Keywords: Intelligent vehicle, Vehicle platoon, Longitudinal control, Lateral control, Multi-model control, Fuzzy control

This thesis would not have been possible without the help and support of so many people in so many ways. I would like to take the opportunity to express my gratitude to all those who contributed to this work.

First of all, my sincere thanks go to my supervisor, Prof. Abdelkader EL KAMEL, for his valuable guidance, continuous encouragement and the share of his research experience.

I would like to thank Prof. Pierre BORNE for his generous cooperation and helpful discussions and the share of his outstanding research experience. A special acknowledgement should be shown to Prof. Shaoping WANG, during her visiting period in LAGIS, I benefited a lot from her helpful suggestions and discussions.

I would like to express my sincere gratitude to Prof. Abdellah EL MOUDNI and Prof. Claude H. MOOG, who have kindly accepted the invitation to be the reviewers of my PhD thesis. My heartfelt thanks go to Prof. Philippe BONNIFAIT and Dr. El Miloudi EL KOURSI, for their kind acceptance to be the members of my PhD Committee.

I am also very grateful to the staff in EC Lille. Virginie LECLERCQ, Marie-Françoise TRICOT, Christine YVOZ, and Brigitte FONCEZ have helped me in the administrative works. Many thanks go also to Bernard SZUKALA, Hilaire ROSSI, Gilles MAR-GUERITE, Jacques LASUE, Patrick GALLAIS and Régine DUPLOUICH, for their kind help and hospitality. I wish to express my special appreciation to Prof. Hélène CATSIAPIS, my French teacher. In her courses, I learned not only the language but also the culture, history, especially the many trips, which enrich my life in France.

I would like also to thank my colleagues and friends, Ismahène, Yahong, Minzhi, Andreea, Lian, Yifan, Pengfei, Yang, Dapeng, Jinlin, Jian, Huarong, Hui, Guoguang, Bo, Wenhua... for their friendship and supports.

Finally, my parents and my brother have provided me with their supports throughout, as always, for which my mere expression of gratitude does not suffice. Thanks to my wife, Ting, for her love, understanding and great patience during the past 3 years, even if that meant sacrificing the time we spent together. Thanks to my son, Pengpeng, for all the joy and happiness he brings to me.

General Introduction

The research presented in this thesis addresses the longitudinal and lateral control strategies for intelligent vehicles in highway, with the main aims of alleviating traffic congestion and improving traffic safety. The background of this research is the significant development of automobile industry in the past decades, which makes the automobiles play an important role in the evolution of industry and even of our society. However, the traffic problems such as traffic congestion, safety, pollution and fuel consumption are becoming more and more serious all over the world. To cope with these problems and to achieve the goal of "Sustainable Mobility", the conception of AHS (Automated Highway System) has been proposed, in which, vehicles can travel together in tightly spaced platoons. In the past two decades, researches on AHS have seen significant progresses. As one of the most active research topics in AHS, the longitudinal and lateral control for automated vehicles is currently being studied by researchers and automotive manufactures.

• Longitudinal control Vehicle longitudinal control system provides assistance to the driver in the task of longitudinal control by using automatic throttle and brake controllers. The first generation of longitudinal control systems like ACC system (Adaptive Cruise Control system) are primarily being developed for improving driving comfort with some potential in increasing vehicle safety. However, the impacts of these systems on highway traffic have been inadequately studied [Swaroop 1999]. In this work, the longitudinal controller design is considered for the operations of vehicle platoon. Thus, we need to consider not only the requirements of driving comfort and vehicle safety but also the challenges of string stability, traffic flow capacity and stability, etc. To meet these challenges, the structure of the longitudinal control system is generally designed to be hierarchical, with an upper level controller and a lower level controller. The upper level controller determines the desired acceleration or speed for the controlled vehicle, while the lower level controller decides the required throttle and brake commands to track the desired acceleration or speed.

The principle design tasks in the upper level control include the design of spacing policy and its associated control algorithm. The spacing policy plays an important role in vehicle longitudinal control because it has great influences on vehicle safety and traffic capacity. In this work, a safety spacing policy (SSP) is proposed, which is a nonlinear function of vehicle velocity. It uses both the information of vehicle's state and braking capacity to adjust the position and velocity of the controlled vehicle.

Furthermore, the special efforts are devoted to the analysis of the string stability, traffic flow capacity and stability of the proposed SSP. A comparison between the SSP and the traditional CTG (constant time gap) policy is also presented.

The nonlinearities and uncertainties in vehicle longitudinal dynamics are the main challenges to be met in the design of throttle and brake controllers (lower level control). For instance, the exact engine model and brake system dynamics are always complex nonlinear models with numerous parameters. And in most cases, these models are hard to get. Another difficulty is that the throttle and brake pedals should work coordinately. To cope with these problems, a coordinated throttle and brake fuzzy control system is proposed. At first, an additive fuzzy controller is proposed to realize the throttle and brake control. The main advantage of this approach is that it can realize the accurate and smooth vehicle speed control without the knowledge of the exact engine and brake system dynamic models. Second, a logic switch is designed to coordinate the two speed actuators.

• Lateral control

As far as lateral control is concerned, the lateral control system generates steering commands to keep the vehicle running along the desired path or steer the vehicle into an adjacent lane. The design requirement of vehicle lateral control is to ensure small lateral errors and small relative yaw angles while maintaining ride comfort under different conditions. Lane keeping and lane changing are the two basic functions of lateral control system. At first, lane keeping control is studied. The vehicle lateral dynamics is presented by the well-known "bicycle model". Since in highway operation, the vehicle parameters such as speed, load, movement inertia, wheel cornering stiffness, may vary in a wide range. The lateral model is thus a LTV (Linear Time Variant) model with parameter uncertainties. A multi-model fuzzy controller is proposed for the lane keeping operation. The proposed solution combines the strong points of multimodel and fuzzy approaches. It can provide stable performances during the whole range of operation speed, and it can also repel the system uncertainties in vehicle load, movement inertia, wheel cornering stiffness, etc.

Second, the main difficulty in the lane changing maneuver is that the vehicle must travel a certain distance without sensor feedback if the onboard sensors can not measure vehicle's location between the adjacent two lanes, for instance, if the magnetmagnetometer sensing system is employed. The virtual desired trajectory (VDT) is then introduced for the lane changing maneuver. By using VDT, the lane changing operation is then investigated as a lane keeping problem. In order to effectuate flexible switch between different lateral operations, such as lane keeping, lane changing, overtaking, and etc, a hierarchical architecture is then proposed for vehicle lateral control system.

Based on the given results in both longitudinal and lateral control, we propose a global control system, which integrates the designed longitudinal and lateral control systems, to realize the final goal of automated vehicle control.

In addition, the vehicle state estimation is also studied as a step towards the application of the proposed vehicle controllers. Since in the controller design process, the required vehicle states are always assumed to be available. However, in practice, this assumption is not always correct. Then the vehicle state observer is required. Considering the sensor system configuration and the required states for the vehicle controllers, we choose the vehicle yaw rate as the parameter to be estimated. Since the control plant is a LTV system, the traditional Luenberger observer is not available in this case. A Kalman-Bucy filter is then designed for the LTV system estimation.

Finally, a reduced scale (1:10) multi-sensor intelligent vehicle prototype is introduced.

The different aspects of the prototype from the multi-sensor system, vehicle structure, communication system, and HMI are presented. This prototype provides a platform for advanced technology integration, reliability analysis, real time control and monitoring. In the first-step tests with the prototype, the basic functions such as vehicle following and lane tracking were realized. In the future work, the more complex scenarios will be tested.

Outline of the thesis

Chapter 1 reviews the developments in automated vehicle control. At first, the background of the current traffic situation and problems are introduced. Second, ITS, AHS, and intelligent vehicle, which are considered as the most promising solutions (at different levels) to the traffic problems, are introduced. Finally, the evaluations of the outstanding projects and the developments in vehicle longitudinal and lateral control have been surveyed in detail.

In Chapter 2, the vehicle longitudinal and lateral models are presented, which will be employed in the controller design in the following chapters. For the longitudinal model, at first, we establish the non-linear longitudinal dynamic model based on the Newton's second law, with the hypothesis of no-slip at the tyre-road interface. Second, the powertrain dynamic model of a passenger car with an automatic gearbox is built, which includes the sub-models of different parts in the powertrain system, the engine, torque converter, automatic gearbox, drive shafts, final drive and differential, as well as the braking system. By using this powertrain model, we can simulate the vehicle behavior thus to test the controllers' performances in the following chapters.

For the lateral model, the kinematic and dynamic models are studied respectively.

The kinematic model provides a mathematic description of the vehicle motion without considering the forces that affect the motion, and it considers only the geometric parameters. A "bicycle" model is adopted to express the vehicle lateral dynamics. Under the assumptions of small steering angle and small slip angle, the bicycle model can be described by a 4 th order linear model.

Chapter 3 concentrates on the vehicle longitudinal control system design. The longitudinal control system architecture is designed to be hierarchical, with an upper level controller and a lower level controller. In the upper level controller design, a safety spacing policy (SSP) is proposed, which uses both the information of vehicle state and vehicle braking capacity to determine the desired spacing from the preceding vehicle. A comparison between the SSP and the traditional CTG (constant time gap) policy is also presented. In the lower level controller design, a coordinated throttle and brake fuzzy controller is proposed. And a logic switch is designed to avoid frequent switching between the two actuators and simultaneous operations of them. Finally, the above proposed longitudinal control system is validated to be effective through a series of simulations.

Chapter 4 is devoted to the vehicle lateral control. A multi-model fuzzy controller is designed to perform lane keeping and lane changing operations. For the lane changing maneuver, the concept of VDT "Virtual Desired Trajectory" is introduced to provide a smooth and efficient lane changing trajectory. In order to effectuate flexible switch be-tween different lateral operations, a hierarchical architecture is then proposed for vehicle lateral control system.

Chapter 5 proposes a global control system, which integrates the longitudinal and lateral control systems that we have given in chapter 3 and 4. By using this system, the vehicle longitudinal controller and lateral controller can work coordinately.

Chapter 6 discusses two aspects relating to the practice, the observation of vehicle states and the design of a reduced scale multi-sensor intelligent vehicle prototype. A Kalman-Bucy filter is introduced to estimate the yaw rate for vehicle later control. And the different aspects of the design of a multi-sensor intelligent vehicle prototype are presented. Accompanying with this augmentation, on one hand, we benefit the vehicles in different aspects. Take Europe for instance, road transport is the largest share of intra-EU transport, which accounts for 44% of freight and around 85% of passenger transport. In addition, the annually growth rate in the above two fields are 2.8% and 1.9% respectively [COMMUNITIES 2006a]. on the other hand, we have to face the spreading traffic problems as traffic congestion, safety, pollution and fuel resources, etc.

Traffic congestion has been regarded as one of the most serious social and economical and environmental problems in the world. Take the Europe Union (EU) as an example, congestion costs amount to e 50 billion per year or 0.5% of Community GDP, and by 2010 this figure could go up to 1% of EU GDP [COMMUNITIES 2006b].

Concerning energy consumption and emissions, in 2002 the transport sector consumed 338 million tonnes oil equivalent (MToe) representing 31% of the total energy consumption in the EU. Road transport consumed 281 MToe, 83% of the energy consumed by the whole transport sector. Road transport CO 2 emissions account for 835 million tonnes per year representing 85% of the total transport emissions [COMMUNITIES 2006b].

Traffic safety is one of the most serious problems that impacts our daily life. According to a WHO1 forecast, by 2020 traffic accidents will rank as the third biggest cause of deaths and disability ahead of such other problems as malaria, HIV/AIDS, and war2 . In 2004, the "Road Safety" has been selected as the theme of the year of WHO.

In the White paper of 2001, the European Commission has set the ambitious aim of halving the number of road traffic fatalities by 2010 (from 50 000 to 25 000). Much progress has been achieved, road fatalities in the EU-25 in 2005 were 41 247, which have been reduced by 18,1% compared with 2001. If the trend continues at the same rate, 32 500 people will die from road accidents in 2010, the EC's goal of 25 000 deaths in 2010 will thus not be achieved. The cost of traffic accidents is around e 200 billion every year, account 2% of EU GDP [START_REF] Hoeglinger | [END_REF]].

One suggestion to the traffic problems is to build adequate highways and streets.

However, the fact that it is becoming increasingly difficult to build additional highway, for both financial and environmental reasons. Data shows that the traffic volume capacity added every year by construction lags the annual increase in traffic volume demanded, thus making traffic congestion increasingly worse. Therefore, the solution to the problem must lie in other approaches, one of which is to optimize the use of highway and fuel resources, provide safe and comfortable transportation, while have minimal impact on the environment. It is a great challenge to develop vehicles that can satisfy these diverse and often conflicting requirements. To meet this challenge, the new approach of "Intelligent Transportation System" (ITS) has shown its potential of increasing the safety, reducing the congestion, and improving the driving conditions. Early studies show that it is possible to cut accidents by 18%, gas emissions by 15%, and fuel consumption by 12% by employing ITS approach [START_REF] Unsal | Intelligent navigation of autonomous vehicles in an automated highway system: Learning methods and interacting vehicles approach[END_REF]].

ITS & Automated Highway System

1.2.1 What's ITS?

The origin of Intelligent Transportation System (ITS) was shown in "Futurama", which is a concept transportation system exhibited at the World's Fair 1940 in New York. After a long story via many researches and projects between 1980 to 1990 in Europe, North America and Japan, today's mainstream of ITS was formed. ITS is a transport system which is comprised of an advanced information and telecommunications network for users, roads and vehicles. By sharing vital information, ITS allows people to get more from transport networks, in greater safety, efficiency, and with less impact to the environment.

The principle of ITS is illustrated in Fig. 1.2. (Source: [Japanese Ministry of Land a])

ITS is actually a big system which concerns a broad range of technologies and diverse activities. According to the Action plan for the deployment of Intelligent Transport System in Europe [START_REF] Communities | Communication from the Commission -Action plan for the deployment of Intelligent Transport Systems in Europe[END_REF]], the six priority areas for action and related measures in the short-to-medium term are:

User

Vehicles Roads The Automated Highway System (AHS) is one of the most important items among the diverse topics in the research of ITS. The AHS concept defines a new relationship between vehicles and the highway infrastructure. The fully automated highway systems assume the existence of dedicated highway lanes, where all the vehicles are fully automated, with the steering, brakes and throttle being controlled by a computer [Tomizuka 1993]. AHS uses communication, sensor and obstacle-detection technologies to recognize and react to external infrastructure conditions. The vehicles and highway cooperate to coordinate vehicle movement, avoid obstacles and improve traffic flow, improving safety and reducing congestion. In brief, the AHS concept combines on-board vehicle intelligence with a range of intelligent technologies installed onto existing highway infrastructure and communication technologies that connect vehicles to highway infrastructure [Cheon 2002].

The potential benefits that might acquire from the implementation of AHS could be summarized in Table 1.1. Note that some of the benefits are fairly speculative, the system they would depend upon are not yet in practical application. In AHS, vehicles travel in closely packed platoons can provide a highway capacity that is three times the capacity of a typical highway [Varaiya 1993].

Safety

Human error is involved in almost 93% of accidents, and in almost three-quarters of the cases, the human mistake is solely to blame [COMMUNITIES 2006b]. Only a very small percentage of accidents are caused by vehicle equipment failure or even due to environmental conditions (for example, slippery roads). Since automated systems reduce driver burden and provide driver assistance, it is expected that the employment of well-designed automated systems will certainly lead to improve traffic safety.

Weather

Weather and environmental conditions will impact little on high performance driving. Fog, haze, blowing dirt, low sun angle, rain, snow, darkness, and other conditions affecting driver visibility and thus, safety and traffic flow will no longer impede progress.

Mobility

All drivers using AHS can be safe, efficient drivers. AHS offers enhanced mobility for the elderly, and less experienced drivers, etc.

Energy consumption and air quality

Fuel consumption and emissions can be reduced. In the short term, these reductions will be accomplished because vehicles travel in a more efficient manner, lesser traffic congestion occurs. In the long term, the AHS can support future vehicle propulsion/fuel designs.

Land use AHS help us to use the road efficiently, thus using the land in a efficient way.

to be continued. . . [START_REF] Andrew | Hearing before the subcommitteee on investigations and oversight of the committee on science, space and technology[END_REF].

Intelligent vehicle control is the vital part of the AHS applications. A variable of vehicle control systems are being developed. In our work, we will concentrate in the design of the two most basic control systems: longitudinal control and lateral control.

Before introducing the state of art technologies in these two systems, we will briefly introduce some of the major electromechanical feedback control systems related to the longitudinal and lateral control, which are under developed in the automotive industry and the research laboratories.

• Adaptive Cruise Control (ACC) systems perform longitudinal control by controlling the throttle and brakes so as to maintain a desired spacing from the preceding vehicle. A significant benefit of using ACC is to avoid rear-end collisions. The

SeiSS study reported that it could save up to 4 000 accidents in Europe in 2010 if only 3% of the vehicles were equipped [START_REF] Abele | [END_REF]].

• Lateral support includes Lane Departure Warning (LDW) and Lane Change Assistant (LCA) systems. The LDW system will warn the driver if his or her vehicle leaves its lane unintentionally, while a LCA will check for obstacles in a vehicle's course when the driver intends to change lanes. The same study estimated that 1 500 accidents could be avoided in 2010 given a penetration rate of only 0.6%, while a penetration rate of 7% in 2020 would lead to 14 000 fewer accidents.

• Collision Avoidance (CA) operates like a cruise control system to maintain a constant desired speed in the absence of preceding vehicles. If a preceding vehicle appears, the CA system will judge the operation speed is safe of not, if not, the CA will reduce the throttle and/or apply brake so as to slow the vehicle down, at the same time a warning is provided to the driver.

• Drive-by-wire technology replaces the traditional mechanical and hydraulic control systems with electronic control systems using electromechanical actuators and human-machine interfaces such as pedal and steering feel emulators. The benefits of applying electronic technology are improved performance, safety and reliability with reduced manufacturing and operating costs. Some sub-systems using "by-wire"

technology have already appeared in the new car models.

• Vehicle navigation system typically uses a GPS navigation device to acquire position data to acquire position data to locate the user on a road in the unit's map database. Using the road database, the unit can give directions to other locations along roads also in its database.

• Automated Vehicle Identification (AVI) and Automated Vehicle Location (AVL) systems: the AVI system was first applied for the Electronic Toll Collection (ETC) system to determine the identity of a vehicle subject to tolls. Most current AVI systems rely on radio-frequency identification, where an antenna at the toll gate communicates with a transponder on the vehicle via Dedicated Short Range Communications (DSRC). While, the AVL automatically determines the geographic location of a vehicle and transmits the information to a requester. Normally, the GPS and a radio communication system are required. As a result of AVI and AVL, processing real-time information on vehicle locations will be possible. A special application of these technologies can be found in vehicle platoon control, will be mentioned in Chapter 3. Although the demonstration showed that the progress had been made, the U.S. DOT withdrew financial support from NAHSC and shifted its priorities to short-term, safety oriented technology development. Also in 1997, the project Intelligent Vehicle Initiative (IVI) Programme was carried out, which is a government-industry partnership to accelerate the development and commercialization of safety, and driver assistance systems. platform between experts in the field, authorities and the public.

Previous research

• Activities in France

In France, PREDIT is a programme of research, experimentation and innovation in land transport, started and implemented by the ministries in charge of research, transport, environment and industry, the ADEME (Agence gouvernementale De l'Environnement et de la Maîtrise de l'Énergie) and the ANVAR (Agence National de Valorisation de la Recherche) [PREDIT ]. Since 1990, the PREDIT has past three phases, the first phase PREDIT 1(1990PREDIT 1( -1994) ) was mainly devoted to technological innovations in vehicles; PREDIT 2 (1996PREDIT 2 ( -2000) ) covered a wider field includ-

Previous research

ing the aspects of human and society sciences and transport services organization, etc. PREDIT 3 (2002PREDIT 3 ( -2006) ) aimed at the goods transportation and energy and environment issues, as well as a diversified research on safety. More recently, the project ARCOS (Action de Recherche pour une COnduite Sécurisée) was founded in 2001, which associates different partners (universities, industries) aiming at the improvement of road safety. Now the PREDIT 4 (2008-) is currently implemented, its objective is to improve 20% of energy efficiency in 2020, priority the other transportation methods (no-road), develop the ecological tax, and etc.

Beside the above national research projects, many universities, institutes, and research centers launched also divers projects aiming at solving current traffic problems. Among them, some results can be cited: the urban congestion problems have been studied by the researchers from SeT (laboratoire Systèmes et Transports) in UTBM (université de Technologie de Belfort-Montbéliard), autonomous vehicle control and traffic signal control using vehicle-infrastructure communication were proposed to improve the traffic efficiency in the intersection,by F. Yan, J.

Wu, and A. El Moudni, see [START_REF][END_REF][START_REF] Wu | [END_REF]]. The problems of vehicle localization and autonomous navigation in the urban areas were studied by the researchers from UTC (Université de Technologie de Compiègne), the GIS-Based (Geographical Information system) localization and navigation systems ,which are adapted to the real-time applications, were proposed in [START_REF] Ph | Real-Time Implementation of a GIS-Based Localization System for Intelligent Vehicles[END_REF][START_REF] Ph | Autonomous Navigation in Urban Areas using GIS-Managed Information[END_REF]. For the automated vehicles in low speed automation, divers results were given by researchers from INRETS (Institut national de recherche sur les transports et leur sécurité), see [START_REF] Nouveliere | [END_REF], Mammar 2004]. An interesting solution called "virtual drawbar" was proposed by the AUTORIS(AUTOmatique pour la Route Intelligent et Sûret). A virtual link is supposed to build a two-car platoon [START_REF] Pf Toulotte | Longitudinal and lateral control for automatic vehicle following[END_REF]]. The issues of bus guidance in station and safe tunnel control were studied in LAGIS, see [START_REF] Kamel | Fuzzy controller for lateral guidance of busses[END_REF][START_REF] Kamel | UML-Based Design and Fuzzy Control of Automated Vehicles[END_REF][START_REF] Kamel | Intelligent Transportation System Design and Monitoring[END_REF]. Special efforts to improve common transport (i.e. railway, bus) safety have been made by researchers from ESTAS (Evaluation des Systèmes de Transport Automatisés et de leur Sécurité), see [START_REF] El-Koursi | [END_REF], EL-KOURSI 2007].

A brief chronology of the ITS development in the world is given in Fig. 1.4. In 1994, the group of PATH has proposed a four-layer control architecture. The proposed four layers are: Link, Coordination, Regulation, and Vehicle dynamics. Among them, the Link layer is on the roadside system and the other three layers are in the vehicle system [START_REF] Hedrick | [END_REF]]. This four-layer constructer can be viewed as the base for the more recently proposed architectures. In 2000, R. Horowitz and P. Varaiya [START_REF] Horowitz | [END_REF]], also researchers from PATH, presented a five-layer architecture, which added a Network layer to the former four-layer constructer. And it can be viewed as a continued work of the former one.

Also in 2000, a group of Japanese researchers proposed an architecture for the AVCSS (Advanced Vehicle Control and safety System), which consists of three layers: vehicle control layer, vehicle management layer, and traffic management layer [START_REF] Tsugawa | [END_REF]].

This architecture has a vehicle centered structure, which will enable well-organized design of the vehicle systems.

Previous research

More recently, another three-layer control architecture was proposed by Simon Halle, this hierarchical architecture was inspired by Tsugawa's architecture [START_REF] Tsugawa | [END_REF]] and other concepts coming mainly from the PATH project [Lygeros 1998]. The resulting architecture has three major layers: guidance layer, management layer and traffic control layer, as indicated in Fig. 1.5. This architecture gives the more detailed descriptions to the coordination activities of the vehicles platoon, such as inter-platoon coordination and intra-platoon coordination. and automotive manufactures for highway vehicle automation [Marsden 2001,Wang 2004a, Zhou 2005]. It provides assistance to the driver in the task of longitudinal control by us-ing automatic throttle and brake controllers. It can be classified into two categories:

"autonomous"and "non-autonomous". An autonomous system means all the required information for the controlled vehicle could be gathered by on board sensors, whereas intervehicle communication or vehicle-road communication are required for a non-autonomous system.

Regarding the longitudinal control system design, it needs to handle several challenges, such as nonlinear vehicle dynamics, spacing policy and its associated control law design, string stability and traffic flow stability, as well as operation at all speed: from high-speed to a complete stop, etc. [START_REF] Rajamani | [END_REF][START_REF] Santhanakrishnan | [END_REF]]. To meet these challenges, the structure of the longitudinal control subsystem is generally designed to be hierarchical, with upper and lower level controllers, see Fig. 1.6. The upper level controller determines the desired acceleration or speed for the controlled vehicle, while the lower level controller decides the throttle and brake commands required to track the desired acceleration or speed [Rajamani 2006, Zhou 2005]. Therefore, we will introduce the state of the arts technologies in the longitudinal control along the two paths.

Lower level control

The nonlinearities and uncertainties in vehicle longitudinal dynamics are the main challenges to be met in the design of throttle and brake controllers. Researches have been pursued for several decades and at many different levels by researchers and automotive manufactures. From 1970s to 1980s, there appeared some researches in the control system design for vehicle engines and brake systems, as shown in [START_REF] Fisher | Brake system component dynamic performance measurement and analysis[END_REF][START_REF] Guntur | [END_REF],Guntur 1980[START_REF] Moskwa | [END_REF][START_REF] Powell | [END_REF]. Since then, some first generation of engine control systems appeared in [START_REF] Cho | [END_REF][START_REF] Grizzle | [END_REF], and some results in the brake system control have obtained great success, such as the ABS (Anti-lock Brake System), which have been widely accepted in the automobile industry.

Based on the above results, and since 1990s, the researches in the longitudinal control combined with throttle and brake control has become steadily more attractive. Ioannou P.A. and Chien C.C. proposed a fixed gain and gain scheduling PID controllers as well as the adaptive control method for vehicle longitudinal control, see [Ioannou 1993]. The controllers were simulated using a validated full order nonlinear longitudinal model and tested also on a real vehicle, and the results are satisfied. However, in order to use these PID based controllers, an exact throttle angle to vehicle speed and position model is required as a premise. To get this model, it needs a lot of experiments to determine the required parameters and in some cases it is confidential. In [START_REF] Gerdes | [END_REF]], Gerdes J.C. and Hedrick J.K. presented a combined engine and brake control system based on multiple-surface. The proposed system consists of three basic elements: an upper sliding controller that incorporates vehicle acceleration as a synthetic input, a logic switch that chooses between throttle or brake control, and lower sliding controllers for the engine and brake operations.

The fuzzy logic is also proposed for this subject. In [Naranjo 2006], Naranjo. J.E. et al. designed a throttle and brake fuzzy control system to perform the ACC+Stop&Go maneuvers. Two separate fuzzy controllers were designed to control the throttle and brake pedals. In order to avoid simultaneous actions of both the pedals, the values of the membership functions of the two controllers were well defined. The constant time gap spacing policy was used to give the desired spacing for the controlled vehicle. This system has been equipped in a two-vehicle platoon. The results showed that the automated vehicle behaved very similarly to human-driven car and was adaptive to the speed variations.

