Evaluation of intersection control strategies for automated vehicles

(1)

ENGINEERING

Henrique Salvaro Furtado

EVALUATION OF INTERSECTION CONTROL STRATEGIES FOR AUTOMATED VEHICLES

Florian´opolis 2017

(2)

(3)

Thesis presented to the Graduate Program in Automation and Sys-tems Engineering in partial fulfill-ment of the requirefulfill-ments for the de-gree of Master in Automation and Systems Engineering.

Advisor: Prof. Rodrigo Castelan Carlson, Dr.

Florian´opolis 2017

(4)

Furtado, Henrique Salvaro

Evaluation of intersection control strategies for automated vehicles / Henrique Salvaro Furtado ; orientador, Rodrigo Castelan Carlson, 2017. 143 p.

Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós Graduação em Engenharia de Automação e Sistemas, Florianópolis, 2017.

Inclui referências.

1. Engenharia de Automação e Sistemas. 2. Veículos automatizados. 3. Controle de interseções. 4. Sistemas inteligentes de transporte. I. Carlson, Rodrigo Castelan. II. Universidade Federal de Santa Catarina. Programa de Pós-Graduação em Engenharia de Automação e Sistemas. III. Título.

(5)

This Thesis is recommended in partial fulfillment of the requirements for the degree of “Master in Automation and Systems Engineering”, which has been approved in its present form by the Graduate Program in Automation and Systems Engineering.

Florian´opolis, December 08th 2017.

Prof. Daniel Coutinho, Dr. Graduate Program Coordinator Universidade Federal de Santa Catarina Dissertation Committee:

Prof. Rodrigo Castelan Carlson, Dr. Advisor

Universidade Federal de Santa Catarina

Prof. Hector Bessa Silveira, Dr. Universidade Federal de Santa Catarina

Prof. F´abio Baldissera, Dr. Universidade Federal de Santa Catarina

Prof. Werner Kraus Jr., Ph.D. Universidade Federal de Santa Catarina

(6)

(7)

(8)

(9)

I would like to first and foremost thank my ever supporting and loving parents, Mafalda and Olinto, as well as my brother, Andr´e, for the meaningful discussions, and for all the rants they’ve had to listen from me. I’m also grateful for all the freedom and guidance provided by my advisor, Prof. Dr. Rodrigo Carlson, and especially for his patience - all that detailed correction!

I must thank CAPES for providing me with the means to develop this work through the scholarship. Special thanks for all the support coming from the PGEAS department. I also can’t forget to thank our beloved UFSC, which has been my home for the past 8 years.

And to finish, I’d like to thank my amazing group of friends who, even after graduating, have sticked together (and have listened to my daily rants), specially to those who have kept me company daily: An-drio, Antonio, Pedro, Rodrigo and Vinicius. Special thanks to the friends who have kept me company throughout grad school, after years of un-dergrad, both in and out of UFSC, Amadeu, Bruno “Bill”, Bruno “Jedi” and Marcelo.

(10)

(11)

O desenvolvimento de ve´ıculos automatizados tem aumentado significativamente desde a virada do século 20 para o 21, e tende a continuar aumentando com a entrada das grandes fabricantes de au-tomóveis anunciando suas próprias iniciativas. Com os avan¸cos das tecnologias de ve´ıculos conectados e automatizados, surge uma série de desafios. Esses desafios não estão somente relacionados com o desenvol-vimento tecnológico em si, mas também com os aspectos operacionais, como o uso em conjunto dessas tecnologias visando tornar o tráfego de ve´ıculos mais seguro e eficiente, particularmente em regiões de conflito, isto é, regiões onde dois ou mais fluxos de tráfego tenham trajetórias conflitantes. Referente a esses aspectos operacionais, a existência des-sas regiões de conflito, como cruzamentos e interse¸cões, torna ne-cessária a cria¸cão de estratégias de controle capazes de coordenar o uso dessas regiões de forma segura e eficiente. Exemplos de melhorias no tráfego são a redu¸cão no atraso dos ve´ıculos, no número de acidentes e na emissão de poluentes, essas melhorais são, por muitas vezes, atingi-das com o uso de técnicas empregando o controle ótimo. Neste trabalho, será desenvolvida uma série de estudos acerca das atuais estratégias de controle de ve´ıculos automatizados em interse¸cões. Estratégias seleci-onadas serão implementadas e comparadas em simula¸cão, sob óticas quantitativas e qualitativas como por, exemplo, ganho de desempenho, escalabilidade e generalidade. Um de nossos prinicipais objetivos é o de criar uma base de compara¸cão para essas estratégias, através do uso dos mesmos parâmetros de simula¸cão e configura¸cões, e as aplicando a diferentes configura¸cões de tráfego.

Palavras-chave: Ve´ıculos Automatizados. Ve´ıculos Conectados. Con-trole de Interse¸c˜oes. Controle ´Otimo. Sistemas Inteligentes de Trans-porte.

(12)

(13)

O desenvolvimento de ve´ıculos automatizados tem aumentado significativamente desde a virada do século 20 para o 21, e tende a continuar aumentando com a entrada das grandes fabricantes de au-tomóveis anunciando suas próprias iniciativas. Com os avan¸cos das tecnologias de ve´ıculos conectados e automatizados, surge uma série de desafios. Esses desafios não estão somente relacionados com o de-senvolvimento tecnológico em si, mas também com os aspectos opera-cionais, como o uso em conjunto dessas tecnologias visando tornar o tráfego de ve´ıculos mais seguro e eficiente, particularmente em regiões de conflito, isto é, regiões onde dois ou mais fluxos de tráfego te-nham trajetórias conflitantes. Referente a esses aspectos operacionais, a existência dessas regiões de conflito, como cruzamentos e interse¸cões, torna necessária a cria¸cão de estratégias de controle capazes de coor-denar o uso dessas regiões de forma segura e eficiente. Exemplos de melhorias no tráfego são a redu¸cão no atraso dos ve´ıculos, no número de acidentes e na emissão de poluentes, essas melhorais são, por muitas vezes, atingidas com o uso de técnicas empregando o controle ótimo. Além dessas melhorias, existe uma série de estudos indicando o poss´ıvel impacto positivo dessa transi¸cão do tráfego em elementos como o es-coamento e a estabilidade do tráfego, potencial aumento de viagens, entre outras, nos mostrando que a tendência dessa transi¸cão é de im-pactar positivamente a sociedade como um todo. Com o surgimento dessas estratégias de coordena¸cão de ve´ıculos, surge também a neces-sidade de se avaliar o desempenho das mesmas, principalmente de forma a tornar poss´ıvel a compara¸cão com os métodos atuais e com outras estratégias de coordena¸cão, possibilitando demonstrar as melho-rias geradas no tráfego através de métricas. Atualmente, as estratégias são, em sua grande maioria, comparadas somente com os métodos atuais de coordena¸cão, como a semaforiza¸cão de tempo fixo, por exem-plo. As poucas compara¸cões realizadas entre estratégias para ve´ıculos automatizados tendem a fazê-las se utilizando dos resultados obtidos diretamente de cada estratégia, sem levar em considere¸cão os detalhes de implementa¸cão ou de simula¸cão. Há uma necessidade de se criar uma base de compara¸cão para essas estratégias de coordena¸cão para ve´ıculos automatizados, de modo que essas sejam avaliadas dentro de um mesmo contexto, utilizando os mesmos parâmetros de simula¸cão e configura¸cões de tráfego, por exemplo. Neste trabalho, será desenvol-vida uma série de estudos acerca das atuais estratégias de coordena¸cão de ve´ıculos automatizados em interse¸cões, de modo a levantar as prin-cipais diferen¸cas de abordagem, referente a quesitos como a existência

(14)

Com esse levantamento de informa¸cões, quatro estratégias selecionadas serão implementadas e comparadas em simula¸cão, tanto entre si quanto com os métodos atuais de coordena¸cão (semaforiza¸cão de tempo fixo). Além disso, as estratégias implementadas serão utilizadas em cinco cenários envolvendo diferentes configura¸cões de tráfego e com diferen-tes valores de demanda de ve´ıculos. Um de nossos prinicipais objetivos ´

e o de criar uma base de compara¸cão para essas estratégias dentro de um mesmo ambiente de simula¸cão e para diferentes aplica¸cões.

