自動車輛駕駛縱向暨橫向控制設計

國

立

交

通

大

學

電機與控制工程系

博 士 論 文

自動車輛駕駛縱向暨橫向控制設計

Longitudinal and Lateral Control Design

for Vehicle Automated Driving

研 究 生：蔣欣翰

指導教授：吳炳飛 教授

李祖添 教授

吳幸珍 教授

自動車輛駕駛縱向暨橫向控制設計

Longitudinal and Lateral Control Design for Vehicle Automated Driving

研 究 生：蔣欣翰 Student : Hsin-Han Chiang

指導教授：吳炳飛 Advisor(s) : Bing-Fei Wu

李祖添

Tsu-Tian

Lee

吳幸珍

Shinq-Jen Wu

國 立 交 通 大 學

電機與控制工程系

博 士 論 文

A Dissertation

Submitted to Department of Electrical and Control Engineering College of Electrical and Computer Engineering

National Chiao Tung University in partial Fulfillment of the Requirements

for the Degree of Doctor of Philosophy

in

Electrical and Control Engineering

February 2008

Hsinchu, Taiwan, Republic of China

自動車輛駕駛縱向暨橫向控制設計

研究生：蔣欣翰

指導教授：吳炳飛 博士

李祖添 博士

吳幸珍 博士

國立交通大學電機與控制工程系博士班

摘

要

車輛駕駛自動化是先進車輛系統(Advanced vehicle systems)主要研究部份

之一，Taiwan iTS-1 是由交通大學自行開發之自動駕駛實驗車。在本論文

中，我們介紹此一多模式自動駕駛之系統，內容包含控制目標之決定、系

統架構設計、車輛動態模型驗証、控制演算法、以及路上測試。此系統實

現於

Taiwan iTS-1 並於真實交通環境高速道路及市區道路測試，驗證其正

確及有效性。我們設計一個階層控制的自動駕駛系統，上層控制(Upper-level

control)判斷道路交通環境並決定是否啟動道路保持、道路切換、定速及適

應巡航控制、以及停走操作模式，並計算該模式操作所需之安全車速及行

駛軌跡，再交由車體控制(Vehicle-body control)來執行。為使系統能像駕駛

人一般控制車輛行駛速度以及轉向，我們採用模糊控制技術來設計車體控

制器，因系統除了具有像駕駛人之模式決策(Decision-making)，也模仿駕駛

人之智能及行為，並展現可與駕駛人比擬之加速、剎車、以及轉向操控。

另外，考慮到車輛縱向及橫向動態耦合(Coupling)之特性，我們發展一種具

有三自由度之非線性車輛動態模型，設計一個整合縱向及橫向之控制器，

並藉由

CarSim 模擬環境來驗證此控制演算法之可行性及實用性。

Longitudinal and Lateral Control Design for Vehicle

Automated Driving

Student：Hsin-Han Chiang

Advisor(s): Dr. Bing-Fei Wu

Dr. Tsu-Tian Lee

Dr. Shinq-Jen Wu

Department of Electrical and Control Engineering

National Chiao Tung University

ABSTRACT

Vehicle automation is an important research topoic of advanced vehicle systems (AVS). Taiwan iTS-1 is an experimental autonomous vehicle developed by National Chiao Tung University (NCTU). In this dissertation, a complete process of developing a multi-mode automated driving system is presented. This process consists of control objectives determination, system configuration design, vehicle dynamics modeling and validation, control algorithm development, and on-road testing. A hierarchical-control structure is proposed in the system to achieve the integrated longitudinal and lateral vehicle control. Upper-level control perceives road environment and determines the proper and safe operation modes including lane-keeping, lane-change, cruise control, adaptive cruise control, and stop-and-go. In each mode, the desired-velocity and reference-trajectory are primarily determined, and then are forwarded to vehicle-body control. To incorporate well driving tasks of human drivers into our system, vehicle-body control utilizes the fuzzy control technique to regulate the vehicle to adapt to the desired command (velocity and trajectory). In addition to the decision-making scheme, our system can mimic a human’s intelligence and behavior to manage throttle, brake, and steering actuators in a driver-compatible way. Besides, to consider the coupling effects between the longitudinal and the lateral motion of a vehicle, a nonlinear three-degree-of-freedom vehicle dynamics is developed for a combined longitudinal and lateral vehicle controlling design. This controller is subsequently evaluated on a virtual vehicle in CarSim with remarkable results. The developed system has been verified repeatedly on highway and urban environments, respectively, with great success.

Acknowledgement

我非常感謝，也非常幸運地，我有三位指導教授─謹向我的指導教授 李祖添老師 致上最感謝之意。感謝老師從碩士班開始的悉心指導，儘管博士班時期老師常在台北， 但仍抽空回來與我們討論，且提供我們良好的研究環境。從老師的言行以及對學問的態 度，影響我甚巨，心裡常記著老師勉勵我們：「要堅持，要認真，還有善良。」非常感 謝指導教授 吳炳飛老師，在博士班的過程中，老師的積極研究態度與訓練要求深切的 感染我，全方位對軟硬體技術以及理論的學問，更是我深感佩服及想學習的目標，永不 忘老師的訓示：「一個人的態度決定一個人的高度。」此外，也向指導教授 吳幸珍老 師致上最深的感謝，從碩士班到博士班，在理論方面指導我甚多，也經由不斷與老師討 論，不斷激發我研究上的思考，也將謹記老師：「以研究來貢獻社會。」的自我期許。 感謝口試委員 鄧清政教授、姚立德教授、以及陳柏全教授，在口試時提出寶貴的 意見，以及不同的思考方向與問題，使得論文內容能更臸完備。 感謝系上老師 廖德誠教授、鄭木火教授、邱一教授，在課程上的指導以及球場上 的交流，讓我感覺亦師亦友的溫暖。 在博士班的過程中，也非常感謝彭昭暐學長，願意不斷地勉勵我以及分享豐富的人 生觀，讓我對幸福的追求有不同的體認，更銘記學長的期勉：「存善心，為善事。」此 外，也感謝實驗室文真學姐、保村學長、冠銘學長和炳榮，學弟忠潔與鎮南，一起度過 實驗室共事的日子。 感謝CSSP Lab 已畢業的學弟岑瑋、俊樺、嘉賢，我永不忘曾經一起沒日沒夜、跑 遍快速道路68 號作實驗的過程，感謝你們在硬體上的幫忙，才以使我的論文更加精彩。 感謝學弟威儀、學妹依庭，在目前持續進行的研究上努力與幫忙。我很榮幸遇到你們這 一群伙伴。 在此也要感謝陪我度過這一段求學過程的所有朋友們，我亦珍惜每一個過程與時 光。最後，非常感謝我摯愛的家人，爺爺、奶奶、爸爸、媽媽和遠在美國的妹妹，你們 的支持、照顧、容忍和深切的期盼是我完成學位的精神支柱，謹將這一份小小榮耀獻給 你們。

Table of Content

Abstract in Chinese i Abstract in English ii Acknowledgement iii Contents ……….. iv List of Figures ……….. vi List of Tables ……….. ix Nomenclature ……….. x 1. Introduction……….………..……….…. 1