Upper level control

The upper level controller determines the desired acceleration or speed of the controlled vehicle. The principle design tasks in the upper level control include the design of spacing policy and its associated control algorithm. The spacing policy denotes the desired spacing that an automated vehicle attempts to maintain with respect to the preceding vehicle [START_REF] Santhanakrishnan | [END_REF], Wang 2004a]. In general, the desired spacing policy is a function of the vehicle velocity but could be also a constant distance or a function of other variables such as relative velocity between the controlled vehicle and the proceeding one.

It plays an important role in vehicle longitudinal control system as it has great influences on vehicle safety and traffic capacity. Spacing policy and its associated control algorithm can be evaluated from the point of view of string stability, traffic flow stability and traffic flow capacity [Swaroop 1999[START_REF] Santhanakrishnan | [END_REF].

A variety of spacing policies have been proposed in early works e.g. [Shladover 1991a[START_REF] Ioannou | [END_REF][START_REF] Rajamani | [END_REF],Wang 2004a,Zhou 2005]. From the traffic capacity point of view, a constant spacing headway of about 1 m was suggested by Shladover [Shladover 1991a].

With such a tight following model, the traffic capacity increases considerably. However, it was shown that the vehicle controller needed information about the leading vehicle of the platoon to ensure string stability [START_REF] Rajamani | [END_REF], Rajamani 2006]. Therefore, an inter-vehicle communication protocol is needed to supply the information of the platoon leader to the followers. At present, the most common spacing policy used by researchers and vehicle manufactures is the constant time-gap (CTG) spacing policy [Wang 2004a].

Unlike the constant spacing policy, the tracking requirement in CTG policy can be easily obtained without any inter-vehicular communication. Much works have been done by using CTG spacing policy, and some manufactures have more recently launched their cruise systems based on CTG algorithms [START_REF] Ioannou | [END_REF], McDonald 1999, Marsden 2001[START_REF] Nouveliere | [END_REF]]. However, there still exists some problems in the use of CTG algorithm:

• Using the CTG policy, the current cruise control system is not suitable for use in high-density traffic conditions, and the operating speed should be higher than 40 km/h [Marsden 2001].

• Using the standard CTG policy, traffic flow stability cannot be ensured [Swaroop 1999].

Lateral control

Lane departure is the number one cause of fatal accidents, and account for over 25,000 deaths annually, almost 60% of the total deaths in the highway crashes in the United

States. It is also reported that the average crash rate in the curves is about 3 times A lane keeping system automatically controls the steering to keep the vehicle in its lane and also follow the lane as it curves around. In [START_REF] Fenton | [END_REF]], Fenton R.E. and Selim I designed a velocity-adaptive lateral controller using an optimization approach. The resulting controller, which is nonlinear with velocity, requires full-state feedback and thus an observer is included. In [Choi 2001], the vehicle is steered to follow the reference yaw rates which are generated by the deviations of lateral distance and the yaw angle between the vehicle and the reference lane. A PI controller was designed to minimize the error between the reference yaw rate and the measured one. In [START_REF] Taylor | [END_REF]], three vision-based lateral control strategies: lead-lag control, full state feedback and input-output linearization were introduced and compared through a series of experiments. Although these unique model based approaches can lead to acceptable control results, their performance may be too sensitive to model mismatch and unmodeled dynamics. Besides, some controllers such as sliding mode solutions in [Zhang 2000], H-infinity controller in [START_REF] Chaib | [END_REF]], and the self-turning regulator in [Netto 2004], appear rather complex for realtime embedded control of autonomous vehicles.

The lane changing system automatically steers the vehicle from the current lane to an adjacent lane. In fact, lane changing and lane keeping maneuvers become virtually identical when the lateral sensor can measure its location in both lanes. One major solution is Look-ahead lateral reference/sensing system (e.g. machine vision system). It can provide a long and wide range measurement of vehicle lateral displacement. By using this measurement, the lateral controller mimics human driver's behavior to perform the lane changing maneuver, see [START_REF] Taylor | [END_REF][START_REF] Lee | [END_REF]]. However, the reliability of machine vision system is susceptible to variations in light or inclement weather conditions. The fact that Look-down lateral reference/sensing system (e.g. magnetic markers installed in the center of highway) improves the reliability of the sensing system can be another solution. But it suffers from the small sensor range. In this case, the lane changing control problem becomes complicated as the lateral sensing system cannot sense both lanes and the vehicle must travel a certain distance without seeing the road reference system.

The virtual desired trajectory (VDT) for a lane change operation is then designed considering passenger's ride comfort and transition time. Four candidate trajectories as

(1) circular trajectory (2) cosine trajectory (3) 5th order polynomial trajectory, and ( 4) trapezoidal acceleration trajectory were evaluated using the transition time as a performance index, the lateral acceleration and jerk as constraints, and vehicle speed as a design parameter. The trapezoidal acceleration trajectory is selected to be the optimal trajectory [Chee 1994[START_REF] Hedrick | [END_REF]]. By using VDT, the lane change maneuver is then investigated as a lane tracking problem. In this way, we consider using a uniform control algorithm to perform the lane tracking tasks for both the lane keeping and the lane changing, so as to make the lateral control system simpler and more compact.

Integrated longitudinal and lateral control

For a totally automated vehicle on automated highway, the combined longitudinal and lateral control should be envisaged. There are two types of combination method: uncoupled and coupled. The uncoupled method neglects the coupling effects between the longitudinal and lateral dynamics, and then the designed longitudinal and lateral controllers are totally independent. Consequently, the global controller can be obtained by simply combining the two separate controllers together. However, in the coupled method, the coupling effects between the two movements are no longer neglected. Therefore, a coupling controller will be considered. Obviously, with the consideration of the coupling effects of the two movements, the controller design task becomes more complex than in the uncoupled case.

Wijesoma and Kodagoda have shown an uncoupled fuzzy control system for a golf car-like AGV (Autonomously Guided Vehicle) [START_REF] Kodagoda | [END_REF][START_REF] Wijesoma | [END_REF]]. In their work, the coupling effects of vehicle speed on steering angle (and hence angular velocity), and vice versa, was not explicitly accounted for. The speed and steering controllers were independent of each other. The proposed fuzzy control system was tested extensively on an AGV prototype and has been demonstrated to operate satisfactory even in the simultaneous operations of the speed and steering control. But, the variation of speed is only from 3 to 7 m/s, which is enough for a Golf car but not sufficient for the highway vehicles. In [Bom 2005], Bom J. et al. proposed a global control strategy for the urban vehicles. The longitudinal control and lateral control are fully decoupled using nonlinear control theory. However, in their experiments and simulations, the maximum speed is only 5 m/s, which appears reasonable for the urban vehicles but very limited for the highway vehicles.

On the contrary, some coupled solutions were also proposed. Lim and Hedrick considered the coupling effects which exist in the vehicle longitudinal and lateral dynamics, and proposed a sliding mode controller to realize automated vehicle following, see [Lim 1999].

The proposed method was validated through simulation and field test, and it was also compared with a PID controller. In [Mammar 2004] and [START_REF] Chaibet | [END_REF]], sliding mode control and backstepping control methods have been proposed for the automated vehicles in the low speed operations (v< 60 km/h). More recently, in [Toulotte 2006], a T-S model based fuzzy control law, which takes into account the coupling between both the longitudinal and lateral modes, was proposed. The "virtual drawbar" strategy was used in the longitudinal and lateral controller design. Simulation results showed that the longitudinal spacing error was less than 5% of safety distance. However, the orientation error (orientation difference between the follower and leader) was more than 40%. In order to limit this orientation error, a communication system was proposed as a possible solution.

Conclusion

This chapter reviewed the developments in automated vehicle control. At first, the background of the current traffic situation and problems were introduced. Second, we briefly introduced ITS, AHS and intelligent vehicle, which were considered as the most promising solutions to the traffic problems. Finally, the evaluation of the outstanding projects and the developments in vehicle longitudinal and lateral control were surveyed in detail.

The automated vehicle control task can be divided into two parts: longitudinal control and lateral control. The vehicle longitudinal control system is designed to be hierarchical with an upper level controller and a lower level controller. The longitudinal controller design needs to meet diverse challenges and requirements as nonlinearities in vehicle longitudinal dynamics, vehicle safety, string stability, traffic flow stability, traffic capacity, driving comfort, etc. In the lateral control design, the complexity in vehicle lateral dynamics, the selection of vehicle reference (measure) system, different operation scenarios, ride comfort are the main problems need to be envisaged. Finally, the coupling effects between the longitudinal and lateral dynamics should be also a question to be considered.

In the following chapters, we will firstly build up a complete vehicle dynamic model, and then the different control strategies for the automated vehicle will be developed.

Introduction

Modeling of the vehicle dynamics is the first step for control system design. It is known that the vehicle system dynamic is normally a complex system where always exists nonlinear parts (tyre, clutch...) and parameter variations (mass, tyre-road friction coefficient, ...). Basically, the modeling of vehicle dynamics is essentially dependent on the forces created at the tyre/road interface and the different mechanical parts of the vehicle.

Firstly, considering the tyre force, different approaches have been studied. For example, Pacejka has developed a series of tyre design models, incorporated these models into vehicle models, and presented an applied understanding of how the tyre influences vehicle behavior [Pacejka 2006]. While, Gim and Nikravesh have proposed a series detailed analyses on tyre modeling by using Finite Element Method [START_REF] Gim | [END_REF],Gim 1991a,Gim 1991b].

Secondly, in order to get the expression of vehicle dynamic, it is necessary to choose a list of mechanical parts need to be considered: tyre, suspension geometry, steering angle, anti-roll bar, etc. The complexity and the accuracy of the expression of vehicle model are depended on the list. Usually, we need to find a compromise between the accuracy and complexity.

The modeling of vehicle dynamic have been pursued at many different levels by researchers and automotive manufactures. Generally, the complexity and accuracy of the vehicle model is always dependent on the final purpose of implementation [START_REF] Td Day | An overview of the HVE vehicle model[END_REF][START_REF] Pham | [END_REF], Hingwe 1997[START_REF] Nouvelière | Commandes Robustes Appliquées au Control Assisté d'un Véhicle à Basse Vitésse[END_REF]]. One of the most complex model with 28 degrees of freedom was proposed by [Lowndes 1998], which included the detailed models for each element of vehicle: sprung mass, independent suspensions, wheels. In [Addi 2005], a complex model with 18 degrees of freedom was employed, which considered rigid body dynamics, dynamics of tyre suspensions system, as well as tyre dynamics. At present, the 6 degrees of freedom model is widely accepted, which can describe the principal movements of vehicle. The six principal movements of a vehicle are as follows: three translation along

x, y and z-axes and three rotational motions about three axes (roll-pitch-yaw).

According to the early literatures, the vehicles models could be classified into three types [START_REF] Nouvelière | Commandes Robustes Appliquées au Control Assisté d'un Véhicle à Basse Vitésse[END_REF]]:

• Longitudinal model of vehicle In this chapter, we will firstly analyse the principle movement of a road vehicle, and then the vehicle longitudinal model and lateral model will be established. The models that we established will be employed in control systems design in the following chapters.

Principle movements of vehicle & decoupling of longitudinal and lateral models

Principle movements of vehicle

The principal vehicle movement can be described as a 6 degrees of freedom system within the vehicle-fixed frame, which includes translations and rotations about the three orthogonal axes: X-Y -Z, as shown in Fig. 2.1.

Decoupling of longitudinal and lateral models

The tyre dynamics is one of the essential elements of the vehicle dynamics. Forces and moments from the road act on each tyre of the vehicle and highly influence the dynamics of the vehicle. The modeling of tyre road interface is difficult because there exists numerous important parameters (tyre pressure, dimension, road condition, weather condition,...) and the variations of their values with time.

One of the most famous tyre model is the "Magic Formula" model, which was proposed by Pacejka and Bakker [Pacejka 2006]. This model provides a method to calculate lateral and longitudinal tyre forces and aligning moment for a wide range of operating conditions including large slip angle and slip ratios as well as combined lateral and longitudinal force generation.

In addition, the conception of "friction ellipse" was proposed by Gillespie [Gillespie 1992].

It was shown that the amount of traction available from the tyre patch is necessarily limited, and hence, there must exist some relationship between the lateral and longitudinal forces. This relationship is generally expressed in the idea of a friction ellipse as shown in Fig. 2.2.

Consequently, there exists the coupling phenomenon between the longitudinal and the lateral motions of the tyre. Thus, the longitudinal and lateral movements of the vehicle are coupled.

However, we can decouple the dynamics of the two movements, under the assumption of small varying velocity and steering angle. Thus, the control problem can be simplified into two separate tasks: longitudinal control and lateral control. In fact, the method of decoupling the two systems are accepted in a many researches [Jia 2000[START_REF] Nouvelière | Commandes Robustes Appliquées au Control Assisté d'un Véhicle à Basse Vitésse[END_REF][START_REF] Wu | [END_REF][START_REF] Chiang | [END_REF][START_REF][END_REF], and it has been tested on automated vehicle prototypes as well as in vehicle platoon operations [Lim 1999[START_REF] Kodagoda | [END_REF].

By using the separate models in stead of the complex coupling model, we can better understand the role of each model in vehicle dynamics and it is easier for us to analyze the different phenomenon in vehicle dynamics. In the following section, we will present

Modeling of Longitudinal Vehicle Dynamics

The vehicle longitudinal dynamics includes two major parts: longitudinal dynamics and powertrain dynamics. The longitudinal dynamics are influenced by longitudinal tyre forces, aerodynamic forces, rolling resistance forces and etc. Modeling of these forces are discussed in section 2.3.1. The powertrain dynamics consists of the dynamics of the subsystems, such as internal combustion engine, torque converter, transmission and wheels. These elements are discussed in section 2.3.2. Finally, the vehicle longitudinal model is set up in section 2.3.3, which sums up the analyses in the two former subsections.

Longitudinal dynamics

Simple vehicle model

The vehicle is considered as one rigid body moving along an inclined road as shown in Fig. 2.3. At each axle the forces in the wheel contact points are combined in one normal and one longitudinal force. The other external forces acting on the vehicle include aerodynamic drag forces, rolling resistance forces, gravitational forces. These forces will A force balance along the vehicle longitudinal axis yields:

mẍ = F xf + F xr -F aero -R xf -R xr -mg sin(α) (2.

Slip ratio

For calculating the longitudinal tyre force, the conception "slip ratio" is widely used.

Slip ratio means the difference between the actual longitudinal velocity at the axle of the wheel V x and the equivalent rotational velocity r ef f ω w of the tyre. The value of slip ration varies according to the vehicle movement:

For traction (r ef f ω w -V x ≥ 0):

s x = r ef f ω w -V x V x (2.2)
For braking (r ef f ω w -V x < 0):

s x = r ef f ω w -V x r ef f ω w (2.3)
where, s x denotes the slip ratio, V x is the actual longitudinal velocity, r ef f represents the effective radius of rotating tyre, ω w means the angular velocity of wheel.

Expression of longitudinal tyre force

The longitudinal tyre forces F xf and F xr are friction forces from the ground that act on the tyres. Assume that the tyre-road interface is dry and the normal force is a constant, the typical variation of longitudinal tyre force as a function of slip ration is shown in Fig. 2.4. From this figure, we can find that in the case where the slip ratio is small (typically in the region of (-0.1 ∼ 0.1)), as in normally driving, the longitudinal tyre force is proportional to the slip ratio. The tyre longitudinal force in the small slip region can be modeled as: (2.4)

F xf = C sf s xf
F xr = C sr s xr (2.5)
where C sf and C sr are the longitudinal tyre stiffness of the front and rear tyres respectively. s xf and s xr are the slip ratio at the front and rear tyre respectively.

Aerodynamic forces

Consider a moving vehicle, the shape of vehicle produces aerodynamic forces, the effect of these forces can be represented by a equivalent force applied at the center of gravity, as shown in (2.6)

F aero = 1 2 ρC d A F (V x + V wind ) 2 (2.6)
where V wind is the wind velocity (positive for a headwind and negative for a tailwind)

Rolling resistance

If a non-rotating tyre has contact to a flat ground, the pressure distribution in the contact patch will be symmetric from the front to the rear. The resulting normal force F z acts in the center c of the contact patch and hence, will not generate a torque around the rotating axis of the tyre.

However, in the case of rotating tyre, the distribution of the normal tyre force is non-symmetric, as shown in Fig. 2.5. The normal force generates the rolling resistance torque

T y = F z x (2.7)
Usually the variable x is difficult to be measured, and the rolling resistance is mod-

R x = R xf + R xr = f (F zf + F zr ) (2.8)
where R x rolling resistance force of vehicle R xf , R xr rolling resistance forces acting on front and rear tyres respectively F zf , F zr normal forces acting on front and rear tyres respectively f rolling resistance coefficient According to the above analysis, we find, to a rolling tyre, it is the rolling resistance torque but not the rolling resistant force that prevents the rolling movement. In fact the rolling resistance force does not exists in reality. However, in order to facilitating the analysis of longitudinal forces, we use the concept of "rolling resistance force", which can be obtained directly from the rolling resistance coefficient, in stead of resistance torque.

Normal tyre force

In order to calculate the normal tyre force on the tyres, we come back to Fig. 2.3, where F zf and F zr denote the normal forces acting on the front and rear tyre respectively. Assuming that the net pitch torque acting on the vehicle is zero, which means the pitch angle of the vehicle is in a steady state value. Then, we can get the moments equation about the contact point of the front tyre:

F zr (l f + l r ) -F aero h aero -mẍh -mgh sin(α) -mgl f cos(α) = 0 (2.9)
Solving for F zr ,

F zr = F aero h aero + mẍh + mgh sin(α) + mgl f cos(α) l f + l r (2.10)
Similarly, the moments equation about the contact point of the rear tyre is written by:

F zf (l f + l r ) + F aero h aero + mẍh + mgh sin(α) -mgl r cos(α) = 0 (2.11)
Solving for F zf ,

F zf = mgl r cos(α) -f aero h aero -mẍh -mgh sin(α) l f + l r (2.12)
Regarding equations (2.10), (2.12), the normal force distribution on the tyres is affected by the acceleration of the vehicle. When the vehicle accelerates, the normal load on the front tyres decreases whereas the normal load on the rear tyres increases.

Effective tyre radius

As the tyre is a flexible body in contact with the road surface, the effective radius is normally slightly less than the nominal tire radius because the tyre deforms under its vertical load when it is rolling. If the rotational speed of the wheel is ω w , the linear speed of the wheel axle is [Kiencke 2005]

V w = r ef f ω w (2.13)
where, r ef f means the effective radius of rotating tyre.

As shown in Fig. 2.6, let ∆ϕ be the angle made by the center line of the wheel to the beginning of the contact patch, 2a be the longitudinal length of the contact patch. We get

a = r 0 sin(∆ϕ) (2.14) cos(∆ϕ) = r s r 0 (2.15)
where, r 0 is the unloaded tyre radius, and r s is the loaded or static tyre radius.

Let t be the time taken by the tyre to move through half of the contact patch. We

V w = r ef f ω w = a t (2.16)
The rotation speed of the wheel is

ω w = ∆ϕ t (2.17) Thus r ef f = a ∆ϕ (2.18)
Replacing a from (2.14),

r ef f = r 0 sin(∆ϕ) ∆ϕ (2.19)
For ∆ϕ is small, the sine-function and cosine-function be approximated by the first terms of its Taylor-Expansion

sin(∆ϕ) ≈ ∆ϕ - ∆ϕ 3 6 (2.20) r s r 0 = cos(∆ϕ) ≈ 1 - 1 2 ∆ϕ 2 ⇒ ∆ϕ 2 ≈ 2(1 - r s r 0 ) (2.21)
Then (2.19) can be rewritten as

r ef f = r 0 ∆ϕ -1 6 ∆ϕ 3 ∆ϕ = r 0 (1 - 1 6 ∆ϕ 2 ) = r 0 (1 - 1 3 (1 - r s r 0 )) = 2 3 r 0 + 1 3 r s (2.22)
The static tyre radius is influenced by the vertical load of the tyre,

r s = r 0 - F z k z (2.23)
where k z is the vertical tyre stiffness.

Powertrain dynamics

In the previous discussions, the vehicle longitudinal dynamics are described in equation ( 2.1), rewrite this equation

mẍ = F xf + F xr -F aero -R xf -R xr -mg sin(α)
where F xf and F xr are the longitudinal tyre forces at front and rear tyres respectively, and they are the primary forces that drive the vehicle moving forward. These two forces depend on the slip ratio of the driving tyre, which is determined by the difference between the actual longitudinal velocity at the axle of the wheel V x and the rotational wheel velocity r e ω w , as discussed in section 2.3.1.2. The rotational velocity ω w is produced by the powertrain system of the vehicle. A typical powertrain system of a vehicle is shown in Fig. 2.7, which includes the subsystems of engine, torque convert, transmission, drive shafts, final drive, and differentials. In the rest of this subsection, the modeling of these subsystems will be discussed.

Engine model

The internal combustion engines are commonly equipped on road vehicles. Normally, we consider the engine output is the engine torque, which is a nonlinear function of the air/fuel ratio, the exhaust gas recirculation (ERG), the cylinder total mass charge, the Various engine models have been proposed in the early researches [START_REF] Powell | [END_REF][START_REF] Cho | [END_REF][START_REF] Sun | Optimal idle speed control of an automotive engine[END_REF]]. But these models are so complex, which always contain many parameters need to be defined, that make them inconvenient to be used in the engine controller design.

An often used alternative to the parametric engine model is one in which engine maps from experimental data are used to replace several parametric functions. For example, the torque T e of a combustion engine can be characterized as a function of its angular velocity ω e and the gas pedal input P th (P th ∈ [0, 1]):

T e = Eng(ω e , P th ) (2.24)
In Matlab Simulink, the Look-up Table block can be used to describe the nonlinear relationships between T e , ω e , P th , an example of engine map is shown in Fig. 2.8.

Torque converter

The torque converter is a type of fluid coupling that connects the engine to the transmission. It includes three major components: pump, turbine and the stator. Torque converter modeling has been studied by different researches [Kotwicki 1982,Assanis 2000[START_REF] Cho | [END_REF]].

Usually, the torque converter model can be described as a quasi-steady model based on

i con = n t n i (2.25) Ψ(i con ) = T t T i (2.26) T i = n i 2 K 2 (2.27)
where, n t rotation speed of turbine

n i rotation speed of pump i con speed ratio Ψ torque ratio T t turbine torque T i pump torque
K capacity factor A torque converter model is shown as a block diagram in Fig. 2.9. Two lookup table blocks are used to convert the speed ration i con to torque ratio Ψ and capacity factor K.

The data that we use in the lookup tables can be obtained from the experiments, which are usually provided by the suppliers. The gearbox allows the gear ration to be adjusted. By shifting the gears manually or automatically, the engine works at its most efficient region while allowing the vehicle to drive at a large range of speed. In our work, a 4-speed automatic gearbox is considered. Let R g be the gear ratio of the gearbox, the value of R g depends on the operating gear. Usually the gear ratio is defined as

Gearbox

Gear transmission basic

R g = ω t ω s = T s T t (2.28)
where, ω t and ω s denote the angular speed of the turbine and the drive shaft. T t and T s denote the turbine torque and the drive torque acting on the drive shaft respectively.

Gear shift schedule

The operating gear is decided by a gear shift schedule that depends on both the The solid and dashed lines denote upshift and downshift thresholds respectively.

Modeling of automatic transmission

The automatic gearbox model is built up on the platform of Matlab/Stateflow. Modeling of the gear shift logic is the kernel in the automatic gearbox modeling.

Traditionally, the gearbox has several fixed gears, 4 or 5 for instance. Under certain conditions, it changes the current gear to an other gear. Thus, the automatic gearbox system is a typical event-driven system with several prescribed states. The FSM (Finite State Machine) theory is then used in the modeling of automatic transmission system. M atlab/Statef low which provides a powerful environment for the analysising&modeling of the finite state machine is then employed in our research.

The stateflow diagram shown in Fig. drive train that cannot be connected directly because of distance or the need for relative movement between them, as shown in Fig. 2.7 . In our work, we neglect the flexibility of the drive shafts and regard them as a rigid connection, the speed ratio and the torque ratio of the drive shaft is always 1.

Final drive & Differential

The basic function of a final drive in the powertrain of an automobile is to provide an additional and constant gear reduction in the transmission system. In the longitudinally mounted engines, two basic types of final drive reduction gear have been used : bevel gear and worm. For the cars with transversely mounted engines, the final drive reduction gears are usually the helical pinions.

In addition, a differential is included in the final drive unit, which is capable of transmitting torque and rotation through three shafts: one input shaft which is connected to the drive shaft or the gearbox layshaft, and two output shafts which drive the driving wheels. The differential allows the two driving wheels to rotate at different speeds, while supplying equal torque to each of them for most vehicles.

As in our work, the vehicle is assumed to drive in the good road condition, the two driving wheels in the both sides always have the same adhesion conditions. Thus the influences of the differential to the vehicle dynamics are neglected. The final drive dynamics are written as:

R f = ω s ω w = T w T s (2.29)
where,

Braking system modeling

The typical automotive brake system is shown in Fig. 2.13. The front and rear wheel brakes (disk brake or drum brake)are connected by a system of tubes and hoses that link each brake to the master cylinder. When we step on the brake pedal, we are actually pushing against the piston in the master cylinder which forces hydraulic oil through a series of tubes and hoses to the braking unit at each wheel.

The braking torque is approximated to be proportional to the pressure in the brake chamber and brake fade is ignored [START_REF] Kienhöfer | [END_REF], Hedrick 1996]:

T b = 2A c P c µ br r br (2.30)
where,

T b braking torque

A c effective area of the brake chamber diaphragm P c brake chamber pressure µ br coefficient of friction between the brake disk and brake pads r br effective radius through which the disk and brake pad friction acts Let K b = 2A c µ br r br , which is a constant that is determined by the vehicle brake system construction. Then equation (2.30) is reduced to

T b = K b P c (2.31)
Considering the deformation of the tubes and hoses as well as the volume nuance of the hydraulic oil during the braking period, the transfer function of the brake demand pressure to the pressure in the brake chamber is approximated as a first order system [START_REF] Kienhöfer | [END_REF]]:

P c = P d 1 1 + τ s e -sT d (2.32)
where, P d brake demand pressure τ time constant of the transient response of the brake system, τ = 0.01s

T d time delay in the brake system

Longitudinal model for simulation

The objective of this subsection is to present the longitudinal model for the simulations in the later chapters. The longitudinal model should consider the most significant phenomenons in the vehicle longitudinal control. As consequence, we build a longitudinal vehicle model which starts from the engine and then the transmission till to the tyre/road, as described in the powertrain system in Fig. 2.7.