Palavras-chave: Ve´ıculos Automatizados. Ve´ıculos Conectados. Con-trole de Interse¸c˜oes. Controle ´Otimo. Sistemas Inteligentes de Trans-porte.

(15)

The development of automated vehicles has been experiencing an increased growth since 2000, and tends to continue growing as ma-jor car manufacturers start their own initiatives. With the advances in connected and automated vehicle technologies, a number of complica-tions arise. These complicacomplica-tions are not only related to the technologi-cal development itself, but also to the operational aspects, such as the seamless usage of these technologies in order to make traffic flow safer and more efficient, particularly in conflict regions, i.e., regions within a traffic network where two or more streams of traffic have conflicting trajectories. Regarding the operational aspects, the existence of conflict regions, such as crossings and intersections, leads to the necessity of creating control strategies that coordinate the safe and efficient usage of those regions. Examples of improvements in traffic flow are the re-duction in vehicle delay, rere-duction in the number of accidents and the emission of pollutants, those improvements are often achieved through the usage of optimal control techniques. In this work, we will study the current automated intersection control strategies and the trends around them. A few chosen strategies will be implemented within the same environment, and compared among them, under quantitative and qualitative analysis, e.g., scalability, efficiency and generality. One of our main goals is to create a base of comparison for strategies, using the same simulation parameters and configuration for all strategies, while applying those strategies to different traffic configurations.

Keywords: Automated Vehicles. Connected Vehicles. Intersection Management. Optimal Control. Intelligent Transportation Systems.

(16)

(17)

2.1 Aerial view of a four way intersection. . . 35

2.2 Intersection atomic model . . . 36

2.3 Intersection as a 5 by 5 grid model . . . 37

2.4 Intersection as a 10 by 10 grid model . . . 38

2.5 Four way intersection and its allowed movements . . . . 39

2.6 Fixed-time traffic light system example . . . 40

2.7 Movements associated with each traffic light phase . . . 41

2.8 Intersection atomic model with a vehicle inside . . . 42

2.9 Intersection as a 5 by 5 grid model with a vehicle inside 43 2.10 Intersection as a 10 by 10 grid model with a vehicle inside 44 2.11 Representation of an intersection using conflict paths . . 45

2.12 Example of the usage of critical sets. . . 46

3.1 Basic scenario proposed by Tachet et al. (2016) . . . 53

3.2 Representation of the algorithm formation strategy . . . 56

3.3 Example of a four way intersection model . . . 59

3.4 Compatibility graph describing a four way intersection . 60 3.5 Representation of an intersection in (MALIKOPOULOS; CASSANDRAS, 2016). . . 67

3.6 General intersection with left and right turns proposed by Zhang et al. (2017) . . . 71

3.7 Representation of an intersection in (CAMPOS et al., 2017) 79 3.8 Visual representation of parameters from (CAMPOS et al., 2017) . . . 85

3.9 Representation of an intersection by M¨uller et al. (2016b) 92 4.1 Scenario 1 modeled for the Slot-Based and Decentralized Framework strategies . . . 100

4.2 Scenario 1 modeled for the Receding Horizon strategy . 101 4.3 Scenario 1 modeled for the OATS strategy . . . 101

4.4 Scenario 2 modeled for the Slot-Based and Decentralized Framework strategies . . . 104

(18)

Framework strategies . . . 118

4.14 Scenario 5 modeled for the Receding Horizon strategy . 119

4.15 Scenario 5 modeled for the OATS strategy . . . 120

A1 Counter example sequence. . . 136

A2 Optimal and executed speed profiles for vehicle #22 with the original formulation. . . 139

A3 Optimal and executed speed profiles for vehicle #22 with the proposed solution. . . 140

A4 Distances22(t) between vehicles #22 and #19, without

and with the solution. Vehicle #19 is ahead of vehicle #22. The safety distance\delta is violated with the original formulation (or is otherwise infeasible) and is respected with the proposed solution. . . 140

(19)

4.1 Vehicle simulation parameters . . . 99

4.2 Simulation results for Scenario 1. Demand: 400 veh/h per approach. . . 102

4.5 Simulation results for Scenario 2. Demand: 400 veh/h from the main freeway, 200 veh/h from the on-ramp. . . 106

4.6 Simulation results for Scenario 2. Demand: 600 veh/h from the main freeway and 400 veh/h from the on-ramp. 107 4.7 Simulation results for Scenario 2. Demand: 800 veh/h from the main freeway and 600 veh/h from the on-ramp. 107 4.8 Simulation results for Scenario 3. Demand: 400 veh/h per approach . . . 111

4.9 Simulation results for Scenario 3. Demand: 600 veh/h per approach . . . 111

4.12 Simulation results for Scenario 4. Demand: 600 veh/h per approach . . . 117

4.14 Simulation results for scenario 5. Demand: 300 veh/h per approach. . . 122

4.15 Simulation results for scenario 5. Demand: 400 veh/h per approach. . . 122

A1 Different formulations for the Decentralized Framework Control . . . 134

A2 Counter example . . . 135

A3 Parameters: (a) intersection . . . 135

(20)

(21)

ACC Adaptive Cruise Control

AIM Autonomous Intersection Management API Application Programming Interface

AV Automated Vehicle . . . . CACC Cooperative Adaptive Cruise Control

CAV Connected Automated Vehicle CR Control Region

CVC Connected Vehicle Center

CVIC Cooperative Vehicle Intersection Control CVXPY Python Convex Optimization Package

CZ Control Zone . . . . DSRC Dedicated Short Range Communication . . . . FCFS First-Come First-Served

FIFO First-In First-Out . . . . HDV Human-Driven Vehicle . . . . IC Intersection Coordinator

iCACC Intersection Management using Cooperative Adaptive Cruise Control

IM Intersection Manager . . . .