1.1 Present Work Survey………...………... 1

1.2 Motivation………...……….…. 2

1.3 Major Contribution………...……….… 4

1.4 Dissertation Overview………...……… 5

2. Vehicle Overview………..………... 6

2.1 Automated Vehicular Equipments………...……….. 6

2.2 Automated Driving System Diagram………...………... 8

2.3 Function-flow………...………...………...… 10

3. Lateral Control system Design.………....…….. 12

3.1 Vehicle Lateral Dynamics………... 12

3.2 Lane-keeping Control Design..………... 16

3.2.1 Observer Design………. 19

3.2.2 Fuzzy Gain Scheduling………... 20

3.2.3 Analysis for the Lateral Controller with FGS……… 24

3.3 Lane-change Control Design……….……. 27

4. Longitudinal Control System Design..……….….. 33

4.2 Longitudinal Automation System Design...………... 37

4.2.1 Adaptive Horizontal Detection Area……….………. 38

4.2.2 Supervisory Control………... 42

4.2.3 Regulation Control………. 49

4.3 Collision Warning/Avoidance Maneuver………... 55

5. Combined Longitudinal and Lateral Control Design……...……….…... 59

5.1 Nonlinear Vehicle Longitudinal and Lateral Coupling Dynamics…………..….. 59

5.2 T-S Fuzzy Modeling for Nonlinear Vehicle Dynamics………..………... 63

5.3 Fuzzy Automated Driving Control Design……….…... 68

5.3.1 Fuzzy Controller Design……….…... 68

5.3.2 Fuzzy Observer Design………... 70

5.4 Numerical Simulations 73 6. Experimental Results…..………... 78

6.1 Test-track Testing………...……….…... 78

6.2 Freeway/Highway Testing…………..………... 81

6.3 Urban-road Testing………...…………. 93

7. Conclusions and Future Works………... 98

References 100 Appendix A. 105 Appendix B. 107 Appendix C. 108 Vita 109 Publication List 110

List of Figures

Fig. 2-1. System architecture in the test-bed vehicle, Taiwan iTS-1………….. 6

Fig. 2-2. Two-level hierarchy of the proposed automated driving system……. 8

Fig. 2-3. Structure of controller/vehicle system………..… 9

Fig. 2-4. Function-flow of the upper-level control………. 10

Fig. 3-1. Bicycle model for front-steering vehicles……… 12

Fig. 3-2. Exampled cornering characteristics of front and rear tires. (Dotted line: high friction road, and dashed line: low friction road)……… 14

Fig. 3-3. The relation between the steering ratio and the average error of measurements……….. 15

Fig. 3-4. The states signal for verification between the model and the vehicle in the case isr= 26. (solid line: model; dashed line: vehicle)... 15

Fig. 3-5. Vehicle lateral dynamics with respect to road geometry……….. 16

Fig. 3-6. Block diagram of the proposed auto-tuning lateral control system….. 21

Fig. 3-7. The membership functions for (a) vx , (b) yLd , and (c) ∆fg …………... 22

Fig. 3-8. The performance of the proposed pure feedback and FGS-feedback as compared to curvature-feedforward approach in [16]………. 23

Fig. 3-9. Closed-loop performance for the normal condition and 10% variation in the cornering stiffness……….……… 24

Fig. 3-10. Equivalent block diagram for the single-point previewed pursuit controller/vehicle system……….. 25

Fig. 3-11. Frequency response characteristics for our steering controller/vehicle system………..………... 26

Fig. 3-12. Illustration of the lane-change maneuver………. 27

Fig. 3-13. Time optimal lateral jerk reference signal in [41]………... 28

Fig. 3-14. Modified lateral jerk reference signal……….. 29

Fig. 3-15(a). Magnitude plot of front-wheel angel to yaw rate Hγ–δf (s)…………... 30

Fig. 3-15(b). Velocity-dependent function hγ–δf (vx) at velocities from 5 to 30 m/s.... 31

Fig. 4-1. Nonlinear model of the vehicle longitudinal dynamics………... 33

Fig. 4-2. Closed-loop configuration employed in the identification of ψ, q1, q2 , and q3 ……….……….. 34

Fig. 4-3. The averaged values of ψ, q1, q2, and q3, verses velocity of the

vehicle………... 35

Fig. 4-4. The I/O responses of the simulation model and its comparison with the real vehicle………... 36

Fig. 4-5. Dual-loop structure of the longitudinal automation system………….. 37

Fig. 4-6. Illustration of the scenario of a vehicle following on curves………… 38

Fig. 4-7. Derivation of the signed distance……….. 49

Fig. 4-8. Membership functions of (a) the fuzzy input and (b) the fuzzy output………. 51

Fig. 4-9. Overall structure of the proposed regulation control structure……….. 51

Fig. 4-10. Constant velocity-tracking performance for (a) proposed PD-based FLC and (b) PID-based FLC……..………... 52

Fig. 4-11. Control surface of the single-input fuzzy control……….... 52

Fig. 4-12. Headway distance for car-following………... 55

Fig. 4-13. The relation between the TTC and the warning evaluate signal with respect to different velocities………..… 57

Fig. 4-14. Warning degree in three zones……….... 58

Fig. 5-1. 3-DOF vehicle model………..… 59

Fig. 5-2. Global sector nonlinearity………...…… 63

Fig. 5-3. Membership functions for z1, z2, and z3………...……… 64

Fig. 5-4. Animation window of Comparison 1……….. 73

Fig. 5-5(a). Lateral offset comparison of the proposed controller against the Autopia approach……… 74

Fig. 5-5(b). Velocity comparison of the proposed controller against the Autopia approach……….. 74

Fig. 5-6. Animation window of Comparison 2……….. 75

Fig. 5-7(a). Trajectory comparison of the proposed controller against the MacAdam model with preview time 1 s………. 76

Fig. 5-7(b). Velocity comparison of the proposed controller against the PI speed controller………. 76

Fig. 6-1(a). The experimental results without FGS on the CDTT (straight lane with flat surface)……….. 79 Fig. 6-1(b). The experimental results with FGS on the CDTT (straight lane with

flat surface)……….. 80 Fig. 6-1(c). The experimental results with FGS on the NVHSTT (straight lane

with irregular surface including single-side lane marking segment)….. 80 Fig. 6-2. The snapshot of the experiment on expressway……….. 81 Fig. 6-3. The sampled history of vehicle following experiments without

adaptive HDA maneuver (Dashed line: reference signal; solid line:

real signal)………... 82

Fig. 6-4. The sampled history of experiments involving the transition between CC and ACC mode (Dashed line: reference signal; solid line: real

signal)……….. 83

Fig. 6-5. Performance of ACC mode (fixed-distance-tracking) in a real traffic

environment………. 84

Fig. 6-6. Experimental results of CC mode switching to ACC mode……… 86 Fig. 6-7. ACC mode operation with throttle and brake actuation……….. 87 Fig. 6-8. Performance of LK mode operation under real-traffic environment in

Highway No. 3……… 88

Fig. 6-9. LK mode operation under crucial curves in Expressway No. 68……… 89 Fig. 6-10. Lane-marking detection in the lane-change scenario from the display

of vision system………... 90

Fig. 6-11. The transition between LK mode and turn-left LC mode………... 91 Fig. 6-12. Turn-right LC mode operation with the velocity 70 km/h……….. 91 Fig. 6-13(a). Turn-right LC mode at 62 km/h with early-switch maneuver…………. 92 Fig. 6-13(b). Turn-left LC mode at 67 km/h with early-switch maneuver…………... 92 Fig. 6-14. The in-vehicle view for stop-and-go maneuver in the Nanliao Harbor

