The result, i.e., logistic coefficient, standard error, and p-value for each feature, is shown in Table 4.1–4.4, but only the p-value is considered to estimate the significance of each feature. Table 4.1: Before backward elimination for Car (Johora and Müller [2021], p .6)

Variable

Coeff.

Std. err.

P-value

OwnSp

-0.6371

0.1178

0.0000

CompetitorSp

0.5841

0.2558

0.0224

NOAI

0.2352

0.1087

0.0305

CarStopped

1.7215

0.3960

0.0000

Angle

0.0755

0.0677

0.2654

CarFollowing

0.0627

0.2533

0.8044

MinDist

-0.0548

0.0244

0.0246

GivewayNr

-0.3577

0.1251

0.0043

Looking at Table 4.1–4.2, it is apparent that from a car’s perspective, all the features but CarFollowing and Angle have a significant impact on the driver’s decisionmaking as the p-value is less than 0.05. Although the Angle feature for the decisionmaking of cars has a higher p-value than our predefined value, we utilize Angle to calculate the car’s utility to maintain higher accuracy. Keeping counts on the number of times a car has been giving way while interacting with pedestrians and utilize this feature while calculating the payoff matrix is out of the scope of this dissertation. We performed some work in this direction in [Hossain et al., 2020]. Table 4.4 shows that OwnSp, CompetitorSp, CarStopped, Angle have a significant impact on a pedestrian when considering deceleration as an action. However, in Table 4.4, it appears like none of the features has statistical significance (p-value > 0.05) for a pedestrian when taking deviation as an action. Therefore, we conduct a sensitivity analysis, and as a result, we keep the variables CompetitorSp, OwnSp, and Angle for determining deviation probability of a pedestrian, even though the regarding p-values indicate otherwise. The calculations of Cc , Cd , Pd , Pcdev , and Pddev are performed using the following p de dev formulae with game parameters Sosp , Scsp , Sfang , Sac ang , Sst , Snoai , Sang , Ssp , and Sang :

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4 GSFM: The Game-Theoretic Social Force Model Table 4.2: After backward elimination for Car (Johora and Müller [2021], p. 6)

Variable

Coeff.

Std. err.

P-value

OwnSp

-0.6363

0.1177

0.0000

CompetitorSp

0.5927

0.2536

0.0194

NOAI

0.2368

0.1084

0.0290

CarStopped

1.7116

0.3936

0.0000

Angle

0.0690

0.0626

0.2698

MinDist

-0.0553

0.0243

0.0229

GivewayNr

-0.3569

0.1250

0.0043

Table 4.3: Before backward elimination (Pedestrian), taken accelerate as the baseline strategy for the logit model Johora and Müller [2021], p. 6)

Accelerate → Decelerate

Accelerate → Deviate

Variable

Coeff.

Std. err.

P-value

Coeff.

Std. err.

P-value

OwnSp

0.5386

0.1140

0.0000

0.2204

0.1489

0.1390

CompetitorSp

-2.3644

0.6279

0.0002

-1.1938

0.7315

0.1027

CarStopped

-0.3278

0.0525

0.0000

-0.0418

0.0728

0.5661

Angle

0.6576

0.3031

0.0300

0.6796

0.3970

0.0869

CarFollowed

1.5395

0.9734

0.1137

-0.9600

0.7152

0.1795

Table 4.4: After backward elimination (Pedestrian), taken accelerate as the baseline strategy for the logit model Johora and Müller [2021], p. 6)

Accelerate → Decelerate

Accelerate → Deviate

Variable

Coeff.

Std. err.

P-value

Coeff.

Std. err.

P-value

OwnSp

0.5429

0.1125

0.0000

0.1175

0.0699

0.0925

CompetitorSp

-2.3320

0.6261

0.0002

-1.3282

0.6926

0.0552

CarStopped

-0.3259

0.0520

0.0000

Angle

0.6805

0.3016

0.0241

0.5662

0.3257

0.0822

4.7 Interactive Decision-Making

77

Cc = –Sosp ∗ CompetitorSp + Scsp ∗ OwnSp + MinDist – Sfang ∗ (Angle ≥ Sac ang ? Angle : 0) Cd = Sst ∗ CarStopped + Snoai ∗ NOAI + Sfang ∗ (Angle ≥ Sde ang ? Angle : 0) p

Pd = 3 – Ssp ∗ OwnSp p

Pcdev = 2 + Ssp ∗ OwnSp + (Angle ≤ 6 ? Sdev ang – Angle : 0) Pddev = Angle ≤ 6 ? Sdev ang – Angle : 0

(4.20) The formulae in Eq. 4.20 to calculate the variables Cc , Cd , Pd , Pcdev , and Pddev are formed by analyzing numerous conflict scenarios and performing sensitivity analysis. Here, a condition ? a variable/value : a variable/value, e.g., Angle ≤ 6 ? Sdev ang – Angle : 0, denotes if-then-else condition.

4.7.2 Pedestrian groups-to-car modeling If a pedestrian group is in a waiting state, all group members decelerate or stop letting the car passes when interacting with a car. Otherwise, the interaction between any pedestrian group (G) and car (C) is handled by playing a Stackelberg game as in Section 4.7.1 with the same payoff matrix (Figure 4.18). However, the distribution of suitable strategies among group members need to be handled separately by considering both clustered and non-clustered group, as formalized in Figure 4.19 and discussed below: – First, the game leader (C) and the group leader (GL ) decide on their strategy among different alternatives (decelerate, accelerate, deviate) by playing a game. – If G splits, all subgroups of G follow the strategy chosen by the group leader GL with 50 % probability 3. – With the other 50 % of the time, all members of the subgroup of G to which GL belongs, perform the strategy of GL and all other subgroups can choose one of the following options: – if C and GL decide to decelerate and accelerate respectively, then all other subgroups (1) either deviate or decelerate, or (2) some subgroups decelerate and others deviate. These decisions can be made based on the interaction angle. – or if C accelerates and GL decelerates, then all other subgroups deviate.

3 The percentage of probability can be calibrated based on real scenarios.

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4 GSFM: The Game-Theoretic Social Force Model

Start

Play a game!

Select strategy

Execute selected strategy

No

Has clusters?

Yes

Who Follow L’s Strategy?

Example L: strategy 1 S: strategy 2

All (A) subgroups

Some (S) subgroups L: strategy 3 S: strategy 1/2

L: selected strategy A: selected strategy

L: selected strategy S: ...

Fig. 4.19: Execution steps of a pedestrian group-to-car interaction with strategy 1, 2 and 3 as the decelerate, deviate and accelerate strategy of road users, respectively (Ahmed et al. [2019], p. 12).

4.7.3 Car-to-car interaction modeling Similar to a pedestrian(s)-to-car(s) interaction, to calculate the payoff matrix for a car-to-car interaction, firstly, all actions of the players are ordinally valued, and then various observable features are added to capture situation dynamics. Let i be a car which interacts with another car j; then the relevant features are the following: ∗0.4 (maximum speed), otherwise – F1 : has value 1, if current speed of j, vj (t) < vmax j –1. – F2 : has value 1, if current speed of j, vj (t) ≥ vmax ∗ 0.5, otherwise 0. j

4.8 Implementation

79

– F3 : has value 1 if i is a car driver following another car j , otherwise 0. – F4 : has value 1 if i as a car is in roundabout, otherwise 0. – F5 : has value 1 if the competitive road user j of i is in roundabout, otherwise 0. The payoff matrix of a game for handling a car-to-car interaction is visualized in Figure 4.20. The calculations of CCc and CCd are performed using the following equations with game parameters Sc1 , Sc2 , Sc3 , and Sc4 : CCc = F1 ∗ Sc1 – F3 ∗ Sc3 + Fc4 ∗ Sc4 CCd = F2 ∗ Sc2 + F3 ∗ Sc3 + F5 ∗ Sc4

(4.21)

Fig. 4.20: The payoff matrix of a game for handling a car-to-car interaction.

4.8 Implementation Up to this point, we represented the conceptual structure of GSFM to model the motion of pedestrians and cars. In this section, we focus on the implementation of GSFM to simulate mixed-traffic scenarios. We start by explaining the process of solving a Stackelberg game. Next, we briefly discuss the LightJason framework [Aschermann et al., 2017b] on which our GSFM model is built. We finish this section by explaining the runtime simulation model with possible inputs and outputs.

4.8.1 Solving Stackelberg games As discussed in Section 4.7, a two-players Stackelberg game is performed to handle any complex conflict situation among road users. The game can be solved (i.e., get the optimal strategy profile for road users) by finding the sub-game perfect Nash equilibrium (SPE). Shoham and Leyton-Brown [2008] defined the subgame-perfect equilibria of a game  G as “all strategy profiles s such that for any subgame G of G, the restriction of s to   G is a Nash Equilibrium of G ", where a strategy profile is a Nash equilibrium (NE)

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4 GSFM: The Game-Theoretic Social Force Model

if, for all agents i, si (own strategy) is a best response to s–i (competitor’s strategy). A SPE is a refinement of the Nash equilibrium in extensive form perfect information game, i.e., every SPE is a NE, but not every NE is a SPE. As visualized in Figure 4.21, each sub-game must include an initial node (i.e., C or P in this example), and all the moves and information sets (i.e., payoffs) from that node.

Fig. 4.21: An example of a Stackelberg game between a pedestrian (P) and a car (C) with arbitrary payoffs. Here, Con, Dec, and Dev denote continue, decelerate, and deviate as road users’ strategy, each orange triangle represents a sub-game of the game, colored utilities are the Nash equilibrium and the red circle denotes the sub-game perfect equilibrium.

The SPE can be inferred by backward induction as formulated in Eq. (4.22) and (4.22). Here, Bsf (sl ) depicts the follower’s best response and the Eq. (4.22) denotes the SPE, where sl , sf , ul , uf and GSl , GSf are the leader’s and follower’s strategies, utilities of the corresponding strategies and their strategy sets, respectively. SPE = {sl ∈ GSl |max(ul (sl ,Bsf (sl )))}, ∀sl ∈ GSl .

(4.22)

Bsf (sl ) = {sf ∈ GSf |max(uf (sf |sl ))}.

(4.23)

4.8.2 Representation of road users in LightJason LightJason is a Java-based multi-agent BDI framework. In LightJason, each agent is formed by following a two-layer structure, i.e., each agent is constituted of a body and a mind, as visualized in Figure 4.22. An agent’s mind is designed using a logical programming language, AgentSpeak(L++), for a symbolic representation of their behaviors and perceived data. The control sequence among different behaviors of an agent (i.e., different modules in GSFM) is handled in Agent’s mind (i.e., the BDI controller in Figure 4.7). The symbolic representation of an agent’s mind is constituted of logical terms and literals, particularly beliefs, rules, plans, goals, actions and variables.

4.8 Implementation

81

– Beliefs are an agent’s knowledge regarding its current state and environment. In LightJason, a belief can be prompted by the agent’s perception of any changes in its environment and also, an agent can conclude new beliefs by combining its current beliefs. – Plans describe an agent’s know-how to direct complex behavior. In LightJason, a plan is constituted of a triggering event, context, plan body, and boolean return value. The triggering event means the event that the plan is intended to handle, the context describes the situations when the particular plan can be used, and the body contains (a set of) action and/or goal(s). – Rules are similar to plans but do not contain context and triggering event. – Goals determine which plans an agent should attempt to execute. – Actions are the way for an agent to interact with its environment and other agents if they exist in the environment. – Variables are for saving dynamic information during runtime.

Fig. 4.22: The representation of an agent in LightJason, split into two parts, i.e., agent mind and body.

On the other hand, the representation of an agent body is formulated using an objectoriented language, Java. An agent body is responsible for executing all actions to achieve the goals and plans triggered from the agent’s mind. An agent’s body handles all physical interaction of an agent with its environment and updates the resulting changes to the agent’s belief base. Also, an agent’s body can trigger plans to the agent’s mind. Agents’ (simulation) environment is also implemented in Java. LightJason also supports the translation of the data between the object-oriented body to a symbolic mind structure. The code fragment in the following listing

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4 GSFM: The Game-Theoretic Social Force Model

10 represents the essential elements of a BDI program, i.e., an agent’s mind, in AgentSpeak(L++). The listing 10 comprising of beliefs (in purple), plans (in blue), and actions (in black). Here, ‘+’, ‘-’, ‘>>’ denote add (plan or belief), remove (belief) and unification (belief), sequentially. The double exclamation mark before calculate/route plan denotes that this plan should run in the current time-step. In contrast, one exclamation mark before a plan (e.g., !walk) indicates the execution of that plan in the next time-step. The environment can also trigger plans. For example, when the interactive decision-making module finishes calculating the road users’ decisions involved in a conflict situation, it triggers the plan update/belief, and the plan related to the decision, e.g., game/accelerate. The complete AgentSpeak(L++) programs of agents are given in the appendix. Sample AgentSpeak(L++) Code Fragment 1 2 3 4 5 6

8 9

11 12 13

15 16

18

19 20

22

23 24

26

27 28 29 30

module(3.0). !main. +!main (module(S), generic /type/ isnumeric (S) && S ==3.0) module(S); -module (S); + module (G). +!game/accelerate: >> (module(S), general /type/ isnumeric (S) && S ==0.0) > (module(S), general /type/ isnumeric (S) && S ==1.0) > (module(S), general /type/ isnumeric (S) && S ==2.0) 2 s), moderate (0.5 s < TTC ≤ 2 s) or short (TTC ≤ 0.5 s) categories. A conflict situation with long TTC is less severe, whereas short TTC indicates that all participants have to react immediately to avoid serious collision.