Assumptions

In order to build a longitudinal model for the controller design in this work, we propose the following hypotheses:

• The vehicle is considered as driving in a straight road, and the vehicle lateral movement has no effect on longitudinal movement, which implies:

δ = 0
where, δ means the steering angle

mẍ = F xf + F xr -F aero -R xf -R xr -mg sin(α) (2.33) Let F t = F xf + F xr -R xf -R xr ,
which means the traction force. Substituting F aero from equation (2.6), vehicle longitudinal motion is then written as:

mẍ = F t - 1 2 ρC d A F V x 2 -mg sin(α) (2.34)
However, this equation is in terms of longitudinal tract force instead of engine and brake torques which are considered to be controlled. Therefore, the powertrain dynamics which we discussed in the section 2. Each wheel can provide a torque equation as:

-F tf r ef f -T bf -T yf = J wf ωwf (2.35) T d -F tr r ef f -T br -T yr =
F tf = 1 r ef f (-J wf ωwf -T bf -T yf ) (2.37) F tr = 1 r ef f (T d -Jwr ωwr -T br -T yr ) (2.38)
Note that the total taction force F t = F tf + F tr , then substituting (2.37) and (2.38) into (2.34), yields:

mẍ = 1 r ef f (T d -T bf -T br -T yf -T yr -J wf ωwf -Jwr ωwr )- 1 2 ρC d A F V x 2 -mg sin(α) (2.39)
In order to simplify the analysis procedure, we make a father assumption that no slip occurs at the wheels. Strictly speaking, this assumption is not true, since in the discussions in the section 2.3.1.2, the longitudinal traction force depends on the slip ratio of the tyre.

However, at the low acceleration conditions in this work for general operation in highway maneuvers, the slip is quite small and thus the tyre slip may safely be neglected. The no slip assumption has been employed in several previous researches [START_REF] Mcmahon | [END_REF][START_REF] Hedrick | [END_REF][START_REF] Hedrick | [END_REF]. Using this assumption, we get:

ωwf = ωwr = ẍ r ef f (2.40)
The next step relates to the drive torque T d . Considering a mechanical transmission system, T d is given by:

T d = T e R g R f (2.41)
where, T e denotes the engine torque, R g , R f refer to the gear ratios of the gearbox and final drive respectively. However, in our work, an automatic transmission system with a hydraulic torque converter is considered, thus by using the expressions of (2.25, 2.26, 2.27), the axel drive torque can be written as:

T d = T e ΨR g R f (2.42)
In case that the torque converter is locked, as appeared in some models for reducing the power loss, the hydraulic transmission is thus regarded as a mechanical transmission system as described in equation (2.41).

Finally, we assume that the distribution of rolling resistance or braking torque on the front and rear axle is always appropriate. And we do not consider the influences caused by the different distributions of the rolling resistance and braking torque on the axels.

We define T y = T yf + T yr and T b = T bf + T br , equation (2.39) is then reduced to:

ẍ(m + J wf + Jwr r 2 ef f ) = 1 r ef f (T e ΨR g R f -T b -T y ) - 1 2 ρC d A F V x 2 -mg sin(α) (2.43)
This final equation represents the longitudinal vehicle dynamics. It considers both the engine and brake torques, and will be used in the controller design in the later chapters.

Simulations

In order to validate the vehicle longitudinal dynamics described in equation 2.43, we build a vehicle longitudinal system diagram as shown Fig. Since, the relationship between the brake torque and the brake oil pressure is approximated to be proportional as described in equation 2.31, therefore, we use brake torque as the input parameter and it is easy to transform, if necessary, the brake torque to the brake oil pressure.

We perform the following operations of throttle and brake pedal to drive the experimental vehicle: at first, we press down slowly the throttle pedal from 0 to 70%, next, we release slowly from 70% to 20%, and then we release the pedal completely. After that, we begin to press down the brake pedal to provide the brake torque from 0 to 400 (n * m), afterwards, we keep the brake operation for 15s, and finally, we release the brake pedal gradually. The operation details of this acceleration and then deceleration scenario are described in Fig. 2.16.

The simulation results are shown in Fig. 2.17. Figure 2.17(a) shows the gear shift history, where we can find the operation trace of the automatic gearbox in this acceleration and then deceleration scenario. In the acceleration period, with the increases both in throttle open and vehicle speed, the gearbox changes up under the following sequence:

1 st → 2 nd → 3 rd → 4 th .
While, in the deceleration period, it changes down reversely as: The engine speed is shown in Fig. 2.17(c). Several peaks in engine speed curve are caused by the gear shift operations. Figure 2.17(d) and 2.17(e) show the evolution of speed and acceleration respectively. Note that in the acceleration curve, there are two sudden oscillations at 10.5s and 13.8s. These oscillations are caused by the gear change shocks between 2 nd → 3 rd and 3 rd → 4 th .

4 th → 3 rd → 2 nd → 1 st . Figure 2.17
The above results are reasonable. They can reflect the interior movements of the different subsystems during the vehicle driving process. Therefore, this model will be employed in the longitudinal controller design in the later chapters.

Modeling of Lateral vehicle dynamics

Lateral kinematic model

The kinematic model of the vehicle motion provides a mathematic description of the vehicle motion without considering the forces that affect the motion. We consider only the geometric parameters in the equations of kinematic model. This model can be used in the low speed application, such as car-like robot.

The vehicle lateral motion can be simplified as a bicycle model, as shown in Fig. 2.18, under the assumptions follows:

• The velocity vectors at front and rear wheels are in the direction of the orientation of • The two wheels in both side of a axle have a same steering angle. Thus, we can combine the two wheels of one axle into a single wheel. The four wheels vehicle is modeled as a two wheels bicycle.

In Fig. 2.18, points A, B and C represent the center of the front, the rear axle and the center of gravity (c.g.) of the vehicle respectively. The point O is the instantaneous rolling center for the vehicle. δ f and δ r represent the steering angle of the front and rear wheel respectively. In the case of front wheel steering, the parameter δ r can be set to zero.

The velocity at the c.g. of the vehicle is V , which has an angle β with the longitudinal axis of the vehicle. The angle β is called the slip angle of the vehicle. R is the radius of the vehicle's path.

We use three coordinates to describe the motion of vehicle: X, Y and ψ. (X, Y ) are inertial coordinates of the location of the c.g. of the vehicle while ψ is the yaw angle of the vehicle. Therefore, the kinematic model of vehicle lateral motion is given by:

         Ẋ = V cos(ψ + β) Ẏ = V sin(ψ + β) ψ = V cos(β) l f + l r (tan(δ f ) -tan(δ r )) (2.44)
where, the vehicle slip angel β is written as:

β = tan -1 l f tan δ r + l r tan δ f l f + l r (2.45)

Lateral dynamic model

At higher vehicle speed, the assumption of zero "slip angle" at each wheel can no longer be made. In this case,the kinematic model cannot be used, and a dynamic model for lateral vehicle motion must be developed.

A "bicycle" model for vehicle lateral dynamics, which has two degrees of freedom, is shown in Fig. According to the Newton's second law for motion along the y axis,

ma y = F sf cos(δ) + F sr (2.46)
where a y is the inertial acceleration of the vehicle at the c.g. in the direction along the y axis, a y = d 2 y dt 2 . F sf and F sr are the lateral tyre forces of the front and rear wheels respectively.

Consider a y , it is composed by two elements: ÿ is due to the motion along the y axis and V x ψ is the centripetal acceleration. Thus

a y = ÿ + v x ψ (2.47)
Substituting from (2.47) into (2.46), the equation of lateral translational motion is given by

m(ÿ + v x ψ) = F sf cos(δ) + F sr (2.48) B X Y O A C lr lf ψ x y ψ d δ V f V r vr θ vf θ f β vr θ vf θ V β V x V y Lane centerline F sf F sr
I z ψ = l f F sf cos(δ) -l r F sr (2.49)
where, l f and l r are the distances of the font wheel and rare wheel respectively from the c.g. of the vehicle.

We assume that the vehicle steering angle is small thus,cos(δ) ≈ 13 , the equations of (2.48) and (2.49) can be rewritten as:

m(ÿ + V x ψ) = F sf + F sr I z ψ = l f F sf -l r F sr (2.50)
On account of the lateral tyre force is proportional to the "slip angle" for small slip angle. The slip angle of a tyre is the angle between the orientation of the tyre and the orientation of the velocity vector of the wheel, as shown in Fig. (2.19). In this figure, the slip angle of the front and rear wheel can be obtained as

β f = δ -θ vf (2.51)
and

β r = -θ vr (2.52)
where δ is the steering angle. θ vf is the angle between the velocity vector of the front wheel and the longitudinal axis of the vehicle, while θ vr is the angle between the velocity vector of the rear wheel and the longitudinal axis of the vehicle.

The slip angle results in a force perpendicular to the wheel's direction of travel-lateral tyre force (cornering force). This lateral force increases approximately linearly for the small slip angle, we can get

F sf = 2C af (δ -θ vf ) F sr = -2C ar θ vr (2.53)
where C af and C ar are the cornering stiffness of each front and rear tyre respectively. The factor 2, in both the two equations, is due to the fact that there are two wheels in each axle of vehicle.

Using the following relations, we can calculate θ vf and θ vr

tan(θ vf ) = V y + l f ψ V x (2.54) tan(θ vr ) = V y -l r ψ V x (2.55)
Using small angle approximations and let V y = ẏ, we can get

θ vf = ẏ + l f ψ V x (2.56) θ vr = ẏ -l r ψ V x (2.57)
Substituting from equations 2.51, 2.52, 2.56 and 2.57 into equation 2.50, the state space model of vehicle lateral dynamics can be written as

Ẋ = AX + Bδ (2.58)
where, X is the state variable, X = [y, ẏ, ψ, ψ] T , and

A =          0 1 0 0 0 - 2C af + 2C ar mV x 0 -V x - 2C af l f -2C ar l r mV x 0 0 0 1 0 - 2l f C af -2l r C ar I z V x 0 - 2l f 2 C af + 2l r 2 C ar I z V x          B =         0 2C af m 0 2l f C af I z        
Equation (2.58) describes the vehicle dynamics using the state variables lateral position and yaw angle. But when our objective is to design a steering control system, it is more practical to utilize a dynamic model in which the state variables are the position and orientation error with respect to the road. Hence, the lateral model described in (2.58) should be re-defined with the new state variables.

We define the following variable as state variables:

• e 1 , the distance of the c.g. of the vehicle from the center line of the lane, as shown in Fig. 2.20.

• e 2 , the orientation error of the vehicle with respect to the road.

From the above definition, we obtain

e 2 = ψ -ψ d (2.59)
where, ψ d denote the desired yaw angle of vehicle (i.e. the orientation angle of the road).

Consider a vehicle traveling with a constant longitudinal velocity V x on a curve of constant radius R. Assume that the curve radius R is large enough so that small steering angle assumption can be made. Then, the desired yaw rate of the vehicle is given by: The desired acceleration along the y axis of the vehicle is then written as:

ψd = V x R ( 2
a yd = V x 2 R = V x ψd (2.61)
From the definition of e 1 , we can get [Rajamani 2006]

ë1 = a y -a yd = (ÿ + V x ψ) - V x 2 R = ÿ + V x ( ψ -ψd ) (2.62)
Then we can get

ė1 = ẏ + V x (ψ -ψ) (2.63)
Substituting from Equations (2.59) and ( 2.63) into (2.49), we get

m ë1 = ė1 -2C af -2C ar V x + e 2 (2C af + 2C ar ) + ė2 -2C af l f + 2C ar l r V x + 2C af δ + ψd -2C af l f + 2C ar l r V x -mV x (2.64)
and

I z ë2 = ė1 -2C af l f + 2C ar l r V x + e 2 (2C af l f -2C ar l r ) ė2 -2C af l f 2 -2C ar l r 2 V x + 2C af l f δ -I z ψd + ψd -2C af l f 2 -2C ar l r 2 V x (2.65)
From ( 2.64) and (2.65), the state space model can therefore be written as

Ẋ = AX + B 1 δ + B 2 ρ (2.66)
where, X is the state variable, X = [e 1 , ė1 , e 2 , ė2 ] T , and

A =       0 1 0 0 0 - 2C af +2Car mV x 2C af +2Car m -2C af l f +2Carlr mV x 0 0 0 1 0 - 2C af l f -2C ar l r I z V x 2C af l f -2C ar l r I z - 2C af l 2 f +2C ar l 2 r I z V x       , B 1 = 0 2C af m 0 2C af l f Iz T , B 2 = 0 - 2C af l f -2C ar l r m -V 2 x 0 - 2C af l 2 f +2C ar l 2

Simulations

In this part, the vehicle lateral kinematic model and dynamic model will be tested using M atlab/Simulink . The kinematic model is given by equation (2.44), while the dynamic model is written by equation (2.66).

Kinematic model simulations

Since the kinematic model considers only the geometric parameters of the vehicle and ignores the forces that will affect its motion. This model is appropriated only in the low speed applications, such as during the parking operation or for the low speed car-like robots. Therefore, we will simulate the model only in the low speed region. In this case, the big steering angle is allowed.

The vehicle longitudinal speed is set to a constant 5 m/s , a typical low speed for a real scale vehicle. The front wheel steering angle is set to 5 • , 10 • and 18 • respectively. The simulation time is set to 10 seconds. The results of vehicle positions are shown in Fig. 2.21. We can find that the two vehicle tracks are two parts of two circles with different radius. These results are reasonable because the kinematic model do not consider the lateral forces that caused by the lateral motion. Thus the vehicle will track a circle in the proposed simulation conditions.

Dynamic model simulations

At first, consider the dynamic model which is given in equation (2.66), the small steering angle assumption is proposed to linearize the lateral model. Thus, in our simulation, the experimental steering angle is set to be small (less than 10 • ) as the first simulation requirement. This requirement is reasonable for the vehicles in highway driving situations. Second, it is known that the vehicle speed varies in a wide range during the highway operations. Therefore, we need to consider a wide range of speed variations in our simulations.

We test the dynamic model with the following conditions. The vehicle longitudinal speed is set to 10 m/s, 20 m/s and 30 m/s respectively. The steering angle is set to be increased from 0 • to 1.2 • during the first 0.9 second, and then it keeps the steering angle of 1.2 • .

The vehicle lateral displacement, lateral acceleration and yaw angle results are shown in Fig 2 .22. We can find that the vehicle responses are varied notably with the variation of vehicle speed, which means the vehicle speed has a great influence on vehicle lateral dynamics. In Fig. 2.22(b), when the vehicle speed is high, v = 30 m/s, the maximum lateral acceleration is about 3.5 m/s 2 , a rather high value, even when the steering angle is small δ = 1.2 • . Generally, for the reason of security, the vehicle lateral acceleration should not exceed 4 m/s 2 , otherwise, there is a risk of rollover. The phenomena that vehicle lateral dynamics is notably affected by the vehicle speed will be an important element to be considered in the lateral controller design.

The two different vehicle lateral model, kinematic and dynamic models, were developed and tested in this section. However, the assumptions for the two models are different.

Thus, when we use these models, the utilization requirements and road conditions are the essential factors to be considered.

Conclusion

In this chapter, we have presented the vehicle longitudinal and lateral models, which will be employed in the controller design in the following chapters.

For the vehicle longitudinal model, at first, we established the non-linear longitudinal dynamic model based on the Newton's second law, with the hypothesis of no-slip at the tyre-road interface. In this model, all the forces that influence the vehicle longitudinal dynamics are expressed in only one equation. Moreover, the engine and brake torques, which are considered to be controlled in the longitudinal controller, are included this equation. This makes it convenient for the controller design. Second, the powertrain dynamic model of a passenger car with an automatic gearbox was built, which includes the sub-models of different parts in the powertrain system, the engine, torque converter, automatic gearbox, drive shafts, final drive and differential, as well as the braking system.

By using this powertrain model, we can simulate the vehicle behavior thus to test the controllers' results in the following sections.

For the lateral model, the kinematic and dynamic models were studied respectively.

The kinematic model provides a mathematic description of the vehicle motion without considering the forces that affect the motion, and it considers only the geometric parameters. This model can be used in the low speed applications. A "bicycle" model was proposed to express the vehicle lateral dynamics. Under the assumptions of small steering angle and small slip angle, the bicycle model can be described by a 4 th order linear model.

Although the bicycle model is simple, it has been proven to be a good approximation for vehicle dynamics when lateral acceleration is limited to 0.4g on normal dry asphalt roads.

Introduction

With the increasing problems of traffic congestion and safety, the idea of using automated vehicles driving in automated highway is growing steadily more attractive. Longitudinal control and lateral control are the two basic functions of the vehicle automation. Longitudinal control system controls the longitudinal motion of the vehicle, such as longitudinal velocity, acceleration or the its longitudinal distance form the proceeding vehicle in the same lane, by using throttle and brake controllers [Rajamani 2006], while the vehicle lateral control system senses the road centerline using a road based reference system and other on-board sensors and generates steering command to keep the vehicle running along the desired path, thus to realize the lane-keeping or lane-changing tasks for the automatic vehicles.

The longitudinal vehicle motion control has been pursued for several decades and at many different levels by researchers and automotive manufactures. From 1970s to 1980s, there appeared some researches in the control system design for vehicle engines and brake systems, as shown in [START_REF] Fisher | Brake system component dynamic performance measurement and analysis[END_REF][START_REF] Guntur | [END_REF], Guntur 1980[START_REF] Moskwa | [END_REF][START_REF] Powell | [END_REF]]. Since then, some first generation of engine control systems appeared in [START_REF] Cho | [END_REF][START_REF] Grizzle | [END_REF], and some results in the brake system control have obtained great success, such as the ABS (Anti-lock Brake System), which have been widely accepted in the automobile industry. Based on these results, and since 1990s, the researches in the longitudinal control combined with throttle and brake control has become steadily more attractive, and a variety of solutions have been proposed in [Tan 1990[START_REF] Mcmahon | [END_REF] and [Hedrick 1991[START_REF] Mcmahon | [END_REF]]. In addition, in 1986, the California PATH (U.S.A.), one of the most fruitful organization in transportation researches, was established. Almost in the same time, the program of AHSS (Advanced Highway Safety System) in Japan, and the program of PROMETEUS (PROgraM for an European Traffic with Highest Efficiency and Unprecedented Safety) in Europe were carried out. These programs have contributed a considerable efforts and encouraging results in such a control system.

Nowadays, the standard Cruise Control (CC) system, which can automatically control the throttle to maintain the pre-set speed, is widely available on passenger cars. Furthermore, the Adaptive Cruise Control (ACC) and the Cooperative Adaptive Cruise Control (CACC) system were developed, which are extensions of the CC system, have the capacity of detecting the preceding vehicle and then maintain a proper distance from it [Marsden 2001, Wang 2004a[START_REF] Van Arem | [END_REF]]. In the case of absence of preceding vehicles, the ACC/CACC vehicle travels as a CC vehicle. Another cruise control system is 3.2. Architecture of longitudinal control system the "collision avoidance" (CA) system. A CA system operates like a cruise control system to maintains a constant desired speed in the absence of preceding vehicles. If a preceding vehicle appears, the CA system will judge the operation speed is safe of not, if not, the CA will reduce the throttle and/or apply brake so as to slow the vehicle down, at the same time a warning is provided to the driver.

A completely different concept proposed by the California PATH Program, is the vehicle "platoon", where the vehicles travel together with a close separation [START_REF] Rajamani | [END_REF]].

It was estimated that the traffic capacity is about three times the capacity of a typical highway if all the vehicles travel in the closely packed platoons [Varaiya 1993].

Inspired by the concept of "platoon", our principal objective is to design a vehicle longitudinal control system which can enhance vehicle safety while at the same time improving traffic capacity. Thus, we need to envisage not only the control problems of a single vehicle but also the behaviors of a string of vehicles and its impacts to traffic flow. This chapter concentrates on the design problems of vehicle longitudinal control system design. At first the longitudinal control system architecture was designed to be hierarchical, with an upper level controller and a lower level controller. And then the design of upper and lower level controllers will be carried out respectively. To validate the proposed controllers, simulation tests will be carried out. And some conclusion will be given in the end of this chapter.

Architecture of longitudinal control system

As we have introduced in chapter 1, the control architecture of an Automated Highway System (AHS) is hierarchical and has 4 layers shown in Fig. 4.18(c). In the (regulation layer), the longitudinal control system is in charge of the steady and transient longitudinal maneuvers. The longitudinal control system is designed to be hierarchical [Rajamani 2006], with an upper level controller and a lower level controller as shown in Fig. 3.1.

The upper level controller determines the desired acceleration or speed for the controlled vehicle, while the lower level controller decides the throttle and brake commands required to track the desired acceleration or speed.

Based on this hierarchical control architecture, the overall longitudinal control system design is thus divided into two steps: (i) upper level controller design, which includes the design of the specific spacing policy and the associated control laws. The spacing policy means the desired spacing that an automated vehicle attempts to maintain with respect to the preceding vehicle. The desired spacing, which is the value of (x i-1 -x i -w i-1 )

i th W i-1 S i X i-1 X i+1 X i

Upper level control

Introduction

As we have introduced in the previous section, the first-generation of longitudinal control systems like CC or ACC systems are primarily being developed from the point of view of increased driving comfort with some potential in increasing vehicle safety. However, the impacts of these longitudinal control systems on highway traffic have been inadequately

studied [Swaroop 1999[START_REF] Santhanakrishnan | [END_REF]]. From the transportation planners' point of view, the automated vehicles equipped with the longitudinal control systems should heavily impact the traffic characteristics, including highway safety, efficiency and capacity because of their more uniform behavior compared with human drivers [Zwaneveld 1998].

Before the longitudinal control systems are widely equipped on automated vehicles, their impacts on string behavior and flow characteristics need to be carefully investigated.

Otherwise traffic congestion may become worse instead of being better.

Two of the most important macroscopic behaviors of ACC vehicles are string stability and traffic flow stability. Such a distinction between the two stability has been first recognized by D. Swaroop [Swaroop 1999]. The string stability of a string of vehicles refers to a property in which spacing errors are guaranteed not to amplify as they propagate towards the tail of the string [Swaroop 1994b[START_REF] Santhanakrishnan | [END_REF]]. This property ensures that any spacing error present at the head of the string does not amplify into a large error at the tail of the string. A general method to evaluate string stability is to examine the transfer function from the spacing error of the proceeding vehicle to that of the following vehicle. If the infinite norm of this transfer function is less than 1, string stability is ensured [Swaroop 1996, Wang 2004a].

Traffic flow stability refers to a macroscopic property associated with speed and density of traffic in a section of a highway. It guarantees that density disturbances attenuate as they propagate upstream. For example, density disturbances may occur as a result of a sudden influx of vehicles from a ramp. An unstable traffic flow characteristic would imply that such density or velocity disturbances are felt at every point upstream from the source without attenuation. A traffic flow is said to be stable when the slope ∂Q/∂ρ is a positive value, where, Q is the traffic flow and ρ denotes the traffic density.

Besides, the early ACC systems are designed mainly for applications where the vehicle speed is higher than 30 km/h and, consequently are not useful in traffic jams or urban driving. This is mainly because the conventional ACC systems only manage the throttle pedal. In an extended version, the brake pedal also needs to be controlled. Stop&Go cruise control system, which includes both throttle and brake control systems, were introduced to overcome this drawback.

Based on the above discussions, the upper level controller, which includes the specific spacing policy and the associated control laws, should be designed to achieve the following objectives:

1. It should guarantee string stability in a string of vehicles.

2. The spacing policy should lead to increased traffic capacity and a stable traffic flow up to a higher characteristic traffic density.

3. The control effort required by the control law should be within the vehicle's traction/braking capability.

4. It should be used for a wide range of speed for vehicle operations in highway, which includes low and high speed scenarios.

The rest of this section is organized as follows: at first the theories of platoon string stability and traffic flow stability, which are required in the design upper level controller, are introduced; next, the traditional spacing policy (CTG: Constant Time Gap policy) will be evaluated; then, the proposed spacing policy will be introduced. It will be evaluated by the objectives that we proposed in this section and will be compared also with the CTG policy. Finally, some simulation results will be given.

String stability

For an interconnected system, such as a platoon of automated vehicles, stability of each component system itself is not sufficient to guarantee a certain level of performance, such as the boundedness of the spacing errors for all the vehicles. This is reasonable because our research object is a string of vehicles instead of only one vehicle. Therefore, besides the individual stability of each vehicle, another stability criterion known as the string stability is also required [START_REF] Horowitz | [END_REF], Rajamani 2006].

Definition of string stability

String stability is generally defined as the spacing errors are guaranteed not to amplify as they propagate towards the tail of the string. In fact, the conditions for string stability were already provided in the works of Sheikholeslam and Desoer [Sheikholeslam 1990],

which indicated that the norm magnitude |G(jω)| < 1 and the impulse response g(t) > 0 of the linear operator G(s), where G(s) maps the deviation in the assigned distances between vehicle i and i -1.

The more formalized and generalized definition of string stability was given by Swaroop [Swaroop 1996]. The mathematical definitions for string stability, asymptotically stability, and l p string stability were made. We use the definitions proposed by Swaroop [Swaroop 1994a, Swaroop 1996]. At first, we use the following notations:

f i (•) ∞ , denotes sup t≥0 | f i (t) |, and f i (0) ∞ denotes sup i |f i (0)|. For all p < ∞, f i (•) p denotes ( ∞ 0 |f i (t)| p dt) 1 p and f i (0) p denotes ( ∞ 1 |f i (0)| p ) 1 p . Consider an interconnected system: ẋi = f (x i , x i-1 , • • • , x i-r+1 ) (3.1) where i ∈ N, x i-j ≡ 0 ∀i ≤ j, x ∈ R n , f : R n × • • • × R n r times → R n and f (0, • • • , 0) = 0.
Definition 3.1 (String stability). The origin

x i = 0, i ∈ N of (3.1) is string stable, if
given any > 0, there exist a δ > 0 such that :

x i (0) ∞ < δ ⇒ sup i x i (•) ∞ < Definition 3.2 (Asymptotically (exponential) stability). The origin x i = 0, i ∈ N of (3.1
) is asymptotically (exponentially) string stable if it is string stable and x i (t) → 0 asymptotically (exponentially) for all i ∈ N.

A more general definition of string stability is given in follow:

Definition 3.3 (l p String stability). The origin x i = 0, i ∈ N of (3.1) is l p string stable if for any > 0, there exist a δ > 0 such that :

x i (0) p < δ ⇒ sup i ∞ 1 |x i (t)| p 1 p <
It is clear that Definition 3.1 can be obtained as l ∞ string stability of Definition 3.3.

The generalized string stability implies uniform boundedness of the system states if the initial conditions are uniformly bounded.