Park. (a) Low speed CC mode; (b) Stop-and-go mode………... 93 Fig. 6-15. Low speed CC mode switches to stop-and-go mode……….. 94 Fig. 6-16. Stop-and-go mode of the supreme 30 km/h……… 95 Fig. 6-17. Experimental results of the vision-based lane-change maneuver……... 96 Fig. 6-18. Experimental results of the GPS-guided lane-change maneuver……… 97 Fig. B-1. Horizontal detection area……… 107

List of Tables

Table 3-1. Rule Base of FGS………..…. 22

Table 3-2. Crossover freq. of controller/vehicle system………..… 26

Table 4-1. (δSW, θ) with varying velocities and radiuses of curves………. 41

Table 4-2. Comparative results between ISO 15622 and adaptive HDA……….... 41

Table 4-3. Rule table of the SFLC………... 51

Table 5-1. DLC performance with different preview distances……….. 77

Table 6-1. Testing conditions of different environmental sets...………. 78

Table 6-2. Performance of CC mode at different velocities……… 85

Table A.1 Specification of Taiwan iTS-1……….... 105

Table A.2 List of equipments in Taiwan iTS-1……….... 105

NOMENCLATURE

Fyf , Fyr Lateral forces of front and rear tires, respectively. Cf , Cr Cornering stiffness of front and rear tires, respectively.

αf , αr Slip angle of front and rear tires, respectively. m Mass of the vehicle.

Iz Inertia moment around the center of gravity (CG) of vehicle. a, b Distance from front and rear tires to CG, respectively. vx Longitudinal velocity in the CG of vehicle.

vy Lateral velocity in the CG of vehicle. γ Yaw rate in the CG of vehicle.

δSW Steering wheel (SW) angle.

δf Front-wheel angle of the vehicle.

isr Steering ratio between the steering wheel and front wheel. ay Lateral acceleration in the CG of vehicle.

Ld Look-ahead distance for previewed navigation.

yLd Lateral offset to the road centerline at a look-ahead distance Ld .

εLd Angle between the tangent to the road and the vehicle axis at a look-ahead distance Ld .

ρLd Road curvature at a look-ahead distance Ld . x State vector of vehicle dynamics.

A, B, E Vehicle linear model matrices. Kfb Full-state feedback control. τ Transport lag of controlling input.

In , Im Identity matrices with dimensions n = 4 and m = 1, respectively. ∆i Tuning gain of the i-th fuzzy rule.

∆fg Inferred gain of fuzzy gain scheduling (FGS). µi The i-th rule strength of FGS.

ycg Deviation of the vehicle’s CG from the lane center. ydes Desired lane-width for lane-change maneuver. Amax Maximum admissible lateral acceleration. Jmax Maximum admissible lateral jerk.

φ Yaw angle with respect to the road. af Acceleration of the following vehicle. afmax Constraint of maximum acceleration. ap Acceleration of the preceding vehicle.

dR Distance in the feasible range of forward-looking sensor (FLS). Ds Signed distance of FLC.

kt Damping gain.

L Minimum distance or typical vehicle length. Rf Radius of the curved road.

R Relative distance between the preceding and the following vehicles. Rdes Desired distance between vehicles

Ri Spacing error for the ith vehicle in a platoon. S Sliding manifold.

Sh Switching line.

Ts Sampling period in the control process. ui Distinct value of the i-th rule output. Vp Forward velocity of the preceding vehicle. Vf Forward velocity of the following vehicle. VC Commanded velocity of the following vehicle. Vdes Driver-selected velocity for the following vehicle. Xp Position of the preceding vehicle.

Xf Position of the following vehicle.

θ Expanded angle in the adaptive detection area.

σ Desired headway time (in seconds).

λ Sliding surface gain.

α Slope of the switching line. Lwb Length of wheelbase.

kD Drag coefficient from aerodynamics.

FT Net force of traction or braking exerted on the tires. f Rotating friction coefficient.

g Acceleration of gravity.

kL Lift coefficient from aerodynamics.

ΨD Desired heading angle with respect to the reference curvature of road.

ρr Reference curvature of the road.

ye Distance from the road center to the sensor mounted at a distance ds ahead of the vehicle’s CG.

Chapter 1

Introduction

1.1. Present Work Survey

The development of automatic driving and highway automation provides an opportunity to relieve the driver from undesired routines of driving task. From the late 1980s, a number of research programs have been aiming to develop various advanced technologies for intelligent transportation systems (ITS) in the United States, Europe and Japan; especially for improving highway-capacity and driving-safety by automation in both highway-system and vehicle-level. This dissertation focuses on achieving automation in vehicle-level. An autonomous vehicle has to execute some or all driving tasks without external intervention. Therefore, intelligence is indispensable for such a vehicle to perform the required driving tasks.

Partners for Advanced Transit and Highways (PATH) program developed an infrastructure-based lane embedded with discrete magnetic markers so that automatic vehicles can circulate autonomously and form platoons [1, 2]. Moreover, in this program, Hessburg and Tomizuka propose a lateral-vehicle-guidance system based on fuzzy logic control (FLC) and successfully implemented it on a Toyota Celica vehicle [3]. The Navigation Laboratory (NavLab) at Carnegie Mellon University demonstrated automated steering control by artificial-vision and neural-network-based control techniques [4]. A navigation system for autonomous lane-keeping and lane-change on their test-bed vehicles (Honda Accord LX) was developed by a team in the Ohio State University (OSU) [5, 6][16]. Dickmanns’ team at University of Bundeswehr in Germany developed an artificial-vision-based automatic driving system installed in a van with automated actuators. It can drive at speeds up to 130 km/h on highway [7, 8]. Alberto Broggi’s team developed the ARGO vehicle at Parma University. ARGO executed an automatic artificial-vision-based steering mission over 2000 km on highway [9]. In AUTOPIA program two Citroen Berlingo vans, which are embedded with fuzzy-logic-based control system for mimicking human driving behavior, carried out driving and route-tracking tasks under urban-like environments [10-12]. Tsugawa’s team in Japan demonstrated their intelligent vehicles with fully automatic driving on normal roads by global positioning system (GPS) and inter-vehicle communications [13, 14]. In China, the

vision-navigation-based intelligent vehicle (THMR-V) developed by Tsinghua University performed autonomous high-speed lane-keeping on a structured road [15].

1.2. Motivation

In general, an automated vehicle possesses two basic control tasks, namely longitudinal control and lateral control. Longitudinal involves speed control and inter-vehicle spacing control with consideration of comfort and safety. Lateral control keeps the vehicle in line with the road centerline and steers the vehicle to an adjacent lane while the good passenger comfort should be maintained.

Assistance in vehicle speed control and car-following is presently one of the most popular research topics throughout the automotive industry and in the filed of intelligent transportation systems (ITS). In the view of improving the safety of occupants of the car by and relieving drivers of tedious tasks, cruise control (CC) systems are developed with the capacity of maintaining a driver-selected speed in the beginning. A much improved version, namely, adaptive cruise control (ACC) systems extend the car-following capability to CC systems. Furthermore, solutions for stop and go situations are now attracting much interest and also highly expected in the catalog of features. Although the procedures for controlling throttle and brake pedal can be based on complicated mathematical models, such a comprehensive longitudinal system of vehicle is very difficult to be linearized. The use of fuzzy logic can avert very complex approximate models which can not be computationally efficient.