94

5 Data Sets and Evaluation Metrics

– PET can be calculated as the minimum time lag for any individual pedestrian in a given conflict scenario. It is concluded by first detecting the intersection point of all conflicting road users and then calculating the required Time at which each one of them will arrive at that point and then calculating the time lag. According to [Pascucci, 2020], PET is utilized to evaluate how close road users were about to collide and PET value less than 4 s does not represent any traffic concern. Due to the stochastic properties of human motion behavior, different road users may behave differently in the same situation [Kaparias et al., 2012]; thus, it is challenging to quantify which way of behaving is better than the other. The abovementioned quantitative evaluation metrics solely may not be sufficient to illustrate the feasibility of a motion model; thus, qualitative analysis of the proposed model, i.e., how it handles different real-world scenarios, is also required.

Chapter 6

Calibration Methodology

The GSFM model has a large number of parameters, which can be broadly categorized into the following categories: – SFM (including extended SFM) interaction parameters, e.g. range of repulsive interaction between a pedestrian and a car. – Safety measurements, for example, the critical spatial distance between two cars. – Game parameters, i.e., a set of parameters that are required to calculate the payoff matrices for game playing. Table 6.1 visualizes the list of parameters of the GSFM model, with corresponding unit of measure. Here, PP, PC, CP, and CC indicate pedestrian-to-pedestrian, pedestrian(s)-to-car(s), car-to-pedestrian1, and car-to-car interactions, respectively. The repulsion range parameter for a car’s repulsion towards a pedestrian (σ(CP)) and a pedestrian’s repulsion to a car (σ(PC)) is kept the same, i.e., σ(PC). Among these parameters, we could not calibrate the game parameters for car-tocar interactions and the parameters for modeling pedestrian groups, because of insufficient scenarios. Thus, we tuned these parameters via qualitative analysis of real scenarios and also based on visual inspection of exemplary scenarios (through simulation). Table 6.2 gives the tuned values of these parameters. We calibrate the rest of the parameters of our model in several steps as shown in Figure 6.1. We start by performing universal calibration (step S1) to get one unique set of values of all parameters for all agents by considering that in the same situation, they all act similarly. The steps S2 to S8 of Figure 6.1 are designated to identify different patterns in pedestrians motion by calibrating and clustering sets of parameters (selected through analysis) given in Table 6.3.

1 In GSFM, in the case of simple interactions, pedestrian-to-car and car-to-pedestrian interactions are different, but in complex scenarios, both count as the same type and are handled in the same way (see Section 4.7.1 and Section 4.7.2).

© The Author(s), under exclusive license to Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2022 F. T. Johora, Modeling Interactions among Pedestrians and Cars in Shared Spaces, https://doi.org/10.1007/978-3-658-38345-9_6

95

96

6 Calibration Methodology Table 6.1: The list of parameters in the GSFM model

Symbol

Type

Description

Unit

Voij (PP)

SFM

Pedestrian-to-pedestrian interaction strength

m2 s–2

Voij (PC)

SFM

Pedestrian-to-car interaction strength

m2 s–2

Voij (CP)

SFM

Car-to-pedestrian interaction strength

m2 s–2

UoiB

SFM

Interaction strength to obstacle

m2 s–2

σ(PP)

SFM

Repulsion range in pedestrian-to-pedestrian interaction

m

σ(PC)

SFM

Repulsion range in pedestrian-to-car interaction

m

γ

SFM

Range of repulsive interaction for obstacle

m

λ

SFM

Anisotropic parameter

—

Satt

SFM

Attraction strength parameter of pedestrian group

—

Svis

SFM

Visibility strength parameter of pedestrian group

—

Dmin (PC)

Safety Critical spatial distance in pedestrian(s)-to-car(s) interaction

m

Dmin (CC)

Safety Critical spatial distance in car-to-car interaction

m

VR

Safety Range of view

m

SAD

Safety Scaling factor for accelerate and deviate actions of pedestrians, i.e., safety distance maintained by pedestrians to cars

m

SC

Safety Scaling factor for conflict recognition

—

Smin dis (PC) Sosp (PC) Scsp (PC) Sfang (PC) Sac ang (PC)

Game

Critical spatial distance for utility calculation

m

Game

Influence of competitive user’s speed

—

Game

Influence of own speed as a car driver

—

Game

Influence of interaction angle

—

Game

Constant value for angle

—

Sst (PC)

Game

Influence of the fact that car is already stopped or decelerating

—

Snoai (PC)

Game

Influence of number of currently active interaction

—

Sde ang (PC) p Ssp (PC) Sdev ang (PC) Sc1 (CC) Sc2 (CC) Sc3 (CC)

Game

Constant value for angle

—

Game

Influence of own speed as a pedestrian

—

Game

Constant value for angle

—

Game

Influence of competitive user’s speed to accelerate

—

Game

Influence of competitive user’s speed to decelerate

—

Game

Influence of the fact that a car (the target agent) is following another car

—

Sc4 (CC)

Game

Influence of the fact that a car is in roundabout

—

6 Calibration Methodology

97

Table 6.2: The list of parameters for car-to-car complex interaction and pedestrian group modeling

Parameter

Value

Sc1

2

Sc2

2

Sc3 Sc4

1

Satt

1

Svis

1

5

Table 6.3: The selection of parameters for performing clustering

Interaction strength: Vo (PP), Vo (PC), Vo (CP), ij ij ij Repulsive interaction range: σ (PP), σ (PC), Anisotropic parameter: λ, Safety distance maintained by pedestrians to cars: SAD

Fig. 6.1: The workflow of model calibration. Here, Θ denotes a set of parameters, and n can be 2 to 10.

For recognizing diverse motion patterns of pedestrians, we calibrate the parameters in Table 6.3 individually for each pedestrian (step S2), then cluster individual parameters using two clustering approaches, specifically the k-means algorithm with Principal Component Analysis (PCA) (step S3), and k-means with step-wise forward selection (FS) method (steps S4 and S5) – more details in Section 6.3.2. The steps

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6 Calibration Methodology

S3 to S5 produce two different sets of clustered groups of pedestrians. Next, we perform group calibration (steps: S6, S7 and S8) so that each clustered group has a unique set of parameters values. For the clustered groups obtained in step S3, we perform group calibration directly. However, for the clustered groups obtained by completing S4 and S5, we perform group calibration in two different phases i.e., S7 and S8 (see Section 6.3.3). Each of these above-mentioned approaches produces a different version of GSFM. In each case, the calibration of model parameters is performed using a genetic algorithm (see section 6.1).

6.1 Genetic Algorithm Genetic algorithms [Zames et al., 1981] are randomized search algorithms that imitate the natural processes of evolution by selecting the fittest individuals of the current population to create offspring for the next generation. We select a genetic algorithm (GA) for calibrating our model parameters because these algorithms are commonly utilized to address optimization problems and parameter calibration [Amirjamshidi and Roorda, 2019, Cunha et al., 2009, Schiermeyer et al., 2016], and straightforward to implement. The main properties of a genetic algorithm are discussed in the following: – Population: The algorithm begins with a population, i.e., a set of individuals. Each individual, also known as chromosome, is a candidate solution to the problem, i.e., in our case, the values of the chosen parameters for calibration. Each parameter in a chromosome is termed as gene. Genes are appended into a string to construct a chromosome. – Fitness function: It calculates the fitness and provides a score to each candidate solution. – Selection operator: It picks individuals as parents from the current population either randomly or by using fitness score as the probability to create offsprings. – Crossover: At this step, the picked parents from the selection phase switch their genes among themselves until the crossover point is reached. A crossover point is decided by, e.g. random choice or arithmetic operations. – Mutation: This process randomly changes the genes of the offspring to maintain population diversity and prevent premature convergence. The workflow between these processes for calibrating our simulation model parameters is represented in Figure 6.2. The algorithm starts with a randomly created population. However, for some parameters (i.e., genes), we set a range of possible values (e.g., 10 to 20) to speed up the algorithm by avoiding generating unrealistic values of parameters. Each chromosome, i.e. set of parameters, is fed into the simulation model to obtain outputs. Then, the simulation outputs are compared with real-world data to calculate the fitness score of the respective chromosome. The

6.2 Calibration of Model Parameters Universally

99

Simulation Simulation Model

Fitness Calculation

Output

Selection No

Is stopping criterion satisfied?

Mutation

Yes

Simulation Input

Crossover

Initial Population

New Generation

Final Generation

Fig. 6.2: The workflow of parameter calibration using a Genetic Algorithm, adapted from (Cunha et al. [2009], p. 8).

types of required simulation output and the fitness function depend on the types of parameters to calibrate (see Section 6.2.1, Section 6.2.2, and Section 6.3.1). An offspring population is created by following the selection, crossover and mutation processes. This feeding populations into the simulation model, fitness calculation and generation of new offspring continues until a precise stopping criterion is satisfied.

6.2 Calibration of Model Parameters Universally As stated earlier, in universal calibration, we calibrate all parameters (except Table 6.2) to get one unique set of values for all agents by assuming they all act similarly in similar situations. The universal calibration process is conducted in two parts, i.e., first, we calibrate all parameters regarding SFM and safety measures (Section 6.2.1) and then calibrate the game parameters (Section 6.2.2). We call our model with universally calibrated parameters as GSFM-U.

6.2.1 Calibration of SFM parameters We calibrate the SFM and safety-related parameters using a genetic algorithm (described in Section 6.1). The calibration procedure is individually performed for the HBS, DUT and CITR data sets. Each input chromosome to the GSFM model is

100

6 Calibration Methodology

formed of all parameters (genes) to calibrate. GSFM simulates all extracted scenarios from the respective data set and outputs the simulated positions of each agent (xsu ) to compare with their real positions (xru ) and assign the fitness score to the respective chromosome using the fitness function denoted in Equation 6.1.  E  U   T   r 2    s f score = xu (t) – xu (t) T U E (6.1) e

u

t

Here, E, U, and T signify the number of scenarios, the number of agents, and the number of time steps, respectively. Table 6.4 shows the SFM and safety parameters of the GSFM model with calibrated values (the last column) of the respective parameters. We presume that some parameters are required to model some general behaviors of agents which are not environment-specific; thus, we only calibrated those parameters based on the HBS scenarios. Table 6.4: Universally calibrated values of the SFM and safety parameters

Symbol

HBS Data Set

DUT Data Set

CITR Data Set

Voij (PP) Voij (PC) Voij (CP)

0.1

0.1

0.1

11.7

4.5

1.5

—

2.27

—

σ(PP)

0.25

0.23

0.18

σ(PC)

0.91

0.27

0.69

λ

0.35

0.41

0.13

Dmin (PC)

7.8

8.0

7.0

VR

18.4

10.0

12.3

SAD

6.0

9.01

7.0

Dmin (CC)

8.0

SC

9.0

UoiB

10.0

γ

0.2

6.2.2 Calibration of game parameters We calibrate the game parameters of the GSFM model for handling pedestrian(s)-tocar(s) interactions using the same genetic algorithm, given in Section 6.1. However, for game parameters calibration, it is preferable to calculate the fitness score using

6.3 Identification of Different Movement Patterns ...

101

Eq. 6.2, as the interactive decision-theoretic module is responsible for selecting decisions (i.e. accelerate/decelerate/deviate) for agents in any conflict situation, not their motion (see Section 4.4). In Eq. 6.2, the simulated (Asu ) and real (Aru ) decisions of each involved road users in each extracted conflict scenario, are compared to calculate the fitness score of the respective chromosome. The simulated decisions, i.e. the decisions of the decision-theoretic module, are estimated using the payoff matrix in Figure 4.18, and the real decisions are manually extracted from the video data. Here, E, and U signify the number of scenarios, and the number of agents.  U    E  1, if Aru == Asu U E (6.2) f score = –1, otherwise e u We use Eq. 6.2 to calibrate the game parameters using the HBS scenarios, but in the case of the CITR and DUT scenarios, Eq. 6.1 is used for calibrating the game parameters due to the difficulty of extracting the real decisions manually. The calibrated values of the game parameters are presented in Table 6.5. Table 6.5: The list of game parameters and their calibrated values

Symbol

HBS Data Set

DUT Data Set

CITR Data Set

Scsp

11.0

4.0

10.4

p Ssp

1.0

0.0

1.0

Sosp

11.0

0.0

6.3

Snoai

3.0

0.0

0.3

Sst

2.0

0.0

1.1

Sfang

1.0

6.6

0.4

Smin dis

7.0

5.0

6.1

Sac ang

7.0

8.0

7.0

Sde ang

5.0

8.0

5.0

Sdev ang

8.0

6.0

8.0

6.3 Identification of Different Movement Patterns of Pedestrians Although the general movement behaviors (e.g., move towards their goal position) of pedestrians are similar, each pedestrian has individual characteristics, e.g., the

102

6 Calibration Methodology

difference in sensitivity while interacting with other road users; thus, the movement patterns of different pedestrians can be diverse. In this section, we attempt to recognize different walking patterns of pedestrians by individually calibrating motionrelated parameters of each studied pedestrian (Section 6.3.1), clustering them into different clustered groups2 based on these parameters values (Section 6.3.2), and finally, performing group calibration (Section 6.3.3) to get a unique set of parameters values for each clustered group 3.