String stability in vehicle following system

In the case of vehicle following system, such as a vehicle platoon as shown in Fig. 3.2, for the ith vehicle, x i is the location measured from an inertial reference, as shown in the same figure. We define the spacing error for the ith vehicle as:

δ i = x i -x i-1 + S i (3.2)
where S i is the desired spacing measured from vehicle i -1 to i, and it includes the preceding vehicle's length W i -1. A sufficient condition for string stability is that [Swaroop 1994a, Swaroop 1996]:

δ i ∞ ≤ δ i-1 ∞ (3.3)
If we define the transfer function from δ i-1 to δ i to be

Ĥ(s) = δ i (s) δ i-1 (s) (3.4)
Chapter 3. Longitudinal Control for Vehicle Platoons where δ i (s) is the Laplace transform of δ i (t). Let h(t) be the impulse response of Ĥ(s), thus the condition (3.3) for string stability becomes

h(t) 1 ≤ 1 (3.5)
due to the result in system theory that

h(t) 1 = sup x∈L∞ δ i-1 ∞ δ i ∞ (3.6)
Then the condition of (3.5) can be replaced by

Ĥ(s) ∞ ≤ 1 and h(t) > 0 (3.7)
This transformation from (3.5) to (3.7) is realized by the following Lemma:

Lemma 3.4 ( [Swaroop 1994a])
If h(t) > 0, then all the Input/Output induced norms are equal.

Proof:

Let γ p be the pth induced norm, i.e.

γ p = sup x∈Lp y p x p (3.8)
Then, from linear systems theory

|H(0)| ≤ Ĥ(jω) ∞ ≤ γ p ≤ h 1 (3.9) If h(t) > 0 then | Ĥ| = h 1 ⇒ γ p = h 1 , as shown below, | Ĥ(0)| = | ∞ 0 h(t)dt| ≤ ∞ 0 |h(t)|dt = h 1 Remark 3.5 As mentioned above, if h(t) > 0, and Ĥ(s) ∞ ≤ 1, results in string stability. However, if h(t) is not positive, then the condition Ĥ(s) ∞ ≤ 1 ⇒ δ i-1 2 ≤ δ i 2
, which means L 2 string stability. L 2 string stability ensures the energy in the signal δ i-1 (t) is less than the energy in the signal δ i (t), but it is not sufficient for the strong condition of δ i-1 ∞ ≤ δ i ∞ for string stability. Therefore, L 2 string stability is less suitable for this type of applications.

We use the condition of (3.7) instead of (3.5), because it is much easier to design the control system to ensure (3.7) is satisfied rather than to design the system to ensure (3.5) is satisfied. In the later Sections, the condition of (3.7) will be used to evaluate the proposed spacing policy for the vehicle longitudinal control system.

Traffic flow stability

As In the late of 1980s, with the development of vehicular technology, the first generation of cruise control systems were developed from the point of view of driving comfort and safety. After that, Adaptive Cruise Control (ACC) system appeared, which is an extension of the standard cruise control system. As the ACC vehicles have the more similar longitudinal behaviors than the manual derived vehicles, the traffic dynamic characteristic of the automated traffic flow is thus deeply influenced by the ACC systems. Therefore, in the design of ACC control systems, its influence on the traffic dynamics is an important aspect to be considered.

Definition of traffic flow stability

The conception of traffic flow stability was proposed to evaluate the traffic flow dynamics [Swaroop 1999]. Traffic flow stability refers to the evolution of density and velocity disturbances. In this work, for the sake of simplicity, a one-lane highway will be considered with every vehicle on the highway is equipped with an ACC system. The traffic flow is modeled as a continuum.

Let x denotes the position of a vehicle at time t, i.e., x = x(X, t), where X is the state of the vehicle at some initial time, t 0 . The velocity of the vehicle is given by v(x, t). ρ(x, t)

denotes the traffic density. Then the traffic flow stability is defined as [Swaroop 1999]: In the following sections, the above definition will be used to judge traffic flow stability of the automated highway traffics.

Effect of spacing policy on traffic flow stability

As mentioned in previous sections, the spacing policy denotes the desired spacing that an automated vehicle attempts to maintain with respect to the preceding vehicle. Clearly, spacing policy has an important effect on the traffic flow dynamics by regulating the spacing of the ACC vehicles. In order to analyze its effect on the traffic flow dynamics, consider the spacing policy is a function of the vehicle velocity,

S = g(v) (3.10)
where, S is the desired spacing for the controlled vehicle. Then, this relation can be translated as the following equation:

1 ρ = g(v) ⇒ v = h(ρ) := g -1 1 ρ (3.11)
Similarly to the fluid dynamics, traffic volume at any point is given by

Q = ρv = ρh(ρ) (3.12)
According to the conservation of mass equation, the evolution of traffic density is According to the above discussions, we can draw the conclusion that if the condition c > 0 or ∂Q/∂ρ > 0 is satisfied, then the traffic flow is a stable traffic flow, otherwise, an unstable traffic flow. This conclusion will be used in the subsequent sections in the design and evaluation of different spacing policies.

Evaluation of the Constant Time Gap spacing policy

At present, the most common spacing policy used by researchers and vehicle manufactures is the constant time-gap (CTG) spacing policy [Wang 2004a]. Much research works have been done in the study of ACC system with CTG spacing policy [Marsden 2001[START_REF] Nouveliere | [END_REF][START_REF] Ioannou | [END_REF]. And some manufactures have more recently launched their ACC systems based on CTG algorithm [McDonald 1999]. However, there still exists some problems in the use of CTG algorithm:

• Using the CTG policy, the current cruise control system isn't suitable for use in high-density traffic conditions, and the operating speed should be higher than 40 km/h [Marsden 2001[START_REF] Zhao | [END_REF]].

• Using the standard CTG policy, traffic flow stability cannot be ensured [Swaroop 1999].

The Traditional Constant Time-gap (CTG) Spacing Policy

The constant time-gap spacing policy is given by:

S i = L + h ẋi (3.17)
where S i denotes to the desired inter-vehicle spacing for the ith vehicle, L is a constant that includes the vehicle length W i-1 of the preceding vehicle as shown in Fig. 3.5. h is the headway time.

i th W i-1 S i X i-1 X i+1 X i Figure 3.5: Vehicle platoon
The spacing error under the CTG policy is given by:

δ i = ε i + L + h ẋi (3.18)
where

ε i = x i -x i-1 .
The corresponding longitudinal controller ensuring that the spacing error converges to zero is described by

ẍi_des = - 1 h ( εi + λδ i ) (3.19)

String stability of CTG

In Section 3.2, we have shown that the ACC control architecture is designed to be hierarchical, with an upper and a lower level controller, as shown in Fig. 3.1. The upper level controller determines the desired acceleration or speed for the controlled vehicle, while the lower level controller decides the throttle and brake commands required to track the desired acceleration or speed. The behavior of this two level control system can be approximated by a first-order system:

τ ȧi + a i = a i_des (3.20)
where a i is the vehicle's actual acceleration, a i_des is the desired acceleration, and τ is a constant time lag.

Substituting a i_des from equation (3.19), we get τ ...

x i + ẍi = - 1 h ( εi + λδ i ) (3.
δ i -δ i-1 = ε i -ε i-1 + h εi (3.24) Differentiating equation (3.24) twice, δi -δi-1 = εi -εi-1 + h ... ε i (3.25)
Using equation (3.23) to rewrite equation (3.25), we obtain hτ ...

δ i + h δi + (1 + λh) δi + λδ i = δi-1 + λδ i-1 (3.26)
Taking the laplace transform of equation (3.26), we get

δ i δ i-1 (s) = s + λ hτ s 3 + hs 2 + (1 + λh)s + λ (3.27)
By using the above transfer function, the string stability of CTG system can be analyzed. Substituting s = jω and evaluating the magnitude of the above transfer function, In fact, the requirement Ĥ(s) ∞ ≤ 1 can be satisfied by choosing a sufficient big value of h based on equation (3.28). However, for the specification that impulse response h(t) > 0, there are no results available that provide a direct design method for ensuring this specification, and it needs to be studied further. The results in [Darbha 2003] show an indirect method for this issues, two necessary conditions are proposed for the non-negative impulse response, 1. The dominant poles of the system should not be a complex conjugate pair.

2. There should not be any zeros of the system that are completely to the right of all poles of the closed-loop system.

Traffic flow stability of CTG

For the CTG policy, the steady-state spacing is given by S = L + hv, where v is aggregate highway velocity, and h is the headway time, this lead to a steady density of

ρ = 1 (L + hv) (3.29)
Solving v in terms of ρ from (3.29), one can get v = (1 -ρL) (ρh), and the traffic flow is

Q = ρv = (1 -ρL) h (3.30)
As we have shown in section 3.3.3.2 that the condition ∂Q/∂ρ > 0 should be satisfied for a stable traffic flow. In equation (3.30) the variable ∂Q ∂ρ = -L h is a negative value, which means the CTG policy is always traffic flow unstable.

Remark 3.7 The results of Shrivastava and Li [Shrivastava 2000, Li 2002] have shown that the CTG policy could ensure traffic flow stability, which appeared to be contrary to the above conclusion that we have just made. In fact, according to [Shrivastava 2000,Li 2002],

traffic flow stability of the CTG system is proofed to be stable in a circular highway without inlets and exits. The premise of road condition can be viewed as a boundary condition for the stability of CTG system. However the specification ∂Q/∂ρ > 0, which we used in this work, can be viewed as a condition for stable traffic flow without any boundary conditions.

Thus the traffic stable with this condition is called unconditional traffic flow stability.

Proposed Safety Spacing Policy

According to the above evaluation results of the traditional CTG policy, and comparing them to the design objectives for the upper level controller proposed in section 3.3.1, it is shown that the CTG policy is not appropriate for the Adaptive Cruise Control systems.

In order to overcome the shortcomings of the CTG policy, we propose a new spacing policy named "Safety Spacing Policy", which considers both the information of the controlled vehicle's state (speed, inter-vehicle spacing) and capacity (braking capacity, reaction time) to maintain a safety headway from the vehicle ahead. In addition, the specifications of string stability and traffic flow stability will also be considered in the design of this new policy. It is expected that this new spacing policy would satisfy the design objectives that we proposed in section 3.3.1.

To begin with, a vehicle platoon is shown in Fig. 3.5. We assume that the following information is available for the controlled vehicle:

• A1: The relative velocity and relative distance between the i -1th and ith vehicle,

i.e. v i-1 -v i , x i-1 -x i -W i-1 .
• A2: The velocity of the controlled vehicle i, i.e. v i .

• A3: The braking capacity j i of controlled vehicle.

Remark: Currently available on board radar and sensors can provide measurements given in A1, A2. And the value of A3 can be obtained from the vehicle manufactures or by experiments.

By using the measurements given in A1-A3, we propose the following safety spacing policy (SSP).

S i = L + t d ẋi + γd i (3.31)
where :

• S i : Desired inter-vehicle spacing for the ith vehicle.

• L: A constant distance that includes the vehicle length W i-1 of the preceding vehicle.

• t d : The time delay of the longitudinal control system. It consists of two components:

One is the time used for recognizing a hard brake in the controller. In current system, the duration of this time delay is about 60ms; The other is the time delay in the brake hardware, which ranges from 10 to 100 ms. Thus the total time delay ranges from 70 to 160ms [Hedrick 1996].

• d i : The ith vehicle's braking distance on horizontal and dry pavement. Let j i be the average deceleration value of the ith vehicle during the maximum brake action, which is always a negative value. Then

d i = -ẋ2 i /(2j i ).
• γ: Safety coefficient, a parameter that could be selected by the driver, which is relevant to road condition and vehicle position in a platoon. For instance, we can select a bigger value of γ if the road surface is wet. In addition, considering the leading vehicle has the greatest impact on safety of a platoon, we give a bigger value of γ for the leading vehicle to improve platoon safety, while we select a smaller γ for the following vehicles thus to improve traffic capacity. In Fig. 3.7, the inter-vehicle spacing is shown as a function of velocity under different Safety coefficient γ. The using parameters are shown in Table 3.1.

δ i = ε i + L + t d ẋi + γd i (3.32)
where

ε i = x i -x i-1 .
In order to ensure the error δ i converges to zero, the dynamic of δ i is set as δi = -λδ i , where λ is a positive control gain. Differentiating (3.32), the desired acceleration with the SSP can be obtained as

ẍi_des = -(λδ i + εi ) (t d - γ j i ẋi ) (3.33)

String stability of SSP

At first, in Section 3.2, we have shown that the ACC control architecture is designed to be hierarchical, with an upper and a lower level controller, as shown in Fig. 3.1. The upper level controller determines the desired acceleration or speed for the controlled vehicle, while the lower level controller decides the throttle and brake commands required to track the desired acceleration or speed. The behavior of this two level control system can be approximated by a first-order system:

τ ȧi + a i = a i_des (3.34)
where a i is the vehicle's actual acceleration, a i_des is the desired acceleration, and τ is a constant time lag. Then, this first order system will be used in the analysis of the string stability of the SSP system.

Recall equation (3.7), the condition for the string stability of vehicle following system is :

Ĥ(s) ∞ ≤ 1 and h(t) > 0 (3.35)
where Ĥ(s) is the transfer function relating the spacing errors of consecutive vehicles, Ĥ(s) = δ i (s)/δ i-1 (s), h(t) is the impulse response of Ĥ(s).

In order to investigate the string stability property of the proposed spacing policy, the SSP system is linearized around a nominal velocity v 0 , i.e. v 0,i = v 0,i+1 = v 0 . And the inter-vehicle spacing is equal to the desired spacing R 0

,i = L + t d v 0 -γ 2j i v2 0 .
At a certain moment, the velocity of the leading vehicle is perturbed, thus introduce disturbance to the tail of the platoon. Let v i = v 0 + ∆v i , vi = ∆ vi , and R i = R 0 + ∆R i , Ṙi = ∆ Ṙi , then for linearized systems the transfer function of the spacing error is the same as that of the velocity variation [Zhou 2005]:

Ĥ(s) = δ i δ i-1 (s) = ∆v i ∆v i (s) (3.36)
Combine (3.34) and (3.33), we can get

τ ȧi + a i = - λδ i + εi t d - γ j i ẋi (3.37) Let T v = t d -γ j i ẋi . Rewrite (3.37): τ ȧi + a i = - λδ i + εi T v (3.38)
Under the assumption that deviations from the nominal velocity is small, and the SSP system is linearized around the nominal speed, differentiating (3.38) to obtain

τ äi + ȧi = - λ δi + εi T v (3.39)
Then we get

T v τ ... v i + T v vi + (λT v + 1) vi + λv i = vi-1 + λv i-1 (3.40)
Using the relation vi = ∆ vi that we mentioned above, equation 3.40 can be rewritten as:

T v τ ∆ ... v i + T v ∆v i + (λT v + 1)∆ vi + λ∆v i = ∆ vi-1 + λ∆v i-1 (3.41)
Taking Laplace transforms of (3.41),

∆v i ∆v i-1 (s) = s + λ T v τ s 3 + T v s 2 + (λT v + 1)s + λ (3.42) Substituting s = jω in equation (3.42), ∆v i ∆v i-1 (jω) = λ + jω -T v τ jω 3 -T v ω 2 + (λT v + 1)jω + λ (3.43)
In order to ensure the string stability, the magnitude of the transfer function should no bigger than 1, i.e. ∆v i ∆v i-1 (s) ≤ 1. Then we obtain,

ω 2 + λ 2 (λ -T v ω 2 ) 2 + ω 2 (λT v + 1 -T v τ ω 2 ) 2 ≤ 1 (3.44)
Following algebraic reduction, it can be shown that this inequality constraint is always satisfied if

T v ≥ 2τ (3.45)
i.e. t d -γ j i ẋi ≥ 2τ . Thus, by using the linearization method, one condition for the string stability of the nonlinear spacing policy was obtained. For example, for the set of values as t d = 0.1s, τ = 0.1s, γ = 0.4, and j i = -7.32m/s 2 , the condition (3.45) is satisfied if One can find, the condition h(t) > 0 is not satisfied when the velocity v = 2 m/s, however, with the increasing of vehicle velocity, when velocity is higher than 5 m/s, the for the condition Ĥ(s) ∞ ≤ 1, thus, in our SSP system, the final string stability condition is v > 5 m/s.

v ≥ 1.83m/s.

Traffic flow stability of SSP

In the traffic analysis, it is assumed that all the automated vehicles possess the same braking capacity j. Recall the expression of the SSP policy given in equation (3.31),

S i = L + t d v i - γv i 2 2j
Then the traffic density at steady state is given by

ρ = 1 L + t d v -γv 2 (2j) (3.
Q = ρj t d -t d 2 + 2γ(L -1/ρ)/j γ (3.48) So that ∂Q ∂ρ = t d j γ - jρ[t d 2 -2 γ j ( 1 ρ -L)] + γ γρ t d 2 -2 γ j ( 1 ρ -L) (3.49)
In order to show the advantages of SSP than CTG in the aspect of traffic flow stability, the Q -ρ (Traffic flow -Density)curves of the two policies are shown in Fig. 3.9. The parameters' values for the SSP are shown in Table 3.1, and the safety coefficient γ = 0.4 is set for the SSP system. For the CTG system, the relationship between Q and ρ is shown in equation (3.30), and the time headway h = 1.5 s is used fot the plot in Fig. 3.9.

One can find that the SSP system holds a stable traffic flow (∂Q/∂ρ > 0) when the density ρ is below a critical density ρ c (≈ 0.069 vehicle/m). However, the CTG system is always traffic unstable for ∂Q/∂ρ < 0.

Traffic flow capacity comparison between SSP & CTG

In this subsection, we consider a highway pipe, a single lane highway without entrances and exits and estimate the maximum possible steady state flow in vehicles per lane per hour through such a pipe. We call this the AHS pipeline capacity [Godbole 2000]. Then, the two spacing policies will be compared using lane capacity in vehicles/lane/hour as a In the case of CTG system, the headway time between 1 and 2 seconds has been widely accepted in the former research [Marsden 2001]. Thus, we choose the headway time h l = 2 s for the leading vehicle of a platoon and headway time h f = 1.5 s for all the following vehicles in a platoon. Here, we select a bigger headway time for the leading vehicle in consideration of improving platoon safety, and a smaller headway time for the following vehicles in consideration of improving traffic capacity. Then the line capacity is given by

Q c = 3600v (L + h f v) + 1 N (L + h l v) (3.50)
In the case of SSP system, we assume that all the vehicles have the same braking capacity. Corresponding to the discussion in Section 3.3.5, we let the leading vehicle's safety coefficient γ l = 1 , and for the following vehicles, γ f = 0.4. Then the lane capacity is:

Q s = 3600v (L + t d v -γ f v 2 2j ) + 1 N (L + t d v -γ l v 2 2j ) (3.51)
The lane capacities given by the two equations above are shown in Fig. 3.11 where N in the plot refers to the corresponding platoon sizes. One can find that the SSP system can provide more traffic capacity than the CTG system. When the aggregate traffic velocity is 100 Km/h (27.8 m/s), the SSP system has about 50% more traffic capacity than that of the CTG system.

Furthermore, as we know in the peak-hour traffic, the aggregate traffic velocity drops down due to the increase of traffic density. In Fig. 3.11, it can be found that with the velocity decreases, the capacity of the SSP system increase notably while that of the CTG system decreases gradually. That means the SSP system can relieve congestion in the peak hour while the situation becomes worse by using the CTG system. At the cruise speed In conclusion, the SSP has the following advantages than the tradition CTG policy:

• The SSP can provide stable traffic flow while the CTG policy failed to do so.

• In the high speed operation, the SSP can provide higher traffic capacity than the CTG. At a common cruise speed of 100km/h, the SSP system can provide about 50% more traffic capacity than the CTG system.

• A significant advantage of SSP is that with the traffic speed drops, the traffic capacity increases notably. This characteristic shows that the SSP can be used to relieve traffic congestion in the peak hour. However, the CTG can provide less traffic capacity in low speed than in high speed, which means the traffic situation becomes worse in peak hour.

Simulation tests

In this section, we test SSP vehicle platoon's behavior when the leading vehicle performs a hard brake and then acceleration scenario. The vehicle lateral movement isn't considered in this scenario. Three platoons of 8 vehicles with different braking capacities were considered as shown in Table 3.2, these values as well as the sequence of each vehicle are set randomly. The vehicle's maximum acceleration limit is assumed to be 0.35g. In simulation, all the following vehicles employ the same SSP controller that described in (3.33), and the safety coefficient γ = 0.4 is used. The platoon performs the following manoeuvres, starting from 27m/s with correct inter-vehicle spacing, after 10 seconds, the leading vehicle of the platoon decelerates with an acceleration of -5m/s 2 for 4 seconds, and comes to a significant low speed of 7 m/s. At t = 40s, the leading vehicle accelerates back up to the initial speed with an acceleration of 2m/s 2 . Then we will test the following vehicles' behavior by using the SSP policy.

In order to avoid to get the results which do not exist in the real world, the following assumptions are made in this simulation test:

• In simulations, if the desired following vehicle's acceleration or deceleration calculated from the control law exceeds the vehicle's acceleration/deceleration limits, then the desired value is made to saturate at the appropriate limit.

• To prevent the vehicles from going backwards on highway, assume that the acceleration of each ACC vehicle becomes to zero as soon as the vehicle stops.

• To prevent the inter-vehicle spacing from being negative, the inter-vehicle spacing of two vehicles keeps zero after the two vehicles happen to collide.

Fig. 3.12(a), 3.12(b) show the time histories of the inter-vehicle spacing and the "ideal" control efforts of all the following vehicles in this hard brake and acceleration scenario with the experiment vehicle platoon 1. Fig. 3.12(a) shows that no mater in the deceleration or acceleration manoeuvres each vehicle can keep a safe headway according to its state and capacity, no collision occurs in this scenario. And it can also be found that all the controlled vehicle can be operated within their corresponding decelerate and accelerate capacity in Fig. 3.12(b).

From the above results, along with the analyses of string stability, traffic flow stability and traffic capacity in the previous three subsections, we can find that the proposed SSP can satisfy the four design objectives that we proposed in section 3.3.1. Thus, we can draw the conclusion that the proposed SSP policy can provide good performances both in safety and in traffic capacity for the ACC system. And it has shown better performances than the traditional CTG policy. It is a promising policy to be implemented on ACC vehicle on today's highway.

Remark 3.8 In the case of using Platoon 2 and 3, the similar results as with Platoon 1 could be obtained. So we don't show them respectively.

Lower level control

Introduction

The vehicle longitudinal control system architecture is typically designed to be hierarchical, with an upper level and a lower level controllers as shown in Fig. 3.1 in section 3.2.

In section 3.3, the issue of upper level controller was studied. In this section, the control problems of the lower level controller will be investigated. And then combine with the two level controllers, we will have a complete longitudinal control system for the automated vehicles.

The design objective of the lower level controller is to decide the required throttle and brake commands to track the desired acceleration/speed which is given by the upper level controller. Obviously, the basic elements of the lower level controller are the throttle controller and brake controller. Two main challenges to be envisaged in the lower level controller design are:

• The nonlinearities and uncertainties in vehicle longitudinal dynamics

• Coordination between the throttle and brake controllers (since a good human driver never uses the throttle and brake pedals simultaneously)

To handel with the model nonlinearities and uncertainties, a combined engine and brake control system based on multiple-surface sliding control method is presented in [START_REF] Gerdes | [END_REF]]. The proposed system consists three basic elements: an upper sliding controller that incorporates vehicle acceleration as a synthetic input, a logic switch that chooses between throttle or brake control, and lower sliding controllers for the engine and brake operations. In [Ioannou 1993], fixed gain and gain scheduling PID controllers as well as the adaptive control method are proposed. The controllers are simulated using a The fuzzy logic is also proposed for this subject. In [Naranjo 2006], a throttle and brake fuzzy control system is proposed to perform the ACC+Stop&Go maneuvers. Two separate fuzzy controllers are designed to control the throttle and brake pedals. In order to avoid simultaneous actions of both the pedals, the values of the membership functions of the two controllers are well defined. The constant time gap spacing policy is used to give the desired spacing for the controlled vehicle. This system has been equipped in a two-vehicle platoon. The results show that the automated vehicle behave very similarly to human-driven car and is adaptive to the speed variations.

Since the using of the fuzzy control approach has the main advantages of no requirement of an exact mathematic model of the controlled system, such as vehicles, where the exact engine and brake dynamics are not always available; and it uses the linguistic expressions to represent the human drivers experiences instead of the mathematical expressions [Naranjo 2006, Zhao 2009a]. Inspired by this, we propose a fuzzy logic control system to perform the throtle/brake control, and a logic switch is used to coordinate the two controllers.

Coordinated Throttle and Brake Fuzzy Controller

Coordinated Throttle and Brake Fuzzy Control System Architecture

To cope the design problems of the lower level controller, we propose a coordinated throttle and brake control system as shown in Fig. 3.13.

At first, a fuzzy logic controller is designed for the task of throttle control. The fuzzy input variables are the speed error E v and the acceleration error E acc , and the output variable is the throttle change T h. In order to facilitate the expression in this work, we use the percentage value for the throttle control signals, where 0% means the throttle valve is fully closed, while 100% means fully opened. Then, the current throttle percentage T h(n) is the summation of the throttle change T h(n) and the throttle percentage at the previous time step T h(n -1), where n denotes the time step number of discrete process:

T h(n) = T h(n) + T h(n -1) (3.52)
Second, from the similar consideration, a fuzzy controller is also proposed for the brake control. Since, for a human driver, the fundamental operation logic for the brake pedal is just the opposite to the throttle pedal, we use the same fuzzy controller that is used in the throttle control. The only difference between the two controllers is the output variable of the brake controller brake torque change Br(n) is always negative to the output of the throttle controller T h(n), i.e.

Br(n) = -T h(n) (3.53)
Similarly, the current brake torque percentage is given by:

Br(n) = Br(n) + Br(n -1) (3.54)
where, Br(n) and Br(n -1) are the values of brake percentage at nth and (n -1)th time step respectively, and 0% means no brake action, while 100% means the maximum brake action.

Next, after each fuzzy controller, there exists a saturation block as shown in Fig. 3.13.

The lower and upper limits of these saturation blocks are set to 0 and 1 respectively, which ensure the throttle and brake percentage do not exceed the range of [0,1].

Finally, a Switch Logic Block is designed to avoid the simultaneously operation of throttle and brake, and to ensure the smooth coordination between the two controllers.

Throttle and Brake Fuzzy Controllers

We begin with the throttle controller. The base knowledge of the fuzzy throttle controller, formed by the inputs, outputs, rules and inference method, is detailed as follows.

Input and output variables: The two fuzzy inputs variables, acceleration error E acc and speed error E v , are given by:

E acc = a des -a (3.55) E v = v des -v (3.56)
where, a des and v des denote the desired acceleration and speed which are given by the upper level controller. a and v mean the real acceleration and speed of the controlled vehicle, which can be obtained from the on board sensors. The output variable of the throttle controller is the throttle change (%): T h.

We define five fuzzy sets for both the two inputs, as Nb, Ns, Null, Ps and Pb. And also five fuzzy sets for the output, as D_inten, D_sof, Null, A_sof and A_inten, described as follows: The proposed fuzzy control rule base is shown in Table 4.5.

{E acc , E v } = {N b, N s, N

Fuzzy Reasoning Process:

The fuzzy reasoning process can be divided into three steps: fuzzification, inference engine and defuzzification. In this work, we use triangle and trapezoids shaped membership function for the fuzzification process as shown in Fig. 3.14.