Two fuzzy controllers for cruise control (CC) and adaptive cruise control (ACC) with stop-and-go maneuver have been demonstrated [10, 11] to be able to overcome the low-speed limitation in conventional ACC systems. However, no transition between CC, ACC, and stop-and-go is developed while encountering a preceding vehicle is required in order to do that. Moreover, the different fuzzy rules for CC and ACC will lead to the more complexity of tuning parameters in FLC. In this dissertation, we use stripe-partition instead of grid-partition for input space in our fuzzy speed control scheme. By doing so, the number of tuning parameters in FLC can be significantly reduced.

As to lateral control system, the issue of maintaining driver compatibility in a wide speed range is solved [17] by proposing a steering control that incorporates variable multiple look-ahead distances. Unfortunately, for the real-time vision system, the look-ahead distance can not be chosen too far because the lane-detection data becomes more erroneous due to

degradation of image resolution [18]. The curvature information at a look-ahead distance is additionally used to improve the steering performance [3][16, 17] while entering/existing curves. However, the correct curvature data is difficult to obtain in practice especially for vision-based approaches. To exhibit adaptive behavior in driver’s steering tasks, a fuzzy gain scheduling (FGS) is proposed to adjust the steering effort by considering the lateral offset at a look-ahead and the instantaneous velocity of the vehicle. Consequently, the crossover model principle is employed to present that our closed-loop steering system provides a driver-compatible way.

Although the look-ahead sensor (such as vision system) replicate human driving behavior in measuring the lateral offset ahead of the vehicle, the road data can not be measured continuously during the transition from one lane to another. It is more difficult for lane-change when there is a so-called “dead-zone” period in which the preview information can not be available due to invalid lane-detection. In an attempt to handle this transition period of “open-loop” characteristics, a reliable time series steering angle command should be developed against adverse disturbances from vehicle-road interaction, uncertainties in vehicle parameters, and actuator nonlinearities.

As described in previous approaches, speed control and steering control are often considered as two separate control problems by assuming that longitudinal and lateral dynamics are independent. However, it is well know that the coupling effects become increasingly significant when the vehicle experiences higher lateral accelerations, larger tire forces, and adverse road conditions. Even though the solution is to merge the two control tasks into single, only a few works have been reported as yet. Sliding control and dynamic surface control methods are used to facilitate the inclusion of the complex, nonlinear coupling effects in the controller derivation [19]. Besides, a series of works have been proposed with nonlinear control techniques based on Lyapunov approach [20]-[22]. Recently, several remarkable works have shown the significant progress toward a coordinated longitudinal and lateral motion control of vehicles. A combined control of longitudinal and lateral motions using robust adaptive control by backstepping is proposed to control the unmatched nonlinear vehicle dynamics even under adverse driving conditions [23]. To compensate the inherent model discrepancies of the vehicle, an on-line adaptive neural module was implemented on top of a proportional plus derivative controller in synthesizing a neuroadpative combined lateral and longitudinal control for highway vehicles in [24].

1.3. Major Contribution

The traffic on real highways remains complex and difficult to be managed such that different functions are required to be performed as well as vehicle control which is necessary to design the decision and the control for an automated vehicle from a safe viewpoint. Taiwan iTS-1 is the first intelligent vehicle developed by National Chiao Tung University (NCTU) in Taiwan [25]. In this dissertation, we propose a hierarchical-control autonomy structure to achieve integrated longitudinal and lateral control on highway and urban-road environments. The upper-level control analyzes the traffic situation and determines a driving mode among several developed modes, while the vehicle-body control executes the real-time control signal based on the determined driving mode. The good driving task depends on the well logical reasoning in underlying systems and dealing with uncertainty related to environment perception. Therefore, it motivates to integrate aspects of human intelligence and behaviors into the vehicle-body control so that driving actuators can be managed in a way similar to humans. Instead of using the mathematical representation of the systems, the behavior and experience of human drivers can be built into the system through fuzzy reasoning which is undeniably a useful feature for emulating the human reactions. Classical approaches frequently fail to yield appropriate models of complex processes, while fuzzy control technique provides an alternative tool for dealing with vehicle and its subsystem complexity. In this way, the controller at vehicle-body level has the same structure across different driving modes at upper-level; besides, the upper-level control is modular and extensible for accommodating to evolutionary modification by easily adding supplementary modes into the decision, and incorporating additional real-time information into the control.

Taiwan iTS-1 is embedded with heterogeneous systems including various sensors, core controller, interfacing, and mechanisms to carry out automatic driving. For lack of support from the vehicle industry, whole equipments including data-acquisition sensors, interfacing circuits, and motor-actuators are self-installed in the vehicle. The developed system on Taiwan iTS-1 has been verified through considerable experiments on test tracks and real highway environments. There are two indicators to access successful testing: a) safety means the system stability (or reliability) and robustness, and b) performance highlights the system consistency and passenger comfort. The designing procedure consists of control objectives determination, sensing system development, actuator design, vehicle dynamics validation, control algorithm design, system integration, and on-road testing. In other words,

development of a successful system demands not only technical understanding of the control problems, but also a sound knowledge of system engineering practice. Every element is crucial in a good mechatronic system design and therefore the success of the testing can be achieved.

In the later part of dissertation, a systematic design of the combined control of vehicle longitudinal and lateral motions for automated driving is presented. The nonlinear 3-degree-of-freedom (3-DOF) dynamic model with the parameters of real vehicle is used. This approach firstly derives the T-S fuzzy model in accordance with the complex nonlinearities and input-coupling characteristics of vehicle dynamics. And then, we can design the fuzzy speed and steering controller such that the vehicle system can be in pursuit of the reference states (i.e., desired vehicle velocity and lateral offset to the road centerline). This controller drives the vehicle to be in line with the desired targets with the assurance of minimum energy consumption [26, 27]. Only the small angle approximation is used. The resulting controlling can be directly solved to obtain the real control inputs of vehicle. The control approach facilitates the inclusion of the complex and nonlinear coupling effects in the controller design. Eventually the proposed scheme is validated and the improved controller performance is demonstrated in the environment of CarSim [28], a general software tool to simulate the dynamic behavior of a road vehicle.

1.4. Dissertation Overview

The rest of this dissertation is organized as follows. Chapter 2 describes the overview of our vehicle platform, namely Taiwan iTS-1. The design of the lateral control system with lane-keeping and lane-change control are presented in Chapter 3. In Chapter 4, the modeling of vehicle longitudinal dynamics and the longitudinal control system design with CC, ACC, and stop-and-go are presented. Besides, the developed collision avoidance/warning scheme is also introduced. In Chapter 5, fuzzy modeling for a nonlinear 3-DOF vehicle dynamics is described and the combined longitudinal and lateral control is achieved by utilization of optimal fuzzy control design. Experimental results under real traffic environment are presented in Chapter 6 to demonstrate the system’s validness. Finally, conclusions are included in Chapter 7.

Chapter 2

Vehicle Overview

2.1. Automated Vehicular System

Fig. 2-1. System architecture of the test-bed vehicle, Taiwan iTS-1.