MILP Mixed Integer Linear Programming MIQP Mixed Integer Quadratic Programming MPC Model Predictive Control

(22)

SAE Society of Automotive Engineers

SDK Software Development Kit . . . . V2I Vehicle-to-Infrastructure

V2V Vehicle-to-Vehicle V2X Vehicle-to-Anything VANET Vehicular Network

(23)

Cri critical set of vehiclei

Da [m] length upstream of approach a that

defines the controlled area Hi [m] end of vehicle’si critical set

Li [m] start of vehicle’si critical set

L [m] distance upstream of an approach that defines the controlled area SL [m] movement length for a left turn SR [m] movement length for a right turn S [m] intersection length

Tsep [s] time gap between to vehicles

Ts [s] step time

XV the approach vehicleV belongs to

Yi(t) communication set of vehiclei at time

t

\Delta [s] delay experienced by a vehicle tV -

atV

\Gamma i,t predicted occupancy interval of the

in-tersection for vehiclei at time t \Omega i set of states before the intersection for

vehiclei

\Upsilon i set of states after the intersection for

vehiclei

\delta safety [m] safety distance gap for vehicles on the same lane

\delta [s] tolerance parameter for time gaps \delta [m] safety distance between two vehicles \bfT \bfone [s] time gap between vehicles from the

same traffic stream

\bfT \bftwo [s] time gap between vehicles from

con-flicting traffic streams \scrA i attraction set of vehiclei

\scrL set of existing lanes \scrN (t) FIFO queue at timet \scrO ordered list of vehicles \scrT set of allowed trajectories abrake [m/s2_{] deceleration rate}

ai(t) [m/s2] acceleration of vehicle i at time t

amax

i [m/s2] maximum acceleration of vehicle i

amin

(24)

conflicting traffic streams

dtail [m] safety distance between to vehicles to avoid tailgating

di movement indicator for vehiclei

hL [s] headway between vehicles travelling from different approaches

hT [s] headway between vehicles travelling from the same approach

lmax [m] maximum length for a vehicle li [m] length of vehiclei

np number of processed vehicles pi(t) [m] position of vehiclei at time t

tV [s] arrival time of vehicleV

tprea [s] earliest allowed arrival time of the preceding vehicle

ta [s] earliest allowed arrival time tres [s] reaction time of a driver/vehicle tci [s] earliest access time for vehicle i to

reach the intersection

tentry_i [s] time vehiclei enters the intersection tf,feas_i [s] feasible safe access time for vehiclei tf

i [s] time instant when vehicle i exits the

intersection tm

i [s] time instant when vehiclei enters the

intersection tmax

a,i [s] maximum feasible arrival time of

ve-hiclei on approach a tmin

a,i [s] minimum feasible arrival time of

vehi-clei on approach a ta

i,t [s] earliest intersection entry time of

ve-hiclei tb

i,t [s] latest intersection exit time of vehicle

i

ui(t) [m/s2] acceleration of vehicle i at time t

umax

i [m/s2] maximum acceleration of vehicle i

umin

i [m/s2] minimum acceleration of vehicle i

va _[m/s] _{maximal allowed speed for a straight} movement

(25)

va

R [m/s] maximal allowed speed for a right turn movement

vi(t) [m/s] speed of vehiclei at time t

vmax

i [m/s] maximum speed of vehiclei

vmin

i [m/s] minimum speed of vehiclei

vi,d [m/s] desired speed of vehiclei

wmax [m] maximum width for a vehicle wi [m] width of vehiclei

(26)

(27)

1 Introduction 27

1.1 Delimitations . . . 29

1.2 Main objective . . . 30

1.3 Specific objectives . . . 30

1.4 Structure. . . 30 2 Background on Traffic Control 31

2.1 Traffic Simulation . . . 31

2.2 Automation Level of Vehicles . . . 32

2.3 Intersection Control Strategies . . . 33

2.3.1 Traffic Lights . . . 34

2.3.2 Connected Intersection Control Strategies. . . 36

2.3.3 Important Aspects . . . 48 3 Implementation 51 3.1 Strategies . . . 51 3.2 Slot-Based Control . . . 52 3.2.1 Basic model . . . 52 3.2.2 Generic model . . . 58 3.2.3 Implementation . . . 62 3.2.4 Discussion . . . 63

3.3 Decentralized Optimal Control Framework . . . 65

3.3.1 Model . . . 65

3.3.1.1 Structure . . . 66

3.3.1.2 Optimization Problem. . . 69

3.3.1.3 Implementation . . . 69

3.3.2 Model supporting left and right turns . . . 70

3.3.2.1 Structure supporting left and right turns . . . 72

3.3.2.2 Implementation . . . 75

3.3.3 Discussion . . . 76

3.4 Cooperative Receding Horizon Control . . . 78

3.4.1 Model . . . 78

3.4.2 Centralized formulation. . . 81

3.4.3 Decentralized formulation . . . 81

3.4.4 Decision order heuristic . . . 84

3.4.5 Receding horizon strategy . . . 86

3.4.6 Implementation . . . 88

3.4.7 Discussion . . . 89

(28)

3.5.2 Implementation . . . 96 3.5.3 Discussion . . . 96 4 Test cases 99 4.1 Scenario 1 . . . 100 4.2 Scenario 2 . . . 104 4.3 Scenario 3 . . . 108 4.4 Scenario 4 . . . 113 4.5 Scenario 5 . . . 118 5 Conclusion 123 5.1 Future Work . . . 124 Bibliography 125 Appendix A 133 Discussion . . . 133 Counter example . . . 133 Solution . . . 137

Simulation & Results . . . 138

Scenario . . . 138

Results . . . 138

Original formulation . . . 138

With the proposed solution . . . 139

(29)

The development of automated vehicles (as defined in (SAE,

2014)) has been experiencing an increased growth since the first years of the XXI century, and continues growing as the major-ity of car factories start their own initiatives. We are reaching a point where the constraints keeping us from actively removing human drivers from the driving loop are legal and operational ones, not technological (MAHMASSANI,2016). Highly and/or fully-automated vehicles will soon become a reality (Public-Private ITS Initiative/Roadmaps,2016). Examples of early demonstrations are VisLab’s endeavours (BROGGI et al., 2012; BROGGI et al., 2015) and the “Bertha Drive challenge” (ZIEGLER et al.,2014).

Connected and automated vehicles are at the spotlight in the field of Intelligent Transportation Systems, enabling the initiatives and predictions mentioned above. While connected and automated vehicles have gained popularity among the scientific community, media has created a myth around their functioning by commonly misusing technical terms, often describing these initiatives using terms as “driverless”, “self-driving” or “autonomous”, leading to con-fusing conclusions for the general public (SHLADOVER,2017). The most commonly accepted descriptions and terminology will be ex-plained below.

Connected vehicles have become popular and generally ac-cepted in the past decade (SHLADOVER,2017), representing a class of vehicles that have the ability to communicate with other vehicles, with road infrastructure, etc., using technologies classified in the lit-erature as Vehicle-to-Vehicle (V2V), Vehicle-to-Infrastructure (V2I), Vehicle-to-Anything (V2X). The development of those technologies enables applications of collision avoidance at intersections, merg-ing zones and within traffic in general. One example of an applica-tion of those technologies is the cooperative adaptive cruise control (CACC) – an “evolution” of the adaptive cruise control (ACC), an automatic speed regulator in cars based on the distance to the vehi-cle ahead and other conditions – that uses connectivity with other vehicles to better regulate the its speed, leading to better traffic con-ditions, increasing efficiency and safety.

Automated vehicles, on the other hand, have been made pop-ular through projects likeWaymo(2017) andTesla(2017), and me-dia coverage, even if often with misleading usage of the terminol-ogy. By definition, automation refers to the replacement of human functions with electronic and/or mechanic devices (HASEGAWA,

2009). SAE’s J3016 standard (SAE, 2014) provides the

(30)

nity with a description of the automated driving levels taxonomy (see Section2.2). Generally, “driverless”, “self-driving” cars and “au-tonomous” cars are, obviously, automated, but not all automated cars are “driverless”, and even those automated ones may only act as truly “driverless” for specific scenarios (driving modes), depend-ing on their level of automation.

With the advances in connected and automated vehicle tech-nologies, a number of complications arise. These complications are not only related to the technological development itself, but also to the operational aspects, such as the seamless usage of these tech-nologies in order to make traffic flow safer and more efficient, par-ticularly in conflict regions, i.e., regions within a traffic network where two or more streams of traffic have conflicting trajectories.