The Mamdani's inference method is employed to solve the fuzzy implication. And we use the centroid method for defuzzification process. In the previous subsections, we designed the throttle and brake controllers, which can be considered as two separate systems working simultaneously. Now, the logic switch is designed to coordinate the operations of the throttle and brake.The basic functions of the logic switch are:

• avoid simultaneous operation at both throttle and brake pedals

• before step down the throttle, it needs to step off the brake, vice versa

• avoid frequent switchings from one pedal to the other

To achieve these functions, our approach is to synthesize the information of speed A "Keep region" is designed to avoid frequent switchings between the throttle and brake actuators. In this region, the Output scheme always keeps in accordance with its current state, as shown in Fig. 3.16. We can find that the procedures from Zero state to T h_con or to Br_con are forbidden when the speed error falls into [-0.1, 0.1], hence to avoid frequent switchings between the two controllers.

error E v (E v = v des -v)
In the Acceleration region, the switch logic works in a similar way as in the Deceleration region. Due to the page limit, we do not give the details. Finally, the above described switch logic can be represented by the flowchart shown in Fig. 3.17. It should be noted that in the process of judging the current state of throttle (brake) pedal, a threshold value of 0.01 is used. It means if the current value of throttle (or brake) value is bigger than 0.01, i.e. T h_s > 0.01, then the current state is throttle (or brake) active: T h_a (or Br_a). If neither of them is bigger than 0.01, than we consider the current sate as ZERO.

Simulation tests

A two-vehicle platoon is considered. The lead vehicle is a manually-driven vehicle, and the following vehicle is an automatic vehicle equipped with the proposed longitudinal control system, which includes the upper level controller that we proposed in equation (3.33) and the lower level controller that we proposed in 3.4.2.2.

The leading vehicle performs a series of operations to change its longitudinal speed, then we test the performances of the longitudinal control system by evaluating the following vehicle's speed, acceleration and inter-vehicle spacing (headway distance), as well as the associated errors, etc. The simulation scenarios are designed to be rather "complex", which include high and low speed cruise, acceleration and deceleration. Furthermore, since the road grade can be regarded as the external disturbances, extended simulations with inclined road conditions are also carried out to test the robustness of the proposed control system.

Longitudinal vehicle model for simulation

A vehicle longitudinal car model is shown in Fig. 3.18 [Ioannou 1993]. There are two control inputs as throttle command and brake command, and the outputs are the vehicle speed and acceleration. The vehicle lateral movement is not considered in this model. Recall the vehicle longitudinal dynamic equation (2.43),

ẍ(m + J wf + Jwr r 2 ef f ) = 1 r ef f (T e ΨR g R f -T b -T y ) - 1 2 ρC d A F V x 2 -mg sin(α)
Then, the vehicle model shown in Fig. 3.18 can be described by the vehicle longitudinal simulation model shown in Fig. 2.15, which has been developed and validated in section 2.3.3.

Horizontal road condition

The horizontal road condition is first considered. The simulation scenario is described as follows: at beginning, the two vehicle run at a constant speed of 10m/s and the following vehicle has 5.6m headway spacing from the leader. From t = 5s to t = 17s , the leading vehicle's speed is gradually increased to a high speed of 26 m/s, and then keeps this speed till to t = 30s. After that, it begins to decelerate, at t = 42s, the speed is decreased to 5m/s. Successionally, from t = 42s to t = 53.3s, the leading vehicle accelerates back to a high speed of 20 m/s, and then keeps this speed. The profile of the leading vehicle's and3 .22(c) show the final control results of the throttle, the brake and the gear shift operations respectively. We can find that the throttle and the brake work coordinately. There is neither simultaneous operations nor frequent switching between the two actuators during the entire period. In addition, the operations of the throttle and brake are rather smooth except several little oscillations in the throttle results.

In fact, the main reason for these little oscillations is the gear shift-up operations in the hydraulic automatic transmission as shown in Fig. 3.22(c).

Inclined road condition

In this simulation, the road grade is considered. We use the same two-vehicle platoon and the same leading vehicle scenario that we used in the former simulation. The road grade is described as follows: for the following vehicle, from t = 0s to t = 5s, the road is horizontal, from t = 5s to t = 25s, it is a downhill with a grade of -2%, from t = 25s to t = 55s, the road becomes to a uphill with a grade of 3%, after that, the road becomes to horizontal again. The road grade profile is given in Fig. 3.23(a).

The results of the following vehicle's speed error and spacing error are given in Fig. 3.23(b),3.23(c). It is shown that good speed tracking and space keeping are achieved by the throttle/brake fuzzy controller even with the road disturbances. The maximum speed error is less than 0.2m/s and that of the spacing error is less than 0.25m.

The control efforts of throttle and brake are shown in Fig. 3.24(a), 3.24(b) respectively.

It is shown that the proposed control system is adaptive to the variations of road grade.

The throttle and brake controller work coordinately.

Conclusion

In this chapter, we concentrated on the vehicle longitudinal control system design. The longitudinal control system architecture was designed to be hierarchical, with an upper level controller and a lower level controller.

In the upper level controller design, the spacing policy and its associated control law were designed with the constrains of string stability, traffic flow stability and traffic flow capacity. A safety spacing policy (SSP) was proposed, which uses both the information of vehicle state and vehicle braking capacity to determine the desired spacing from the preceding vehicle. It was shown that the proposed SSP could ensure both the string stability and traffic flow stability. In addition, through the comparisons between the SSP and the traditional Constant Time Gap (CTG) policy, we could find the obvious advantages of the SSP system in improving traffic capacity especially in the high-density traffic conditions.

In the lower level controller design, a coordinated throttle and brake fuzzy controller was proposed. This controller can deal with the nonlinearity in the engine and brake dynamic systems. And a logic switch was designed to avoid frequent switching between the two actuators and simultaneous operations of them.

The above proposed longitudinal control system was validated to be effective through a series of simulations. In the past two decades, the Automated Highway System (AHS)-with the main goal of eliminating traffic congestion and enhancing traffic safety -has seen significant progresses.

Vehicle lateral control is one of the crucial subsystems for the AHS vehicles. It senses the road centerline using a road based reference system and other on-board sensors and generates steering command to keep the vehicle running along the desired path or steer the vehicle into an adjacent lane. The design requirement of vehicle lateral control is to ensure small lateral errors and small relative yaw angles while maintaining ride comfort under different conditions. Lane-keeping and lane-changing are the two basic functions of vehicle lateral control system [START_REF] Huang | [END_REF], Shladover 1991b]. A lane keeping system automatically controls the steering to keep the vehicle in its lane and also follow the lane as it curves around. In [START_REF] Fenton | [END_REF]], Fenton R.E. and Selim I designed a velocity-adaptive lateral controller using an optimization approach. The resulting controller, which is nonlinear with velocity, requires full-state feedback and thus an observer is included. In [Choi 2001], the vehicle is steered to follow the reference yaw rates which are generated by the deviations of lateral distance and the yaw angle between the vehicle and the reference lane. A PI controller was designed to minimize the error between the reference yaw rate and the measured one. In [START_REF] Taylor | [END_REF]], three vision-based lateral control strategies: lead-lag control, full state feedback and input-output linearization were introduced and compared through a series of experiments. Although these unique model based approaches can lead to acceptable control results, their performance may be too sensitive to model mismatch and unmodeled dynamics. Besides, some controllers such as sliding mode solutions in [Zhang 2000], H-infinity controller in [START_REF] Chaib | [END_REF]], and the self-turning regulator in [Netto 2004], appear rather complex for realtime embedded control of autonomous vehicles. The lane changing system automatically steers the vehicle from the current lane to an adjacent lane. In fact, lane changing and lane keeping maneuvers become virtually identical when the lateral sensor can measure its location in both lanes. One major solution is Look-ahead lateral reference/sensing system (e.g. machine vision system). It can provide a long and wide range measurement of vehicle lateral displacement. By using this measurement, the lateral controller mimics human driver's behavior to perform the lane changing maneuver, see [START_REF] Taylor | [END_REF][START_REF] Lee | [END_REF]. However, the reliability of machine vision system is susceptible to variations in light or inclement weather conditions. The fact that Look-down lateral reference/sensing system (e.g. magnetic markers installed in the center of highway) improves the reliability of the sensing system can be another solution. But it suffers from the small sensor range. In this case, the lane changing control problem becomes complicated as the lateral sensing system cannot sense both lanes and the vehicle must travel a certain distance without seeing the road reference system.

The virtual desired trajectory (VDT) for a lane change operation is then designed considering passenger's ride comfort and transition time. Four candidate trajectories as (1) circular trajectory (2) cosine trajectory (3) 5th order polynomial trajectory, and ( 4) trapezoidal acceleration trajectory were evaluated using the transition time as a performance index, the lateral acceleration and jerk as constraints, and vehicle speed as a design parameter. The trapezoidal acceleration trajectory is selected to be the optimal trajectory [Chee 1994[START_REF] Hedrick | [END_REF]]. By using VDT, the lane change maneuver is then investigated as a lane tracking problem. In this way, we consider using an uniform control algorithm to perform the lane tracking tasks for both the lane keeping and the lane changing, so as to make the lateral control system simpler and more compact.

Considering the vehicle lateral dynamic system is a typical system where driving models, sensorial information, objectives, constraints, and control actions are under uncertainty, see [Naranjo 2008], in this work, a multi-model fuzzy controller is proposed. We choose this method for two main reasons. On one hand, there are two main advantages in fuzzy logic control: (1) The possibility of effective usage of drivers' knowledge and skills using linguistic control rules. ( 2) The lack of requirements for a quantified model of the control vehicles, see [Lee 1999]. In [START_REF] Kamel | Fuzzy controller for lateral guidance of busses[END_REF], the authors have proposed a knowledge-based fuzzy controller for lateral guidance of buses during final approach, which involve a nonlinear model and uniquely 40 rules. On the other hand, the multi-model control appears as a powerful technique to deal with complex, non-linear and/or ill-defined systems, and is a potential solution for systems with large parameter variations. In [EL KAMEL 2000a, EL KAMEL 2000b], the multi-model approach was studied, and a multi-model controller for the vehicle longitudinal control has been suggested [START_REF] Kamel | UML-Based Design and Fuzzy Control of Automated Vehicles[END_REF]. Therefore, we propose a multi-mode fuzzy controller, and expect to combine the strong points of these two methods.

Based on the above discussions, the following design objectives are proposed for the vehicle lateral control system:

1. It can provide a framework in which the divers lateral operation scenarios can be performed (such as lane keeping, lane changing, overtaking...) 2. It can ensure small lateral errors and small relative yaw angles while maintaining ride comfort under different operations.

3. It is robust to variations of vehicle parameters (such as velocity, load mass, tyre cornering stiffness, road conditions ... )

The following of this chapter is organized as follows: section 4.2 introduces the basic theory of multiple model approach. In section 4.3, the lateral control system architecture is presented. The vehicle lateral dynamics is analyzed in section 4.4. Section 4.5 illustrates the design of 3 lateral controllers: PID with anti-windup, fuzzy controller, and multi-model fuzzy controller. Simulation tests are given in section 4.6.

Methodology-Multiple model approaches

Introduction

With the increasing complexity of process plant, vehicles and other engineered systems, the task of controller design for these complex systems is obviously a difficult problem. For such a situation, Zadeh has described the principle of incompatibility: "As the complexity of a system increases, our ability to make precise and yet significant statements about its behaviour diminishes until a threshold is reached beyond which precision and significance (or relevance) become almost mutually exclusive characteristics [Zadeh 1973]." One obvious result that we can drive from this principle is that models and analysis of complex systems will be less precise than for simple systems. Inspired by this, it appears an idea that we could look for other model representations and tools that can make use of less precise system knowledge than the traditional approaches which worked well for low and medium complexity modelling and control problems in the past. This idea just represents the trend in the filed of intelligent control where fuzzy logic, neural networks, expert systems, etc, are being developed [START_REF][END_REF], Åström 1992[START_REF] Antsaklis | [END_REF].

A common experience in daily life, as well as in engineering fields, to solve complex problem is the divide-and-conquer strategy, which means a complex problem can be divided into a number of simpler subproblems that can be solved independently, and these individual solutions yield the solution of the original complex problem. This strategy can be then applied in the modeling or control problems for complex systems. A complex system (nonlinear or time-varying) can be divided into a number of simpler subsystems, then the solutions for each "local" subsystems compose the solution for the global system. This is the principle of the multiple model approaches. One of the key to successful applying this approach is to find the appropriate axes along which the problem can be partitioned.

One important approach to realize the partition is the operating regime approach.

The basic of the operating regime approach is to partition the operating range of the system thus to solve modeling and control problems. The operating regime approach leads to multiple model or multiple controller approaches, see Fig. 4.2 [Murray-Smith 1997].

We can see different local models or controllers work under different operating conditions, and a supervisor or scheduler will coordinate these local models or controllers. Then, the operating regime approach and multiple model/controller approach will be introduced in the subsequent sections. or controllers. In fact, the combination process is to decide when and how to "switch" between the local models or controllers. In this process, the problems of the overlap between the operating regimes, and whether a sudden switch of a smooth transition should be addressed. In previous literatures, the methods of mode switching, finite state automata, interpolation methods, fuzzy logic, and probabilistic approaches were proposed as the possible solutions for the combination of the local models [START_REF] Hilhorst | [END_REF], Zhang 1994, Johansen 1993b, Zadeh 1973[START_REF] Jacobs | [END_REF]]. In the following of this subsection, we will take the mode switching and interpolation method for instance to illustrate how the combination process works.

Hard partitions and model switching

The basic idea of hard partitions is that at each operating point, there exist exactly one local model or controller as a deterministic function of the operating point. In this condition, the mode switching method is always employed. For example, a complex system can be decomposed into 4 operating regimes numbered from 1 to 4, see Figure 4.6. For each operating regime i, i ∈ 1, 2, 3, 4, there is a corresponding local model, named as f i .

Then the total control system could be realized by using a number of logical statements of the form

If x 1 is HIGH, AN D x 2 is LOW,
T HEN the system is operating in the Regime 4 (4.1) In practice, the type of hard partitions operating regime based models or controllers can be implemented using the methods from the simple discrete logic to sophisticated expert systems. A supervisory system based on discrete logic that supervises the traditional control systems to handle various situations, such as start, shut down, product change, has become the standard approach to dealing with wide operating range plants in manufacturing industry.

To give a general description of this method, we assume a modeling problem is a static function approximation problem, where the local models f 1 , f 2 , • • • f n are known for each operating regime. The operating regimes must cover the full operating range, and have not overlap between them. Then the global approximation is

f (u) = n i=1 f i (u)r i (u) (4.2)
where r i (u) is the characteristic function for the set of points that defines the operating regime with index i.

Architecture of lateral control system

operating regimes, and the weighting functions satisfy

n i=1 ρ i (u) = 1 (4.4)
for all u. In the case fuzzy logic inference, then

ρ i (u) = r i (u) n j=1 r j (u) (4.5)
The function r i is the membership function for the fuzzy set that represents the operating regimes with index i.

Conclusion of multiple model approach

In order to deal with the increasing complexity of process plant, the multiple model approach provides an effective method. Inspired by the "divide-and-conquer " strategy, a complex system (nonlinear or time-varying) can be divided into a number of simpler subsystems, then the solutions for each "local" subsystems compose the solution for the global system. This is the principal strategy of the multiple model approach. Two key steps to successful applying this approach are: find the appropriate axes along which the problem can be partitioned; decide when and how to "switch" between the local models or controllers.

Architecture of lateral control system

The architecture we adopted for vehicle lateral control system is base on a two-level control model [Naranjo 2008]. This architecture is also inspired by Halle's architecture [START_REF] Halle | A collaborative driving system based on multiagent modelling and simulations[END_REF]]. The resulting architecture represents the basic human driver's behavior in vehicle lateral operations, as shown in Fig. 4.8.

The intelligent sensing module gets the information from sensors for speed, acceleration, yaw rate, lateral displacement etc. The planning module is a decision-making module. It receives and checks all the sensing data, then selects the right operation mode (lane keeping or lane changing) to continue the automatic driving. Usually, the planning module decides the vehicle keeping in its lane by using the road reference/sensing system. When a lane changing operation starts, it changes the road reference to the VDT, and then the lane changing controller stars to control the vehicle to trace the VDT. As the VDT is designed with consideration of ride comfort and transit time, the changeover between the two control modes is then assured to be smooth and efficient.

The module of upper level controller receives the decision from the planning module and uses the sensor data to give out the desired steering angle for the automated vehicle. A multi-model fuzzy control algorithm is designed for the lane tracking tasks in both the lane keeping and lane changing controllers. In our work, there are two major differences between the lane keeping and lane changing controllers. The first is that the two controllers use the different desired trajectories, as we mentioned earlier. The second is the method of obtaining the lateral position of the vehicle. For the lane keeping, the lateral position can be measured directly by the lateral rference/sensing system. While, the lateral position for the lane changing controller is obtained indirectly by integrating twice the data of the lateral accelerometer.

The lower level controller receives the target steering angle from the upper level controller and generates the appropriate control signals for the Steering Actuator (e.g. DC motor), hence, to control the vehicle moving in the desired direction. On account of the lower level controller is a typical DC motor control system, a PID controller will be competent.

Analysis of vehicle lateral dynamics

Bicycle Model

For the propose of designing an effective vehicle lateral controller, at first, we need to know the characteristics of the vehicle lateral dynamics. Since in section 2.4, we have already built the vehicle lateral kinematic model and dynamic model based on different assumptions and for different application conditions. In this chapter, our objective is to design a lateral controller for highway vehicle operations, thus the lateral dynamic model should be considered, and the kinematic model is not the case.

Recall the bicycle model described in equation ( 2.66), which is a 4 th order system in the standard state space form,

Ẋ = AX + B 1 δ + B 2 ρ (4.6)
where, X is the state variable, X = [e 1 , ė1 , e 2 , ė2 ] T , and

A =       0 1 0 0 0 - 2C af +2Car mVx 2C af +2Car m -2C af l f +2Carlr mVx 0 0 0 1 0 - 2C af l f -2Carlr IzVx 2C af l f -2Carlr Iz - 2C af l 2 f +2Carl 2 r IzVx       , B 1 = 0 2C af m 0 2C af l f Iz T , B 2 = 0 - 2C af l f -2Carlr m -V 2 x 0 - 2C af l 2 f +2Carl 2 r Iz T .
The meaning of the symbols in (4.6) are listed in Table 4.1.

Although the bicycle model is simple, it has been proven to be a good approximation for vehicle dynamics when lateral acceleration is limited to 0.4g on normal dry asphalt roads.

Open-Loop Response to the Parameter Variations

If we fix the values of the parameters used in the system matrices in (4.6), the bicycle model represents a linear time-invariant (LTI) model. However, the longitudinal velocity of vehicle will not always be a constant in highway driving, the LTI model is then replaced by a LTV (Linear Time Variant) model. In addition, other parameters, such as the vehicle load and cornering stiffness of wheels are not always constant. The variations of these parameters will lead to the different vehicle lateral behaviors. Therefore, we use bode 4.9(a) shows the bode diagrams of the frequency response under vehicle speeds of 30, 60, 90 km/h respectively. In the phase-angle plot, with the changing of speed, the shapes of the curves change a lot, especially in the frequency region of [1,20] rad/s, which is a common frequency region for vehicle operation. Figure 4.9(b) shows the bode plots under the loads of 0.8m, m, 1.3m respectively, with the vehicle speed of 60 km/h (m denotes the vehicle mass, and its value is shown in table 4.1) . It is clear that the load variation has a very little influence on the log-magnitude curves, and the influence on phase angle curves is also very limit compared with the influence caused by speed.

ρ road curvature (1/m) m mass (1485kg) V x /V y longitudinal/lateral velocity (m/s) I z yaw moment of inertia (2872kgm 2 ) l f /l
From the above discussion, the very important conclusion is that the vehicle longitudinal velocity has a great influence on vehicle lateral dynamics which should be considered in lateral controller design.

Lateral controller design

In the previous sections, the lateral control system architecture and vehicle lateral dynamics have been discussed. In this section, our task is to design a lateral controller, which works in the hierarchical lateral control architecture and is competent to deal with the parameter variations in vehicle lateral dynamics. The design processes of PID controller with anti-windup, fuzzy controller, and multi-model fuzzy controller will be presented, and results of these control algorithms will be compared, so as to find out the appropriate lateral control system. 1)

d i T s T s + + + e(t) u(t) Set point
u(t) = K p e(t) + 1 T i t 0 e(τ )dτ + T d de(t) dt (4.7)
where, K p is the proportional gain, T i is the integral time, and T d is the derivative time.

u(t) is the control effort, and e(t) is the error. The three elements of the PID controller produce outputs with the following nature:

• P element: proportional to the error at the instant t, which is the "present" error.

• I element: proportional to the integral of the error up to the instant t, which can be interpreted as the accumulation of the "past" error.

• D element: proportional to the derivative of the error at the instant t, which can be interpreted as the prediction of the "future" error.

By tuning the three constants in the PID controller, the controller can provide control action designed for specific process requirements. There are several prescriptive rules used in PID tuning. Two of the most effective methods were proposed by Ziegler and Nichols [Ziegler 1942], and they have been widely utilized either in the original form of in modified forms.

In our case, in order to find the values of parameters of PID, equation (2.66) is used to represent the vehicle lateral dynamic model, we choose the steering angle as the system input and the lateral displacement is the system output. And the vehicle velocity is chosen as 50 km/h. By using Matlab/Simulink, we can find the step response of the vehicle lateral system is not a S-shaped curve, thus the first method of Ziegler-Nichols is not available for our case. Then we use the Second Ziegler-Nichols method to determine the values of the parameters. .11), increase K p from 0 to a critical value K cr at which the output first exhibits sustained oscillations. Thus we can get the critical gain K cr = 2.6 and the corresponding period P cr = 0.693 s. using the formulas suggested by Ziegler and Nichols shown in table 4.5.1.1, we can calculate the coefficients K p , T i , and T d :

Plant p K + e(t) u(t) r(t) c(t)
K P = 1.56, T i = 0.347, T d = 0.087 (4.8)
K p T i T d P 0.5K cr ∞ 0 PI 0.45K cr 1 1.2 P cr 0 PID 0.6K cr 0.5P cr 0.125P cr
Then, with the above values, we can get the step response of the PID control system, as shown in figure 4.12. It is clear that the result is not satisfied, the transit response is oscillatory, the setting time is about 20 s, which means the amplitude decays slowly.

In addition, the overshoot is rather big, and the maximum overshoot is 69%. Thus, additional fine-tuning should be done in order to get a good performance. Since, the most urgent requirement is to decrease the setting time as shown in Fig. 4.12, then we increase the value of T d with a step of 0.05 by using a simple Matlab program, and we check the result in Matlab/Sumulink. Once the setting time gets into 3 s (allowable tolerance is 0.5%), we exit the program and it return the final value of T d . By using this method, we get the modified value: T d = 0.385. Thus the new parameters values are:

K P = 1.56, T i = 0.347, T d = 0.385
The step response of the PID controller with the new set of parameters is shown in Fig. 4.13. It should be noted that another benefit of increasing T d is the decrease of overshoot. The control performance becomes much more better than the former one. The setting time is less than 3 s, and the maximum overshoot decreases to less than 25%. Although the above designed PID controller has a good performance in this step response test, however, it should be noted that the PID output at the step time is a very big value which is far more than 45 • , the mechanical limit of the steering system of road vehicles. In addition, for a road vehicle, the ride comfort is another constraint need to be considered, thus a limit of 0.175 rad (or 10 • ) should be introduced to our lateral control system. A saturation block is then added in the PID control system, as shown in Fig.

Fuzzy control for vehicle steering

It is known that fuzzy logic is a very useful nonlinear control method, that can be used to control very complex models or plants, which are difficult to model. As the vehicle lateral dynamic system is a typical system where driving models, sensorial information, objectives, constraints, and control actions are under uncertainty, thus different fuzzy logic controllers were proposed for the vehicle lateral control [START_REF] Chunyan | [END_REF]].

In [START_REF] Chunyan | [END_REF]] an adaptive fuzzy logic controller was designed, which has two inputs, one output, and an adaptive fuzzy search table deduced by lingual information from experienced drivers. Simulations and experiments have been done in straight lane with the speed of 80 km/h and in curve lanes with the speeds of 40 km/h. The given results showed the effectiveness of the proposed fuzzy approach. However the tracking results in low speed have not been shown in this work.

Works carried out by [START_REF] Wijesoma | [END_REF]Kodagoda [Wijesoma 1999, Kodagoda 2002] have shown a fuzzy lateral controller for a golf car-like AGV (Autonomously Guided Vehicle). In their works, the coupling effects of vehicle speed on steering angle (and hence angular velocity), and vice versa, was not explicitly accounted for. Thus, two independent controllers of longitudinal controller and lateral controller were designed. Simulation experiments were carried out with the variation of vehicle loads and vehicle velocities.

However, the variations of vehicle speed is only from 3m/s to 7m/s ([10.8 km/h, 25.2 km/h]), which is reasonable for their Golf Car but not sufficient for the highway vehicle operations, because this speed region covers only the low speed region for the vehicles driving in highway.

As we know the fact that vehicle velocity has great influences on vehicle lateral dynamics, then it is interesting to investigate how the above mentioned fuzzy controllers deal with this problem using the uncoupled model of the longitudinal and the lateral controllers. In the following of this subsection, we will take the fuzzy controller in [START_REF] Chunyan | [END_REF] as an example to find out how lateral controller works with out considering the influences of vehicle speed. The vehicle model used in [START_REF] Chunyan | [END_REF]] is a kinematic model as shown in Fig. 4.17.

And it has the following formulas:

             θ(t) = tan ϕ(t) v(t) L ẏ(t) = sin θ(t)v(t) ẋ(t) = cos θ(t)v(t) ϕ(t) = f (θ, t) (4.10)
where L is the wheelbase, θ is the yaw angle, and ϕ is the steering angle.

Input and output variables

The fuzzy controller has two input variables: lateral displacement Y and its change ratio Ẏ ; and it has one output: steering angle ϕ. For each variable, there are 7 fuzzy sets, described as follows: s2, s3, ce, b1, b2, b3} (4.11) The normal distribution function as formula (4.12) is used for the membership distribution description.

{ Y, Ẏ , ϕ} = {s1,
µ(x) = exp -( x -a b ) 2 , (b > 0) (4.12)
Then the membership function of the input and output variables are shown in Fig. 4.18.

Fuzzy control rules

The fuzzy control rules are in the form of "IF (Premise) THEN (Consequent)". There are totally 49 fuzzy control rules deduced from experienced drivers, as shown in Table 4.3.

Simulation tests

In order to check whether the tracking performance of this fuzzy controller is robust to the variation of vehicle speed, a simple step input is used, and we will perform this step input at different vehicle speeds.