As shown in Fig. 2-1, Taiwan iTS-1 (a prototype of Mitsubishi Savrin wagon) is equipped with a throttle, a brake, and a steering-wheel (SW) actuating system. Two internal state sensors, namely the speedometer and an inertia measurements unit (IMU), are used to sense the vehicle’s velocity, acceleration and angular rate, respectively. Besides, the utilized primary sensors include a real-time kinematical differential GPS (RTK-DGPS), an image processor with a monochromatic CCD camera, and a laser range finder. Initially, the in-vehicle controller is developed in a dSPACE Microautobox (MABX), a real-time hardware with a rapid prototype for control design and verification [29]. At present, the in-vehicle controller is successfully realized by a DSP-based stand-alone board [30, 31]. The in-vehicle controller communicates with various sensors through an interface board, and can be

reprogrammed onboard with data analysis and calibration via a notebook. Through environmental perception from primary sensors, the in-vehicle controller runs the driving control algorithm and sends throttle, brake, and SW controlling commands to actuating motors to achieve vehicle longitudinal and lateral control.

An AC servomotor is installed in the SW column to enable automatic steering. The angle of SW is measured by a steering angle sensor which is set around the axis of SW. Both the vision system [18, 32] and RTK-DGPS can provide lateral information such as the deviation from the centerline and the orientation with respect to a reference trajectory. The vision system is a look-ahead sensor while RTK-DGPS is a look-down sensor, and the fundamental difference between these two sensors is the difference in the range of the lateral information. The vision detects the lane-markings ahead of the subject-vehicle, and provides the look-ahead relative positions of the vehicle with respect to the lane center. Based on RTK-DGPS, the relative position data are compared with a digital map on which the target route has been previously specified to be tracked.

As for longitudinal control, a throttle valve is driven by a mounted DC servomotor avoiding any change to vehicle’s internal-components. A throttle position sensor (TPS) is composed of an A/D converter encoding an analog voltage into a normalized digital signal [33]. The brake pedal is automated by using a DC servomotor which is connected to a brailed steel cable via an electromagnet. Its position is measured in terms of voltage variation output from a linear position transducer [30]. The main sensor for longitudinal control is the range finder which provides the current headway distance between the subject-vehicle and a preceding-vehicle in the same lane.

The specification of Taiwan iTS-1 and the utilized sensors, signal processors, and actuators are given in Appendix A.

2.2. Automated Driving System Diagram

Fig. 2-2. Two-level hierarchy of the proposed automated driving system.

We use a two-level hierarchical architecture as shown in Fig. 2-2 to achieve automated driving or driver assistance in a highway/freeway and urban-road environment. Mimicking human driver observing the traffic situation and the course of the road, the upper-level control determines the driving modes, namely lane-keeping (LK), lane-change (LC), cruise control (CC), adaptive cruise control (ACC), and stop-and-go. This level is concerned with ensuring that the system fits the suitable driving to the existing road-condition and the traffic. After determination of driving mode, the upper-level control then provides the vehicle-body control with the reference velocity (for CC, ACC, and stop-and-go) and the reference trajectory (for LK and LC).

The vehicle-body control is the lowest level in the hierarchy, but has the highest priority at the same time because of the task of transforming the desired variables into suitable control values. As comparing sensory information to these reference data, vehicle-body control will generate SW-, throttle-, and brake-control commands to motor drivers. In addition to stability requirement, the vehicle-body control must handle uncertainties in vehicle subsystems such as engine, driveline and brake, and compensate for disturbances such as tire-road adhesion or changes in gradients. Another important factor is the transmission latency in transmitting data.

There are two major delays which come from (a) the sensor processing time such as image processing of the vision system and scanning period of the laser range finder, and (b) the actuation of servo motor. Since these delays are quite substantial, this factor have been explicitly considered into the upper-level control or the vehicle-body control design which depends on our designing approach.

Fig. 2-3. Structure of controller/vehicle system.

The two levels can be described with “controller/vehicle” system, as illustrated in Fig. 2-3. In this figure, a division into longitudinal and lateral control is made. The upper-level control requires good knowledge about road-environment, while the vehicle-body control focuses on providing driver-comparable control behavior in carrying out the control of throttle pedal, brake pedal, and SW angle. The upper-level control is responsible for calculating the reference values of velocity (for CC, ACC, and stop-and-go) and trajectory (for LK and LC) for the longitudinal controller and lateral controller, respectively. The reference velocity changes frequently and is rather dependent upon the road traffic. The objective for the longitudinal controller is to keep the reference velocity as exactly as possible. The general task for the lateral controller is to keep the lateral error to zero, i.e., the reference trajectory is the centerline of the road. While LC mode is activated, the reference trajectory will be previously calculated in terms of desired values of lateral offset such that the vehicle can be steered from the current lane to an adjacent lane. It should be noted that either the upper-level control or the vehicle-body control is designed to be adaptive with vehicle states such as current velocity, real-time lateral error, and headway distance. In practice human drivers also

perform several driving tasks which are adaptive to these vehicle states.

By receiving the throttle-, brake-position, and SW-angle commands from the vehicle-body control, a proportional-integrate-differential (PID) controller is used to manage the AC-motor attached to the SW column to reach the target position for LK and LC mode, and another two PID controllers are used to drive DC-motors to adjust the throttle degree and the brake position for executing CC, ACC, and stop-and-go mode. This architecture, based on the cascade-control paradigm [34], is particularly useful to get over time-delay from controlling signals to action signals: rapid control can be achieved by intermediate signals which will provide faster response than the control signals.

2.3. Function-flow

Fig. 2-4. Function-flow of the upper-level control.

In Fig. 2-4, the function-flow between LK, LC, CC, ACC, and stop-and-go mode in the upper-level control is presented. This system will initially activate LK mode or CC mode, or both simultaneously according to on-line detected traffic condition. In LK mode, the system retrieves real-time sensory information, calculates the deviation from a reference trajectory, and then generates a SW-control command. In CC mode, the subject-vehicle tracks a desired velocity profile set up by a human driver or the limited highway-velocity. As the vehicle

velocity is more than 40 km/h, the control scenario in ACC mode includes both safety-distance and fixed-distance tracking control. The former operation guarantees the safety-spacing keeping from the vehicle ahead while the later operation keeps a constant inter-vehicle spacing for the purpose of increasing the capacity of traffic flow. As a new event is detected, switching from CC mode to ACC mode is automatically activated. The system is defaulted in CC mode for clearance at road-ahead, and switches to ACC mode as a valid-target is detected. A valid-target is defined to satisfy the following conditions:

(a) it is in a designated range which is well defined to the feasible field of the utilized laser range finder;

(b) the velocity of a valid-target is slower than that of the subject-vehicle.

In ACC mode, the safety-distance is derived from constant headway-time policy. The value of fixed-distance can be set according to roadway control [35]. While the vehicle is driven under the velocity 40 km/h, it is reasonably to be assumed that the subject-vehicle is moving in an urban environment or a situation of heavy traffic such that stop-and-go mode will be activated if a valid-target is detected ahead. The preceding-vehicle might come to a complete stop owing to a traffic jam or a stop light. The modes-selection logic scheme is constructed in the upper-level control. The desired reference velocity in each mode will be filtered out, and then passed onto the vehicle-body control.

While the request of LC mode is given by the driver, the system steers the subject-vehicle from the current lane to an adjacent lane. The autonomous changing lane for overtaking a slower vehicle or an obstacle will be further developed in our system. Two schemes of lane-change maneuvers (GPS-guided lane-change and free lane-change) using RTK-DGPS and the vision system, respectively, are developed in our system. In the GPS-guided lane-change scenario, the reference trajectory calculated in the upper-level control is directly added on the lateral position of a specified route on the GPS map. This scheme guarantees the reference path-tracking stability issue, but limits the lane-change maneuver to specific locations where the map must be obtained beforehand. In the free lane-change scenario, the reference trajectory is transformed into the reference steering command that causes the subject-vehicle to track that reference. Without requiring the map information, however, the major difficulty in the free lane-change scenario is the extreme sensitivity of the system performance with respect to sensor noises and parameters variations in vehicle/road model.

