anandnaik ms thesis

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ROLE OFVEHICLEDYNAMICMODELINGFIDELITY

WITHHAPTICCOLLABORATION INSTEER BYWIRE

SYSTEMS

by

ANAND PNAIK

JULY 2007

A thesis submitted to the Faculty of the Graduate School of the State University

of New York at Buffalo in partial fulfillment of the requirements for the degree of

MASTER OF SCIENCE

Department of Mechanical and Aerospace Engineering

State University of New York at Buffalo

Buffalo, New York 14260


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To My Family and Friends


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Abstract

Steer-By-Wire (SBW) systems offer many benefits ranging from mechanical

isolation of steering wheel from the road, weight reduction in the steering system, relaxed

packaging constraints, to facilitating advanced driving-safety systems. However, there is

also the loss of proprioception (road feel) which is a critical feedback element for

manual vehicle control. To this end, haptic interfaces for SBW systems have been

proposed to restore the intimacy of interactive control back to the driver.

Candidate solutions for mimicking the steering feel have ranged from direct

instrumented-pickup and feedback of road-wheel interactions (using

accelerometers/force-sensors) to steering torque prediction schemes based on

mathematical dynamics models (of tire-road, suspension, power-steering systems) in

conjunction with selected real-time measurements. While the latter approach offers the

most promise, real-time implementations at high sampling rates in noisy environments

pose challenges. A careful selection of fidelity of the underlying dynamic model as well

as good matching of haptic model-device capabilities is critical.

The degree of realism for the user-vehicle interaction is dependent on the fidelity

of the underlying computational vehicle dynamics model. Hence, in this work we focus

on creation, implementation and preliminary testing of varying fidelity vehicle-dynamic

models for haptic steer-by-wire driving tasks. Additionally the SBW paradigm can

simplify implementation of shared/collaborative control (steering) of the underlying

mechanical system (vehicle). In this thesis we implement and evaluate various


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possibilities for sharing of control between multiple individual users and/or between user

and automation technology.

Quantitative performance evaluation is conducted to understand the role of

vehicle dynamics modeling fidelity for haptic SBW tasks along with the evaluation of 3

modes of shared control, user automation control vs. individual control. In particular,

preliminary experimental analyses with five subjects using three performance metrics

(Error Value Parameter, FFT Power Ratio and Free Control Oscillations) were evaluated

to quantify vehicle models and collaboration modes performance.


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Acknowledgment

Many people have influenced my life in the time it took to complete the work

described in the pages that follow. First and foremost, it has been my graduate advisor

and mentor, Dr. Venkat Krovi. He provided the imagination and guidance to turn mere

notions into reality. Many of the ideas in this thesis were developed at his suggestion. I

was fortunate enough to find someone like him who shared the same passion and

realization of our responsibility as engineers for conducting quality research. I want to

sincerely thank Dr. Krovi, without whom this work would not have been possible.

I also want to sincerely thank Dr. Roger Mayne and Dr. Puneet Singla for serving on

my thesis defense committee. Special thanks to Dr. Mayne who has played a very

important role in my education at UB. These 5 years of your advisement and support

have been invaluable.

I have had the pleasure of working with some great lab-mates like LengFeng, CP,

Glenn, Mike, Rajan, Kun when I first joined ARM Lab in 2005. Special thanks to

LengFeng, Madhu and CP for the countless hours they spent in discussing my thesis

during its final stages. Thanks to all new ARM Lab members, Shrikant, Pat, Yao, Quishi,

Hao for their support. Most importantly, I want to thank all the lab members in making

the lab a fun and enjoyable place, and for never once complaining when I said, just one

more data set during the experimental analysis.

Most importantly, it goes without saying that my Mother, Father and Sister have been

my biggest support throughout all these years. Thank You! for without your emotional,

support this would never have been possible.

I have made a lot of friends in Buffalo. I want to thank all of you, Ashwin, Devan,

Maddy, Joel, Sidharth and many more for your support and for standing by me whenever

needed. A special thanks to Priya, for her never-ending encouragement and support right

from the day one of this thesis.