6.3.1 Individual calibration At this stage, to get individual motion characteristics, we calibrate the set of parameters given in Table 6.3 for individual pedestrian using the genetic algorithm discussed in Section 6.1. We simulate only the target pedestrian during individual calibration and update the states of her surrounding road users as their real trajectories. The simulated positions of the target pedestrian are then compared with her real positions to calculate the fitness score of the corresponding chromosome, as formalized in Eq. 6.3. Here, T signifies the number of time steps.

f score =

T 



xru (t) – xsu (t)

2  

T

(6.3)

t

6.3.2 Clustering on individuals’ parameters Similar to [Alahi et al., 2017], we apply the K-means clustering algorithm to group the pedestrians with similar walking patterns. K-means is a simple, fast and commonly used clustering algorithm for grouping data based on the euclidean distance between the data points. Moreover, we utilize two different approaches to reduce the number of parameters before clustering using K-means, namely, Principal Component Analysis and step-wise forward selection method. We compare the performance of K-means with Principal Component Analysis and K-means with the step-wise forward selection method in Section 7.2.2.2. More details regarding these clustering approaches are given in the following sections.

6.3 Identification of Different Movement Patterns ...

103

Fig. 6.3: The elbow method with the k-means clustering algorithm.

6.3.2.1 K-means with Principal Component Analysis K-means starts with randomly selecting and assigning data points to clusters (k). Then at each iteration, for each cluster, the distance between each data point and the cluster center is calculated, and data points switch clusters such that the algorithm finishes with clusters where data points within each cluster are nearest neighbors [Marutho et al., 2018]. In K-means algorithm, the number of clusters needs to be defined before the algorithm starts. We represent each individual pedestrian’s calibrated parameters’ values as each data point and decide on the number of clusters using the elbow method. In the elbow method [Marutho et al., 2018], k-means is executed on the examined data with the number of clusters from 2 to 10. The idea is to choose the correct number of clusters through computing and displaying the Within-Cluster-Sum-of-Squares (WCSS) to find the elbow, as shown in Figure 6.3. Here, WCSS is the sum of squares of the euclidean distances between each data point of each cluster and its center. Principal Component Analysis [Marutho et al., 2018] is a method to reduce a larger number of parameters to a smaller set which are linear combinations of the original parameters and contains most of their information. As stated in [Ding and He, 2004], reducing the dimension of data using Principal Component Analysis (PCA) is beneficial for k-means clustering. Therefore, we use PCA to reduce the number of parameters given in Table 6.3. Next, we perform k-means on the reduced set of parameters to cluster pedestrians into groups with similar movement patterns.

2 Here, the keyword group is used to denote a set of pedestrians with a similar movement pattern, not the social group (e.g., visualized in Figure 4.12). 3 This work is conducted in collaboration with Dongfang Yang during my research stay in the USA.

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6.3.2.2 K-means with Forward Selection Forward selection (FS) is a simple but frequently used feature (or parameter) selection method. FS begins with an empty model which contains no parameters, then continues by adding the most important parameter one after another until a preset stopping criterion has been fulfilled or if all present parameters are already in the model [Borboudakis and Tsamardinos, 2019]. The steps of the forward selection method with k-means is formulated in the following Algorithm. Algorithm 3 takes the number of clusters K, a set of parameters Ap , and a preset silhouette score Cs as inputs and returns the collection of most significant parameters among Ap . The significance of a or a set of parameter(s) is calculated by executing k-means for some K and measuring the clustering performance using the silhouette score. The algorithm terminates if Cs has been reached. The silhouette value is a measure to check if a data point is closer to its own cluster than to other clusters [Rousseeuw, 1987]. After performing feature selection using Algorithm 3, we perform k-means on the reduced set of parameters to cluster pedestrians into groups where each clustered group signifies a walking pattern. Figure 6.4 displays different clustered groups of pedestrians from the DUT data set derived by executing k-means with FS method, and k-means with PCA approaches, from left to right. We perform both these approaches separately for each data set.

Fig. 6.4: Different clustered groups of pedestrians from the DUT data set with different motion patterns.

6.3.3 Group calibration In Section 6.3.2, we prepared two sets of different clusters representing different walking patterns of pedestrians. For the clustered groups created in Section 6.3.2, i.e., using K-means with PCA, we calibrate the parameters in Table 6.3 for each group. However, for the clustered groups computed in Section 6.3.2.2, we perform

6.3 Identification of Different Movement Patterns ...

105

Algorithm 3 Forward Selection with k-means Input: Number of clusters K, Set of parameters Ap , Predefined score Cs Output: Set of chosen parameters for clustering Sp 1: Sp ← {} 2: Csint = 0 ⊲ initialize clustering score to 0 3: temps = 0 4: tempp ← {} 5: while Csint < Cs do 6: for each p ∈ Ap do 7: if Sp == ∅ then 8: perform k-means clustering for p 9: else 10: tp = Sp ∪ {p} 11: perform k-means clustering for tp 12: end if 13: score = silhouette score of clusters 14: if temp_s < score then 15: temps = score 16: tempp = p 17: end if 18: end for 19: Sp = Sp ∪ {tempp } 20: Ap = Ap \ {tempp } 21: Csint = tempp 22: end while

group calibration in two phases: (1) we individually calibrate the chosen parameters by the FS method for each clustered group while maintaining the other parameters’ values the same (derived in Section 6.2) for all groups, and (2) we calibrate all parameters given in Table 6.3 for each clustered group. Each clustered group is calibrated individually by simulating all extracted scenarios of a particular data set to get a unique set of parameter values. However, a single conflict scenario can involve pedestrians from different clustered groups. Therefore, while simulating a particular scenario for calibrating parameters for a specific clustered group (C), only the pedestrians from C simulate using the genes (i.e., parameter values) of chromosomes (in the genetic algorithm) and other agents use the universally calibrated parameters. In group calibration, for each clustered group, the simulated positions of all pedestrians in that group are compared with their real positions to calculate the fitness score of the corresponding chromosome using Eq. 6.1. After performing the clustering and calibration processes, we got several sets of parameters’ values, which results in different versions of our model. Specifically,

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Table 6.6: The calibrated values of model-specific parameters in GSFM-M1. Here, G1, G2, G3 are the clustered groups.

Symbol Voij (PP) Voij (PC) Voij (CP) σ (PP) σ (PC) λ SAD

HBS Data Set G1 G2 G3 1.1 0.5 0.1 17.2 11.9 19.3 — — — 0.29 0.17 0.16 0.3 0.8 0.1 0.43 0.37 0.8 11.0 9.0 3

DUT Data Set G1 G2 0.01 0.01 4.87 2.77 2.437 1.387 0.22 0.53 0.12 0.37 0.459 0.59 5.0 8.0

G3 0.01 4.25 2.125 0.31 0.13 0.47 10.0

CITR Data Set G1 G2 G3 0.11 0.1 0.4 1.52 1.52 0.075 — — — 0.19 0.3 0.1 0.68 0.61 3.0 0.17 0.37 0.53 6.87 7.3 4.9

GSFM-M1 denotes the model obtained by performing k-means with PCA. GSFMM2 and GSFM-M3 are the models that combine k-means with the FS method, but GSFM-M2 obtained by calibrating all parameters in Table 6.3 during group calibration, whereas GSFM-M3 is derived by calibrating only the selected parameters by FS during group calibration. Table 6.6, Table 6.7 and Table 6.8 display the calibrated values of parameters of individual clustered group in the GSFM-M1, GSFM-M2, and GSFM-M3 models, respectively with clustered groups GX, e.g., G1. Summing up, in this section, we propose a calibration methodology that combines an optimization algorithm, i.e., a genetic algorithm, two feature selection methods (i.e., step-wise backward and forward selection methods), and clustering approaches (i.e., PCA with k-means and k-means with the FS method) to calibrate model parameters and recognize heterogeneous motion patterns of pedestrians. The calibration of parameters is conducted in several ways: universal calibration, individual calibration, and group calibration. Table 6.8: The calibrated values of model-specific parameters in GSFM-M3. Here, G1, G2, G3 are the clustered groups.

Symbol Voij (PP)

HBS Data Set G1 G2 G3 — — —

DUT Data Set G1 G2 — —

CITR Data Set G1 G2 G3 0.1 0.1 0.5

λ SAD

0.1 6.0

1.11 8.0

0.5 —

0.11 9.0

0.28 6.0

0.61 8.0

0.3 —

0.33 —

6.3 Identification of Different Movement Patterns ...

107

Table 6.7: The calibrated values of model-specific parameters in GSFM-M2. Here, G1, G2, G3 are the clustered groups.

Symbol

HBS Data Set

DUT Data Set

CITR Data Set

G1

G2

G3

G1

G2

G1

G2

G3

Voij (PP)

0.1

0.1

1.9

0.01

0.1

0.2

0.1

0.4

Voij (PC)

15.1

17.3

11.9

1.52

3.4

0.2

2.6

0.075

Voij (CP)

—

—

—

0.76

1.7

—

—

—

σ (PP)

0.17

0.24

0.25

0.17

0.18

0.1

0.2

0.25

σ (PC)

0.1

0.7

0.2

0.11

0.14

1.5

0.39

1.1

λ

0.35

0.339

0.42

0.43

0.16

0.15

0.59

0.52

SAD

7.6

12.0

7.8

6.0

7.0

6.1

8.4

8.3

Chapter 7

Evaluation

7.1 Goals and Methodology So far, we have proposed a motion model to reproduce different movement behaviors and interactions of pedestrians and cars in mixed-traffic environments, most specifically in shared spaces. In the following, we describe and perform several experiments to quantitatively and qualitatively evaluate our model in terms of realistic and safe trajectory modeling. For interpreting the results of the experiments, the research goal can be broken down into the following questions: 1. Are the trajectories generated by the GSFM model realistic? We interpret a motion model as a realistic model if it can reproduce (1) observed behaviors (e.g., car following or courtesy) of real road users and (2) trajectories of road users with a minimal error, i.e., less deviation from the real trajectories. – To evaluate that our model can reproduce observed behavior patterns of pedestrians and cars in shared spaces, we perform case studies with different scenarios extracted from different environments, including various types of interactions in Section 7.2.1. – In Section 7.2.2, we compare the simulated trajectories of our model with real trajectories using metrics discussed in Section 5.2 to quantitatively evaluate the performance of our model. 2. Is our model generalizable, i.e., easily transferable to new environments and capture a large variety of behaviors, both fundamental and environment-specific behaviors of road users? Generalizability is an important property of a motion model as it saves time and effort in modeling the motion behavior of road users of any new environment from scratch. Generalizable models can be more easily reused. In Section 7.2.2, we report two experiments to evaluate the generalizability of the GSFM model.

© The Author(s), under exclusive license to Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2022 F. T. Johora, Modeling Interactions among Pedestrians and Cars in Shared Spaces, https://doi.org/10.1007/978-3-658-38345-9_7

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3. How does our model perform in terms of realistic trajectory modeling compared to other motion models? To answer this question, we compare the GSFM model with the classical social force model (in Section 7.2.1 and 7.2.2) and with a Deep Learning model, LSTM-DBSCAN, in Section 7.2.4. 4. Is our model able to reproduce realistic trajectories in terms of traffic safety? We experiment in Section 7.2.3 to see if our model can produce both collision-free and near-collision scenarios. Scenarios with accidents are not considered in this study, as the examined data sets do not contain any accident data.

7.2 Description of Experiments and Results The GSFM model is implemented on the scalable, multi-threaded, java-based BDI multi-agent framework LightJason [Aschermann et al., 2017b]. We run the GSFM simulation model for all experiments multiple times on an Intel Core™i5 processor with 16 GB RAM. In simulating in the GSFM model, we apply the following settings: gt

– The goal of each agent i is estimated by extending its last observed position (xi ) in real trajectory using Eq. (7.1) with the extended length ldes = 5 m or 10 m. gt

st st xdes i = xi + ldes · (xi – xi ),

(7.1)

– We calculate the desired speed v∗i of a pedestrian i by one of the following ways: – For each pedestrian, averaging all the speed values of that pedestrian to obtain her v∗i . – Identifying the walking portion of each pedestrian’s trajectory, i.e., where that pedestrian’s speed is larger than a threshold vwalk and then, we average all the speed values of i to obtain v∗i . We set vwalk = 0.8 ms–1 . – Taking the general desired speed of pedestrians from literature, i.e., the Gaussian distribution with mean 1.34 ms–1 and standard deviation (std) 0.26 ms–1 [Helbing and Molnar, 1995]. – A car’s desired speed is set to: mean(vi ) + std(vi ) ∗ 0.5, where vi is the set of all the speed values of car i. – For both pedestrians and car, their maximum speed is extracted from their real trajectories. – Based on the discussion in Section 5.1, the weight wp in Eq. (4.18) is set to 1 for the CITR scenarios, otherwise 0 and the weight wc in Eq. (4.19) is set to 1 for the DUT scenarios, otherwise 0. In the following sections, to evaluate the GSFM model, we perform several experiments and discuss subsequent results.