Regarding the operational aspects, the existence of conflict re-gions, such as crossings and intersections, leads to the necessity of creating control strategies that coordinate the safe and efficient us-age of those regions. In the applications of controlling intersections and crossings, a multitude of techniques have been proposed in re-cent years, as summarized byRios-Torres and Malikopoulos(2016) and Chen and Englund (2016). Coordination in this thesis refers to the action of coordinating vehicles movements within conflict re-gions in order to guarantee their safety and traffic efficiency. The reader should not confuse it with the coordination of traffic lights in traditional traffic control, e.g., for providing the known green waves of traffic.

While there has been a great deal of coordination techniques developed, as well as some studies regarding the possible impacts of the transition to a fully connected and automated traffic, such as the impact on traffic throughput and stability (TALEBPOUR; MAH-MASSANI, 2016), the potential increase in travel (HARPER et al.,

2016) and others, there’s still a lot of room for growth, specially in the operational aspects of that transition (MAHMASSANI,2016).

Most of the techniques proposed so far (RIOS-TORRES; MA-LIKOPOULOS, 2016;CHEN; ENGLUND, 2016;DRESNER; STONE,

2004; DRESNER; STONE, 2005; ZOHDY et al., 2012; ZOHDY; RAKHA, 2016; LEE; PARK, 2012; TACHET et al., 2016; M ¨ULLER et al., 2016b; MALIKOPOULOS; CASSANDRAS, 2016), are evalu-ated with respect to current intersection control methods, i.e., traf-fic lights or on the basis of a theoretical increase of capacity of the intersection (throughput). However, those comparisons should be made among other automated intersection control strategies un-der the same conditions. Other aspects should also be taken into

(31)

account, e.g., qualitative results such as flexibility, generalization, among others.

With that in mind, and focusing on the coordination strate-gies for vehicles crossing conflict regions, it becomes interesting to evaluate the strategies not only regarding their impacts on traffic when compared to the current solution for conflicts (traffic lights, mostly), but also with regards to how well they compare against each other in a series of categories, like safety, reinitialization capa-bilities. Such comparisons are lacking in current developments.

One of the first steps in the literature towards the definition of such criteria was taken byFortelle and Qian(2015), where the authors elect a set of criteria to be considered in intersection control strategies, such as: the balance of safety and efficiency, whether the strategy has a planned or reactive behavior, the system’s nature – centralized or distributed – its heterogeneity – whether it focus on cooperation or self-optimization, and how those criteria relate to real properties and to the system’s implementation.

This master’s thesis aims to study current automated inter-section control strategies using connected and automated vehicles and to gather hands-on experience through the implementation of a few chosen strategies under the same simulation environment, as well as to compare those strategies that were implemented in even grounds.

1.1 DELIMITATIONS

The work here presented is limited to scenarios where all ve-hicles are at least conditionally automated (see Section 2.2), i.e, the vehicle is considered capable of performing all aspects of the dynamic driving task involved, relying on the human driver solely on cases of failure for at least one specific driving mode, thus re-ducing the reaction time considered when simulating the vehicles. There is no formal analysis performed in this work. The discussions in this work are mostly from a qualitative nature and results from the implementation, simulation and observation of strategies. Quan-titative results presented are the average of a total of twelve replica-tions using the Traffic Simulator AIMSUN (TSS,2015). Simulations were done considering only constant demand values.

(32)

1.2 MAIN OBJECTIVE

The implementation and comparison of selected automated intersection control strategies under the same simulation environ-ment.

1.3 SPECIFIC OBJECTIVES

\bullet Implementation of selected strategies;

\bullet Application of the strategies to different types of infrastructure with simulation;

\bullet Evaluation of the strategies performances;

1.4 STRUCTURE

This thesis is structured as follows: Chapter 2 will cover the basic concepts involved in traffic control, focusing on the basics of traffic simulation and on the basics of intersection control strategies, starting at the current control method and reaching the state-of-the-art strategies. Chapter 3 will detail the strategies that were chosen to be evaluated in this work, as well as discuss the details of their implementation and the general analysis of each strategy. Chapter 4 presents the simulation scenarios that were used to evaluate the strategies as well as the results. Chapter 5 concludes this work and points out the direction of our future works.

(33)

In this chapter we present basic concepts related to traffic simulation, automated vehicles and traffic control. We mainly cover the subject of automated intersection control strategies, describing the problem they attempt to solve. We also present a brief literature review and point out the state-of-the-art, as well as a brief analysis of the important aspects involved in a intersection control strategy.

2.1 TRAFFIC SIMULATION

According toGerlough and Huber (1976), traffic simulation originated naturally from the necessity (or desire) to conduct experi-mentation, be it a model validation or the evaluation of a particular parameter or constant. The authors also provide a brief historical note on the matter of traffic simulation: how its origin dates back to as early as 1949, only to have the first computational results af-ter 1954, and to be widely accepted as a possible and feasible tool around 1960. Simulation has evolved since then into three different approaches: Macroscopic, Mesoscopic and Microscopic.

Macroscopic modelling models the relationships of basic traf-fic flow’s attributes, such as density, speed and flow, not focusing on the discrete elements (the vehicle itself, for instance) but rather on the traffic stream behavior. The first widely accepted macroscopic model was proposed by Lighthill and Whitham (1955) with the idea of it being comparable with fluid streams. It has been devel-oped since then, culminating in other models, one of them being the well-known Cell-Transmission Model proposed byDaganzo(1994). Mesoscopic models analyze transportation elements in small groups, within which elements are considered homogeneous. A typ-ical example is vehicle platoon dynamics and household-level travel behavior (BURGHOUT et al.,2006).

Microscopic traffic simulation instead models the behavior of each vehicle, based on car-following models (that simulate the pair human-car driving behavior) first introduced by Chandler et al.(1958) as the General Motors’ model. Nowadays other models are also used together with car-following models to better replicate human behavior.

More recently, there’s been development in the modeling of connected vehicles behavior (be it human-driven or automated)

Talebpour et al.(2016), offering a framework that enables a more “realistic” simulation of the new emerging technologies involving

(34)

connected/fully-automated vehicles, such as (TALEBPOUR; MAH-MASSANI,2016).

2.2 AUTOMATION LEVEL OF VEHICLES

There are a number of nomenclatures used to describe cur-rent connected and automated vehicle technologies: autonomous, self-driving, driverless, automated, etc, to name a few. In order to standardize and facilitate cooperation/communication regarding those technologies, the SAE International has defined in 2014 a common taxonomy and definitions to describe the levels of driving automation and other associated characteristics, for example, the driver’s role (SAE,2014).

The standard defines six levels of driving automation, start-ing at “No Automation” and reachstart-ing “Full Automation”. The word “System” here may refer to the driver assistance system, to a

com-bination of driver assistance systems, or to the automated driving system. Key terms are described in the standard:

\bullet Dynamic Driving Task: includes the operational (steering, braking, accelerating, monitoring the vehicle and roadway) and tactical (responding to events, determing when to change lanes, turn, use signals, etc) aspects of the driving task, but not the strategic (destinations, waypoints) aspect.

\bullet Driving mode: type of driving scenario with characteristic dy-namic driving task requirements, e.g., expressway merging, high speed cruising, low speed traffic jam, closed-campus op-erations, etc.

\bullet Request to intervene: notification by the automated driving system to a human driver that he should promptly begin or resume performance of the dynamic driving task.