Figure 4.19 shows the step responses of the fuzzy controller. We can find the results at 80km/h and 40km/h are quite good, however the results become bad with the speed decreases. This results combined with the results in [START_REF] Chunyan | [END_REF] show that this fuzzy controller can provide adaptive lateral performances in middle and high speed region, however the control performances in low speed region are not acceptable. Therefore, if we want to design a adaptive lateral controller which is qualified in all vehicle speed, then the factor of speed variation must be taken into account.

An issue need to be mentioned is that the vehicle model used in the work of [START_REF] Chunyan | [END_REF]] is a kinematic model which is just a simplified version of the equation (2.44) given in section 2.4. As we have discussed already that the kinematic model neglects the dynamic factors which is acceptable in the low speed operations. However, it is not the case for highway vehicles.

Since we have obtained step responses with both the fuzzy controller and PID controller which are shown in Figures 4.19 and 4.16 respectively. Then it is interesting to compare the two control results. Although the two vehicle models are not the same, but nevertheless we can find some rough conclusions by comparing the two results: • It seems that the fuzzy controller works better that the PID, because at the speed of 80, 40, and 20 km/h, the fuzzy controller has always less overshoot and less set time than that of the PID controller.

Multi-model fuzzy control

In the previous two subsections, the PID with Anti-Windup and fuzzy control algorithms have been studied. Although the fuzzy control method has shown some advantages than the PID, the results are still not satisfied if the vehicle velocity varies. This is because the above mentioned methods did not consider the influences of the variations of vehicle speed. However, for a highway vehicle, the operation speed varies in a wide range from low speed to high speed. Therefore, in the rest of this section, we will dedicate to the The proposed fuzzy control rule base is shown in Table 4.5. This rule base is used for all the four local controllers.

Fuzzy Reasoning Process: The fuzzy reasoning process can be divided into three steps -fuzzification, inference engine and defuzzification. In this work, we use triangle and trapezoids shaped membership function for the fuzzification process as shown in Fig. 4.22.

The Mamdani's inference method is employed to solve the fuzzy implication. And we use Centroid method for defuzzification process.

Virtual desired trajectory for lane change maneuver

In the design of VDT, passenger's ride comfort, transit time are the main factors to be considered. The trapezoidal acceleration trajectory has been selected to be the optimal trajectory for a lane changing maneuver, see [Chee 1994[START_REF] Hedrick | [END_REF][START_REF][END_REF]]. The acceleration profile is specified in Fig. 4.23, where a max and J max represent the lateral acceleration limit and the lateral jerk limit of the trapezoidal acceleration trajectory respectively. From Fig. 4.23, the desired lateral acceleration ÿd can be described as

ÿd = J max t • u(t) -J max (t -t 1 ) • u(t -t 1 ) -J max (t -t 2 ) • u(t -t 2 ) + J max (t -t 3 ) • u(t -t 3 ) +J max (t -t 4 ) • u(t -t 4 ) -J max (t -T ) • u(t -T ) (4.15)
where, u(t) is a unit step function. Integrating (4.15) twice with respect to time and with zero initial conditions, then the lateral position can be written as:

y d = J max 6     t 3 • u(t) -(t -t 1 ) 3 • u(t -t 1 )- (t -t 2 ) 3 • u(t -t 2 ) + (t -t 3 ) 3 • u(t -t 3 ) +(t -t 4 ) 3 • u(t -t 4 ) -(t -T ) 3 • u(t -T )     (4.16)
Set y d (T ) = d, where d means the lateral distance between the target lane and the origin lane, i.e. lane width. The temporal parameters for this trajectory, t 1 ,t 2 ,t 3 and t 4 can be obtained as

t 1 = a max J max , t 2 = -t 2 1 + t 4 1 + 4t 1 d J max 2t 1 t 3 = 2t 1 + t 2 , t 4 = t 1 + 2t 2 (4.17)
The transit time T for the lane change maneuver can be written as:

T = 2(t 1 + t 2 ) = a max J max + ( a max J max ) 2 + 4 d a max (4.18)
By selecting the values of design parameters d, a max and J max , one can obtain the desired trajectory and the transit time from (4.16) and ( 4.18) respectively. The trapezoidal acceleration trajectory is easy to be parameterized. And it provides a direct method to design a desired trajectory only with several main performance constrains, which facilitates finding the optimal trade-off between the transit time and ride comfort constrains.

Simulation tests

In this section, we will test the performance of the proposed vehicle lateral control system throughout a series of simulations. The lane keeping and lane changing will be assessed

Test 1: Lane keeping control at different speeds (1)

In this simulation, the lane keeping performance will be tested. A 600-meter trajectory includes a segment of 5-meter lateral deviation is designed, see Fig. 4.25. The test vehicle will pass through the designed trajectory at the speeds of 30, 60, 90 km/h respectively, and the simulation results of steering angle, lateral position error and lateral acceleration are shown in Figs. 4.26(a), 4.26(b), 4.26(c) respectively. We can find that the experimental vehicle can steer accurately to trace the desired trajectory at all the three test speeds. In the three output results, all the maximum values occur at the speed of 90 km/h, and the results at 30 and 60 km/h are more accurate and more smooth. However, even at the speed of 90 km/h, the maximum lateral position error is less than 0.08 m, and the maximum lateral acceleration is less than 1.1 m/s 2 . In general, the lateral acceleration should not exceed 4 m/s 2 for the rollover and 2 m/s 2 for passenger comfort [START_REF] Ackermann | [END_REF]]. Since the lateral acceleration is always below 2 m/s 2 , the passenger comfort is then ensured in this scenario. 4.6.2 Test 2: Lane keeping control at different speeds (2) In this simulation, the experimental vehicle will perform two times of 3-meter lateral deviation during the periods of 4 to 10 s and 15 to 22 s, see Fig. The objective of this scenario is to test the performance of the lateral control system when it performs a same lateral deviation during the same time, however at different speeds.

The vehicle speed is set to 30, 60, 90 km/h respectively. Figure 4.28(a) shows the steering results corresponding to the three test speeds. The steering operations are rather smooth in this scenario, and the steering angle at 30 km/h is bigger than the results at the higher speed. This is reasonable, because when the speed is slow, we need bigger steering angle to reach the same lateral position. In this simulation, the issue we address is the influences caused by the variations of vehicle mass and wheel cornering stiffness. With the variation of vehicle mass, as a result, the moment of inertia will change correspondingly. We use the same input trajectory that we used in the former simulation as shown in Fig. 4.27, and the vehicle speed is set to 60 km/h. The variations of the parameters are listed in Table 4.6. The vehicle mass changes from 1300 kg to 2300 kg, the movement inertia of vehicle body changes from 3000 kgm 2 to 4400 kgm 2 , and the wheel cornering stiffness changes from 36500 N/rad to 55000 N/rad.

Test 4: Lane changing scenarios at different speeds

The VDT for the lane changing is described in equation (4.15). In our case, the lateral acceleration limit a max for the VDT is set to 0.05 g, and the jerk limit is set to 0.1 g/s, We perform the lane changing scenarios at the speeds of 30, 60 and 90 km/h respectively. Fig. 4.31(a) shows the tracking errors for the three cases. The peak tracking error is about 0.06 m, which appears at the speed of 90 km/h scenario. With the speed drops down, the peak tracking errors at 60 km/h and 30 km/h decrease to about 0.04 m. Figure 4.31(b) shows the lateral acceleration results. One can find that the lateral acceleration responses are always less than 1 m/s 2 . Furthermore, the three curves are very similar, which means the proposed lateral controller working together with the VDT can provide stable performances under different operation speeds.

Cornering Stiffness

In this test, we will test the robustness of the lane changing controller under the variations of the vehicle load and wheel cornering stiffness. We use the VDT as shown in Fig. 4.30.

Two sets of vehicle parameters are shown in Table 4.6. Two simulations are carried out separately with the two sets of parameters, while the vehicle speed for these tests is set to 60 km/h. Figs. 4.32(a), 4.32(b) show the tracking error results and lateral acceleration results respectively. Although the values of the vehicle parameters change a lot in the two cases, the results are very similar. This shows the proposed controller is robust under the variations of these parameters.

Conclusion

In this chapter, we presented a lateral control system, which was capable of performing lateral operations for the autonomous vehicles. This system was built on a hierarchical control architecture, with this architecture we could perform the basic lateral operations of lane keeping and lane changing. By combining the two basic operations, we could reach the more complex operations, such as overtaking, etc. One major difficulty in lane changing control is that the vehicle need to travel a certain distance without seeing any road references when the on-board sensors' range cannot cover both the two adjacent lanes. By using the concept of "Virtual Desired Trajectory"(VDT), the lane changing problem is then transferred to a lane tracking task.

Since the vehicle lateral dynamic is deeply influenced by the vehicle longitudinal speed, a multi-model fuzzy controller, which includes four local controllers and a fusion block, was then proposed for the lane tracking tasks in both the lane keeping and lane changing controllers. Simulations showed that it could provide good tracking performances while at the same time ensuring ride comfort in the whole range of operation speed, and it could also repel the system uncertainties such as changes in vehicle load, movement inertia and wheel cornering stiffness. Furthermore, as in each local controller, there are only 3 linguistic values for the input variables and 5 linguistic values for the output variable, and there are totaly 9 fuzzy rules. Thus the calculation procedure is not complex, and is rather rapid. It appears a promising control algorithm for realtime applications and to be embedded in our reduced scale vehicle platoon platform.

Introduction

In chapter 3, we have proposed a longitudinal control system, which includes an upper controller and a lower level controller, to perform the vehicle longitudinal speed control by using brake and throttle control. In chapter 4, a multi-model fuzzy control system has been proposed to perform the lateral control tasks for the autonomous vehicles. However, the objective of our work is to design a global control system which can perform the automatic driving in highway. Therefore, the above proposed longitudinal and lateral control systems should be integrated into a global control system which can perform the two control tasks simultaneously. In this control system, the longitudinal controller block represents the longitudinal control system which includes the upper and the lower level controllers, as we have shown in Fig. 3.1. The upper level controller in the longitudinal control system is the SSP spacing policy that we have proposed in equation (3.33), written as:

System integration

ẍi_des = -(λδ i + εi ) (t d - γ j i ẋi )
The details of the upper level controller are described in section 3.3.5. The lower level controller included in the longitudinal control system is the coordinated throttle and brake fuzzy controller that we have proposed in section 3.4.

For the task of lateral control, we use the multi-model controller that we have proposed in section 4. 5.3,see Fig. 4.21.

With this integrated control system, we can mange either the longitudinal movements or the lateral movements of autonomous highway vehicles. Furthermore, some more complex maneuvers, which require simultaneously operations both in longitudinal and lateral directions, could also be achieved in this integrated control system.

Simulation experiments

Since in sections 3.3.6 and 4.6, the independent longitudinal controller and lateral controller have been already examined and validated through a series of simulation tests. In this section, we will test the experiment vehicle's behavior in a more practical case where the longitudinal and lateral controllers operate simultaneously, as this will give us some results under the coupling effects between the steering and driving systems.

The values of the parameters used for the simulation are shown in Table 5.1. shows the longitudinal spacing error of the controlled vehicle during the experiment period.

The maximum longitudinal spacing error is about 0.22 m when the desired inter-vehicle spacing is about 19.7 m, thus at this time ,the spacing error is only around 1.1%. The results of the lateral position error and lateral acceleration are shown in Figs.

5.5(b) and 5.5(c) respectively. One can find that the maximum lateral position error is less than 0.05m, and the maximum lateral acceleration is less than 0.8 m/s 2 , which mean the tracing accuracy and ride comfort are ensured during this simultaneous operations of the longitudinal and lateral controllers.

Conclusion

In this chapter, we concentrated on the problem of designing a global control system, which could control both the longitudinal and lateral movements of the automated vehicle by using the longitudinal controller and lateral controllers that we have proposed in chapter 3 and 4. Since, in our work, the vehicle longitudinal speed has been demonstrated as a key parameter that can influence the vehicle lateral dynamics, and we use it to build up a multi-model lateral controller. Thus, the uncoupled longitudinal and lateral control system is no longer available in our case.

Therefore, we proposed a global control system, in which the longitudinal and the lateral controllers were connected by the vehicle longitudinal speed. In this way, the designed longitudinal control system and the multi-model fuzzy control system can work coordinately. The simulation experiments showed that the proposed global control system could provide good performances in the scenario where the steering operations and acceleration(or deceleration) operations were performed simultaneously. With this control system, we can achieve the more complex scenarios where different longitudinal and lateral operations are required.

Introduction

In the previous chapters, the intelligent vehicle motion control systems have been studied.

In the controller design process, we assume that all vehicle states are accurately measured by different type of sensors, such as longitudinal and lateral acceleration, velocity, intervehicle spacing, yaw angle, lateral displacement, etc. In practice, however, some states are not measurable, or some states are measurable but due to the high cost of sensors and rigorous installation requirements, we can not measure them directly. Then we need to design observers to estimate unavailable state variables. In addition, even for the states that can be directly measured, on account of the sensor noise which will degrade the control performance, and sensor fault diagnosis, the observer design is also an important issue need to be considered. This chapter is devoted to two aspects relating to the practice: the observation of vehicle states and a multi-sensor intelligent vehicle prototype. At first, the vehicle sensor system configuration is discussed. Second, the principe of the Kalman-Bucy filter is introduced. Then a Kalman-Bucy filter is designed to estimate vehicle yaw rate and lateral velocity by using lateral acceleration measurement. Finally, a reduced scale multisensor intelligent vehicle prototype will be introduced.

Observation of vehicle states

Introduction

The effectiveness of a vehicle dynamic control system relies on accurate knowledge of vehicle states. Generally, the vehicle states are directly measured by the onboard sensors.

However, some states are not measurable, in addition, even for the measurable states, due to the limitations in sensor accuracy, cost, reliability, we can not always get the vehicle states directly from onboard sensors. Thus the vehicle state estimation is a very important aspect in vehicle control system design. It should be noted that estimation is also one of the key technologies for onboard fault diagnosis.

Vehicle state estimation problem can be divided into four aspects: sensor configuration, physical model, estimation algorithm and parameter adaption [START_REF] Yu | [END_REF]].

According to the divers application objectives, the typical estimation states are vehicle speed, yaw rate and side-slip angle. Take ABS (Anti-lock Brake System) and ESP (Electronic Stability Program) as an example, which are the most two typical active security systems in today's market. ABS highly depends on the estimation of vehicle speed. And ESP needs the yaw rate as an important control input, although the gyroscope sensor can provide direct measurement of yaw rate, the high price of gyroscope sensor (compared to the other sensors) makes the ESP system can be only equipped in the high-end models.

Using state estimation, the yaw rate can then be estimated (indirectly measured) through other already employed and low cost sensors, such as lateral acceleration sensor.

Selection of state to be estimated Since our work mainly concerns two aspects in vehicle motion control: longitudinal control (spacing control) and lateral control (steering control). In the longitudinal control system, the required information such as: longitudinal acceleration, speed, inter-vehicle spacing can be obtained by using the acceleration sensor, wheel rotation sensor and radar (or infrared sensor). While, in the lateral control system, the vehicle lateral displacement and yaw angle are two input parameters. Normally, the Magnet-Magnetometer reference system (look down system) can provide the lateral displacement measurement. Then the yaw angle is the parameter to be estimated.

Observation methods in former researches

Different observation algorithms have been proposed in former literatures. For the linear system observation, the traditional Luenberger observer and Kalman filter are widely used [Luenberger 1971[START_REF] Kalman | A new approach to linear filtering and prediction theory[END_REF]]. The Luenberger observer, which is based on the pole-placemen of LTI system (Linear Time Invariant), was proposed to estimate the states in vehicle lateral dynamics [Kiencke 1997]. However, the problem for this method is that the poles are shifting, caused by changes of the system parameters (for example, the vehicle speed v). In [Venhovens 1999], the application of Kalman filter in vehicle dynamics estimation was discussed. An example of using Kalman filter to estimate lateral velocity was introduced. Gao Z.H. has proposed a "soft measurement" of vehicle yaw rate by using discrete Kalman filter [Zhenhai 2003]. The results showed that the proposed Kalman filter could provide accurate estimation of yaw rate, however, the experiment vehicle speed was assumed to be a constant (22 m/s). The results under the variations of vehicle speed have not been provided.

While, for the nonlinear system, different solutions have been proposed, such as Extend Luenberger observer, Extend Kalman filter, sliding-mode observer are the conven-tional nonlinear observers [Stephant 2004, Shaozhong 2009]. Besides, some other nonlinear observers have been also proposed for the vehicle state estimation, such as estimation based on H ∞ algorithm, neural network estimate and fuzzy logic, and etc., see [START_REF] O'brien | A comparison of H ∞ with Kalman Filtering in vehicle state and parameter identification[END_REF], SASAKI 2000[START_REF] Shuming | [END_REF]].

In conclusion, considering the vehicle controller requirements together with sensor system configuration, we choose the yaw rate as the state to be estimated. Since in chapter 2, we have shown that the vehicle lateral dynamic equation (2.58) is a LTV (Linear Time variant) system with the consideration of vehicle parameters variations, such as the variation of vehicle speed. Therefore, the traditional Luenberger observer is not available in our case. We choose the Kalman filter to estimate the yaw rate.

Kalman-Bucy Filter for LTV system

The famous Kalman filter, based on the state-space formulation of linear dynamic systems, provides a recursive solution to the linear optimal filtering problem. The Kalman filter is a set of mathematical equations that provides an efficient computational means to estimate the state of a process, in a way that minimize the mean of the squared error. The mathematical algorithms was original provided in [START_REF] Kalman | A new approach to linear filtering and prediction theory[END_REF]] for the discrete system and [Kalman 1961] for the continue system. The Kalman-Bucy filter is the continue version of the Kalman filter.

Let us consider here LTV system defined by the following state space model:

ẋ(t) = A(t)x(t) + B(t)u(t) + G(t)w(t), y(t) = C(t)x(t) + v(t) (6.1)
where x(t) is the state vector, y(t) denotes the measured signal, u(t) is the control input, w(t) and v(t) represent the process and measurement noise respectively. The noises are assumed to be independent (of each other), white, Gaussian and with the following covariance matrices:

E{w(t)w T (t )} = Q(t)δ(t -t ), E{v(t)v T (t )} = R(t)δ(t -t ), E{v(t)w T (t )} = 0, E{v(t)x T (0)} = 0, E{w(t)x T (0)} = 0, E{x(0)x T (0)} = P 0 , (6.2)
where, δ(t) is the Dirac delta, and x(0) is a random variable with the expected value m 0 ,

x(0) = x(0) -m 0 .
The filter consists of two differential equations, one for state estimate and one for the covariance: 6.4) where the second equation is a Riccati equation, and the Kalman gain is given by:

ẋ(t) = A(t)x(t) + B(t)u(t) + K(t)[y(t) -C(t)x(t)] (6.3) Ṗ (t) = A(t)P (t) + P (t)A T (t) + G(t)Q(t)G T (t) -K(t)R(t)K T (t) (
K(t) = P (t)C T (t)R(t) -1 (6.5)
Equations ( 6.3), (6.4) and (6.5) define the continues-time Kalman-Bucy estimator, which is also called the Kalman-Bucy filter [START_REF] Kalman | A new approach to linear filtering and prediction theory[END_REF], Kalman 1961, Borne 1990].

6.2.3 Yaw rate and lateral velocity estimation using Kalman-

Bucy filter

The issue of vehicle lateral dynamics has been discussed in Chapter 2. The well known two degree-of-freedom "bicycle model" was introduced. Recall the bicycle model, as shown in Fig. 6.1.

Rewrite the vehicle lateral dynamic equation in the state space form:

Ẋ = AX + Bδ (6.6)
where, X is the state vector, X = [y, ẏ, ψ, ψ] T , y and ψ denote the vehicle lateral displacement and yaw angle respectively, δ represents steering angle, and

A =          0 1 0 0 0 - 2C af + 2C ar mV x 0 -V x - 2C af l f -2C ar l r mV x 0 0 0 1 0 - 2l f C af -2l r C ar I z V x 0 - 2l f 2 C af + 2l r 2 C ar I z V x          B =         0 2C af m 0 2l f C af I z        
the variables in the matrices A and B are shown in table Since the lateral acceleration sensor is a common sensor can be easily obtained, in our system, the lateral acceleration ÿ is selected as the measured variable. Then from equation (6.6), we can get:

6.1. B X Y O A C lr lf ψ x y ψ d δ V f V r vr θ vf θ f β vr θ vf θ V β V x V y Lane centerline F sf F sr
ÿ = a y = - 2C af + 2C ar mV x ẏ + -V x - 2C af l f -2C ar l r mV x ψ + 2C af m δ (6.7)
From equation ( 6.7), one can find that only the state variables ẏ and ψ are related with the measured variable ÿ, while the state variables y and ψ do not have an one-to-one mapping to the measurement ÿ. We eliminate the states y and ψ from equation (6.6).

Then, the simplified state space model for observation and measurement equation can be given by:

= C ar = 42000N/rad) Ẋ = A 1 X + B 1 δ + G 1 w ÿ = C 1 X + D 1 δ + v (6.8)
where, X is the state vector, X = [ ẏ ψ] T . ÿ is the measurement. δ, steering angle, is the system input, w is the process noise, w = [w 1 w 2 ] T , v is the measurement noise, and

A 1 =    - 2C af + 2C ar mV x -V x - 2C af l f -2C ar l r mV x - 2l f C af -2l r C ar I z V x - 2l f 2 C af + 2l r 2 C ar I z V x    , B 1 =    2C af m 2l f C af I z    , C 1 = - 2C af + 2C ar mV x -V x - 2C af l f -2C ar l r mV x , D 1 = 2C af m , G 1 = 1 0 0 1 ,
the meaning of the parameters in the above matrices are shown in table 6.1.

From equation( 6.8), one can find that the system matrices A 1 and C 1 are functions of longitudinal velocity V x . Since in our work, the vehicle speed variation is considered as an important factor in the lateral controller design (see chapter 4). The speed variation should also be considered in the estimation process. Therefore, the vehicle state estimation problem described by equation ( 6.8) is a LTV system estimation problem.

At first, we need to validate the observability of the system described in equation (6.8).

The observability matrix of the system is

M = N 0 N 1 (6.9)
where, N 0 = C 1 , and

N 1 = N 0 A 1 + dN 0 d(V x ) d(V x )
dt . Then we can get,

M =    a 1 V x -V x - a 2 V x -a 3 + a 2 1 -a 2 a 3 -a 1 a cc V x 2 (-a cc -a 1 -a 4 + a 2 a cc -a 1 a 2 -a 2 a 4 V x 2 )    , rank of M is 2. (6.10)
where a cc is the vehicle acceleration, and

a 1 = - 2C af + 2C ar m , a 2 = 2C af l f -2C ar l r m , a 3 = - 2l f C af -2l r C ar I z , a 4 = - 2l f 2 C af + 2l r 2 C ar I z
Therefore, the system is observable.

Then, a Kalman-Bucy filter can be designed by following the equations (6.3), (6.4) and (6.5), which can be used to estimate the state variables lateral velocity and yaw rate by using the lateral acceleration measurement.

Estimation results

In this subsection, we will test the performance of the designed observer by using Matlab/ Simulink. The vehicle parameters are given in table 6.1. The vehicle performs a sinusoidal steering operation, the steering angle is given by: 6.11) where, the unit of δ is rad, t denotes the time, and 0.1N (t) represents the steering input noise caused by the steering mechanism and uncertainties of road conditions, N (t) is assumed to be a normal distribution with mean 0 and standard deviation 1, N (t) ∼ N (0, 1) (6.12) Figure 6.5: Two-car platoon

δ = 0.1 sin( t 2.5 + 0.1N (t)) (
• Infrared telemeter: it measures the changing between the outgoing wave and the phototransistor that receives it after reflection on an obstacle.

• Ultrasonic sensors: they use the propagation time of a short ultrasonic impulsion which is proportional to the distance between vehicles.

The two distance measurements are sent to the intelligent system which compares them and deduces the reliable data based on a data fusion process.

Sensors for trajectory tracking

The road (or desired trajectory) is represented by a white line drawn on the ground that the platoon has to follow. The position of the vehicle with respect to the white line is given by an integrated system camera/microprocessor. Thus, with the given color of the line, the microprocessor of the camera is able to compute the barycenter of the line and to send it digitally to the intelligent central system.

However, since the line tracking is a critical function for the vehicle and hence cannot accept any misleading without dramatic consequences, a magnet/magnetometer system is also introduced. The magnetic plots are fixed on the lane center, and two magnetometers placed on the left and right sides of the front bumper. We can compare the tensions delivered by each one and thus get the exact position with respect to the lane, see Fig.

Sensors for lateral detection

In order to enable the vehicle to implement complex driving scenarios such as the insertion of a vehicle in the platoon, the lateral detection becomes essential. Indeed, to determine for instance whether a vehicle can be inserted or not, we need to be sure that there is not any other vehicle on the side. Two ultrasonic telemeters on front and end sides of the vehicle are used.

Other sensors

We need to know at any time the specific data of each vehicle. The velocity, acceleration and steering angle are used as feedback variables for longitudinal and lateral controls. Besides, for safety reasons, the information is sent to the supervisor using a wireless communication.

Thus, we use a sensor of angular rotation to measure the steering angle, an optical velocity sensor to determine the velocity and an accelerometer to determine the acceleration of the vehicle.

The microcontroller

The core of intelligent system is the microcontroller. An Infineon CS167 microcontroller has been chosen to gather all sensors' information, compute the control law, and manage the communication system. As the load of the microcontroller appears rather high and a master/slave architecture is a new solution proposed to devote a specific microcontroller to one task, communication for instance, while the second is devoted to sensor management and control strategies and an exchange protocol is developed to communicate with the main controller.

Wireless communication

The communication system is one of the core parts of the system. Many options are available as radio telecommunications, Wifi, Bluetooth, ZigBee. Due to the technology limitation, cost and availability in the market for the moment, a Bluetooth socket plugged on the RS-232 port of the microcontroller communicating with the PC which transmits the information to the other vehicles, see Fig.

Integration

One of the main difficulties of the prototype design is to integrate all the technologies and make them work together. The integration process is explained as follows.

We have designed and built a complete architecture for the cars which takes into account interference and power issues. Figure 6.9 shows the general structure of a vehicle.

It should be noted that all the devices have been organized and optimized around the microcontroller. The more complex scenarios will be carried out in the future works.

Conclusion

This chapter is devoted to two aspects relating to the practice, the observation of vehicle states and the design of a multi-sensor intelligent vehicle prototype.

At first, we considered the sensor configuration problem for our intelligent vehicle control system (longitudinal and lateral control system). Due to the cost limit, the yaw rate, which is useful in the lateral control system, is not available in our multi-sensor system. Then an observer is required to estimate the yaw rate by using the available lateral acceleration measurement.

Second, since the vehicle lateral dynamic system is a LTV system, thus the traditional observe method for LTI system (such as Luenberger observer) is not applicable in this case. A Kalman-Bucy filter was then designed to estimate the vehicle states. The designed filter can provide accurate estimation results even with the noisy lateral acceleration measurement and a wide range of speed variation.