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7.2.1 Realistic trajectory modeling In this section, we qualitatively evaluate the GSFM model in terms of realistic trajectory modeling using extracted scenarios from the HBS, SPG, DUT, and CITR data sets to show the differences in these data sets and our model’s capability to address these differences. The example scenarios include various types of interactions among pedestrian and cars, namely, multiple-user conflict, multiple conflicts, interconnected conflict, car-following behavior, and longitudinal interactions. In all figures, the dotted lines indicate the real trajectories, and the solid lines denote the simulated trajectories of road users. In Figure 7.1–7.6, the real and simulated trajectories are represented at two specific subsequent time steps. The black lines in Figure 7.5 and Figure 7.7 denote the trajectories of car, and the color-coded lines represent the trajectories of pedestrians.

(a) Trajectory difference. The left plot visualizes a conflict situation. In the right plot, the conflict shows to be resolved by the road users.

(b) Game tree Fig. 7.1: Multiple conflicts scenario among pedestrians and cars from the HBS data set. (a) The dotted lines represent the real trajectories and the solid lines are the simulated trajectories. Trajectories are visualized at two subsequent time steps. (b) extensive form representation of a car-to-pedestrian game.

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Figure 7.1 represents a complex pedestrians road crossing example with cars coming from two directions, i.e., a MC, extracted from the HBS data set. Both in simulation and reality, both vehicles stop to let the pedestrians cross first, which is a common phenomenon in HBS scenarios. In the GSFM model, this situation is handled by playing a game with car 127 as the leader, its nearest competitive user pedestrians 437 as the follower, and also by considering all other road users involved in the scenario. Car 127 decides to decelerate, car 97 follows the decision of leader and both pedestrians continues. As visualized in Figure 7.1, road users’ actual and simulated trajectories are mostly overlapped; thus, our model realistically reproduces this situation.

(a) Trajectory difference

(b) Game tree

(c) Real scenario

Fig. 7.2: A multi-user conflict scenario among pedestrians and cars from the SPG data set. (a) Comparison of the real and simulated trajectories of road users. The dotted lines represent the real trajectories, and the solid lines are the simulated trajectories. Trajectories are visualized at two subsequent time steps. (b) a snapshot of the real scenario. (c) extensive form representation of a car-to-car game. The colored leaf denotes the optimal strategy pair.

Figure 7.2 also represents a pedestrians-to-vehicles interaction in an intersection area, extracted from the SPG data set. The GSFM model manages this scenario

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113

differently, as here, all road users are co-dependent, unlike the previous scenario, where vehicles do not need to consider other vehicles as competitive users. At first, as pedestrians already start crossing, both cars decelerate re-actively (i.e., Istop ) to evade collision with pedestrians, and when pedestrians have crossed them, both cars play a game to decide on who will go next, see Figure 7.2b. The GSFM model realistically models this scenario and results in similar behaviors for all involved road users.

(a) Trajectory difference

(b) Car 33 to pedestrian 118 game tree Fig. 7.3: A scenario from the HBS data set containing pedestrians-to-cars crossing and carfollowing interactions. (a) The dotted lines represent the real trajectories and the solid lines are the simulated trajectories. Trajectories are visualized at two subsequent time steps. The subplot (b) represents the extensive form representation of games. The colored leaf is the optimal strategy pair.

Figure 7.3 visualizes a conflict scenario that includes two interconnected interactions from the HBS data set. We choose this scenario to emphasize the car-following behaviors of cars in shared spaces. In both real and simulated scenario, car 33 decelerates to let the pedestrians cross first and car 34 responds by decelerating to follow car 33. In the simulation, car 33 decides to decelerate for avoiding conflicts with pedestrians by playing a game, and the car-following behavior of car 34 is captured by Ifollow . In the simulation, road users maintain a large safety distance compared to the real situation. Although the simulated trajectories of road users do not completely overlap their real trajectories, our model could reproduce all road users’ real behaviors in this scenario.

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(a) Trajectory difference

(b) Car 28 to pedestrian 112 game tree

(c) Car 29 to pedestrian 114 game tree

Fig. 7.4: A interconnected conflict scenario from the HBS data set. (a) The dotted lines represent the real trajectories and the solid lines are the simulated trajectories. Trajectories are visualized at two subsequent time steps. The subplot (b) and (c) represent the extensive form representation of games. The colored leaf denotes the optimal strategy pair.

Figure 7.4 also represents a conflict situation from the HBS data set, including several interconnected interactions. More specifically, this scenario contains two pedestrian(s)-to-car interactions and a car-following behavior of cars. Both in reality and in simulation, car 29 follows car 28 instead of overtaking. Car 28 decelerates to let pedestrian 112 and pedestrian 113 cross and similarly car 29 lets pedestrian 114 continues as the result of two individual games. Even though the simulated trajectories of pedestrians deviate from their real trajectories, simulated and real road users behave similarly. We zoom in the left image of Figure 7.3a to clearly visualize the difference in simulated and real trajectories. Figure 7.5 presents a multiple pedestrians-to-car interaction scenario from the DUT data set. The first and second rows display the real trajectories and the simulated trajectories of the involved road users, respectively. Most of the DUT scenarios contain many pedestrians, as displayed in Figure 7.5. Similar to the real situation, in simulation, the car first continues driving, and pedestrians wait (decided by the game shown in Figure 7.5b), later the car decides to decelerate to give the faster pedestrians cross (determined by the game tree shown in Figure 7.5c). As visualized in Figure 7.5, even though the way of reacting is somewhat different, the reacted behaviors

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115

of road users are similar in real and simulated scenarios. Our model satisfactorily simulates this large scenario.

(a) Trajectory difference

(b) Car 2 to pedestrian 10 game tree

(c) Car 2 to pedestrian 11 game tree

Fig. 7.5: Pedestrians-to-car interaction from the DUT data set. (a) The first row denotes the real trajectories and the second row presents the simulated trajectories of road users, at two subsequent time steps. Car’s trajectories are in black color. Extensive form representation of (b) Car 2to-pedestrian 10 game (c) Car 2-to-pedestrian 11 game. The colored leave denotes the optimal strategy pair. ID of the road users are extracted from the data set.

Figure 7.6 represents two sub-subsequent (somewhat interconnected) pedestriansto-car interaction scenarios from the HBS Data set. In reality, when interacting with pedestrian 83, pedestrian 84, and pedestrian 85, car 17 decides to continue and the pedestrians deviates. In this scenario, the GSFM model makes error in predicting

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the strategies of road users, i.e., car 17 decelerates to let these three pedestrians pass. The game tree is visualized in Figure 7.6b. In simulation, while car 17 stopping to let pedestrian 83, pedestrian 84, and pedestrian 85 pass, other pedestrians also continues to cross the road, as there was no other vehicles at that time. In reality also, car 17 stops for letting pedestrian 1, pedestrian 2, and pedestrian 55 pass. As visualized in 7.6, due to the error in the decision-making process, there is a significant difference between the simulated and real trajectories of road users. We zoom in the left image of Figure 7.6a to distinctly show the difference in simulated and real trajectories of pedestrians and the car.

(a) Trajectory difference

(b) Car 17 to pedestrian 85 game tree Fig. 7.6: Subsequent pedestrians-to-car interactions from the HBS data set. (a) The dotted lines represent the real trajectories and the solid lines are the simulated trajectories. Trajectories are visualized at two subsequent time steps. The subplot (b) represents the extensive form representation of games. ID of the road users are extracted from the data set.

Figure 7.7 shows a pedestrians-to-car longitudinal interaction scenario from the CITR data set. To show the impact of considering heterogeneous pedestrian motion patterns, we simulate the same scenario in the GSFM-U and GSFM-M2 models. As shown in Figure 7.7, GSFM-U models all pedestrians by following a single motion pattern, whereas, in GSFM-M2, pedestrians follow different movement patterns.

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117

(a) Real trajectories

(b) Simulated trajectories in SFM

(c) Simulated trajectories in GSFM-U

(d) Simulated trajectories in GSFM-M2

Fig. 7.7: Pedestrians-to-car interaction from the CITR data set. The trajectories of road users: (a) real, (b) simulated in the classical SFM (the dotted line denotes the real trajectory of the car), (c) simulated in GSFM-U, and (d) simulated in GSFM-M2 are visualized. Here, the arrow lines indicate the movement direction of pedestrians.

Thus, the generated trajectories of pedestrians in GSFM-M2 are more similar to the real trajectories than the trajectories simulated by GSFM-U. Moreover, to qualitatively compare the performance of our model with the classical SFM model, we simulate this same scenario using SFM. As SFM only models pedestrians’ trajectories, the car moves according to its real trajectory during the simulation. As shown in Figure 7.7b, the trajectories of pedestrians simulated in the SFM model are very different from both the real and simulated trajectories in our model. To summarize, in this section, we qualitatively evaluate the GSFM model. Our model realistically simulates different types of complex interactions among pedestrians and car(s), such as, multi-user conflict, multiple conflicts and interconnected conflict scenarios. In most cases, road users could accurately detect and classify interaction and behave respectively in simulation. As visualized in Figure 7.6, GSFM sometimes makes errors in predicting the observed decisions of road users, which results in deviation of simulated trajectories of road users from their real trajectories; even though the real and simulated road users choose different strategies to handle the same conflict situation, the situation is resolved in both cases, i.e., no collision detected. As the error in decision-making is one of the main reason for the deviation of simulated trajectories from the real, more work in this direction will be beneficial. Moreover, as visualized in Figure 7.7, consideration of heterogeneity in pedestrians motion pattern improves our model performance, and our model performs qualitatively better than the SFM model. However, there are still differences in the movement patterns of real

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and simulated (in GSFM) road users, indicating more work is required to identify heterogeneity in pedestrians’ motion, e.g., by considering other individual factors of pedestrians like demographics. The quantitative evaluation of our model is given in the following Section.

7.2.2 Model generalizability We perform two separate experiments to evaluate our model in terms of its transferability (i.e., the ability to adapt new behavior patterns from new environments efficiently) and generalizability (i.e., the model’s transferability together with its ability to capture a large variety of motion behaviors of road users). – Transferability: We develop, calibrate and validate our model (V4 in Figure 4.24) based on the HBS data set and then evaluate its transferability by simulating scenarios from the DUT data set, which are different from HBS in terms of traffic conditions, spatial layout and social norms. We analyze the new environment and explicitly change our model parameters (based on sensitivity analysis) and methods so that it can capture the social norms of the new environment (see Section 7.2.2.1). The main drawback of this approach is that it results in different versions of our model for each different environment. – Generalizability: With the aim of a general model, we incrementally integrate new movement behaviors from new data sets to GSFM and utilize a well-defined and largely automated calibration method to adjust model parameters to the new environment (see Chapter 6). At this level, we evaluate the performance of our model in terms of capturing various motion behaviors from different environments using three data sets, the DUT, HBS, and CITR data sets, discussed in Section 7.2.2.2. The CITR data set contains unique interaction scenarios which are not observed in the other two data sets (see Section 5.1).

7.2.2.1 Experiment on transferability As stated earlier, at this point, the GSFM model is calibrated using the HBS data set. Figure 7.8 shows the difference between real and simulated trajectories and speeds of road users involved in the extracted scenarios from the HBS data set. The mean and standard deviation in the speed difference are: for cars, 1.385 ms–1 (meter per second) and 0.584 ms–1 and for pedestrians, 0.345 ms–1 and 0.199 ms–1 . The trajectory difference are 4.935 m (meter) and 3.773 m for cars; 1.80 m and 1.383 m for pedestrians.

7.2 Description of Experiments and Results

(a) Trajectory Difference

119

(b) Speed differences

Fig. 7.8: The difference in trajectory and speed of real and simulated pedestrians and cars of the HBS data set (Johora and Müller [2021], p. 7).

We simulate the DUT scenarios in the GSFM model (calibrated using the HBS data set), and the results are visualized in Figure 7.9. The deviation of simulated trajectories of road users from their real trajectory are: for cars, mean error is 6.581 m and standard deviation (std) is 4.229 m; for pedestrians, mean is 5.4578 m and std is 9.1073 m. The mean and standard deviation error of simulated speeds of all road users in the DUT scenarios are: 2.043 ms–1 and 0.9656 ms–1 (for cars); 0.540 ms–1 and 0.1954 ms–1 (for pedestrians).

(a) Trajectory Difference

(b) Speed differences

Fig. 7.9: The difference in trajectory and speed of real and simulated pedestrians and cars of the DUT data set (Johora and Müller [2021], p. 8).