Levels 0-2 are defined as environments monitored by the hu-man driver, while levels 3-5 are monitored by the automated driving system:

\bullet Level 0 - No Automation: the human driver is fully respon-sible for all aspects of the dynamic driving task, even when enhanced by warnings or intervention systems. An example is a vehicle equipped with a parking sensors;

(35)

\bullet Level 1 - Driver Assistance: a driver assistance system is re-sponsible for either steering or accelerating and decelerating during a specific driving mode using information about the en-vironment. It is expected that the human driver will perform all remaining aspects of the dynamic driving task. An example is a vehicle equipped with Adaptive Cruise Control;

\bullet Level 2 - Partial Automation: one or more driver assistance systems are responsible for steering, accelerating and deceler-ating during a specific driving mode using information about the environment. It is expected that the human driver will per-form all remaining aspects fo the driving task. An example is a vehicle combining both Adaptive Cruise Control and a Lane-Keeping Assistance system;

\bullet Level 3 - Conditional Automation: an automated driving sys-tem is responsible for all aspects of the dynamic driving task during a specific driving mode, including to monitor the envi-ronment. The human driver is expected to respond appropri-ately to a request to intervene. An example is a vehicle capable of changing lanes and deciding how to respond to dynamic in-cidents on the road, while still relying on the human driver as fallback system;

\bullet Level 4 - High Automation: an automated driving system is re-sponsible for all aspects of the dynamic driving task during a specific driving mode, including to monitor the environment. For those specific driving modes, the vehicle is expected to stay in control even if a human driver does not respond appro-priately to a request to intervene. An example is the Google’s Self Driving Car (WAYMO,2017);

\bullet Level 5 - Full Automation: an automated driving system is re-sponsible for all aspects of the dynamic driving task under all roadway and environmental conditions.

2.3 INTERSECTION CONTROL STRATEGIES

Intersections are one of the reasons why traffic dynamics can be highly non-linear and difficult to predict, acting as natural bottle-necks, adding constraints in space and time to the traffic dynamic (ROESS et al., 2010). They are the regions where roads coming

(36)

One can look at intersections as a shared resource (physi-cal place) wanted by other elements of the system (vehicles), but, for safety reasons, the access to this resource must be coordinated. There are some complexities and differences to how we can model these shared regions, related to how one chooses to represent it. Ex-amples of possible approaches can be seen inFigure 2.2,Figure 2.3

andFigure 2.4, showing, respectively, an intersection modelled as an atomic resource, meaning that only one vehicle would be al-lowed to be inside it for a given time, and as a series of smaller resources (cells) that can be allocated to vehicles at a given time. The smaller those resources are, the more efficiently the intersec-tion can be used, because one needs only to reserve the effective space a vehicle would require, while the remaining cells can be used by other incoming vehicles.

In order to allow the safe access to that shared resource, we must coordinate the movement among vehicles with incompatible paths. This vehicle coordination is what we call an “Intersection Control Strategy”, i.e., a strategy that will, based on a representa-tion of the intersecrepresenta-tion, create a crossing sequence for the incoming vehicles, guaranteeing that the vehicles will not collide with each other. This coordination1 _{can be achieved through many ways. An} example would be, much like the scheduling problem in computer science, the definition of time slots to be distributed to the vehi-cles. This section will cover the most proeminent strategies in the literature and cover briefly the most common way of dealing with intersections.

2.3.1 Traffic Lights

Nowadays, the common approach to ensure the safe usage of intersections is the traffic light system. Coordination of crossing vehicles is achieved by switching among a combination of phases, each phase allowing only compatible movements to cross the inter-section for a certain period of time.

The fixed time approach has been around since the early 1900s, and consists of cycling through a sequence of phases, i.e., the system has a fixed periodCycle Length, ranging from 35 s to 120 s, usually, where, for a given amount of time calledPhase, it allows 1_{It is important to notice that coordination here means the action of creating}

a crossing sequence for the vehicles approaching the intersection, and not the coordination of traffic lights, e.g., for the creation of green waves.

(37)

Figure 2.1: Aerial view of a four way intersection. Coordinates: 42.331601, -71.053131 c\bigcirc Google 2017.

a set of non-conflicting movements to pass. A typical intersection with four approaches and twelve possible movements is depicted in

Figure 2.5. An example of the fixed time approach can be seen in

Figure 2.6andFigure 2.7, showing, respectively, the cycle informa-tion (length, phases and sequence) and the movements allowed for each phase.

Control of traffic lights is a field well researched in the Intel-ligent Transportation Systems, where fixed time control is not the only way, nor the most efficient option. There is research regarding the dynamic control of traffic lights, while the principle remains the same: usage of time slots allowing only non-conflicting moves to share the intersection at a given time, the definition of each phase’s duration is dynamic. For example, one can find in the literature techniques using artificial intelligence (fuzzy logic, reinforcement learning, etc) (FAVILLA et al., 1993; ABDULHAI et al., 2003; EL-TANTAWY et al., 2013), dynamic programming (CAI et al., 2009),

etc.

Those techniques often rely on using loop detectors to gather traffic data, but with the development and popularization of

(38)

con-W N E S L L L L

Figure 2.2: Representation of the intersection in Figure 2.1 as an atomic model. The intersection conflict region (grey area) can be interpreted as a resource that can only be allocated to one user at a time. The area formed by a lengthL upstream from each approach is usually defined as the “Control Zone”, defining an area in which vehicles are considered as being part of the system. In this example, there are four approaches N, S, W and E, related to the North, South, West and East approaches.

nected vehicles, methods gathering data through the use of vehicu-lar communication have gained popuvehicu-larity in the 2000s (MASLEKAR et al., 2011;GRADINESCU et al., 2007) and continue to gain trac-tion. That adds a new level of flexibity to the strategies, in which the system now does not have to rely on information gathered from a statically positioned device, but rather on the moving vehicles di-rectly, making it possible to anticipate traffic information.

2.3.2 Connected Intersection Control Strategies

Advances in both vehicle connectivity and automation, like the developments of Vehicular Networks (VANETs) (MOUSTAFA;

(39)

W N E S L L L L

Figure 2.3: Representation of the intersection inFigure 2.1as a set of smaller resources, in this case a 5 by 5 grid. The intersection conflict regions (grey boxes) can be interpreted as resources that can only be allocated to one vehicle at a time.

ZHANG,2009) and Dedicated Short Range Communication (DSRC) (CSEH, 1998; DELGROSSI; ZHANG, 2012), have been closely fol-lowed by the development of new strategies to control access to intersections. Differently from the technologies developed in the dynamic traffic light systems, these new strategies tend to com-municate directly to each vehicle, increasing the flexibility of such approaches by allowing vehicles to move as independent elements rather than a set of movements.

Strategies using connected and automated vehicles started appearing around the 1990s, allowing cooperative driving among vehicles for changing lanes and platoon merging (TSUGAWA,2002). This new approach of treating vehicles as individuals rather than as incoming flow led to the development of what is called “Autonomous Intersection Management” (AIM), a term coined by

(40)

W N E S L L L L

Figure 2.4: Representation of the intersection inFigure 2.1as a set of smaller resources, in this case a 10 by 10 grid. The intersection conflict regions (grey boxes) can be interpreted as resources that can only be allocated to one vehicle at a time.

treats vehicles as if they were individuals, thus they are capable of negotiating their crossing with the intersection’s infrastructure and/or with other vehicles nearby. Considering vehicles as individu-als creates additional complexity to the coordination problem, due to its combinatorial problem, i.e., the number of sequences possi-ble. The new challenges are then not only coordinating vehicles in-dividually, but also finding a way to achieve this coordination with safety, efficiency and with real-time application feasibility. Whereas with traffic lights one would optimize the cycle lenghts and phase lengths, with AIM one can optimize the travel time of each vehicle or the fuel consumption, for example.