Chapter 3

Lateral Control System Design

3.1. Vehicle Lateral Dynamics

In this chapter, the model for vehicle lateral dynamics is introduced to design the lane-keeping and lane-change control. As stated in [16, 32][36], the longitudinal and the lateral dynamics can be separated if the moving velocity does not vary too much. If roll movement is neglected, the vehicle lateral dynamics can be well represented by the so-called “bicycle model”. The bicycle model which dominates the lateral and yaw dynamics is useful in designing the steering controller to stabilize the vehicle keeping within the lane. As shown in Fig. 3-1, the bicycle model couples two front and two rear wheels together by assuming that the vehicle body is symmetric about the longitudinal plane, and the roll and pitch motion of vehicle are neglected.

Fig. 3-1. Bicycle model for front-steering vehicles.

From Newton’s law, the net lateral forces and the net torque at the center of gravity (CG) of the vehicle can be obtained as

( _{y x} ) _yf cos _{f yr}

m v + ⋅v γ =F δ +F (3-1)

z yf yr

I γ=F ⋅ +a F ⋅b (3-2)

Based on the assumption of the small steering angle (cosδf ≈ 1) and the linear tire model, the lateral force of tire can be taken as linear proportional to the slip angle with a constant proportionality called cornering stiffness as

yf f f yr r r F C F C α α = ⎧ ⎨ ₌ ⎩ (3-3) The cornering stiffness of front and rear tire Cf, r considered here is the slope of side force characteristics at the origin on a normal road condition. The slip angles αf and αr can be approximated as the functions of the vehicle’s kinematic parameters

y f f x a v v γ α =δ − + y r x b v v γ α = − (3-4)

The state equation of bicycle model can be rewritten in the following 1 2 1 3 4 2 y y f a a b v v a a b δ γ γ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ₌ ⎡ ⎤₊ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦⎣ ⎦ ⎣ ⎦   (3-5) where ₁ f r , ₂ r f , x x x C C bC aC a a v Mv Mv + − = − = − 2 2 3 , 4 , r f r f z x z x bC aC b C a C a a I v I v − − = = 1 , 2 f f z C aC b b M I = = .

Remark: In (3-1)-(3-5), the linear tire mode is used by taking the cornering stiffness Cf , r to be constant. In reality, it is found that the lateral tire force will initially increase with tire slip angle, and then saturate for a given tire/road friction condition [55-57], as shown in Fig. 3-2. To capture the saturation property of lateral tire/road friction, several nonlinear tire models were proposed. Bakker and Pacejka proposed a famous “magic formula” which represents that the lateral tire force not only depends on its slip angle but also on vehicle side slip angel αf , r , steering angle δf , and yaw rate γ. Without assuming small angles, the stability condition and bifurcation phenomenon with varying cornering stiffness and different velocities are presented in our previous work [57]. Besides, the front-wheel steering vehicle will become unstable due to the existence of saddle-node bifurcation which is derived in [57] and heavily depends on the rear-tire cornering force characteristics [55].

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0 1000 2000 3000 4000 5000 6000 7000 cor n er in g f o rc e ( N )

slip angle (rad) Front tire

Rear tire Front tire

Rear tire

Fig. 3-2. Exampled cornering characteristics of front and rear tires. (Dotted line: high friction road, and dashed line: low friction road)

To validate the bicycle model with the real vehicle dynamics is critical to obtain precise tracking results of steering control. The bicycle model in (3-5) varies with the vehicle speed vx. Notably, the actual input to our vehicle platform is the SW angle δSW rather than the front-wheel angle δf . According to vehicular steering mechanics [37], the SW angle can be expressed as a product of the steering ratio isr and the front-wheel angle δf

SW isr f

δ = ⋅δ (3-6) Because the compliance and steering torque gradients vary with increasing steering angles and load on the front tires, tire pressure, coefficient of friction, etc, in general, isr is not a fixed value for the power steering of the vehicle. However, the constant ratio can be practically used for control design. The steering ratio isr can then be adjusted slightly to yield a response that is more similar to that of the real vehicle platform. The measured SW angle was used as the input to the model. Besides yaw rate, the predicted lateral acceleration from the model can be approximately calculated by

y x y

a ≅ v ⋅ − γ v (3-7)

The average errors between the measurements and the model with respect to isr are illustrated in Fig. 3-3, and the minimum point is in the case of isr = 26. Figure 3-4 compares experimental results with the bicycle model predictions for a transient maneuver at around 60 km/h. The lateral acceleration of model agrees with the obtained experimental data in Fig. 3-4(a), and the predicted yaw rate of the vehicle also shows consistent correlation with the

experimental results in Fig. 3-4(b). Several other quantities were also measured and compared with the bicycle model. Results show that the bicycle model (3-5) can faithfully represent the lateral dynamics of the vehicle platform (Taiwan iTS-1).

Fig. 3-3. The relation between the steering ratio and the average error of measurements.

0 5 10 15 20 25 30 35 40 45 50 -0.4 -0.2 0 0.2 0.4 lat er al acc el er at ion ( g-uni t) 0 5 10 15 20 25 30 35 40 45 50 -10 -5 0 5 10 ya w r ate ( de g/ s) time (sec) (a) (b)

Fig. 3-4. The states signal for verification between the model and the vehicle in the case of isr = 26. (solid line: model output; dashed line: measured)

3.2. Lane-keeping Control Design

Fig. 3-5. Vehicle lateral dynamics with respect to road geometry.

The relationship between the lateral dynamics of the vehicle and the desired previewed navigation at a look-ahead distance Ld is plotted in Fig. 3-5. The valid amount of Ld is determined from the vision system [18, 32]. The previewed dynamics can be described as

Ld y d x Ld

y =v +L ⋅ +γ v ⋅ε (3-8)

Ld vx Ld

ε = − ⋅γ ρ (3-9) where the parameters have been defined in Nomenclature.

The bicycle model (3-5) is combined with the previewed dynamics (3-8) and (3-9) to form a linear state-space equation

Ld x = Ax+ Bu+Eρ (3-10) with 1 2 1 3 4 2 0 0 0 0 0 0 , , 0 1 0 0 0 1 0 0 0 d x x a a b a a b A B E L v v ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ = = = ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ₋ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦

where the state vector x = [ , , , ]T y Ld Ld

v γ y ε , the control input u =δf , and the previewed road curvature ρLd is viewed as an exogenous disturbance of the system.

The linear system in (3-10) is parameterized with the longitudinal vehicle speed vx . As vx increases, the poles of the system move toward the imaginary axis, reducing the stability. Notably, changing the look-ahead distance Ld does not affect the poles location in the transfer function from δf to the previewed lateral offset yLd . If Ld is regarded as being close to the front of the vehicle, then the damping of the zeros in system (3-10) declines drastically and a

high-gain controller drives the closed-loop poles toward the zeros, resulting in a poorly damped closed-loop system. However, Ld can not be chosen too distant from the reliable field of the vision system. The image resolution at far look-ahead distance will be degraded such that collected data includes more errors. As the result of numerous experimental verifications, the reliable value of Ld is chosen as 10 ~ 15 m according to the developed vision system [18].