As visualized in Figure 7.8 and Figure 7.9, the performance of the GSFM model decreases for the new data set. For checking the statistical significance of the differences in results obtained for the HBS and DUT data sets, we perform Mann–Whitney U tests. We set the alternative hypothesis for the tests, as GSFM makes fewer errors while simulating the HBS scenarios than simulating the DUT scenarios. The results

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of Mann–Whitney U test in trajectory difference are U = 859.0, p-value ≈ 0.0 for pedestrians and U = 1217.0, p-value = 0.0011 for cars. The results of Mann–Whitney U test in speed difference is U = 729.0, p-value ≈ 0.0 ( for pedestrians) and U = 1084, p-value = 0.0001 (for cars). According to the experiment results, we can deduce that our model’s performance significantly declines for the DUT data set in all cases. These results correspond with our observation, discussed in Section 5.1, that the motion patterns of road users in these two environments differ in many aspects. Consequently, we attempt to integrate the observed differences in the DUT data set to GSFM (calibrated on HBS) so that it can capture the new situations more realistically. – We adjust the way of utility calculation for game playing to handle complex interactions among road users. – We decrease the value of the view range VR and safety distance Dmin parameters by performing a sensitivity analysis similar to [Chen et al., 2018b]. – We skip reactive stopping behavior of car Istop . The adjusted way to capture the impacts of situation dynamic on car-to-crowd interactions from the DUT data set is formulated in Eq. (7.2). Cc , Cd , Pd , Pcdev , and Pddev variable are used in Figure 4.18 in Section 4.7.1 to calculate the payoff matrix for capturing complex conflict scenarios extracted from the DUT data set. For the DUT data set, the MinDist feature is modified and divided into two parts: PedestrianMinDist: has value dij , if manhattanDistance(i,j) < Dmin and dij - manhattanDistance(i,j) ≤ M, otherwise 0 and CarMinDist: has value high

manhattanDistance(i,j), if manhattanDistance(i,j) > N and vi (t) > vi (i as a pedestrian), otherwise 0. dij signifies the euclidean distance between i and j. Sdev , M, and N are new parameters. The tuned values of Sdev , M, N, reduced Dmin and VR are 9, -2, 10, 7 and 12 respectively. Other parameters utilized in Eq. (7.2) have the calibrated values of these parameters for the HBS data set, e.g., Sdev ang = 8.

c f ac Cc = Sdev ∗ (Angle ≤ 6 ? Sdev ang – Angle : 0) + Ssp ∗ OwnSp – Sang ∗ (Angle ≥ Sang ? Angle : 0)

Cd = –Sst ∗ CarStopped + Snoai ∗ NOAI – CarMinDist Pd = 3 – PedestrianMinDist Pcdev = 2 + OwnSp + (Angle ≤ 5 ? Sdev ang – Angle : 0) Pddev = Angle ≤ 6 ? Sdev ang – Angle : 0 (7.2)

7.2 Description of Experiments and Results

(a) Trajectory Difference

121

(b) Speed differences

Fig. 7.10: The difference in trajectory and speed of real and simulated road users of the DUT data set on the adjusted model (Johora and Müller [2021], p. 8).

We simulate all the DUT scenarios on the adjusted GSFM model and visualize the differences between simulated and real speeds and trajectories of road users in Figure 7.10. The mean and standard deviation in the difference of real and simulated speeds of road users are for cars 1.787 ms–1 and 0.9736 ms–1 ; for pedestrians, 0.5823 ms–1 and 0.2352 ms–1 . The deviation in simulated trajectories from real trajectories of road users are: mean is 4.6778 m and std is 3.1293 m for cars; mean is 3.739 m and std is 1.734 m for pedestrians. Compared to the results visualized in Figure 7.9, the current results present a substantial improvement in the performance of the GSFM. We also perform Mann–Whitney U tests to check if this performance enhancement is statistically significant. In terms of modeling cars’ trajectory, the performance of the adjusted GSFM model is improved (Mann–Whitney U test, U = 415.5, p-value = 0.004). Moreover, the speed performance of cars also has a slight enhancement (Mann–Whitney U test, U = 514.0, p-value=0.06). However, according to the pvalues, for both trajectory modeling (p-value = 0.95) and maintaining realistic speed profile (p-value = 0.75) of pedestrians, the adjusted model has no significant advance. Overall, the modified model gives improved performance by only integrating a few normative aspects in the utility calculation process of games, reducing the value of VR and Dmin , and skipping Istop .

7.2.2.2 Experiment on generalizability This section investigates the performance of the general1 GSFM model (V5 in Figure 4.24). As discussed in Section 6.3, for recognizing diverse motion patterns of pedestrians, we applied several approaches combining calibration and clustering of model parameters, resulting in different versions of the GSFM model, i.e., each contains different value sets of parameters. We compare these different versions of the general GSFM model, namely the GSFM-M1, GSFM-M2, GSFM-M3, and GSFM1 A single model that can reproduce scenarios from all examined data sets.

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U models, with the classical SFM (proposed in [Helbing et al., 2000]) models on the HBS, DUT and CITR data sets. The evaluation is performed using metrics discussed in Section 5.2, namely, Adjusted Final Displacement Error (aFDE), Adjusted Average Displacement Error (aADE), and Speed Deviation (SD). Table 7.1 and Table 7.2 show the performances of these models in modeling pedestrians trajectories and cars trajectories, respectively. In column entries of Table 7.1 and Table 7.2, we summarized three scores that are aADE, aFDE, and SD, respectively. In both tables, the bold number denotes the best score. Table 7.1: Quantitative results i.e., aADE(m) / aFDE(m) / SD(ms–1 ) of the classical SFM and all versions of GSFM in modeling pedestrians trajectories. Here, the bold number denotes the best score.

GSFM-M1 GSFM-M2 GSFM-M3 GSFM-U SFM

HBS 0.7552/0.8262/0.3364 0.7431/0.8059/0.3357 0.7542/0.8342/0.3365 0.7535/0.8345/0.3366 1.122/1.164/0.376

DUT 0.5757/0.8999/0.2389 0.5567/0.8345/0.2410 0.6030/0.9714/0.2408 0.6202/1.0306/0.2379 1.4990/2.260/0.2630

CITR 0.5757/0.8760/0.1740 0.5728/0.8691/0.1741 0.5785/0.8821/0.1741 0.5772/0.8794/0.1741 1.1850/1.7910/0.2566

For a fair comparison, like the GSFM model, we calibrate all parameters of the classical SFM for each data set using the genetic algorithm in Section 6.2.1 and the fitness function in Eq. (6.1). As shown in Table 7.1, the GSFM-M2 model outperforms the other versions of our model. In the case of the DUT data set, the performance of our model is significantly improved by considering heterogeneous motion patterns of pedestrians. In comparison, the enhancement in quantitative performance by considering heterogeneity in pedestrians motion is negligible for the other two data sets. One possible reason could be that the DUT data set is captured from a crowded environment, whereas HBS and CITR scenarios contain comparatively fewer pedestrians (see Section 5.1). As visualized in Table 7.2, the performance of our model in cars trajectory modeling did not improve by considering different motion patterns of pedestrians, except for the DUT data set. All versions of the GSFM model always perform better than the SFM model in terms of modeling realistic pedestrians’ trajectories. We only compare the trajectories of pedestrians generated in GSFM with the SFM model as the classical SFM model only considers pedestrians. In SFM, while simulating the extracted real scenarios, the cars follow their real trajectories. For all data sets, the mean errors of our best-performed model in trajectory modeling, i.e. aADE and aFDE, is in the range of 0.5 m to 1 m for pedestrians, which counts as a good result given the stochasticity in pedestrians motion behaviors and also similarities with the results shown in [Sadeghian et al., 2019], a state-of-the-art trajectory prediction model of pedestrians that designed and assessed by pedestrianonly scenarios.

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Table 7.2: Quantitative results i.e., aADE(m) / aFDE(m) / SD(ms–1 ) of all versions of the GSFM model in modeling the trajectories of cars. Here, the bold number denotes the best score.

HBS

DUT

CITR

GSFM-M1 1.4336/3.4282/1.098 1.4655/3.4899/1.007

2.5142/5.3766/1.1839

GSFM-M2 1.3014/3.4214/1.096 1.4844/3.5279/1.021

2.5041/5.3199/1.1785

GSFM-M3 1.2896/3.4327/1.092 1.5120/3.8180/1.079

2.5056/5.3456/1.1835

GSFM-U

1.2893/3.4321/1.092 1.5523/3.9589/1.1126 2.5041/5.2974/1.1815

However, the aADE and aFDE scores of the GSFM model for cars is relatively higher than pedestrians, i.e. bigger error, mainly for the CITR data set. One possible reason behind this is the notable difference in simulated and real speeds of cars. Thus, improving the motion model of vehicles, e.g., by considering different movement patterns and speed profiles of cars, is needed. To sum up, Table 7.1 and Table 7.2 visualize that our model performs satisfactorily for all data sets. Therefore, the GSFM model could model scenarios from new data sets efficiently (i.e. CITR and DUT) by adding new types of interactions into the model and using a largely automated calibration process. This can be considered as minimal effort compared to traditional approaches, i.e., starting modeling process from scratch for each new case, or the approach in Section 7.2.2.1, explicitly change the model’s methods for individual data set. This evaluates the generalizability of our model. However, we only evaluate the generalizability of our model in capturing new interaction scenarios of pedestrians and cars from new environments, but evaluating the ability of GSFM to capture a new type of road user with minimal effort is not considered. The results of our quantitative evaluation state that in the case of the DUT data set, the performance of our model is significantly improved due to heterogeneous motion patterns of pedestrians by using K-means with feature selection method (GSFM-M2) or K-means with PCA (GSFM-M1) compared to the universal model GSFM-U.

7.2.3 Traffic safety In shared spaces, pedestrians and motorized vehicles share the same space; thus, pedestrians safety becomes a crucial traffic concern in such areas. This section is dedicated to analyzing pedestrian safety in mixed-traffic areas that captured in the HBS, DUT, and CITR data sets. All the examined data sets in this study do not contain any collision data. No visible collision is detected in real and simulated scenarios, indicating that road users resolve their conflict before any serious conflicts happen. Therefore, following the work in [Pascucci, 2020], we apply surrogate

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safety measures, namely, Time To Collision (TTC) and Post Encroachment Time (PET) metrics, to capture near-collision situations between pedestrians and cars, as discussed in Section 5.2. We analyze both simulated and real scenarios by utilizing these safety measures2. Similar to [Pascucci, 2020], to calculate TTC and PET, at each time step of any specific scenario, we predict the future trajectories of each road user by extrapolating their current and past three positions. Next, we loop through the predicted positions of each pedestrian to get the point when the distance between her and a car is the lowest and less than five meters. If so, we calculate the TTC and PET metrics; otherwise, we set NaN (i.e, Not a Number) for values of both metrics. Finally, we set all TTC values to NaN if the minimum relative distance (d) between the respective road users is not less than 2. Because according to [Pascucci, 2020] only the situations with d < 2 are considered as conflicts. Also, we want to distinctly visualize small d values with short TTC values. In Figure 7.11 – 7.13, we plot the values of TTC and PET for all pedestrians from all extracted scenarios of the respective data set, unless both TTC and PET values of any pedestrians are NaN (i.e., no traffic concern), which occurs only if both participants resolve their conflict before their relative distance become less than 5 m. The NaN values in these figures represent that the respective pedestrians were with distance less than 5 meters to the cars but wasn’t in the distance below 2 meters at any second.

(a) On real data

(b) On simulation data

Fig. 7.11: Surrogate safety measurement of pedestrians on the HBS data set. TTC and PET are measured in seconds. TTC can be classified in terms of severity [Kaparias et al., 2013]: TTC ≤ 0.5 is short, 0.5 < TTC ≤ 2 is moderate, and TTC > 2 is long. PET > 4 has no traffic concern [Pascucci, 2020].

In the case of the HBS data set, out of 211 road-crossing trips of pedestrians, the situation considered as safe (i.e., both TTC and PET are NaN) is 81 in real scenarios 2 This experiment extends the bachelor project work of my students, Ghaith Al Akad and Mohamad Yasser Fares.

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and 181 in simulation. Moreover, any case with TTC ≥ 5 and PET ≥ 4 is also regarded as safe, according to [Pascucci, 2020]. As visualized in Figure 7.11, in simulation, the number of near-collision scenarios is comparatively less than in real scenarios.

(a) On real data

(b) On simulation data

Fig. 7.12: Surrogate safety measurement of pedestrians on the DUT data set. TTC and PET are measured in seconds. TTC can be classified in terms of severity: TTC ≤ 0.5 is short, 0.5 < TTC ≤ 2 is moderate, and TTC > 2 is long. PET > 4 has no traffic concern.

Among all 607 DUT scenarios, the situation when both TTC and PET are NaN is 265 in real scenarios and 242 in simulation. From these numbers and also as visualized in Figure 7.12, we can infer that while modeling crowded scenarios, our model performs realistically in terms of safe trajectory modeling of pedestrians.

(a) On real data

(b) On simulation data

Fig. 7.13: Surrogate safety measurement of pedestrians on the CITR data set. TTC and PET are measured in seconds. TTC can be classified in terms of severity: TTC ≤ 0.5 is short, 0.5 < TTC ≤ 2 is moderate, and TTC > 2 is long. PET > 4 has no traffic concern.