Dresner and Stone(2004) andDresner and Stone(2005) pro-pose a new strategy to grant the right-of-way to vehicles approach-ing an intersection. Their strategy considers that the vehicles are driven by agents fully capable of self-operating, the vehicles

(41)

commu-N

S

W E

Figure 2.5: An example of a four way intersection, with eight ap-proaching lanes and twelve possible movements (dashed lines).

nicate with road infrastructure, the so called “Intersection Manager” (IM), in order to reserve the spaces they will use when crossing the

intersection. The authors also introduced the concept of “granular-ity” of an intersection, by dividing the intersection in ann by n grid in cases where the intersection has a squared shape. Other shapes could be represented with grids of varying dimensions or with cells of different shapes as well, but then granularity would have to be referred to differently. Figures 2.8, 2.9 and 2.10 show the spaces a vehicle would have to reserve at a certain give time for an inter-section of granularity one, five and ten, respectively. The “Intersec-tion Manager” is responsible for comparing the vehicle request with other vehicles’s reservations and allow the reservation or not, ne-gotiating with the vehicle. This granularity approach was the first approach to introduce the concept of “conflicting regions” that a lot of strategies would use later.

Following this definition of “granularity”, the definition of “conflicting regions” inside the intersection started to appear. For example,Mehani and Fortelle(2007) andFortelle (2010) propose

(42)

Cycle Length Phase 1 Intergreen Phase 2 Intergreen Phase 3 Intergreen Phase 4 Intergreen

Phase 1 Phase 2 Phase 3 Phase 4

Figure 2.6: An example of the fixed time approach for traffic lights, considering the intersection shown inFigure 2.5. It operates looping through a cycle of a defined length. In this example, there are four phases, and each phase give right of way for a given set of non-conflicting trajectories. The intergreen time is composed by the sum of the yellow time and the red-clearance interval, an interval where all trajectories are denied access, in order to increase safety.

a very similar strategy as the one by Dresner and Stone (2004), but with the usage of defined conflict points. Neither strategies had yet tried to optimize the efficiency directly, but rather only focus on guaranteeing the safety of crossing vehicles, i.e., the total time spent by each vehicle was not considered in the problem solution. The efficiency can be calculated through the difference from a base-line case where the vehicle makes follows its entire trajectory with free flow speed.

Still in the multiagents field, the strategies proposed byJin et al.(2012a),Jin et al.(2012b) andJin et al.(2013), started initially as a simple agent-infrastructure negotiation, much likeDresner and Stone(2004) did. The strategy evolved into the “Intersection Man-ager” (IM) not only being able to grant the vehicles requests in cases where those were conflict-free, but also being able to solve an optimization problem in order to enhance traffic flow. Using the in-formation of all vehicles currently under the communication range of the IM, an optimization problem is solved in order to minimize the total travel delay. Vehicles were still supposed to make reser-vations, but those reservations would be adapted (within feasible ranges for each vehicle) by the IM, according to the optimization problem solution.

(43)

N S W E (a) Phase 1 N S W E (b) Phase 2 N S W E (c) Phase 3 N S W E (d) Phase 4

Figure 2.7: Representation of the movements associated with each one of the traffic light phases shown inFigure 2.6. As expected, only non-conflicting movements are allowed within the same phase.

Zohdy et al. (2012) and Zohdy and Rakha (2016) pro-posed a new approach using optimization tools, the “Intersection Management using Cooperative Adaptive Cruise Control” (iCACC). The strategy uses vehicle’s “Cooperative Adaptive Cruise Control” (CACC) in order to optimize vehicles movements when crossing the intersection. The system communicates with the vehicles and con-trols their speed profile under a defined area, aiming to minimize total drive delay and avoid any collisions. The iCACC also uses con-flict points.

Conflict regions were also used in the strategies proposed byM¨uller et al. (2016a) and M¨uller et al. (2016b). The “Intersec-tion Coordinator” (IC) communicates with the vehicles and controls

(44)

W N E S L L L L

Figure 2.8: Representation of the intersection in Figure 2.1 as an atomic model, i.e., a granularity of 1. In this approach, only one ve-hicle at a time can be inside the intersection. The red color indicates that the resource is occupied.

their speed profiles when approaching the intersection. The IC aims to minimize the total travel delay and to guarantee the crossing safety, by keeping vehicles accessing the same conflict regions apart in time by what the authors define as “headways”.

With the same idea of keeping vehicles accessing the same conflict regions apart in time, Tachet et al.(2016) proposed a co-ordination strategy based on time-slots reservation using heuristics, with two different approaches: a First-Come First-Served (FCFS) al-gorithm and a Platoon-Based alal-gorithm. The authors use queueing theory to show that the formation of platoons leads to a capacity increase of the intersection. It is also one of the few strategies that mention the concept of starvation, i.e., cases where one traffic flow would never be allowed to cross the intersection. This strategy has a centralized controller responsible for calculating each vehicle’s time slot. In similar fashion, the strategy proposed byMalikopoulos and

(45)

W N E S L L L L

Figure 2.9: Representation of the intersection inFigure 2.1as a set of smaller resources, in this case a 5 by 5 grid, i.e., a granularity of 5. In this approach, only one vehicle at a time can use each resource. The red color indicates that the resource is occupied.

Cassandras(2016) uses a decentralized approach, following a FCFS approach, where vehicles are expected to calculate their own time slots following a set of heuristic rules that ensure safety. Both ap-proaches consider the intersection as one resource, while allowing non-conflicting moves to cooperate inside the intersection.

Still with the usage of time slots, but now with an optimiza-tion approach,Campos et al.(2017) proposed a fully decentralized approach, where vehicles, following a negotiated decision order that depends on a set of heuristic rules, must calculate their own time slots aiming at minimizing their speed deviation from a de-sired speed value while operating under safety constraint. A Model Predictive Control (MPC) approach with a receding horizon is used. This strategy considers the intersection as one atomic resource, and no two movements are allowed to performed inside the intersection at the same time, even if they are non-conflicting. The strategy

(46)

pro-W N E S L L L L

Figure 2.10: Representation of the intersection inFigure 2.1as a set of smaller resources, in this case a 10 by 10 grid, i.e., a granularity of 10. In this approach, only one vehicle at a time can use each resource. The red color indicates that the resource is occupied.

posed byMakarem and Gillet (2013) has a very similar approach, using an MPC scheme to minimize the vehicles speed deviation and to guarantee the safety constraints, with additional modifications to the cost function in order to allow the formation of platoons of vehicles. The authors use the approach of conflicting paths and in-troduce the definition of a critical set, as shown inFigure 2.11and

Figure 2.12.

Conflict regions are not the only approach to intersection con-trol, however, as seen in the strategy proposed by Lee and Park

(2012), in which the authors define a new scheme called “Cooper-ative Vehicle Intersection Control” (CVIC). Again, like other strate-gies, the intersection is equipped with infrastructure capable of com-municating with incoming vehicles. The CVIC is based on the mini-mization of “trajectory overlap” within the intersection, guarantee-ing the safety of vehicles. Failure handlguarantee-ing is also discussed.

(47)

[L1, H1] [L2, H2] [L3, H3] [L4, H4] W N E S p1 p2 p3 p4 L L L L

Figure 2.11: Representation of an intersection using conflict paths. The thicker lines represent “Critical Sets”, i.e., the portion of a tra-jectory in which vehicles are inside the intersection. For a given path pi,[Li, Hi] is the the Critical Set.