The control objective for vehicle lane-keeping is to regulate the offset at the look-ahead yLd to zero. Moreover, the controller is well anticipated to ensure that the vehicle lateral acceleration does not exceed 0.4g (g is 9.8 m/s2) during the control process, such that smooth responses and the comfort of the passengers can be achieved. Given the vehicle model as (3-10), the state feedback control seems to be naturally applied with u =− Kfb x where

[ _{y Ld Ld}]

fb v y

K = k kγ k kε . Here the pole-placement design approach is adopted to consider

that the control effort required is related to how far the open-loop poles are moved by the feedback. The objective of pole-placement aims to fix specifically the undesirable aspects of the open-loop response, and avoids either large increases in bandwidth or efforts while poles are moved [38]. Moreover, it typically allows smaller gains and thus smaller control efforts by moving poles that are near zeros rather than arbitrarily assigning all the poles. The closed-loop poles for the system with high order (>2) can be chosen as a desired pair of dominant second-order poles with the rest poles which correspond to sufficiently damped modes, so that the system will mimic a second-order response with the reasonable balance between system errors and control effort. The closed-loop bandwidth for the look-ahead lateral offset is chosen at 5.35 rad/s to mimic human responses [16]. As for comfort requirement, the corresponding closed-loop poles are chosen to ensure that the lateral acceleration above 0.5 Hz will not be amplified during the steering path. Besides, the pole-selection can also be specified by the bandwidth requirement with regard to the transfer function yLd (s)/ρLd (s) with the maximal allowable yLd to reasonable step changes of ρLd [3-6]. From the computer simulations for the closed-loop system response with the step change in curvature, it is found that the complex poles with a damping ratioζ =0.707 will meet the constraint of lateral acceleration. Therefore, the natural frequency ωn of the prototype second-order system can be determined by [39]

1 / 2

2 4 2

BW =ω_n⎣⎡(1 2− ζ )+ 4ζ −4ζ +2⎤_{⎦ ,} (3-11)

and then we have the conjugate dominant poles as s1,2 =−3.58±3.58j. The other two poles are chosen as those in the original system. Notably, increasing the speed will reduce the stability

of the closed-loop system since the poles move close to the imaginary axis.

Recall the system matrix A in (3-10) is time-varying with the longitudinal vehicle velocity vx. The feedback control is supposed to be designed under the highest speed of interest such that the stability for lower velocities can be guaranteed by applying the convex nature of the lateral vehicle dynamics. The following proposition summarizes this approach of using full state feedback control design.

Proposition 1: If a constant feedback control Kfb is chosen such that

min min 0 T CL CL A P PA+ < (3-12a) and max max 0 T CL CL A P PA+ < (3-12b)

where min min

max max ( ) ( ) CL x fb CL x fb A A v BK A A v BK = − = −

for a matrix P > 0, than the closed-loop system is stable for varying velocities of the range vxmin ≤ vx ≤ vxmax .

Proof:

The closed-loop matrix at a velocity vx can be represented as a convex combination of ACL(vxmin) and ACL(vxmax), namely

min max ( ) ( ) (1 ) CL x x fb CL CL A v A v BK A A µ µ = − = + −

whereµis a parameter whose values depend on the vehicle velocity vx and at the range 0≤µ( ) 1v_x ≤ .

By choosing Lyapunov candidate as _{V = x Px}T _{, we can obtain its derivative as}

min min max max

( ( ) ( )) ( ) (1 ) ( ) 0 T T T T CL x CL x T T T T CL CL CL CL V x Px x Px x A v P PA v x x A P PA x x A P PA x µ µ = + = + = + + − + <  _{ }

The proof is complete.

Furthermore, the transport lag is also emphasized in the lateral controller design. The transport lag is caused by the SW motor which arises while the desired command is sent to force the actuator, and also includes image processing delay. The further phase lags are added over the range of frequencies, and severely destabilizing the overall system. Thus a

pure transport lag element e-sτ is included into the designed lateral controller. The input can be described as _{u =e u}−sτ 0 _{with u}0₌−_K

fb x. By using the approximation of first-order Pade polynomial, 1 ₂ 1 ₂ s s e s τ τ τ − _≅ − + (3-13) and the input becomes

0 0 2 ( ) u u u u τ = − −   0 2 (u u) K Ax Bu E_fb( ρ_Ld) τ = − + + + 2 2 ( ) ( ) fb n fb m fb Ld K A I x K B I u K Eρ τ τ = − + − + (3-14) By combining the system (3-10) with (3-14), we obtain the augmented system:

2 2 ( ) ( ) Ld fb fb n fb m A B _E x x K E u K A I K B I u ρ τ τ ⎡ ⎤ _{⎡ ⎤} ⎡ ⎤_{=⎢ ⎥}⎡ ⎤ + ⎢ ⎥ ⎢ ⎥ _{⎢ − − ⎥}⎢ ⎥ ⎣ ⎦ _{⎣ ⎦}⎣ ⎦ ⎣ ⎦   (3-15)

The stability of the transport-lagged system is determined by the characteristic roots of the system matrix in (3-15); consequently, the feedback controller Kfb is designed to guarantee the stability of the closed-loop system (3-15) with a transport lag at the highest velocity (145 km/h in our system).

Remark 1: Due to the presence of nonzero term ρLd , the states in (3-15) will not all converge to zero when the vehicle is traveling on a curve even through the closed-loop matrix ACL is asymptotically stable.

Remark 2: The transport lag comes from the transmission delay in two latencies: 0.04 s for the complete processing of the vision system and measurements available to the controller, and 0.52 s for the average duration gathered by the step response and sine wave tracking between the command and the reaction of servo motor. We choose the transport lag 0.6 s in stable controller design.

3.2.1. Observer Design

Based on the state space model of vehicle lateral dynamics, the full-state feedback control strategy, i.e., all the states must be measurable, is applied in the previous section. However, it is difficult to measure the lateral velocity vy of vehicles directly from general available sensors. In addition, it is not expected for rapid response in control due to the sensor noise in high

frequency. Thus, the observer design is naturally adopted for the lateral control system. By considering the system (3-10) again and feeding back the error between the measured and estimated outputs, the equation for the observer scheme can be described as

(

)

( )_{x o} x = A v x+Bu L y C x+ −  (3-16) y Cx= (3-17) with 0 1 0 0 0 0 1 0 0 0 0 1 C ⎡ ⎤ ⎢ ⎥ = ⎢ ⎥ ⎢ ⎥ ⎣ ⎦

wherex denotes the estimated states.

The measurements in previewed lateral offset yLd and angle εLd can be obtained from the real-time vision system [18], while the yaw rate γ can be provided from optic gyro.

The observer gain matrix Lo∈ℜ4x3 is chosen to achieve satisfactory error characteristics in a number of ways. Here, the pole-placement technique is adopted for the pole-selection convenience of feedback control. As with the control design, the best estimator design keeps the balance between good transient response and low-enough bandwidth such that sensor noise does not significantly impair actuator [38]. Hence, the observer pole locations are selected to be slower than two times the controller poles, and this yields the overall system with lower bandwidth and more noise reduction.

3.2.2. Fuzzy Gain Scheduling

Although the static feedback control strategy suffices to meet the requirements of vehicle lateral control, it is sensitive to the parameters of the system, such as vehicle mass, cornering stiffness, and road curvature, and thus solid reflected by feedback signals. The desire to steer the vehicle in a more human fashion and to provide a smooth automated steering control process, motivates the adoption of a fuzzy inference scheme as part of the lateral controller designing strategy. Based on fuzzy set theory, an adaptation scheme using fuzzy gain scheduling (FGS) is proposed to improve the lateral controller of the vehicle.