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In the CITR scenarios, out of 208 scenarios, the situation that considered as safe (i.e., both TTC and PET are NaN) is 69 in reality and 119 in simulation, i.e., our simulation model generates more collision-free trajectories. As shown in Figure 7.13, similar to the HBS scenarios, the number of near conflict scenarios is comparatively less in simulated scenarios. To summarize this section, in the case of the HBS and CITR scenarios, our model generates a larger number of safe trajectories of pedestrians than it is seen in the real scenarios. This means that in simulation, road users resolve conflicts before they come very near to each other, i.e., they maintain a large safety distance. However, for crowded scenarios from the DUT data set, the recognized number of safe trajectories of pedestrians are comparable in real scenarios and simulation. These results indicate that although our model can capture both near-conflict and collision-free trajectories, it is mostly over conscious about modeling safe trajectories; thus, it deviates from reality. In future, it would be beneficial to calibrate our model’s parameters in term of realistic safety-related behavior.

7.2.4 Comparing GSFM with a deep learning model As discussed in Section 3.4, existing multi-agent-based simulations for road users’ behavior modeling can broadly be categorized into expert-based and data-driven approaches. Our GSFM model falls into the expert-based category as it combines symbolic modeling and reasoning with explicit analysis of decision logic to model agents motion. In-depth comparisons of expert-based and data-driven models for trajectory modeling of road users are currently missing. In joint work with Hao Cheng, we compare our model (third stage of GSFM, visualized in Figure 4.24) with a data-driven model (i.e., LSTM-DBSCAN) by creating a common framework to run these two models for ensuring a fair comparison. LSTM-DBSCAN, Long Short-Term Memories with Density-Based Spatial Clustering of Applications with Noise [Cheng et al., 2019], is a data-driven model, more specifically, a deep learning (DL) model that derives and predicts trajectories based on, e.g., video data.

7.2.4.1 LSTM-DBSCAN The LSTM-DBSCAN model contains two modules: a mapping module for interaction pooling and an LSTM module for motion planning, as visualized in Figure 7.14. The mapping module is responsible for pooling the target agent’s interactions with other neighboring agents at each time step. Like the repulsive force in SFM, this module maps the collision probability based on the safety distance (d) kept by the target (i) and neighboring (j) agents, denoted by probability density mapping (PDM). As shown in Figure 7.14, d is estimated by the approximate mass points from i to j. PDM increases exponentially if d decreases. In Figure 7.14, the egg shapes with estimated radius (extracted from real-world interactions) indicate pedestrian’s

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127

personal space and car geometry. The mapping module also includes a DBSCAN cluster [Ester et al., 1996] to detect and relax on close interactions among pedestrian group members, as in social groups, less inter-distance does not usually mean high collision probability. At each time step during the observation time, existing agents are clustered. A neighboring agent is considered as a group member for i if they co-exist in the same cluster over 90 % of the observed time steps. The LSTM module is responsible for motion planning. It takes the target agent’s coordinates and the mapping module’s output as input at each observed time step. In contrast, in prediction time, it uses the encoded information from observed time steps to predict the next positions of i. The prediction process in LSTM-DBSCAN for a target agent i is formulated in Eq. (7.3). For simplicity, the time step is omitted in the equation. Here, f(.,.) denotes LSTM, φ( .) is PDM, and ψ(.,.) indicates DBSCAN. For each target agent i, LSTMDBSCAN takes Xi (positions in the observed time steps) as input and outputs Yˆ i , i.e., the future positions of i. ˆ i∈N = f(Xi∈N ,φ(ψ(Xi∈N ,Xj∈N,j≠i ))) Y

(7.3)

Fig. 7.14: The structure of the LSTM-DBSCAN model for any target agent i. ⊗ stands for the concatenation of the mapping module’s output and the target agent’s position at each time step (Cheng et al. [2020a], p. 6).

7.2.4.2 Data Sets, Evaluation Metrics, and Experiment Setup The prediction task of both DL model LSTM-DBSCAN and expert-based model GSFM is to generate realistic and collision-free future trajectories of road users based on their locations at observation time steps. To evaluate the prediction performance of GSFM and LSTM-DBSCAN, we use the HBS and DUT data sets (see Section 5.1). Table 5.1 summarizes the statistics of both data sets. We used the first 1200 of 3620 time steps from the HBS data set and twelve clips (eight from the intersection

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and four from the roundabout-like open space) from the DUT data set for extracting various interaction scenarios to evaluate our models. The rest of the two data sets are utilized to fine-tune the GSFM model and train the LSTM-DBSCAN model. There is no overlap between the evaluation and training data.

We evaluate the performance of GSFM and LSTM-DBSCAN in terms of realistic trajectory prediction (by considering both conflict-avoidance and behavior modeling) using two displacement errors (Euclidean and Hausdorff distance) and the heading error as metrics (see Section 5.2). In most cases, the displacement error increases with the increment of time steps. We also perform case studies to evaluate the GSFM and LSTM-DBSCAN models qualitatively using different real-world scenarios.

(a)

(b) Fig. 7.15: The performance of GSFM and LSTM-DBSCAN on (a) the HBS data set and (b) the DUT data set (Cheng et al. [2020a], p. 9).

As mentioned in Section 4.8, GSFM is implemented in Java using the LightJason framework. On the other hand, LSTM-DBSCAN is implemented in Python using tensorflow [Abadi et al., 2015] framework. The LSTM units have a size of 128 and one vertical layer. It is trained by RMSProp optimized with a learning rate of 0.003 and batch size of 16 for 300 epochs. The observation sequence length is fixed to six time steps but the prediction sequence length can vary with a minimum length of six time steps. Both GSFM and LSTM-DBSCAN are evaluated on real-world scenarios lasting the varying length of time steps, unlike models in [Alahi et al., 2016, Gupta

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129

et al., 2018, Sadeghian et al., 2018] that can only predict trajectories of a fixed length of time steps.

7.2.4.3 Quantitative Results for Individual Models Figure 7.15 visualizes the difference (i.e., error) between the real trajectories and the predicted trajectories by LSTM-DBSCAN and GSFM along time horizon on HBS and DUT, measured by Euclidean distance error (ADE), Hausdorff distance error, and heading error. As shown in Figure 7.15, in general, the performance of both models decreases on both data sets with the increase in time step due to increased uncertainty in future. Figure 7.15a shows that LSTM-DBSCAN works better in short-sequence prediction (roughly 25 time-steps) than GSFM by all the evaluation metrics for the HBS data set. However, the HBS data set includes several long-sequence interaction scenarios and with the increasing time steps, the performance of the LSTM-DBSCAN model drops faster than GSFM. As visualized in Figure 7.15b, the prediction performance of LSTM-DBSCAN on the DUT data set is notably better than GSFM by all measures possibly because the scenarios from the DUT data set are shorter and for short-sequence LSTM-DBSCAN performs better than GSFM. However, both the LSTM-DBSCAN and GSFM 3 (V3 in Figure 4.24) models show limited performance on the DUT data set. As stated in Section 5.1, the DUT scenarios are more complicated as this data set is collected from highly dense traffic areas compared to the HBS data set.

7.2.4.4 Qualitative Results for Individual Models Figure 7.16 to Figure 7.19 visualize the trajectory predictions of GSFM and LSTMDBSCAN in three interaction scenarios from the HBS data set and one from the DUT data set. In situations that involve a small number of road users (scenarios extracted from the HBS data set), both the GSFM and LSTM-DBSCAN models generate reasonable trajectories. However, while modeling dense traffic in the DUT data set, both models face difficulties.

3 At this stage, the GSFM model does not include an automated calibration process, thus it shows limited performance on any new data set (e.g., the DUT data set).

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(a) The GSFM model

(b) The LSTM-DBSCAN model

Fig. 7.16: HBS scenario one. Here, the real trajectories are in black and the predicted trajectories are color-coded (Cheng et al. [2020a], p. 10).

As presented in Figure 7.16, the predicted trajectories by the GSFM model overlays the ground truth well and exceeds the LSTM-DBSCAN model when the trajectories have a steady heading direction. However, when road users frequently change their heading direction, GSFM faces difficulty mimicking this behavior. As shown in Figure 7.17, GSFM predicts straight forward and homogeneous trajectories of pedestrians because the model designates a limited number of motion patterns allowing relatively fixed speed (i.e., a Gaussian distribution of speed) of road users. In contrast, LSTM-DBSCAN can automatically capture both the speed and orientation attributes of individual agent based on a short observation time. In Figure 7.18, the GSFM model makes the error in predicting the selected decisions of road users to handle the conflict situation. Unlike real situation, in GSFM, the car decelerates and lets the pedestrian proceed. Still, GSFM predicts reasonable trajectories for both road users. On the other hand, the short-term prediction of LSTM-DBSCAN is similar to the real situation, i.e., the car continues and the pedestrian waits, but in the long-term it predicts that both road users slow down; thus, in this scenario, LSTM-DBSCAN also fails to optimally predict the trajectories of road users. GSFM and LSTM-DBSCAN manage conflict situations differently. GSFM handles conflicts explicitly using the social forces, where the repulsive force rises exponentially when two road users come closer, or by game playing to negotiate the priority over the shared space. On the other hand, LSTM-DBSCAN automatically learns col-

7.2 Description of Experiments and Results

(a) The GSFM model

131

(b) The LSTM-DBSCAN model

Fig. 7.17: HBS scenario three. Here, the real trajectories are in black and the predicted trajectories are color-coded [Cheng et al., 2020a].

(a) The GSFM model

(b) The LSTM-DBSCAN model

Fig. 7.18: HBS scenario three. Here, the real trajectories are in black and the predicted trajectories are color-coded.

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lision avoidance based on the training data with probability density mapping. Thus, these models may produce different negotiating results when handling the same interactions. As an example, Figure 7.19, both GSFM and LSTM-DBSCAN do not optimally predict road users’ trajectories in a situation involves a car approaching a large number of pedestrians. Unlike real situation, in GSFM, for handling the conflict situation, the car decelerates and let all pedestrians continue. In contrast, LSTM-DBSCAN predicts a very unrealistic and aggressive behavior of the car, resulting in a (near) collision situation.

(a) The GSFM model

(b) The LSTM-DBSCAN model

Fig. 7.19: DUT scenario. Here, the real trajectories are in black and the predicted trajectories are color-coded.

Table 7.3: List of Pros and cons of the GSFM and LSTM-DBSCAN models (Cheng et al. [2020a], p. 10) Model

GSFM

Pros

generate collision-free trajectories, transparent and explainable architecture, no requirement for labeled data, easy to control

require domain knowledge, contain complicated rules, Cons homogeneous predictions, less flexible in scaled problems, limited performance in heavy traffic

LSTM-DBSCAN require less domain knowledge, not based on rules, good for short-term predictions, realistic predictions in simple situations not transparent, not explainable, collision-free trajectories are not guaranteed, computationally expensive, hard to control, limited performance in dense traffic, need labeled data, can be over-fitted

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133

To summarize this section, both the GSFM and LSTM-DBSCAN models have respective strengths and shortcomings; we outline those in Table 7.3. The above experiments and discussion lead us to think about a combined model of GSFM and LSTM-DBSCAN for generating collision-free, explainable, and heterogeneous trajectories of agents. Moreover, some pioneer research [Hu et al., 2016, Pedreschi et al., 2019] point that a hybrid or combined model can be utilized to achieve the collective advantages of both kinds of modeling approaches. There are very few exciting works in combining these two approaches for trajectory modeling of road users. To predict traffic congestion in crowded environments, Kim and Kim [2020] combined a deep artificial neural network (ANN) with a cellular automaton. The ANN helps the CA-based simulation model by predicting its parameters and functions. Antonucci et al. [2020] proposed a unique approach merging a physicsbased model (SFM) and a learning-based model (feed-forward neural network) to model pedestrians motion and their interaction with static obstacles. We take a first attempt to develop a combined model of GSFM and LSTM-DBSCAN, presented in Chapter 8.

7.3 Interpretation of Results Although we already discussed the results of each experiment in the respective sections. In this section, we explain in total if our model was able to answer all research questions defined in Section 7.1: 1. Based on the case studies in Section 7.2.1, we can deduce that our model can reproduce both the fundamental behavior of road user (e.g., car-following) and also complex scenarios like multiple pedestrians-to-car interaction realistically. The results of our quantitative evaluation process in Section 7.2.2 indicate that our model achieves significant performance for each three data sets regarding all metrics. Especially in terms of modeling trajectories of pedestrians, but trajectory modeling of cars could be improved. Summing up the results of both experiments, we can infer that our model simulates realistic trajectories of pedestrians and cars in shared spaces. 2. From the experiments in Section 7.2.2, we can also conclude that our model is a general model (i.e., can capture new behaviors from new environments with limited effort) for modeling trajectories of pedestrians and cars. 3. From the results of the experiments in Section 7.2.1 and 7.2.2, it is evident that our model performs better than the SFM model in terms of realistic trajectory modeling. Based on the qualitative and quantitative experiments in Section 7.2.4 we conclude that both the GSFM and LSTM-DBSCAN models have their shortcomings and advantages. For example, in quantitative results, the LSTMDBSCAN model performs better than the GSFM model, but it can not guarantee collision-free trajectories.