Another possible approach is the use of queueing theory, as proposed byMiculescu and Karaman (2014), with a strategy that models the coordination problem as a polling system with two queues and one server. The polling system is used to define the sequence of arrival times assigned to each vehicle approaching the intersection, and a coordination algorithm is responsible of finding safe trajectories for each vehicle, respecting their assigned arrival times. Simulations have shown that the strategy tends to favor the formation of platoons with the increase in traffic loads. The authors show that their approach has provable guarantees both in safety and performance.

Yet another approach is presented by Makarem and Gillet

(2011) andMakarem and Gillet (2012), with a strategy based on the definition of a decentralized navigation function responsible of safely guiding vehicles through the intersection. The strategy as-sumes that vehicles can communicate with each other, and that each vehicle has a desired speed, allowing the calculation of an expected arrival time for the vehicles. The navigation function is responsible to calculate the adequate safe control inputs in order to minimize

(48)

p1 p2 H1 L1 H2 L2

Figure 2.12: Visual representation of a pair of critical sets. The lines represent two possible safe trajectories for vehicles following paths p1 and p2. The solid line represents the sequence of movements

in which the vehicle followingp2 crosses the intersection first, and

the dashed line represents the other possibility. The rectangle rep-resents the union of both critical sets, representing the states that violate the condition of no two vehicles occupying the intersection at the same time. The critical set of a pathpi is defined as the

inter-val[Li, Hi].

the speed deviation from the desired value while keeping a safe tra-jectory, by keeping a defined safe time gap among vehicles crossing the intersection. The authors mention that their navigation function is defined in a way that prevents deadlocks within the network and that it offers different crossing priorities for vehicles depending on their inertia.

Another approach to the coordination problem was intro-duced byNaumann et al.(1997). The authors propose a decentral-ized procotol for vehicles to wirelessly negotiate their right-of-way, assuming that the vehicles are connected and automated and that they are able to instantly compute their priority, that continues to evolve during the trajectory prior reaching the intersection. Depend-ing on the received messages, vehicles with a lower priority will wait behind a stop line until the vehicles with higher priority have crossed. Something interesting about this strategy is that this is one of the very few strategies to have stated their formal requisites, by dividing the system in two parts: a discrete model, modelled us-ing Predicate/Transition Petri-Nets, enablus-ing the formal analysis of properties like the existence of deadlocks, the safeness and the

(49)

fair-ness of the collision avoidance algorithm, and a continuous part, for which the authors used simulation to evaluate performance as flow rate, global energy comsuption, etc. The strategy also treats the intersection as a series of smaller conflict regions, where only one vehicle is allowed at a time.

Still within the more formal approaches, Ahmane et al.

(2013) propose a simple control strategy using wireless vehicle in-formation and aiming to minimize the sum of the queue lengths requesting to cross the intersection. The strategy works by giving a green signal to each vehicle when it is that vehicle’s time to cross the intersection. They have modelled the strategy using Timed Petri Nets, and the control strategy was analyzed using structural analy-sis, proving that there is no deadlock present.

More recently, we have seen the appearance of strategies binding together a mix of all the different approaches presented in this chapterAltch´e et al.(2016) andAltch´e et al.(2017) propose a series of robust strategies based on the usage of a Mixed Integer Quadratic Programming (MIQP) formulation, while still using the definition of conflicting regions/paths in order to formally establish safety of their strategy. All this is performed through what the au-thors call a “Supervisor”, that monitors the human driver’s inputs to the vehicle, and in cases where unsafe situations are detected, the “Supervisor” will override the control inputs in order to guarantee the vehicle’s safety. The authors prove that their strategy prevents collisions and deadlock situations. This is one of the few works that mentioned that the framework developed is capable of supporting a variety of traffic conflicting regions, like intersections, merging lanes and roundabouts.

Lin et al.(2017) proposed a strategy that uses a solution sim-ilar to the reservation of time slots for each vehicle. The strategy uses roadside infrastructure in what the authors call a “Connected Vehicle Center” (CVC), and vehicles are expected to communicate with the CVC following standard communication protocols for ve-hicular environment. A big improvement from the majority of the strategies is that the authors take into consideration the possibility of communication failures through an assignment failure handling process. The strategy considers both “Automated Vehicles” (AVs) and “Human-Driven Vehicles” (HDVs), another improvement. The strategy uses regular traffic lights for the HDVs. Regarding the ac-tual representation of the intersection, the authors define a “con-flict section”, much similar to other strategies that use con“con-flict re-gions/points within the intersection. Optimization of the total travel

(50)

time of all vehicles is used to define adequate crossing spans for each vehicle, and a simple three-segment linear function is used to define the required speed profile to ensure that the vehicle crosses the intersection during its assigned span.

When reviewing the literature, we have encountered a clear lack of use of formalisms. Very few strategies have mentioned prop-erties like deadlocks, starvation, liveness, fairness, etc. Specially when proposing the strategy, a lack of a formal definition of what the authors want to achieve makes the actual evaluation of the strat-egy a challenging task to be performed. Modelling such systems and strategies, in a way that allows formal verification pose a great chal-lenge ahead, and should be the main concern for future work in the field.

2.3.3 Important Aspects

Observing the current lack of clear desired properties and the lack of a consensus on what those properties should be for auto-mated intersection control strategies,Fortelle and Qian(2015) and

Qian et al.(2017) presented and discussed five pairs of criteria that they believe must be considered and evaluated when designing the strategies. They also observed how those criteria relate to real prop-erties of the system.

The first pair of criteria is the existing balance of a system being bothrobust and efficient, those relate to two of the main de-sires for a strategy, its safety and its efficiency. Robust here means a system that would allow a bigger margin for failure and efficient means a system where the vehicles’s total time spent are closer to free flow time. The authors note that, in most cases, to increase robustness, i.e., make the system safer, the most common trade-off is the efficiency. One example of that trade-trade-off is, for the cur-rent method of traffic control, the traffic lights system design favors heavily the safety, at the cost of efficiency, with the existence of yel-low and red clearance times. As for the case of automated control strategies, most of the approaches would allow to increase head-ways among vehicles or to reduce the intersection’s granularity and so on.

The second pair of criteria relates to the time-frame involved in the decision making process for the vehicles, and it is an evalua-tion on what is the main feature of a stratregy: if the system is de-liberative or reactive, i.e., if the system is flexible enough to allow changes in decisions already made (trajectories or speeds, for

(51)

exam-ple) or not. A deliberative system is a system where decisions are made based on current information and on expected states of the system (planning). A reactive system is a system where decisions are made based on past and current information, without relying on the expectation of future states. The authors think it is truly im-portant that an automated intersection control strategy seeks the balance between those two. A system fully deliberative, i.e., fully planned, for example, would not be able to properly adapt to possi-bly dangerous changes.

The third pair of criteria relates to the practical aspects in-volved in the implementation of such a system, classifying the sys-tems incentralized or decentralized. Both approaches have their advantages and drawbacks. A centralized system avoids informa-tion inconsistency and increases efficiency. The drawback is that such a system is not completely feasible, because of issues relating to scalability, e.g., the centralized controller becoming a bottleneck in the processing of information in high traffic load scenarios. A decentralized system can be much more scalable, but at a harder implementation design in order to ensure information consistency. According to the authors, a hybrid system is what a strategy should aim for, having a centralized high-level decision making with local trajectory planning, for example.