Finally, a reduced scale multi-sensor intelligent vehicle prototype was introduced. The different aspects of the prototype from the multi-sensor system, vehicle structure, communication system, and HMI were presented. In the first-step tests, the basic functions such as vehicle following and lane tracking were realized. In the future work, the more complex operations such as platoon control with more vehicles, lane changing, join (or split from) a platoon will be carried out.

Conclusions and Perspective

Conclusions

This thesis is devoted to the intelligent control strategies for vehicle platoons in highway, with the main aim of resolving the traffic congestion and traffic safety problems. The whole document is structured around five themes:

1. Modeling of four wheeled vehicles The main contributions of this thesis include the following:

• At the upper level of longitudinal control system, the spacing policy and its associated control law were designed with the constraints of string stability, traffic flow stability and traffic flow capacity. A safety spacing policy (SSP) was proposed, which uses both the information of vehicle state and vehicle braking capacity to determine the desired spacing from the preceding vehicle. It was shown that the proposed SSP could provide good performances both in traffic safety and traffic capacity for highway operations. In addition, through the comparison between the SSP and the traditional Constant Time Gap (CTG) policy, we can find that the SSP system has the obvious advantage in improving traffic capacity especially in the high-density traffic conditions, i.e., it can relieve traffic congestions in peak hour.

The corresponding results were published in "IEEE Intelligent Vehicle Symposium 2009", see [Zhao 2009c].

• At the lower level of longitudinal control system, a coordinated throttle and brake fuzzy controller was proposed. One main advantage of using fuzzy approach in this case is that we can achieve the control objectives by using the linguistic expressions of driver's experiences instead of the exact mathematic model of the controlled system (such as engine or brake dynamics). The proposed controller can deal with the nonlinearity in the engine and brake dynamics. Another highlight of the lower level controller is that a logic switch is designed to coordinate the two actuators (throttle and brake pedals). It was shown that the proposed controller could successfully deal with different driving scenarios and road disturbances. The corresponding result will be published in the "IEEE Conference on Intelligent Transportation Systems 2010", see [Zhao 2010a].

• The vehicle lateral control system was designed based on a hierarchical lateral control architecture, which could effectuate flexible switch between different lateral operations. Considering the vehicle lateral dynamics is a typical LTV system which is deeply influenced by the vehicle longitudinal velocity, a multi-model fuzzy controller was then proposed. The proposed controller contains four local fuzzy controllers which correspond to four velocity intervals. In order to avoid the undesired peaks which may appear during the commutation of the different local controllers, a fusion block was designed. Simulations showed that it could provide good tracking performances while at the same time ensuring ride comfort in the whole range of operation speed, and it could also repel the system uncertainties in vehicle load, movement inertia, etc. The corresponding results can be found in [Zhao 2009b, Zhao 2010c].

• In order to reach the final goal of automated vehicle operation, the longitudinal and lateral control system should be integrated into a global controller. Since we have shown that the vehicle longitudinal velocity is a key parameter which influences the lateral controller, an integrated longitudinal and lateral control system is then proposed, in which the two controllers are connected by the vehicle longitudinal velocity. The proposed integrated system is different from the existing uncoupled control systems (such as the one in [START_REF] Kodagoda | [END_REF][START_REF] Wijesoma | [END_REF]). And it is appropriate to the real vehicle dynamics in highway than the uncoupled control system. Simulation results showed that the longitudinal controller and lateral controller could work coordinately in this global control system. The corresponding results can be found in [Zhao 2009a, Zhao 2010b].

• For the purpose of application, the estimation of vehicle states is an important issue to be considered. In our case, the vehicle yaw rate is a parameter unavailable for our lateral control system. Considering the vehicle lateral dynamics is a LTV system, a Kalman-Bucy filter was designed, which could estimate the vehicle states in lateral dynamics by using the available lateral acceleration measurement. The designed filter can provide good estimation results even with the noisy lateral acceleration measurement and a wide range of speed variation. Finally, a multi-sensor intelligent vehicle prototype, which was developed in our research team, was presented.

Perspective

Based on the results given by this thesis, several perspectives should be considered:

• In this thesis, the fuzzy logic control was used for the vehicle automation: the coordinated throttle and brake fuzzy controller and the multi-model fuzzy lateral controller. Compared with the traditional fuzzy controller, the proposed approaches provide new ways to achieve more robust and accurate control performances than the traditional approach. Based on these results, the following two suggestions should be considered for the further works:

1) In this work, the stability of the proposed control algorithms was only tested by simulations in different scenarios with different disturbances. The theoretical stability analysis of the fuzzy algorithm (multi-model fuzzy system) has not been given. In fact, we choose the fuzzy control because it is a powerful approach for very complex system, non linear system and system with uncertainties... And the design of a fuzzy controller does not depend on an exact mathematic model. However, it is just the above mentioned advantages make it is often difficult or even impossible to apply nonlinear analysis techniques (such as Lyapunov method) to the fuzzy applications. In fact, to develop a mathematical theory for verification and certification of fuzzy system is still a problem for today's fuzzy controller researchers.

2) The fuzzy control rules and parameters are derived from the driver experiences and time consuming simulation experiments. In order to get the "optimized" fuzzy rules and parameters, we could also introduce the Genetic algorithms or neural network to optimize the fuzzy controllers.

• The two main advantages of vehicle platoon control shown in this work are increasing traffic capacity and improving traffic safety. The related analyses were carried out with the assumption that all the vehicles are automated controlled. However, in a mixed traffic condition, where automated vehicles operate together with manually driven vehicles, the traffic flow, traffic safety as well as fuel consumption and pollution levels are the interesting issues to be studied.

• A multi-sensors intelligent vehicle platform is introduced. In the first step experiments, some basic functions such as vehicle following and lane tracking have been realized. In the future, we need to test some more complex scenarios, such as platoon control with more vehicles, lane changing, overtaking, join (or split from) a platoon, etc. Thus, we can provide a theoretical and practical groundwork for those near term applications such as safe tunnel control, ACC system, driver assistance systems, and also for those long term applications like AHS, fully automated vehicles, etc.

• In our reduced scale vehicle platform, a communication system (Bluetooth) is introduced to communicate between the PC (supervisor) and the cars. Thus, we can supervise the system states and perform more complex scenarios. However, with the using of system communication, an important issue need to be envisaged is the time-delays which may degrade the control performance. Some constructive solutions for the time-delay problems have been proposed, such as [START_REF] Ch Moog | The dynamic disturbance decoupling problem for time-delay nonlinear systems[END_REF][START_REF] Márquez-Martınez | [END_REF], Márquez-Martinez 2004]. However to solve the time-delay problem in the vehicle platoon control is still an attractive topic.

• Considering the fact that a fault from any part of the vehicle control system (sensor, actuator, microcontroller, etc.) may cause serious results for vehicle safety, a fault tolerant control system is safety critical for intelligent vehicles. The subjects of fault tolerant control and reliability analysis have been studied by the researchers in BUAA (Beihang University), see [Wang 2009, Wang 2005, Wang 2004b]. In the frame of the cooperation between the two research teams from BUAA and LAGIS, the subject of fault tolerant control system for intelligent vehicles will be emphasized.

Résumé étendu en français

Organisation du document

Le premier chapitre présente l'état de l'art sur les systèmes de conduite automatisée.

Dans un premier temps, le contexte et les problèmes du trafic sont mis en place. Ensuite, nous présentons les solutions les plus intéressantes : ITS, AHS et Véhicule intelligent.

Enfin, les évaluations des grands projets en cours ainsi que l'évolution des contrôles longitudinal et latéral sont présentées en détail. Finalement, une synthèse de ces travaux de thèse est effectuée afin d'évaluer les résultats déjà obtenus ainsi que les perspectives futures.

v

  List of Tables1.1 Potential benefits of AHS . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.1 Potential benefits of AHS . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.1 Parameters for longitudinal controller . . . . . . . . . . . . . . . . . . . . . 80 3.2 Platoon vehicles' braking capacities (m/s 2 ) . . . . . . . . . . . . . . . . . . 87 3.3 Fuzzy Rule Base . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 4.1 Nomenclature of Bicycle Model . . . . . . . . . . . . . . . . . . . . . . . . 118 4.2 Ziegler-Nichols tuning rule based on critical gain K cr and critical period P cr (Second Method) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 4.3 Fuzzy Rule Base . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 4.4 Membership Function Variables . . . . . . . . . . . . . . . . . . . . . . . . 133 4.5 Fuzzy Rule Base . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 4.6 Parameter Variations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 5.1 Parameters for longitudinal controller . . . . . . . . . . . . . . . . . . . . . 146 6.1 Nomenclature of Bicycle Model . . . . . . . . . . . . . . . . . . . . . . . . 157 xvii Acronyms ACC -Adaptive Cruise Control AHS -Automated Highway System CTG -Constant Time-Gap spacing policy LTI -Linear Time Invariant LTV -Linear Time Variant SSP -Safety Spacing Policy VDT -Virtual Desired Trajectory xix

  Figure 1.1: World motor vehicle production

  Figure 1.2: Intelligent Transportation System (ITS) illustration

  After the first appearance of the concept of automated driving in the 1940 World's Faires, in the late of 1950s, RCA(Radio Corporation of America) in collaboration with the GM (General Motors) proposed the concept of Automated Highway System. The full AHS concept was initially examined by GM with sponsorship from U.S. department of Transportation (DOT) during the late 1970s. With the rapid evolution of automobile and the appearance of the problems of congestion around the big cities, the program PATH (Partners for Advanced Transit and Highways), one of the most fruitful organization in transportation researches, was created by the Caltrans (California Department of Transportation) and ITSUC (Institute of Transportation Studies of the University of California) in Berkeley in 1986 [PATH ]. The current research projects are mainly in the following three fields: , the U.S. Department of Transportation launched the National Automated Highway System Consortium (NAHSC). The consortium attempted to expand the programme's expertise and resources, and contribute to the goal of fully automated highway systems. In 1997, a demonstration was conducted in San Diego by PATH programme. Eight fully automated cars traveled together in a tightly spaced platoon guided by the magnetic plots fixed on the center of the road, see Fig. 1.3. This demonstration is regarded as the first milestone of the AHS programme, and showed the feasibility of the AHS.

Figure 1 . 3 :

 13 Figure 1.3: Vehicle platoon in the NAHSC demonstration

Figure 1 . 4 :

 14 Figure 1.4: ITS development chronology in the world

Figure 1 . 5 :

 15 Figure 1.5: Hierarchical architecture for automated driving

Figure 1 . 6 :

 16 Figure 1.6: Two-level structure for longitudinal control

  that for straight segments[A.A.S.H.T.O 2008]. Vehicle lateral control systems provide a possible solution to cope with the steering problems of vehicles. It senses the road centerline using a road based reference system and other on-board sensors. Then, it generates steering commands to keep the vehicle running along the desired path or steer the vehicle into an adjacent lane. The design requirement of vehicle lateral control is to ensure small lateral errors and small relative yaw angles while maintaining ride comfort under different conditions. Lane-keeping and lane-changing are the two basic functions of vehicle lateral control system[START_REF] Huang | [END_REF]].

Figure 2 . 1 :

 21 Figure 2.1: Six degrees of freedom vehicle model

-

  Longitudinal movement: translation along the x axis -Lateral movement: translation along the y axis -Vertical movement: translation along the z axis • Rotation motions: -Roll angle φ: Rotation about the x axis -Pitch angle θ: Rotation about the y axis -Yaw angle ψ: Rotation about the z axis

Figure 2 . 2 :

 22 Figure 2.2: Friction ellipse represents the interdependence of longitudinal and lateral forces for several constant value of the slip angle

Figure 2

 2 Figure 2.3: Vehicle on a inclined road

Figure 2 . 4 :

 24 Figure 2.4: Longitudinal tyre force as a function of slip ratio

Figure 2 . 5 :

 25 Figure 2.5: Pressure distribution at a non-rotation and rotation tyre

Figure 2 . 6 :

 26 Figure 2.6: Calculation of tyre effective radius

Figure 2

 2 Figure 2.7: Vehicle powertrain system

Figure 2

 2 Figure 2.8: Example of engine map

Figure 2 .

 2 Figure 2.9: Block diagram of torque converter subsystem

Figure 2 .

 2 Figure 2.11: Model of automatic gear shift control

Fig. 2 .

 2 Fig. 2.11 shows the automatic gear shift model. This model includes two subsystems: the Threshold calculation and the Gear shift logic. The Threshold calculation subsystem receives the input signals of throttle angle and the current gear number, and then it calculates the upshift threshold speed and downshift threshold speed for the vehicle at current gear. These two threshold speeds combined with the current vehicle speed are then transferred to the Gear shift logic subsystem, where the vehicle current speed is compared with the upshift and downshift threshold speed, and then it determines whether or not to perform an upshift or a downshift operation.

Figure 2 .

 2 Figure 2.12: Stateflow diagram of the gear shift logic

Figure 2 .

 2 Figure 2.13: Typical braking system

  3.2 should be added in the expression of longitudinal dynamics. The diagram of the different forces acting on the body and wheels of a rear drive vehicle during a acceleration driving is shown in Fig 2.14.

  2.15. The basic elements in longitudinal powertrain system are modeled as Engine, Torque converter, Gear box (Stateflow model) and Final drive, respectively. The Vehicle longitudinal dynamics subsystem is built upon the equation 2.43. The system inputs are throttle and brake, and the output is vehicle longitudinal speed. In our work, the throttle is expressed by the value of open

Figure 2 .

 2 Figure 2.15: Vehicle longitudinal system diagram

Figure 2 .

 2 Figure 2.16: Throttle and brake input for simulation

Figure 2 .Figure 2 .

 22 Figure 2.17: Simulation of longitudinal model

  2.19. The two degrees of freedom are denoted by the vehicle lateral position y and the vehicle yaw angle ψ. Two coordinate systems are used in this analysis: the global coordinate system is fixed to the ground, denoted by X, Y axes. The body fixed coordinate system is fixed to the vehicle body, denoted by x, y axes, the origin of this system, C, is the c.g. of the vehicle. Point O is the rotating center. The longitudinal velocity of the vehicle at the c.g. is denoted by V x .

Figure 2 .

 2 Figure 2.19: Bicycle model for vehicle lateral dynamics

Figure 2 .

 2 Figure 2.20: The vehicle lateral system

.

  Consider the simplified vehicle lateral dynamic model shown in (2.66), it is a 4 th order linear model and a LTI model as well, when all the parameters in the matrices A, B 1 and B 2 are constant. If the parameters' values vary, for example the vehicle velocity V x or tyre cornering stiffness C a varies, the LTI model is then replaced by a LTV (Linear Time Variant) model. : Kinematic model results with different steering angles δ

Figure 2 .

 2 Figure 2.22: Dynamic model results with different speeds

  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.2 Architecture of longitudinal control system . . . . . . . . . . . 65 3.3 Upper level control . . . . . . . . . . . . . . . . . . . . . . . . . 66 3.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 3.3.2 String stability . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 3.3.3 Traffic flow stability . . . . . . . . . . . . . . . . . . . . . . . . 71 3.3.4 Evaluation of the Constant Time Gap spacing policy . . . . . . 74 3.3.5 Proposed Safety Spacing Policy . . . . . . . . . . . . . . . . . . 78 3.3.6 Simulation tests . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 3.4 Lower level control . . . . . . . . . . . . . . . . . . . . . . . . . . 89 3.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 3.4.2 Coordinated Throttle and Brake Fuzzy Controller . . . . . . . . 90 3.4.3 Simulation tests . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

  Figure 3.1: Two-level structure for longitudinal control

Figure 3 . 2 :

 32 Figure 3.2: Vehicle platoon

  Figure 3.3: Fundamental diagram

Definition 3. 6 ( 2 .Figure 3 . 4 :

 6234 Figure 3.4: Main lane and inlet ramp

  partial equation, let ρ 0 be a base solution for the density. In order to study the stability of the base solution, consider some density perturbations ερ p to the base solution. Neglecting second-order terms in ε and defining c as c := h(ρ 0 ) + ρ 0 16) describes the evolution of a density disturbance of the traffic flow.Thus, the behavior of the solution to the linear partial differential equation (3.16) depends on the sign of c. It is clear that the sign of c is dependent on the density of base flow, ρ 0 .The solution of equation (3.16) is a traveling wave, i.e., ρ p = F (x -ct). If c > 0, the solution is a forward traveling wave. If c < 0, the solution is a backward traveling wave.Thus, in the traffic flow dynamics, when c < 0, arbitrarily small density disturbances are propagated upstream without any attenuation. According to the Definition 3.6, the traffic flow is thus unstable when c < 0. In contrast, the traffic flow stability can be ensured when c > 0.

Figure 3 . 6 :

 36 Figure 3.6: Impulse response of the CTG system

Figure 3

 3 Figure 3.7: Inter-vehicle spacing with different safety coefficients γ

  Another condition for string stability is h(t) > 0, as shown in equation (3.45). Consider the transfer function shown in equation (3.42), we use the following values: t d = 0.1s, τ = 0.1s, γ = 0.4, j i = -7.32 m/s 2 , λ = 0.4. Then the impulse responses of the transfer function (equation (3.42)) at different velocities can be obtained and shown in Fig. 3.8.

  Figure 3.8: Impulse responses at different velocities of the SSP system

Figure 3

 3 Figure 3.9: Q -ρ curves of the CTG and SSP

  Figure 3.10: Single lane highway

Figure 3

 3 Figure 3.11: Q -v curves of CTG and SSP

  Figure 3.12: Results of longitudinal control

Figure 3

 3 Figure 3.13: Coordinated throttle and brake control system diagram

  Figure 3.14(a), 3.14(b) and 3.14(c) show the input and output variables' membership functions. The values that we give to each fuzzy set are derived from expert experiences and simulation experiments.Fuzzy rule base: The expert's knowledge and experience are represented by a fuzzy rule base, with the fuzzy control rules in the form of "IF (premise) THEN (consequent)".

Figure 3

 3 Figure 3.14: Variables of fuzzy throttle controller

  Figure 3.15: Block diagram of logic switch

  scheme** Th_a Th_con Br_a Br_con Zero Br_con

  Figure 3.17: Flowchart of switch logic

  Figure 3.18: Longitudinal car model

Figure 3

 3 Figure 3.19: Leading vehicle's speed and acceleration

Figures 3 .

 3 Figures 3.21(a),5.4(b) show the time history of the inter-vehicle spacing and the spacing error between the two vehicles respectively. The following vehicle can always keep a safe spacing from the proceeding one, which is decided by the Safety Spacing Policy (SSP) described in (3.33). The maximum spacing error is always less than 0.25 m, which means the vehicle safety is ensured during this test.

Figures 3 .

 3 Figures 3.22(a), 3.22(b) and 3.22(c) show the final control results of the throttle, the

FigureFigure 3 Figure 3

 33 Figure 3.20: Following vehicle's speed and speed error

Figure 3 .

 3 Figure 3.23: Road grade, speed error and spacing error (inclined road)

Figure 3 .

 3 Figure 3.24: Control results of throttle and brake (inclined road)

Figure 4 . 1 :

 41 Figure 4.1: Road fatalities in U.S.A.

Figure 4 . 4 :Figure 4 . 5 :

 4445 Figure 4.4: Hierarchical decomposition of a complex system

Figure 4 . 6 :

 46 Figure 4.6: Hard partitions example

Figure 4 . 8 :

 48 Figure 4.8: Hierarchical architecture for vehicle lateral control

  r distance between the C.G. and the front/rear wheels (1.1/1.58m) C af /C ar cornering stiffness of the front/real wheels (C af = C ar = 42000N/rad) diagram to investigate the changes caused by the variations of vehicle parameters. The results of this investigation are important to have an insight of vehicle lateral behavior and to design the vehicle controller.

Figure

  Figure 4.9(a) shows the bode diagrams of the frequency response under vehicle speeds

  Bode graph at different vehicle speeds (System Input: δ; Output: e1 ) Bode graph under different loads (System Input: δ; Output: e1 )

Figure 4 .

 4 Figure 4.9: Open-loop responses to parameter variations

Figure 4 .

 4 Figure 4.10: Block diagram of PID controller

Figure 4 .

 4 Figure 4.10 shows a block diagram of PID controller. The PID algorithm is described by :

Figure 4 .

 4 Figure 4.11: P control system

Figure 4 .Figure 4 .

 44 Figure 4.12: Step response of PID controller after the first tuning

Figure 4

 4 Figure 4.15: PID controller with Anti-Windup

Figure 4 .

 4 Figure 4.16: PID with anti-windup control system: step responses at different speed

Figure 4 .

 4 Figure 4.17: Simple bike model

Figure 4 .

 4 Figure 4.18: Membership functions

Figure 4 .

 4 Figure 4.19: Traditional fuzzy controller: step responses at different speeds

Figure 4 .

 4 Figure 4.20: Decomposition of operating regimes

Figure 4 .

 4 Figure 4.21: Lateral controller: Multi-model fuzzy controller block diagram

Figure 4 .

 4 Figure 4.22: Variables in multi-model fuzzy controller

Figure 4 .

 4 Figure 4.24: Multi-model fuzzy controller: step responses at different speeds

  4.27. This input trajectory is different from the trajectory shown in Fig. 4.25. In the latter one, we give out the time history of the desired lateral displacement. If the test vehicle performs this

Figure 4

 4 Figure 4.25: Desired trajectory (1)

Figure 4 .

 4 Figure 4.26: Lane keeping control results at different speeds (1)

Figure 4 .

 4 Figure 4.28(b) shows the time history of lateral position errors. We can find the proposed multi-mode fuzzy controller can assure good tracking performances in different speed scenarios. The maximum lateral position error occurs at 90 km/h, and the maximum value is less than 0.05 m.Figure 4.28(c) shows the lateral acceleration curves. The

Figure 4 .

 4 28(c) shows the lateral acceleration curves. The maximum value of lateral acceleration is about 0.6 m/s 2 , which means the ride comfortable is ensured. Furthermore, the acceleration results are very similar even there are big difference between the operation speeds. This shows the proposed multi-model controller can provide stable performances in a wide range of operation speed.

4. 6 . 3

 63 Test 3: Lane keeping control under different loads and Cornering Stiffness

Fig. 4 .

 4 Fig. 4.29(a) and Fig.4.29(b) show the time history of the lateral position error and lateral acceleration respectively. In both the two figures, the differences between the two cases are very small. The proposed controller shows a strong adaptability to the variations of vehicle load, moment inertia and wheel cornering stiffness.

Figure 4

 4 Figure 4.27: Desired trajectory (2)

Figure 4 .

 4 Figure 4.28: Lane keeping control results at different speeds (2)

Figure 4 .

 4 Figure 4.29: Lane keeping control results under different loads

  Figure 4.30: Virtual Desired Trajectory

Figure 4 .

 4 Figure 4.31: Lane changing control results at different speeds

Figure 4 .

 4 Figure 4.32: Lane changing control results under different loads

Figure 5 . 2 :

 52 Figure 5.2: Integrated control system

  the controlled vehicle will trace a desired trajectory in which the steering operations are required. The profile of the proceeding vehicle's speed and the desired lateral displacement are shown in Fig.5.3. In Fig. 5.3(a), one can find that during the period of[5, 10] s, the controlled vehicle needs to accelerate from 10 m/s to 26 m/s (36 km/h to 93.6 km/h), and than during the period of[25, 37] s, the vehicle decelerates from 26 m/s to a low speed of 5 m/s (18 km/h). While, in Fig.5.3(b), it shows that the controlled vehicle needs to perform a 3-meter deviation during the accelerate period and it needs to steer back during the decelerate period.The results of the longitudinal control system, which include the upper and lower longitudinal controllers, are shown in Fig.5.4. The time history of the proceeding and the following vehicles' speeds are shown in Fig.5.4(a). We can find that the following vehicle can follow smoothly the speed variations of the proceeding vehicle.

Figure 5

 5

Figure 5 .Figure 5 . 3 :

 553 Figure 5.4(c) shows the coordinated throttle and brake controller results. One can find the throttle and brake actuators can work coordinately, and smoothly. However, there are three little oscillations in the throttle curve. In fact, these oscillations are induced by

Figure 5 .

 5 Figure 5.5 shows the results of the lateral control system. The result of the steering angle of the controlled vehicle is shown in Fig. 5.5(a). One can find the controlled vehicle can steer accurately and smoothly to trace the desired trajectory, and there is no high frequency oscillation in the steering output.

Figure 5

 5 Figure 5.4: Longitudinal control results

Figure 5 . 5 :

 55 Figure 5.5: Lateral control results

Figure 6 . 1 :

 61 Figure 6.1: Bicycle model for vehicle lateral dynamics

Figure 6 . 6 :

 66 Figure 6.6: Multi-sensor system

  6.8. The communication between the supervisor and a vehicle is based on a general communication protocol using a specific framework. Therefore the development of a human machine interface (HMI) is required to help the user communicate with the platoon of vehicles. The HMI is in charge of different types of data flows[START_REF] Kamel | Intelligent Transportation System Design and Monitoring[END_REF].

Figure 6 .

 6 Figure 6.8: Platoon communication system

Figure 6 .

 6 Figure 6.9: Vehicle structure

2 .