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4. Based on the analysis in Section 7.2.3, we can deduce that our model can capture both collision-free and near-collision trajectories. However, it generates a large number of safe trajectories of pedestrians than it is observed in the real scenarios for the HBS and CITR data sets and produces more trajectories with traffic concern in the case of the DUT scenarios. Thus, although our model performs satisfactorily, there is still room for improvement of the performance of our model in terms of modeling safe trajectories.

Chapter 8

Towards Combining Expert- and DL-based Models

As discussed in Section 7.2.4, both expert-based and deep learning (DL) approaches have respective strengths and shortcomings in realistic trajectory modeling, and the combination of both methods has the penitential for improved performance. Thus, in collaboration with Hao Cheng, we conduct a preliminary work to combine the expertbased GSFM model with a deep learning model, LSTM-DBSAN, by considering the possibility of conflict as the basis of choosing between GSFM and LSTM-DBSCAN for predicting trajectories in any specific situation. We name the combined model as GSFM-w-LSTM; it is discussed in same detail in the following section.

8.1 Agent Architecture in GSFM-vs-LSTM Table 7.3 in Section 7.2.4 sums up the strengths and weaknesses of the GSFM and LSTM-DBSCAN models. Until now, we focus only on the most prominent (from our perspective) strength and shortcoming of these models to utilize it for combining them. Specifically, LSTM-DBSCAN can not always guarantee collisionfree trajectories, but when it does, it captures heterogeneous motion patterns of road users. On the other hand, the GSFM model generates collision-free trajectories of road users but often fails to capture the heterogeneity in their trajectories. To generate collision-free and heterogeneous trajectories of road users, we combine the GSFM and LSTM-DBSCAN models. The workflow of predicting the trajectories of all road users in any interaction scenario using the GSFM-w-LSTM model is visualized in Figure 8.1 and discussed in the following: – Both the GSFM and LSTM-DBSCAN models predict the trajectories of respective road users by perceiving the same information from the environment. – The predicted trajectories of road users using the LSTM-DBSCAN model is then cross-checked for collision avoidance. Suppose road users’ predicted trajectories

© The Author(s), under exclusive license to Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2022 F. T. Johora, Modeling Interactions among Pedestrians and Cars in Shared Spaces, https://doi.org/10.1007/978-3-658-38345-9_8

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collide, and the time to collision, i.e., the difference between the time-stamp of the intersection point of their trajectories, is less than one second. In that case, the predicted trajectories will be considered as collided. – If the predicted trajectories by LSTM-DBSCAN are conflict-free, these trajectories will be executed; otherwise, the predicted trajectories of road users by the GSFM will be performed. In the following sections, we quantitatively and qualitatively evaluate the performance of the GSFM-w-LSTM model in terms of realistic trajectory modeling.

GSFM

Start a game

Leader (a car)

Activate or Deactivate

Path Planning

LSTM DBSCAN

Nearest competitive user of leader (a pedestrian)

Observed Trajectory

Trigger Solve the game and select strategy pair (Ls, Fs)

Interactive decision-making

Yes

Leader car and follower car execute Ls Activate or Deactivate

Trajectory Prediction

Percepts

Percepts Actions

Trigger

BDI Controller

No Both Activate players or Deactivate Multiple followers?

execute selected Force-based modeling stategies

All pedestrian followers execute Fs

Trigger Percepts

Percepts

Yes

Environment Model

Conflicts in Prediction?

No

Predicted Trajectory

Fig. 8.1: The conceptual architecture of a agent in the combined model, GSFM-w-LSTM. The GSFM component denotes the conceptual structure of GSFM, and the LSTM-DBSCAN component represents the general structure of the DL model. Both models share the same input from the observation. The prediction of the trajectories of road users are conducted using both the expertbased model GSFM and the DL model LSTM-DBSCAN. A conflict checking box is applied to postprocess the LSTM-DBSCAN model’s trajectory prediction and used to choose the final prediction from either of the two models [Johora et al., 2020].

8.2 Quantitative Results for Combined Model The performance of the GSFM-w-LSTM model in realistic trajectory modeling of pedestrians and cars is measured by Euclidean and Hausdorff distance, and heading error metrics. Figure 7.15 presents the difference in the performance of GSFM-wLSTM (shown in blue color) in comparison with the GSFM and LSTM-DBSCAN models.

8.3 Qualitative Results for Combined Model

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The GSFM-w-LSTM model outperforms GSFM by all measures on both the HBS and DUT data sets. Compared to the LSTM-DBSCAN model, GSFM-w-LSTM performs better in long-sequence trajectory prediction, i.e., on HBS, after 25 time steps and on DUT, after 13 time steps. However, LSTM-DBSCAN beats the GSFMw-LSTM model in predicting short-sequence trajectories; still, the difference in the performance of the GSFM-w-LSTM and LSTM-DBSCAN models is less than that observed for GSFM and LSTM-DBSCAN. Overall, the preliminary version of the combined model shows improved performance in trajectory prediction of pedestrians and cars.

(a)

(b) Fig. 8.2: The performance of the GSFM-w-LSTM model compared to the LSTM-DBSCAN and GSFM models estimated by Euclidean and Hausdorff distance, and heading error (a) on the HBS and (b) DUT data sets (Johora et al. [2020], p. 2).

8.3 Qualitative Results for Combined Model In this section, we qualitatively evaluate the performance of GSFM-w-LSTM in comparison with the single models, i.e., GSFM and LSTM-DBSCAN.

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Fig. 8.3: Comparison of the predictions by the GSFM model and the combined model. Ground truth trajectories (GT) shown in black color and predicted trajectories are color-coded. Cars are traveling diagonally.

Figure 8.3 and Figure 8.4 visualize the difference in the performance of the single model and the combined model on the HBS data set. Figure 8.5 shows the comparison for trajectory prediction between the single and the combined models on the DUT data set. For all these figures, the left side shows the visualization before combination and the right side presents the prediction by the GSFM-w-LSTM model. As visualized in Figure 8.3 without combination, the GSFM model wrongly predicts that the car yields to the pedestrians crossing in both scenarios. On the other hand, GSFM-w-LSTM predicts that the vehicle keeps approaching, which is very similar to the ground truth. But the combined model suggests a faster crossing speed for the pedestrians. However, when the time step increases, even the combined model gives wrong predictions for the pedestrians.

Fig. 8.4: Comparison of the predictions by the LSTM-DBSCAN and the combined models. Ground truth trajectories (GT) shown in black color and predicted trajectories are color-coded. Cars are traveling diagonally.

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The scenario demonstrated in Figure 8.4 shows that the combined model predicts that the car yields to the pedestrians similar to the real scenario but with a decelerated speed. On the other hand, the single model on the left side predicts an accelerated speed for the car, forcing the pedestrians to deviate from their destination.

Fig. 8.5: Comparison of the predictions by the GSFM model and the combined model. Ground truth trajectories (GT) are in black color, predicted trajectories are color-coded. The car is traveling from the right to the left direction.

In Figure 8.5, neither the single and combined model give an optimal prediction for the car navigating in a large number of pedestrians. However, from the visualization, the combined model performs noticeably better than the single model. It suggests a more conservative driving behavior for the vehicle and also correctly predicts some of the trajectories for the pedestrians. Summing up the results of the quantitative and qualitative analysis, compared to the expert-based model, the combined model can model more realistic trajectories and interactions among pedestrians and cars. On the other hand, in the combined model, the expert-based model takes over the DL model when its predictions give faulty or dangerous trajectories. Hence, collision-free trajectories are always guaranteed. However, the performance of the combined model is limited in dealing with high density of traffic, especially on the DUT data set. Up to this point, the combined model is purely based on a conflict checking mechanism that decides the output of which individual models will be selected. Other factors need to be considered for performing this selection process, such as checking if the complete trajectory is realistic. It will be also interesting to investigate ways to integrate the DL model’s output directly into the expert-based model, such as a hybrid model that can cope with challenging interactions in shared spaces in the prediction process. The performance of the combined model solely depends on the performances of the GSFM and LSTM-DBSCAN models. The versions of these two models used at this stage are not the updated versions. The performance of both models has been

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improved later on by using more open-source data sets of shared spaces for training and evaluation. Thus, further work is needed to investigate the performance of the combined model with the updated GSFM and LSTM-DBSCAN models.

Chapter 9

Conclusions and Perspectives

In this chapter, we summarize this research work, discuss limitations of the proposed model, and outline future research opportunities related to improving and extending it.

9.1 Conclusions As briefly described in Chapter 1, the research aim of this dissertation is to develop a microscopic motion model of pedestrians and vehicles that can realistically simulate a large variety of interactions among road users from different shared space schemes. The motivation towards this work is that such models can be utilized (1) to assess the effectiveness of future urban space designs, and (2) in the advent of autonomous cars, e.g., to generate synthetic data or train autonomous cars to learn how to interact with other road users. To understand the requirements for realistically modeling mixed-traffic situations, aka shared spaces, and the necessity of such places, in Chapter 2, we investigated (1) shared space design principles, e.g., the objectives and observed advantages of shared spaces, (2) the typical motion behaviors of most frequently observed modalities in shared spaces, namely, pedestrians, social groups, bicyclists, and vehicles, and (3) different modeling paradigms. We conclude that for realistically modeling shared space operations, we must recognize and classify typical interactions among road users in shared spaces and find suitable methodologies to capture different levels of motion behaviors of road users. In Chapter 3, we discussed several methodologies for planning optimal paths, controlling movements and capturing decision-making processes of road users to select suitable methods for this research. We also reviewed the state-of-the-art of behavioral models of road users in mixed-traffic contexts, to identify and state the research gap.

© The Author(s), under exclusive license to Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2022 F. T. Johora, Modeling Interactions among Pedestrians and Cars in Shared Spaces, https://doi.org/10.1007/978-3-658-38345-9_9

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In Chapter 4, based on the discussion in Chapter 3, we compared several methods and selected the A* algorithm as the path planning algorithm, the social force model to control the motion of road users and a non-cooperative game-theoretic model, more specifically, the Stackelberg game, as the decision-theoretic model, to reproduce movement behaviors of pedestrians and vehicles. As our first contribution, we proposed a modeling process to design a general motion model of road users that outputs the game-theoretic social force model (GSFM). According to our first research objective, we analyzed and classified the interactions among shared space users depending on the complexity of interaction (i.e., simple and complex interaction), the types of participants involved (e.g., car-to-car or pedestrian-to-car interaction), the number of road users involved (e.g., multiple conflicts among pedestrians and cars), and the angle of interaction (e.g., lateral or back interaction), visualized in Figure 4.3. We also analyzed the environment-specific behaviors of pedestrians and cars. We proposed Algorithm 1 to detect and classify interactions among them based on our classification of interaction types and shared spaces (i.e., road and intersection zones). To fulfill our second research objective, we proposed GSFM for realistically modeling the motion behaviors of pedestrians and cars in shared spaces. We presented the multi-layer architecture of the proposed GSFM model, including the workflow among the path planning, force-based modeling and interactive decisionmaking layers (or modules) in this chapter. Up next, the detailed description of these modules, such as how we extended the classical SFM model for vehicles or how we modeled complex interaction among pedestrian groups and cars using the Stackelberg game, and the implementation of the GSFM model are presented. The calibration and evaluation of the GSFM model are performed using four mixedtraffic data sets, namely the HBS, DUT, CITR and SPG (for evaluation only) data sets, and several commonly-used evaluation metrics (e.g., Average or Final Displacement Error), which are discussed in Chapter 5. We proposed a calibration methodology, combining optimization algorithm (i.e., a genetic algorithm), feature selection methods (step-wise backward and forward selection methods), and clustering approaches (i.e., Principal Component Analysis (PCA) with the k-means algorithm and k-means with the forward selection method) to calibrate model parameters and detect heterogeneous motion patterns of pedestrians in Chapter 6. To evaluate the proposed model as our third research objective, we address the following questions: Are the trajectories generated by the GSFM model realistic? is our model generalizable? Is GSFM able to reproduce realistic trajectories in terms of traffic safety? and How does it perform compared to other motion models? The results of our experiments indicate that the GSFM model can reproduce both the fundamental behaviors (e.g., free-flow movement) and complex interactions (crowd-to-vehicle interaction) of road users realistically. However, the performance of GSFM in the modeling of car trajectories could be improved. As discussed in Chapter 5, the examined data sets differ from one another concerning observed types of interactions, environmental structure, traffic culture and density. For each

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data set, the GSFM model gave satisfactory performance in both quantitative and qualitative evaluation, indicating that by following a systematic process with a precise calibration methodology, our model can adapt to a new environment and capture a large variety of interactions. The results of our experiments on traffic safety analysis indicate that GSFM can generate both conflict-free and near-collision trajectories, but it mostly generates a larger number of safe trajectories than is observed in real scenarios. We also examined if the performance of GSFM improves by considering heterogeneity in pedestrians motion, and the results support the hypothesis that it does so mainly when capturing crowded environments. To answer the last question, we compared our model with the classical social force model and a Deep Learning model, LSTM-DBSCAN. The results show that the GSFM model outperforms the SFM model in terms of realistic trajectory modeling. Also, both the GSFM and LSTM-DBSCAN models have their limitations and strengths, e.g., LSTM-DBSCAN mostly predicts trajectories more accurately than GSFM but does not guarantee collision-free trajectories like the GSFM model, which indicates the potential of a hybrid or combined model. Consequently, in Chapter 8, we proposed a preliminary version of GSFM-w-LSTM, combining the GSFM and LSTM-DBSCAN models. We focused on these models’ most prominent strengths from our viewpoint, i.e., guaranteed collision-free trajectories in GSFM and prediction of heterogeneous motion patterns in LSTM-DBSCAN. We compared the performance of the combined model with the single models, i.e., GSFM and LSTM-DBSCAN, and GSFM-w-LSTM outperforms the single models in terms of predicting collision-free, realistic, and heterogeneous trajectories. Even though this work is preliminary, but it introduces a promising direction for future research. To conclude, this dissertation presents a novel agent-based, realistic and general motion model of pedestrians and (human-driven) cars that can reproduce a large variety of interactions from different shared space environment settings. The proposed GSFM model can be applied to assess future shared spaces in the planning stage and utilized in the advent of autonomous cars. Although our model performs satisfactorily, there is still room for improvement of the performance of GSFM, which are discussed in the following section.