The fourth pair of criteria is the balance between what is most benefitial for the system and what is most benefitial for one specific vehicle, characterizing acooperative system and a egoistic system. A cooperative system seeks the global system optimum, even if at the expense of vehicles’s own objectives. An egoistic system allows vehicles to seek their own local optimums, comfort or fuel consump-tion, for example, what does not necessarily lead to the global sys-tem’s optimum. The authors consider that strategies should aim at allowing both approaches to co-exist.

The last pair of criteria addresses an assumption that is of-ten made in the strategies: that all the vehicles are homogeneous, i.e., have the same parameters, e.g., width, length, maximum speed values, acceleration values, etc, dividing the strategies in either ho-mogeneous or heterogeneous strategies. According to the authors, it is a requirement that, for real applications, the strategies must ac-cept at least a certain level of heterogeneity of vehicles.

(52)

(53)

In this chapter we will describe the four strategies that have been chosen for implementation. We will cover in detail the func-tioning of each strategy, as well as provide comments regarding de-tails and the challenges involved in their implementation. There will also be a discussion for each strategy mentioning those aspects described in section 2.3.3. They were all implemented using the Python Programming Language (ROSSUM, 1995), using the API provided by the AIMSUN Traffic Simulator (TSS,2015). Optimiza-tion problems were modelled using the CVXPY OptimizaOptimiza-tion Pack-age (DIAMOND; BOYD,2016).

3.1 STRATEGIES

The strategies were chosen taking into consideration how re-cent they were, as well as to how well-received and well-cited they were by academia. Another factor that weighed heavily was the amount of supporting information they had, including the number of iterations each strategy had received. The strategies are:

\bullet “Revisiting Street Intersections Using Slot-Based Systems” ( TA-CHET et al., 2016): a coordination strategy based on time-slots reservation using heuristics, with two different ap-proaches: a First-Come First-Served (FCFS) algorithm and a Platoon-Based algorithm. The authors presented proofs of the theoretical intersection capacity increase enabled by the size of a platoon. This strategy has a centralized controller respon-sible for calculating each vehicle’s time slot.

\bullet “Decentralized Optimal Control for Connected and Automated Vehicles at Intersections Including Left and Right Turns” ( ZHA-NG et al., 2017): another coordination strategy based on time slots reservation using heuristics, with a Come First-Served (FCFS) approach. This strategy is similar to the one mentioned above, making it possible to compare these two strategies. This strategy has a decentralized approach, where each vehicle is supposed to calculate its own time slot by com-municating with specific vehicles.

\bullet “Traffic Coordination at Road Intersections: Autonomous Deci-sion-Making Algorithms using Model-Based Heuristics” ( CAM-POS et al., 2017): a coordination strategy based on au-tonomous decision making, i.e., where each vehicle is

(54)

sible for the calculation of its own optimal access time, al-beit respecting an imposed crossing sequence. The crossing sequence can be defined with different approaches, as FCFS and Model-Based Heuristic. This is a decentralized strategy and vehicles are assumed to negotiate with each other to cal-culate their time slots.

\bullet “Time Optimal Scheduling of Automated Vehicle Arrivals at Urban Intersections” (M ¨ULLER et al., 2016b), a coordina-tion strategy based on a centralized “Interseccoordina-tion Coordinator” (IC), responsible for calculating each vehicle’s time slots, but based on an optimization problem aiming at minimizing the delay experienced by each vehicle (decreasing travel time). Ve-hicles are assumed to communicate with the IC.

3.2 SLOT-BASED CONTROL

The slot-based control strategy for autonomous vehicles is based on the assignment of time slots to each vehicle willing to cross the intersection, using two different heuristics to assign the time slots: one following a First-Come First-Served basis (FCFS) and an-other favoring the formation of platoons of vehicles. The slot-based strategy will be covered in detail in the following sections.

3.2.1 Basic model

In this basic model, there are two crossing streets of length L, as shown inFigure 3.1. Cars approach the intersection of length S coming from North (N) or East (E). The cars have length \ell and speedv.

The strategy guarantees crossing safety by utilizing two de-fined distances, namely: the tailgate distancedtail for cars coming

from the same approach and the stopping distance dstop for cars

coming from conflicting approaches, withdtail< dstop.

Under the assumptions that cars from the same approach travel at similar speeds, the tailgate distancedtail, defined asdtail =

v(tres+ \delta ), is chosen to avoid tailgating and ensures a time

separa-tion between two vehicles by being transformed into a scheduling time \bfT \bfone , with:

\bfT \bfone =

dtail

v =

v(tres+ \delta )

(55)

N E \ell S dtail dstop

Figure 3.1: Basic scenario proposed byTachet et al.(2016). Source:

Tachet et al.(2016). The tailgating distancedtail = v(tres+ \delta ) is the

distance vehicles coming from the same approach must keep be-tween them upon crossing the intersection,tres is the reaction time

and \delta a safety parameter. The stopping distance dstop = v

2

2abrake is

the distance vehicles coming from different approaches must keep between them upon crossing the intersection, allowing that the ve-hicle can stop before reaching the intersection in case of disruptions

andabrakeis the deceleration rate the vehicle can impose.

withtres the reaction time,\delta a tolerance parameter and v the

vehi-cle’s current speed.

The stopping distance dstop is informally defined as the

dis-tance between the point at which the vehicle system (or driver) detects a dangerous situation and the point at which the vehicle comes to a complete stop. This notion of distance is transformed into another scheduling time \bfT \bftwo (speed-dependent, unlike \bfT \bfone ):

\bfT \bftwo = \bfT \bftwo (v) =

dstop(v)

v + txing(v) (3.2)

(56)

intersection area anddstop= v

2

2abrake, withabrakethe deceleration rate

imposed by the vehicle. Thus:

\bfT \bftwo (v) = tres+

v

2abrake

+ \ell + S

v (3.3)

The authors define an optimum speedv\ast _{for a specific intersection}

configuration asv\ast ₌_{\sqrt{} 2a}

brake(S + \ell ).

With the scheduling intervals \bfT \bfone and \bfT \bftwo , the authors

pro-pose two algorithms to assign time slots to each arriving car, both algorithms rely on what is called “access request”, a request issued by each vehicle upon entering the area covered by the “Intersection Manager” (IM):

\bullet FAIR, a First-Come First-Served (FCFS) approach that priori-tizes fairness. In this approach the arriving vehicle service time \bfT is defined as \bfT = \bfT \bfone , if the last serviced vehicle belongs to

the same approach as the arriving one, and \bfT = \bfT \bftwo otherwise.

\bullet BATCH, that aims at maximizing capacity by forming platoons of vehicles coming from the same approach, prioritizing the shorter scheduling time \bfT \bfone .

It does so by utilizing a batch formation strategy, in which arriving vehicles’s access requests are gathered during a speci-ficed time interval or until the batch reaches a specified size N and divided in two groups according to the vehicles’s ap-proaches.

Access times are then sequentially assigned to each group (fol-lowing FAIR’s rule), starting by the group whose approach was last given access to, so it starts using the shorter scheduling time (\bfT \bfone ). Two basic rules are followed: i) batches of size

larger than one should be formed only when the system starts to experience delays, thus avoiding the possibility of delay variance increase, and ii) an upper boundN for the batch size cannot be exceeded, to address the possibility of starvation due to one approach having a higher load than the others. A delay here is when a vehicle access time is greater than its earliest arrival time, i.e., the time it would take to reach the intersection at free flow speed.

The batch formation strategy is illustrated inFigure 3.2. and its details can be seen in Algorithms 1and2. The FAIR