 2 Longitudinal control (upper level controller, lower level controller, string stability, traffic flow stability, etc) 3. Lateral control (lane keeping control, lane changing control) 4. Integration of longitudinal and lateral control 5. Vehicle state observation and multi-sensor intelligent vehicle prototype design

•

  Ce mémoire est consacré à la mise en oeuvre de commandes d'un train de véhicules intelligents ayant pour objectifs premiers la réduction de la congestion et l'amélioration de la sécurité routière. Au cours de ces dernières décennies, l'industrie automobile a vécu un développement considérable et par suite le secteur automobile a joué un rôle important dans l'évolution industrielle et même de notre société. Néanmoins, les problèmes de transport tels que la congestion du trafic, la sécurité routière, la pollution et la consommation de carburant sont de plus en plus graves dans le monde entier. La conception d'AHS (Automated Highway System) a été proposée pour faire face à ces problèmes et atteindre l'objectif d'une "mobilité durable", avec des véhicules pouvant rouler à terme en formation de "train de véhicules". Depuis les deux dernières décennies, des recherches sur l'AHS ont vu des progrès significatifs. Les contrôles longitudinal et latéral du véhicule représentent l'un des sujets les plus étudiés, actuellement, par les chercheurs et les constructeurs automobiles. Le contrôle longitudinal Le système de contrôle longitudinal offre son assistance au conducteur pour contrôler le véhicule en utilisant les commandes d'accélérateur et de frein. La première génération de ces systèmes est principalement développée pour améliorer le confort de conduite avec une certaine amélioration de la sécurité. En revanche, les impacts de ces systèmes sur le trafic sont insuffisamment étudiés[Swaroop 1999]. Dans ce mémoire, nous envisageons le contrôle longitudinal pour un train de véhicules, donc nous devons tenir compte non seulement des contraintes de confort et de sécurité, mais aussi des exigences de stabilité de la chaîne, de stabilité des flux de trafic ainsi que de l'augmentation de capacité de trafic. Pour répondre à ces exigences, la structure du système de contrôle longitudinal est conçue pour être hiérarchique avec un contrôleur de niveau supérieur et un contrôleur de niveau inférieur. Le contrôleur de niveau supérieur détermine l'accélération (ou la vitesse) désirée pour le véhicule contrôlé, tandis que le contrôleur de niveau inférieur décide des commandes d'accélération et de freinage pour suivre l'accélération (ou la vitesse) désirée.Les tâches principales pour la conception du contrôleur de niveau supérieur sont la conception d'une régulation d'inter-distance entre les véhicules et l'algorithme de contrôle associé. La régulation d'inter-distance détermine l'espacement entre le véhicule contrôlé et le véhicule précédent, qui a des grandes influences sur les de poursuite. Le suivi et le changement de trajectoire sont les deux principales opérations.Nous étudions, tout d'abord, la loi de commande pour le suivi de trajectoire. Le modèle latéral est un modèle de type "bicyclette" avec une description du pneumatique dans des conditions de faible glissement. Etant donné que les paramètres du véhicule, comme la vitesse, la masse, le moment d'inertie, la rigidité du pneu, etc., ne sont pas toujours constants, le modèle latéral est donc un système LTV (Linear Time-Variant). Nous proposons une loi de commande de type multi-modèle floue qui hérite les points forts de la commande multi-modèle et de la commande floue. Cette loi peut donner de bonnes performances pour la gamme de vitesses de conduite. Par ailleurs, elle peut maîtriser les incertitudes du système (la masse, le moment d'inertie, la rigidité du pneu, etc.).La principale difficulté dans l'opération de changement de trajectoire est que le véhicule doit traverser une certaine distance sans les retours des capteurs si les capteurs ne peuvent pas mesurer la position du véhicule entre les deux voies, par Enfin, nous présentons un prototype multi-capteurs de véhicule intelligent à échelle réduite (1 :10). Les différents aspects du prototype tels que la structure du véhicule, le système de communication ainsi que l'IHM (Interface Human-Machine) sont présentés. Ce prototype offre une plate-forme pour l'intégration des technologies, l'analyse de la fiabilité, le contrôle en temps réel et la surveillance. Les performances des divers algorithmes de commande proposées dans ce mémoire ont été testées par simulations numériques, et les résultats ont été confirmés par les premières expériences en utilisant ce prototype.

Dans

  le deuxième chapitre, nous réalisons, tout d'abord, les modèles de la dynamique longitudinale et latérale, afin d'élaborer des lois de commande pour la régulation de la position du véhicule suiveur dans la suite des travaux. On établit le modèle longitudinal en utilisant la formule de Newton. Puis, la description mécanique du comportement du groupe motopropulseur est présentée. Ce dernier comprend les sous-modèles des différentes parties : le moteur, le convertisseur de couple, la boîte de vitesses automatique, les arbres de transmission et le différentiel. En ce qui concerne le modèle latéral, nous présentons à la fois le modèle cinématique ainsi que le modèle dynamique. Le modèle cinématique fournit une description mathématique du mouvement du véhicule sans tenir compte des forces influant le mouvement. Quant au modèle dynamique, le modèle retenu est un modèle de type "bicyclette" avec une description du pneumatique dans des conditions de faible glissement. Les modèles longitudinal et latéral sont utilisés par la suite pour générer les lois de commande dans les chapitres suivants. Dans le troisième chapitre, nous développons la loi de commande longitudinale. Le système de contrôle longitudinal est conçu pour être hiérarchique avec un contrôleur de niveau supérieur et un contrôleur de niveau inférieur. Pour le contrôleur de niveau supérieur, une régulation d'inter-distance (SSP, Safety Spacing Policy) est proposée. Elle utilise à la fois les états du véhicule et la capacité de freinage pour déterminer la distance désirée pour le véhicule suiveur. Nous présentons aussi une comparaison entre la SSP et la régulation d'inter-distance traditionnelle CTG (Constant Time Gap spacing policy). Quant au contrôleur de niveau inférieur, on propose un contrôleur de type commande floue coordonnée pour gérer l'accélérateur et le finage. Enfin, on teste le système de contrôle longitudinal par simulation numérique. Le quatrième chapitre est consacré au contrôle latéral. Nous proposons une loi de commande multi-modèle floue afin d'effectuer les opérations de suivi et de changement de trajectoire. Une trajectoire virtuelle VDT (Virtual Desired Trajectory) est introduite pour fournir une trajectoire lisse et efficace pour l'opération de changement de trajectoire. Afin de réaliser des commutations flexibles entre les différentes opérations, nous proposons aussi une architecture hiérarchique pour le système de contrôle latéral. A partir des lois de commande proposées dans les chapitres précédents, le chapitre 5 présente un système complet intégrant le contrôle longitudinal et le contrôle latéral. Ce système complet permet de réaliser une conduite automatisée pour les véhicules sur AHS. Le dernier chapitre s'attache d'écrire, d'une part, l'estimation des variables d'états du véhicule, et d'autre part l'introduction d'un prototype multi-capteurs de véhicule intelligent à échelle réduite. Nous proposons un filtre de Kalman-Bucy pour estimer des états du véhicule de la dynamique latérale. En outre, les différents aspects pour réaliser le prototype de véhicule intelligent sont présentés.

Table 1

 1

		.1: Potential benefits of AHS
	Elements	Benefits
	Road capac-
	ity

Table 1

 1

			.1: Potential benefits of AHS
	Elements	Benefits
	Travel time	AHS can save travel time by reducing congestions in urban highway
	saving		travel, and permitting higher cruise speed than today's driving.
	Commercial	More efficient commercial operations and transit operations. Com-
	and	transit	mercial trucking can realize better trip reliability and transit opera-
	efficiency	tions can be automated, extending the flexibility and convenience of
			the transit option to increase ridership and service.
	1.2.3 Intelligent vehicle

Implementation of AHS requires automatically controlled vehicles. Nowadays, automobiles are becoming more and more "intelligent", with increasingly equipping with electromechanical sub-systems that employ sensors, actuators, communication systems and feedback control. Thanks to the advances in solid state electronics, sensors, computer technology and control systems during the last two decades, the required technologies to create an intelligent transportation system is already available, although still expensive for full implementation. According to Ralph K

[Ralph 2008

], today's cars normally have 25 to 70 ECUs ( Electronic Control Unit), which perform the monitoring and controlling tasks. Few people realize, in fact, that today's car has four times the computing power of the first Apollo moon rocket

  Established in 1999, the ITSC (National Intelligent Transport Systems Center of Engineering and Technology) aims at improving traffic safety and efficiency by using the communication and information technologies, and it is supported by the

	Ministry of Science and Technology. Its current research projects cover a wide field
	from society science to technology: Electronic toll collection and short range com-
	munication, traffic data analysis, safety monitoring and early-warning technology
	for commercial vehicles, automated snow sweeping vehicle, policy consultation and
	planning, and etc.
	1.3.1.3 Projects in Europe

• Activities in China

[ITSC ]

In Europe, a number of projects have been carried out since 1970s. The development of ALI (Autofahrer Leit und Information System) was promoted in the middle of 1970s in Germany. The programme PROMETHEUS ( PROgraM for a European Traffic with Highest Efficiency and Unprecedented Safety) was implemented during 1986 and 1994, leaded by EUREKA (Europe Research Coordination Agency). Its objective was to improve traffic safety and the management of road transport. Contemporaneously, the programme DRIVE (Dedicated Road Infrastructure for Vehicle Safety in Europe) and DRIVE II (1989-1994) studied traffic infrastructure such as road pricing and park and ride for reducing the volume of traffic in city area. These programmes have been succeeded by the current PROMOTE (Programme for Mobility in Transportation in Europe) Programme and the Telematics Applications Programme. In 1991, ERTICO -ITS Europe was founded, which is a multi-sector, public/private partnership pursuing the development and deployment of Intelligent Transport System and Services [ERTICO ]. More recently, the programme ADASE (Advanced Driver Assistance Systems) was promoted to improve road safety, efficiency and comfort. It provided the communication and dissemination

  According to longitudinal dynamics described in equation 2.1, considering the assumptions in the previous subsection, we get the new equation of longitudinal dynamics,

	• Negligible roll, pitch and vertical motions
	• Negligible wind speed
	2.3.3.2 Longitudinal model

Table 3

 3

	.1: Parameters for longitudinal controller
	Parameters	L	w i	t d	λ	j
	Value	6.5 m 4.5 m 0.1 sec 0.4 -7.32 m/s 2

Table 3 .

 3

		2: Platoon vehicles' braking capacities (m/s 2 )
				Vehicle No. in platoon
		1	2	3	4	5	6	7	8
	Platoon 1	-7.62 -7.32 -6.72 -7.08 -7.8 -6.9 -7.26 -6.54
	Platoon 2	-7.93 -6.85 -7.42 -6.53 -7.84 -7.64 -7.18 -7.24
	Platoon 3	-6.76 -7.88 -7.69 -7.42 -6.93 -7.61 -6.69 -7.17

Table 3

 3

				.3: Fuzzy Rule Base
				Input 2: Acceleration Error
			Nb	Ns	Null	Ps	Pb
	Input 1: Nb D-inten D-inten D-sof D-sof	Null
	Speed	Ns D-inten D-sof D-sof	null	A-sof
	Error	Null	D-sof	D-sof	Null	A-sof	A-sof
		Ps	D-sof	Null	A-sof A-sof A-inten
		Pb	Null	A-sof	A-sof A-inten A-inten

Table 4

 4

		.1: Nomenclature of Bicycle Model
	e 1	distance of the Center of Gravity
		(C.G.) of the vehicle from the cen-
		ter line of the lane (m)
	e 2	orientation error of the vehicle
		with respect to the lane (rad)
	δ	steering angle (rad)

Table 4 .

 4

		2: Ziegler-Nichols tuning rule based
	on critical gain K cr and critical period P cr
	(Second Method)
	Type	of
	controller

Table 4

 4

						.3: Fuzzy Rule Base
								Input 2: Y
						s1 s2 s3 ce b1 b2 b3
		Input 1: s1 b3 b3 b2 b2 b1 ce ce
			Y		s2 b3 b3 b2 b2 b1 ce ce
					s3 b3 b3 b2 b1 ce s2 s2
					ce b3 b3 b2 ce s2 s1 s1
					b1 b2 b2 ce s3 s2 s1 s1
					b2 ce ce s3 s2 s2 s1 s1
					b3 ce ce s3 s2 s2 s1 s1
		1.5
	Lateral position (m)	0 0.5 1										step input v=80 km/h v=40 km/h v=20 km/h
												v=10 km/h
		-0.5	0	1	2	3	4	5	6	7	8	9	10
								Time (s)

Table 4 .

 4

			4: Membership Function Variables
				Local controllers
			Low	Medium-Low Medium-High	High
	y l /y r (m)	-0.2/0.2	-0.3/0.3	-0.4/0.4	-0.5/0.5
	a l /a r (deg)		-10/10	-6/6		-4/4	-3/3
	δ lmax /δ rmax (deg) -20/20	-12/12		-8/8	-6/6
			Table 4.5: Fuzzy Rule Base
				Input 2: Angular Error
				Left	Center Right
	Input 1:	Left	RightB RightS Center
	Lateral Center RightS Center LeftS
	Error		Right Center LeftS	LeftB

Table 5

 5

			.1: Parameters for longitudinal controller
	Parameters	L	w	t d	λ	j
	Value	6.5 m	4.5 m	0.1 sec	0.4	-7.32 m/s 2
	Parameters	m	I z	l f /l r	C af /C

ar Value 1485 kg 2872 kgm 2 1.1/1.58 m 42000 n/rad

We build a scenario which requires the simultaneous operations of the longitudinal and lateral controllers. In this scenario, the controlled vehicle is supposed to follow a leading vehicle which will perform accelerate and decelerate operations. And at the same time,

Table 6

 6

		.1: Nomenclature of Bicycle Model
	ψ	yaw angle (rad)
	δ	steering angle (rad)
	ρ	road curvature (1/m)
	m	mass (1485kg)
	V x /V y	longitudinal/lateral		velocity
		(m/s)
	I z	yaw (2872kgm 2 ) moment	of	inertia
	l f /l r	distance between the C.G. and
		the front/rear wheels (1.1/1.58m)
	C af /C ar cornering	stiffness	of	the
		front/real wheels (C af

WHO: World Health Organization.

The first and second causes are Ischemic heart disease and Unipolar major depression. Source:" The Gloval Burden of Disease," by theWHO, 1996.

The assumption of small steering angle is reasonable for the vehicles in highway driving conditions. In this work, a small steering angle means δ ∈ [-15 • , 15 • ].

A.A.S.H.T.O.: American Association of State Highway and Transportation Officials

comportements du véhicule et ainsi sur le trafic. Dans ce travail de recherche, nous proposons une régulation de sécurité (SSP, Safety Spacing Policy), comme fonction non-linéaire de la vitesse du véhicule. Elle utilise à la fois les informations sur l'état du véhicule et la capacité de freinage afin d'ajuster la position et la vitesse du véhicule contrôlé. En outre, des efforts particuliers sont consacrés à l'analyse de la SSP dans les aspects de la stabilité de chaîne, et de la stabilité des flux de trafic ainsi que la capacité de trafic. Enfin, une comparaison entre la SSP et la régulation d'inter-distance traditionnelle CTG (Constant Time Gap spacing policy) est également présentée. Les non-linéarités et les incertitudes dans la dynamique longitudinale du véhicule sont les principaux défis à relever pour la conception de contrôleurs d'accélération et de freinage (Contrôleur de niveau inférieur). Par exemple, les modèles exacts du moteur et de la dynamique du système de freinage sont toujours des modèles nonlinéaires avec de nombreux paramètres. Par ailleurs, dans la plupart des cas, ces modèles sont difficiles à obtenir. En outre, afin d'avoir des opérations acceptables comme un bon conducteur humain, la commande d'accélérateur et la commande de freinage doivent être coordonnées. Pour relever ces défis, nous proposons un contrôleur de type commande floue coordonnée pour gérer l'accélérateur et le freinage. Dans un premier temps, deux commandes floues pouvant effectuer des actions additives sur les pédales d'accélération et de freinage sont proposées. Le principal avantage de cette approche est qu'elle peut réaliser le contrôle de vitesse rapidement et efficacement sans exigence de modèles exacts de moteur et de freinage.Ensuite, nous proposons une logique de commutation permettant de coordonner les actions des deux pédales (accélérateur et freinage).• Le contrôle latéralEn ce qui concerne le système de contrôle latéral, il pilote l'angle de braquage du véhicule pour que le véhicule puisse suivre la trajectoire ou en changer. La loi de commande doit assurer une bonne qualité de conduite et une faible erreur

exemple, si on utilise le capteur de type magnétomètre. Nous utilisons la trajectoire virtuelle désirée (VDT, Virtual Desired Trajectory) qui peut fournir une référence virtuelle pendant l'opération de changement de trajectoire. Afin d'effectuer des commutations flexibles entre les différentes opérations latérales, telles que le suivi de trajectoire, le changement de trajectoire, le dépassement, etc., nous proposons aussi une architecture hiérarchique pour le système de contrôle latéral. Sur la base des résultats des commandes longitudinale et latérale, nous proposons un système de contrôle complet intégrant ces contrôles. Avec ce système complet, le contrôle pour la conduite automatisée peut être réalisé sur autoroute. En outre, l'estimation des variables d'états du véhicule est discutée. Pour les lois de commandes que l'on a proposées, on suppose que toutes les variables utilisées sont disponibles. Néanmoins, cette hypothèse n'est pas toujours vraie dans la pratique (indisponibilité de la technologie, prix. . . ). Par conséquent, l'observation d'état du véhicule est incontournable. Compte tenu de la configuration du système de capteurs et les états utilisés pour les contrôleurs du véhicule, nous avons choisi la vitesse de lacet du véhicule en tant que paramètre à estimer. Etant donné que la dynamique du véhicule latérale est un modèle LTV, on propose un filtre de Kalman-Bucy pour l'estimation des variables du système LTV.

Acknowledgments

The PhD work presented in this thesis has been done at "Laboratoire d'Automatique, Génie Informatique et Signal" (LAGIS) in Ecole Centrale de Lille, from September 2007 to September 2010. This work is partly supported by the China Scholarship Council (CSC).

The decomposition of a system's full range of operation into a number of sub-regimes is illustrated in Fig. 4.3. In each operating regime, a local model or controller is applied. Of course, the final goal is a global model or controller, and it can be realized by combining the local models or controllers in some ways. Thus, the operating regime approach includes typically the following tasks [Murray-Smith 1997]:

• Decompose the system's full range of operation into several operating regimes.

• Select simple local model or controller structures within each operating regime. The local model or controller structures are usually parameterized by certain variables that must be determined.

• A method for combining the local models or controllers into a global one.

In the case of a complex system in which there has a large number of variables affecting the behaviour of system, the decomposition of the operating regimes will be a high dimensional problem. To deal with the complexity and high-dimensionality, a common method is hierarchy, which could be found in almost every area of science [START_REF] Mesarovic | [END_REF]]. The first step of this idea is to decompose roughly the full operating range into several operating regimes according to the most important characteristic variables. Now each of these

Dilemma between local and global

Obviously, in the operating regime approach, a trade-off between the number of operating regimes and the complexities of the local models should be made.

Combination of local models and controllers

In the previous subsections, we have discussed briefly the issues of operating range decomposition and local controller selection, then the nest step is to combine the local models

Soft partitions and interpolation method

In the case of hard partitions of operating regime, there exist a sudden change between two adjacent operating regimes. However, in some cases, the sudden change between the operating regimes is not natural. For instance, the system behavior changes gradually as the operating point moves between different operating regimes. In such cases, the operating regimes can be described as overlapping sets and perform a smooth deterministic transition between them.

Consider again the decomposition shown in Fig. 4.6. If the boundary between the operating regimes characterized by LOW and HIGH is soft, which means there is a overlapping region between the classifications LOW and HIGH. Then a mixture of the local models or controllers should be applied.

Methods that can be applied to describe such soft boundaries between operating regimes includes fuzzy logic and interpolation methods, see [Zadeh 1973, Takagi 1985] and [Johansen 1993b]. In fuzzy logic, the logic statement described in (4.1) acts as a fuzzy rule, which is interpreted in terms of fuzzy sets defined as LOW and HIGH, as shown in Fig. 4.7. The inference system of fuzzy logic can then be built based on a series fuzzy rules. The resulting inference mechanism can be viewed as an interpolation algorithm that gives a certain weight on the local models or controllers in the different operating regimes, depending on the operating point.

where the smooth weighting functions ρ 1 , ρ

The saturation block is a nonlinear element, and it will induce the integrator windup phenomenon in the PID control system, which will make worse the performance of the PID controller and even the stability of the control system. Different anti-windup algorithms have been proposed in former researches, such as the Set Point Limitation, Incremental

Algorithms, Back-calculation, etc. [Åström, K.J. 2002]. In this work we use the traditional back-calculation method to deal with the anti-windup phenomenon.

The back-calculation method works as follows: When there is a output saturate, the integral term in the controller is recomputed so that its new value gives an output at the saturation limit. is fed to the input of the integrator through gain 1/T t . A rule of thumb that has been suggested is to choose T t = √ T i T d = 0.366 [Åström, K.J. 2002]. Therefore, the values of the PID with anti-windup control system parameters are:

Then we will test the proposed controller with a simple step input. As we have already shown the fact that the vehicle velocity has great influences on vehicle lateral dynamics in Section 4.4, then it is interesting to test whether the above mentioned controller is robust to the variation of vehicle speed. Therefore, the test will be performed at 80, 40, 20, 10 km/h respectively.

Figure 4.16 shows the step responses of the PID with anti-windup. It can be found that the results at 80 and 40 km/h are quite similar, which are better than the results in task of designing a lateral control method which is robust to the velocity variations.

In section 4.2, the multiple model approach has been introduced as an effective method to deal with the complex systems where nonlinearity and wide range of parameter variations exist. Thus we will use this method to deal with the problem of velocity variations in vehicle lateral controller design.

Decomposition of the operating regime

The first step of the application of multiple model approach is to find the appropriate axes along which the control system can be partitioned. Obviously, the vehicle velocity is the "appropriate axe" in our case. In highway operations, the vehicle speed varies in a wide range from low to high speed, normally in the range of [0, 120] km/h. Then, how to decompose the vehicle speed into the operation regimes is the problem need to envisaged.

Two questions should be answered in this procedure:

1. How many operating regimes should be decomposed? (It is associated with the question that how much is the speed interval that one operating regime should cover.)

2. Whether an overlap is required for two adjacent regimes? (It concerns the question of which kind of partition should be selected: hard partition or soft partition.)

How many operating regimes should be decomposed?

Consider the first question, since the velocity is the sole "axe" used to decompose the operating regime in our case, the decomposition procedure is then less complex than the systems with several decomposition "axes". Then, we need to decide how many operating regimes that the full velocity range should be divided. In this procedure, a trade-off between the number of operating regimes and the complexities of the local models should be made (see the discussions in section 4.2.2).

One feasible idea is that we divide the full speed range into fine partitions, and a simple local model is proposed for each partition. For example, we can divide the speed range into 12 equal operating regimes as: [0, 10], [10, 20], • • • , [110, 120] km/h. Since the partitions of speed are rather fine, then in each operating regime, we consider the vehicle lateral dynamic behaviors are similar when the speed varies in each regime. For each regime, a simple local controller can be designed, such as a PID controller, which can be designed using the method that we have shown in section 4.5.1. Thus, a candidate method with 12 operating regimes and 12 local PID controllers could be generated.

On the contrary, another idea is that we divide the full velocity range into several rough partitions, and a more complex local controller is proposed for each partition. For example, we can divide the speed range into four operating regimes, and each regime coves an interval of 30 km/h as: [0, 30], [30,60] Compare the two methods suggested above, the latter one is considered to be better.

Two main reasons contribute to this choice. One main reason is that, from the system constructer point of view, the latter method has only 4 local controllers which is more simple and clear than the former one, which has 12 local controllers. A further reason is that the fuzzy controller is more accurate and more adaptive than the PID controller, as shown in section 4.5.2.

Whether an overlap is required for two adjacent regimes?

Then we need to consider the second question that whether an overlap is required for two adjacent regimes. As we have discussed in section 4.2.2, the hard partitions with model switch method will induce discontinuities in the global control control law. Besides, undesirable peaks which may appear very detrimental to the vehicle in terms of quality of service and passenger comfort. Therefore, an overlap should be introduced to the operating regimes which can perform a smooth deterministic transition between them.

Thus, the soft partition method is used in this work.

Consider the four operating regimes that we have just proposed: [0,30], [30,60], [60,90],

[90,120] km/h, we make an overlap of 10 km/h for every two adjacent regimes. Then the modified four regimes are: [0,35], [25,65], [55,95], [85,120] km/h. For the sake of expression, we give each regime a name, as : Low, Medium-Low, Medium-High, and High.

Then the decomposition of the operating regimes is shown in Fig. 4.20.

In the following sections, we will design the multi-model controller based on the above operating regimes.

Multi-model fuzzy controller design

In this subsection, we propose a multi-model fuzzy controller to perform the lane tracking tasks for the lane keeping maneuver. At first, according to the four operating regimes that we have just proposed, four fuzzy logic-based local controllers are designed respec-

In this chapter, at first, we will establish a global control architecture which includes the longitudinal and lateral control systems, and then we will test the performance of the global control system throughout a series of experiments based on Matlab/Simulink.

Finally, some conclusions will be given.

System integration

Uncoupled longitudinal and lateral control system

In the former researches, Wijesoma and Kodagoda have shown a global control architecture for a golf car-like AGV (Autonomously Guided Vehicle) [START_REF] Kodagoda | [END_REF][START_REF] Wijesoma | [END_REF]. In their works, the coupling effects of vehicle speed on steering angle (and hence angular velocity), and vice versa, was not explicitly accounted for. Thus a global control system contenting the independent longitudinal controller and lateral controller was proposed in Fig. 5.1. In this control system, the longitudinal and lateral control are achieved through separate uncoupled controllers. The single longitudinal control performance and lateral control performances were tested to be effective in their works. In addition, the simultaneous operations of the longitudinal and lateral control were also considered. But, the variation of speed is only from 3 m/s to 7 m/s, which is reasonable for the Golf Car but not sufficient for the highway vehicle operations, because this speed region covers only the low speed region for the vehicle driving in highway.

Integrated longitudinal and lateral control system

Although in our previous works, the longitudinal and lateral controllers have been designed Although the vehicle velocity varies in a wide range, and the lateral acceleration measurement is noisy, the estimated lateral velocity and yaw rate can closely follow the variations of the true values during the whole experiment period. The designed Kalman-Bucy filter is proved to be effective in the vehicle lateral dynamic estimation.

Presentation of reduced scale multi-sensor intelligent vehicle prototype

In this section, a reduced scale (1:10) multi-sensor intelligent vehicle prototype will be introduced [START_REF] Kamel | Intelligent Transportation System Design and Monitoring[END_REF]. This prototype provides a platform for advanced technology integration, reliability analysis, real time control and monitoring... An overview of the platoon is shown in Fig. 6.5. The different parts of the car are to be explained in the following sections.

Technologies

Multi-sensor system

At first, the multi-sensor system, which is necessary to perform the control strategies, will be introduced. A cost oriented principle was established when choosing the most advanced technologies which meet the operation requirements for the reduced scale cars.

The multi-sensor system diagram and configuration are shown in Fig. 6.6.

Sensors for longitudinal control

We propose to determine distance between vehicles by using two kinds of sensors, both chosen because of their 2m-range which makes them efficient and reliable at our scale:

Abstract

This PhD thesis is dedicated to the control strategies for intelligent vehicle platoon in highway with the main aims of alleviating traffic congestion and improving traffic safety. After a review of the different existing automated driving systems, the vehicle longitudinal and lateral dynamic models are derived. Then, the longitudinal control and lateral control strategies are studied respectively.

At first, the longitudinal control system is designed to be hierarchical with an upper level controller and a lower level controller. For the upper level controller, a safety spacing policy (SSP) is proposed. It is shown that the proposed SSP can ensure string stability, traffic flow stability and improve traffic capacity. Then, a coordinated throttle and brake fuzzy controller (lower level controller) is designed, in which a logic switch is designed to coordinate the two actuators (throttle and brake pedals).

Second, for the lateral control, a multi-model fuzzy controller is designed. And a hierarchical lateral control architecture is also proposed, which can effectuate flexible switch between different lateral operations. After that, the integration of the longitudinal controller and lateral controller is also studied.

Finally, the estimation of vehicle states is discussed. A Kalman-Bucy filter is designed to estimate vehicle states in lateral dynamics. Moreover, a reduced scale multi-sensor intelligent vehicle prototype is also presented. The performances of the divers control algorithms proposed in this thesis have been tested in numerical simulations, and the first step experiments with the reduced scale vehicle prototype gave encouraging results.