9.2 Limitations In the following, we summarize some aspects of our model which require to be improved or explored. – As discussed in Section 7.2.2, the performance of the GSFM model in modeling car trajectories requires to be improved. Moreover, there is still room for improvement in pedestrian behavior modeling. So far, we considered that each pedestrian

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has only a single desired speed. However, a pedestrian’s desired speed can change based on the situation context. – As discussed in Section 7.2.1, the prediction performance of the game model could be improved. – As stated in Section 4.3, explicit interaction (i.e., with explicit communication, e.g., by hand or eye contract) among road users is observed in shared spaces, but is not addressed in this dissertation. – We only consider modeling motion behavior of regular-size and small cars, not large motorized vehicles like micro-buses or buses. – In the GSFM model, during the simulation, each agent checks for conflicts with all other agents in the environment at each time step. While simulating a large environment, this can slow down the runtime performance of GSFM. – As stated in Section 7.2.3, our model is over conscious about the safety concerns of pedestrians, i.e., it generates more conflict-free trajectories than it is observed in real scenarios. Thus, reducing this deviation from reality is required. – Even though we devote much of work to identifying heterogeneity in pedestrians’ motion, there is still more work required as discussed in Section 7.2.1. Moreover, recognizing and modeling different motion patterns of vehicles is not considered in this dissertation. – So far, we only evaluate the generalizability of our model in capturing new interaction scenarios from new settings but did not evaluate the model’s generalizability in terms of integrating a new type of road user. – As mentioned in Chapter 8, the combined model is incomplete; so far, it makes decisions regarding which model will be active completely based on a conflict checking mechanism. Moreover, GSFM-w-LSTM did not build on the current version of the GSFM and LSTM-DBSCAN models.

9.3 Perspectives In addition to the above-listed limitations, few aspects are realized during this dissertation where further research is advisable, discussed in the following.

9.3.1 Model improvements To enhance the performance of the GSFM and also GSFM-w-LSTM models, we need to consider the following steps as future work:

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– Automatic detection of selected strategies of road users in real-world conflict situations is a necessary step to improve the game model and also generalizability of GSFM (or any motion model). – Improve the motion model of cars, e.g., by considering different motion patterns and speed profiles of vehicles and utilizing state-of-the-art controllers for the vehicular physical model. – Moreover, analyzing the causal relationship between situation context and pedestrians’ desired speed by considering the physical limits of humans is necessary for future research in realistic trajectory modeling. For example, a pedestrian walks faster when she has to catch a train. However, there is a certain limit of how fast and how long she can continue this speed, which varies from pedestrian to pedestrian but might be possible to clusters based on demographics. Modeling such individual behavior is one specialty of the multiagent system approach. – Boosting up the scalability of GSFM is essential. Possible approaches to do that are: (1) Dividing the simulation environment into regions, and then agents only consider other agents who are within their region. In this case, agents’ status (regarding in which region they belong) need to be updated when they move from one region to another. (2) At any time step, each agent can only consider and has information about the position and velocity of nearby agents instead of considering all agents in the environment. This can be achieved by storing the state of every agent using an efficient data structure, e.g., KD tree. (3) Combining both approaches. – To recognize new behavior patterns of pedestrians and cars and further enhance (e.g., calibrate parameters regarding pedestrian groups and interactions among cars) and evaluate the performance of our model, we need to explore new data sets, preferably with larger scenarios and a large number of interactions. – More works on the proposed combined model are required. First of all, we need to combine the updated version of the GSFM and LSTM-DBSCAM models, as lately several efforts have been made to improve the performance of both these models, and the performance of both models has been significantly enhanced. To activate the appropriate model in GSFM-w-LSTM, considering other factors, e.g., checking if the complete predicted trajectory is realistic, together with the conflict checking mechanism, would be beneficial. Moreover, it will also be fascinating to investigate ways to develop a hybrid model. For example, creating a hybrid model where GSFM is used to detect conflicts and come up with a solution to avoid them, whereas the LSTM-DBSCAN model takes as input observations on the previous k, e.g., 6, time steps and the decision from GSFM as input to predict trajectories for the next time steps. Then, GSFM executes the trajectories predicted by LSTM-DBSCAN until a new conflict situation arises. Such a hybrid model could promise collision-free trajectories and also exhibit explainability. – Implement the explicit interaction among road users, e.g., by reproducing hand signal or eye contract using message passing mechanisms in the LightJason

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framework, to analyze its impact on the decision-making processes of road users for resolving any conflict situations.

9.3.2 Considering new modalities Until now, we worked on modeling the motion behaviors of pedestrians and vehicles in shared spaces. There are other types of road users which often observed in shared space like cyclists or even buses, and in the near future, autonomous cars may also share the space with humans. Thus, these modalities also need to be incorporated into the simulation model to analyze the application of shared space schemes accurately.

9.3.2.1 Autonomous Vehicles The advent of automotive technology to build intelligent traffic modalities such as autonomous cars makes it essential to analyze strategic interactions between such systems and the human [Rudenko et al., 2020]. How such systems will anticipate human behavior and how humans interact with them needs to be analyzed before they share the same environment with humans. Humans may react differently with autonomous cars than with human drivers. There is ongoing research on both these topics. – Autonomous driving: Autonomous driving is a multi-agent setting where the host vehicle needs to consider other road users while performing a maneuver, e.g. overtaking, following the car in front or pushing ahead in unstructured urban roadways. Recent works on modeling autonomous driving are either focused on reinforcement learning [Shalev-Shwartz et al., 2016, Galceran et al., 2015], most significantly DRL, deep multi-agent reinforcement learning [Isele et al., 2018, Wang et al., 2018b] or imitation learning [Sun et al., 2018, Rehder et al., 2017]. DRL for interaction handling deals mainly by learning driving behaviors in highend simulation models. Such models are beneficial for analyzing what-if situation, such as if only one pedestrian in the current environment runs weirdly from one side to another side of the road, or if half of the road users behave selfishly, what situation will arise. On the other hand, the goal in imitation learning is to learn the behavior of a human driver from recorded driving experiences [Grigorescu et al., 2020]. A realistic simulation model that captures all possible interactions among road users can be used for generating data that isn’t easy to collect or find, to train autonomous cars. Current works on autonomous driving are mainly focused on highway driving, i.e. interaction between autonomous cars and other (human-driven or autonomous) cars, rather than on how an autonomous car will behave while interacting with other types of users like pedestrians or bicyclists in urban areas.

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– Analyzing humans’ behaviors with autonomous vehicles: So far, research on how humans will behave with autonomous vehicles indicate that safety is the utmost priority for autonomous cars and human might take advantage of this situation and dominate the traffic [Michieli and Badia, 2018]. Traffic planners need to consider this case, as they might need to make new traffic regulations for fair traffic [Michieli and Badia, 2018]. Thus, further investigation is required in this direction. Decision-theoretic models such as Game Theory have been used to interpret the human decision-making process in traffic environments [Elvik, 2014]. Such models have good potential to analyze humans interaction with autonomous systems and the impact of different traffic rules on road users for promising future traffic. A game-theoretic model like Level K game [Li et al., 2019] can capture the bounded rationality of human, which is an undeniable need, as not all humans are rational and will follow traffic regulations. To this end, the possible interactions of humans, e.g., pedestrians, cyclists, and human-driven vehicles with autonomous vehicles, need to be investigated, e.g., by considering new traffic rules and rational and irrational human behaviors.

9.3.2.2 Other Modalities Cyclists are frequently observed in shared spaces, and their movement patterns are quite different from pedestrians or motorized vehicles. Some existing works focused on modeling movement behavior of bicyclists [Rinke et al., 2017, Schönauer, 2017, Luo and Ma, 2016, Twaddle et al., 2014]. However, very few works focused on modeling bicyclist group behaviors [Trenchard et al., 2015] and the interactions of cyclists or cyclist groups with autonomous vehicles. Modeling the movement behavior of cyclist groups, including their intragroup interactions and interactions with other modalities, e.g., pedestrians and (autonomous and human-driven) vehicles, is essential. However, modeling cyclist behaviors is very challenging, e.g., they can change role by getting off the bicycle to become a pedestrian, which also needs to be considered when modeling them. The public buses and good transports are also observed in the shared spaces like the one in Sonnenfelsplatz Graz, Austria. Modeling such motorized vehicles is different from modeling cars, not only because of their size, but one might also need to consider appropriate stops for such vehicles for loading and unloading. Also, urban traffic is predicted to increase further [UN-DESA, 2018], and more new traffic modalities, such as tram buses, people and cargo movers, scooters, or cargo bikes, will emerge. Analyzing the behaviors of these modalities are required before they share the same space with traditional road users.

Publications

Journal papers related to this dissertation Johora, F.T. and Müller, J.P., 2021. On transferability and calibration of pedestrian and car motion models in shared spaces. Transportation letters 13, 172–182. Johora, F.T., Yang, D., Müller, J.P. and Özgüner, Ü., 2021. On the generalizability of motion models for road users in heterogeneous shared traffic spaces. arXiv preprint arXiv:2101.06974. (Accept with minor revision for IEEE ITS Transactions journal)

Peer-reviewed conference papers related to this dissertation Johora, F.T. and Müller, J.P., 2020. Zone-specific interaction modeling of pedestrians and cars in shared spaces. Transportation Research Procedia 47, 251–258. Johora, F.T., Cheng, H., Müller, J.P. and Sester, M., 2020. An agent-based model for trajectory modelling in shared spaces: A combination of expert-based and deep learning approaches, in: Proceedings of the 19th International Conference on Autonomous Agents and MultiAgent Systems, IFAAMAS. pp. 1878–1880. Johora, F.T. and Müller, J.P., 2018. Modeling interactions of multimodal road users in shared spaces, in: 2018 21st International Conference on Intelligent Transportation Systems (ITSC), IEEE. pp.3568–3574. Ahmed, S., Johora, F.T. and Müller, J.P., 2019. Investigating the role of pedestrian groups in shared spaces through simulation modeling, in: International Workshop on Simulation Science, Communications in Computer and Information Science, vol 1199. Springer. pp. 52–69, Cham. Cheng, H., Johora, F.T., Sester, M. and Müller, J.P., 2020a. Trajectory modelling in shared spaces: Expert-based vs. deep learning approach?, in: International Workshop on Multi-Agent Systems and Agent-Based Simulation, Lecture Notes in Computer Science, vol 12316. Springer. pp. 13–27, Cham.

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2022 F. T. Johora, Modeling Interactions among Pedestrians and Cars in Shared Spaces, https://doi.org/10.1007/978-3-658-38345-9

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Other publications Hossain, S., Johora, F.T., Müller, J.P. and Hartmann, S., 2020. A conceptual model of conflicts in shared spaces, in: 2020 The 6th International Conference on Industrial and Business Engineering, pp. 228–235. Yang, D., Johora, F.T., Redmill, K.A., Özgüner, Ü. and Müller, J.P., 2021. Sub-goal social force model for collective pedestrian motion under vehicle influence. arXiv preprint arXiv:2101.03554.

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Chapter 10

Appendix

This chapter contains the complete AgentSpeak(L++) scripts of road users and the host agent and also the UML class diagram of our model implementation. AgentSpeak(L++) Code for Road User 1 2 3 4 5

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module(3.0). !main. +!main (module(S), generic /type/ isnumeric (S) && S ==3.0) module(S); -module (S); + module (G). +!game/accelerate: >> (module(S), general /type/ isnumeric (S) && S ==0.0) > (module(S), general /type/ isnumeric (S) && S ==1.0) > (module(S), general /type/ isnumeric (S) && S ==2.0) >(canceldetour(S), generic /type/ isnumeric (S) && S > 0.0) >(canceldetour(S), generic /type/ isnumeric (S) && S == 0.0)