Fig. 3-6. Block diagram of the proposed auto-tuning lateral control system.

As presented in Fig. 3-6, FGS is designed to auto-tune the lateral controller. The kernel of the proposed FGS is the inference rule base, which constitutes a natural environment in which engineering judgment and human knowledge can be applied to the vehicle steering controller. FGS supports more human-like driving behavior during the process of keeping to the lane. The system mimics humans’ driving more aggressively at low speeds, and more gently at high speed, even when the deviation between the vehicle and the centerline of the road is large. Accordingly, the linguistic input variables are the immediate velocity of the vehicle and the lateral offset from the centerline at the look-ahead distance. FGS yields the proper tuning gain, based on the following rules

i-th rule: If vx is A and yLd is B , then ∆i is C (3-18) where A, B, and C are corresponding linguistic terms,

A ={LOW, MED, HIGH} B ={NB, NS, ZO, PS, PB} C={S, M, L}

where the notation NB: negative big, NS: negative small, ZO: zero, PS: positive small, PB: positive big, S: small, M: medium, L: large.

Table 3-1 shows the rule base of FGS. These parameters of the membership functions for prior and consequent expressions are tuned manually to ensure satisfactory steering performance. The shapes chosen in FGS are trapezoidal for vx, and triangular for yLd and ∆fg ,

respectively, as shown in Fig. 3-7. In the defuzzification strategy, the center of area (COA) method is adopted to determine the gain

15 1 15 1 i i i fg i i µ µ = = × ∆ ∆ =

∑

∑

(3-19)

(

)

min ( ), ( ) i A vx B yLd µ = µ µ (3-20) Finally, the terminal front-wheel steering quantity is thus obtained by

δc = −∆fg⋅ Kfb x (3-21) TABLE 3-1. Rule base of FGS.

vx

yLd LOW MED HIGH

NB L L M NS L M S ZO M S S PS L M S PB L L M (a) (b) (c) Fig. 3-7. The membership functions for (a) vx , (b) yLd , and (c) ∆fg .

As mentioned in Remark 1, during a vehicle steers on curves, the road curvature serves as an exogenous input to the previewed dynamics (3-8)-(3-9). In straight roads (zero curvature) case, both the look-ahead lateral offset and heading angle will be regulated to zero. For the

case of non-zero curvature, these two states will be stabilized to non-zero steady-state values as in Fig. 3-5. Although the curvature information at a look-ahead distance is useful to improve the steering performance while entering/existing curves, it is difficult to obtain the correct information of road curvature in practice. An additional curvature estimator is proposed for feedforward control [16] to improve the transient behavior as the vehicle enters and exits curves. By examining (3-8) and (3-9), changes in curvature ahead can be anticipated by the varying lateral offset ahead. Therefore, FGS is able to compensate the effect from this unknown curvature information: if the lateral offset ahead of the vehicle increases, then the steering control will be increased. Figure 3-8 shows that yLd response with respect to step change of ρLd (300-1 m-1 within 3 ~ 14 s) at a look-ahead distance 15 m is improved by FGS as compared with the pure feedback design. It can be seen that FGS possesses comparable performance with the curvature feedforward approach in [16].

Fig. 3-8. The performance of the proposed pure feedback and FGS-feedback as compared to curvature-feedforward approach in [16].

Another important factor that influences closed-loop performance of the lateral controller is the variation of the cornering stiffness. When the vehicle turns, the mass would transfer onto the external wheels such that the tires pressure increase which leads to variations in the cornering stiffness. Stephant et al. have presented that the variations caused by this factor are

normally less than 10% even at speed to 90 km/h [56]. As shown in Fig. 3-9, the comparisons between the nominal value and the 10% variations of the front- and rear-tire cornering stiffness are given. The vehicle velocity is 90 km/h, and turning on a curve with the radius 200 m between 3 s and 16 s. It can be seen that our designed lateral controller still keeps the closed-loop stability and exhibits the robustness against the 10% variation in the cornering stiffness. 0 5 10 15 20 25 30 -5 0 5 vy ( km /h ) 0 5 10 15 20 25 30 -10 0 10 20 r ( deg /s ) 0 5 10 15 20 25 30 -4 -2 0 2 yL d ( m ) 0 5 10 15 20 25 30 -10 -5 0 5 ph i ( de g) time (sec) Normal 10% variation

Fig. 3-9. Closed-loop performance for the normal condition and 10% variation in the cornering stiffness.

3.2.3. Analysis for the Lateral Controller with FGS

To achieve the persuasive performance of the steering control, the so-called crossover model principle is applied to examine the utility of the designed lateral controller. This principle has been empirically demonstrated to be applicable for driver’s steering and any good driver model is expected to yield results that conform to this principle [40]. Therefore, it is expected to achieve the evidence of crossover model principle for our proposed lateral controller. By modifying Fig. 3-6 into a single-loop preview pursuit of lateral position, as

shown in Fig. 3-10, where Gv(s) = [sIn − A]-1B represents the controlled-element transfer matrix of vehicle dynamics, and δC(t), the servo control, is related to the feedback control δf0(t) through the FGS and a transport lag. The straight-line regulatory control test for the controller/vehicle system in Fig. 3-10 reveals the direct-loop frequency response, as shown in Fig. 3-11, which relates the output previewed lateral offset yLd to the error e. This system exhibits a slope of around -20 dB/decade for ω ≈ ωc , despite low and high vehicle velocities, i.e., the open-loop transfer function of the controller/vehicle system can be approximated as

ωc /s around the crossover frequency ωc (phase margin = 90°). This result is consistent with the crossover model principle of the human operator. Besides, the included transport lag can be viewed as an “effective” time delay similar to the inherent limitation of human sensing, processing, and actuation to steer, such that the open-loop ratio of the system can be described by the transfer function (ωc /s)e-sτ.

Fig. 3-10. Equivalent block diagram for the single-point previewed pursuit controller/ vehicle system.

By viewing Fig. 3-11, not only the frequency response in the vicinity of the crossover frequency ωc is determined but also the crossover frequency at high velocity is lower than that at low velocity. This fact is also consistent with the experimental results concerning the crossover model principle [40], which is responsible for the lower crossover frequency and the difficulty of the drive task at higher velocity. For the skilled drivers, the smoother steering behavior will be employed to avoid excessive response especially under high velocities regardless the characteristics of vehicles. In Fig. 3-11, the characteristics of direct loop

response exhibit the smaller magnitude of high frequency at high velocity than that at low velocity. Table 3-2 shows that the crossover frequency is higher especially at a high velocity without FGS compensation. This result certainly meets the originality of FGS compensation design within the lateral controller. As the crossover frequency ωc increases, the bandwidth of the closed-loop system increases thereby causing unexpected noise that may destabilize the system.

(a) Low velocity (about 60 km/h)

(b) High velocity (about 110 km/h)

Fig. 3-11. Frequency response characteristics for our steering controller/vehicle system.

TABLE 3-2. Crossover frequency of controller/vehicle system. Diving velocity W/O FGS With FGS

About 60 km/h 2.90 rad/s 2.86 rad/s About 110 km/h 3.94 rad/s 2.78 rad/s