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Contents

Abstract .............................................................................................................................. iii

Acknowledgment ................................................................................................................ v

Contents ............................................................................................................................. vi

List of Figures .................................................................................................................... ix

List of Tables ................................................................................................................... xiii

1 Introduction....................................................................................................... 1

1.1 Motivation..........................................................................................................1

1.2 Steer-By-Wire for Automotive Application ......................................................2

1.2.2 Advantages of a Steer-By-Wire System ...................................................3

1.3 Haptics ...............................................................................................................4

1.3.1 Haptic Systems Architecture.....................................................................6

1.3.2 Classification of Haptic Devices and Haptic Applications.......................8

1.4 Research Issues ................................................................................................10

1.4.1 Principal Issues and Thesis Contribution................................................13

1.5 Thesis Organization .........................................................................................15

2 Literature Survey ............................................................................................ 16

3 Mathematical Model Development................................................................. 24

3.1 Vehicle Dynamics............................................................................................24

3.1.1 Model A: Spring-Mass-Damper Analogy (No Slip Model) ...................25

3.1.2 Model B: The Bicycle Model with Linear Tire Model...........................27


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3.1.3 Model C, D: Vehicle Model (With and Without Suspension)

Using DynaFlexPro.................................................................................40

3.1.4 Steering Column and Steering Force Design..........................................44

3.1.5 Model Validation ....................................................................................46

3.1.6 Collaborative Haptic Driving..................................................................49

4 Implementation ............................................................................................... 55

4.1 MATLAB Simulink Implementation...............................................................55

4.2 MATLAB GUI Implementation ......................................................................61

5 Experimental Setup and Results ..................................................................... 63

5.1 Error Value Parameter (EVP) Evaluation........................................................65

5.1.1 Comparison across Vehicle Models (EVP) ............................................67

5.1.2 Comparison Across Collaboration Modes (EVP)...................................69

5.2 Fast Fourier Transform (Power Ratio) Evaluation ..........................................71

5.2.1 Comparison Across Vehicle Models (Power Ratio)...............................73

5.2.2 Comparison Across Collaboration Modes (Power Ratio) ......................74

5.3 Free Control Evaluation...................................................................................76

5.3.1 Comparison Across Vehicle Models (Free Control) ..............................78

5.3.2 Comparison across Collaboration Modes (Free Control) .......................80

5.4 Result Summary...............................................................................................81

6 Conclusion ...................................................................................................... 84

6.1 Research Question Revisited ...........................................................................84

6.2 List of Thesis Contributions.............................................................................86

6.3 Future Work.....................................................................................................87


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Bibliography ..................................................................................................................... 89

Appendix A : Development of vehicle Model C and D in DynaFlexPro ......................... 94

A.1 Model D Development DynaFlexPro-Tire Package ........................................94

A.2 Maple Simulation Code Development...........................................................102

A.3 Model C Development DynaFlexPro-Tire Package ......................................106

A.4 Simulink Implementation of Model C and D ................................................107

A.5 Generation of User Defined Parametric Surface in VRML

Environment...................................................................................................108


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List of Figures

Figure 1-1: (a) Conventional steering system; (b) Rack and Pinion Assembly; (c)

Recirculation Ball Bearing. [Courtesy: (b), (c)-www.howstuffworks.com] .............. 2

Figure 1-2: (a) Steer-By-Wire (SBW) Automotive Steering System; (b) General Motors

Hy-Wire; (c) BMWs concept SBW. ...................................................................... 3

Figure 1-3: Architecture of Haptic Interface ...................................................................... 7

Figure 1-4: Haptic modality can be implemented to enhance the Human Environment

Interaction ................................................................................................................... 8

Figure 1-5: Classification of Haptic Devices...................................................................... 9

Figure 1-6: Haptic Applications........................................................................................ 10

Figure 1-7: Challenges faced in implementing Haptics.................................................... 11

Figure 1-8: Sensor Latency............................................................................................... 12

Figure 1-9: Challenges faced due to high refresh rates..................................................... 12

Figure 2-1: Experimental Steer-By-Wire Vehicle (Courtesy Dynamic Design Lab

Stanford University).................................................................................................. 17

Figure 2-2: Three different laws used to provide steering feel [20] ................................. 18

Figure 2-3: The Virtual Teacher [16]................................................................................ 19

Figure 2-4: Cornering Stiffness: Lateral Force vs. Slip Angle Curve [Courtesy: [38] [37]]

................................................................................................................................... 20

Figure 2-5: CARSIM simulating car handling characteristics [Courtesy: Mechanical

Simulation]................................................................................................................ 22

Figure 2-6: DynaFlexPro-Tire: Latest pneumatic tire models incorporated for building

system equations [Courtesy: Maple Soft/DynaflexPro-Tire] ................................... 22


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Figure 3-1: (a) Steering System modeled with rotational spring mass damper analogy, (b)

simple bicycle kinematics model (no slip)................................................................ 25

Figure 3-2: Bicycle Model State Description ................................................................... 27

Figure 3-3: The Bicycle Model......................................................................................... 30

Figure 3-4: Tire Forces and Moments .............................................................................. 32

Figure 3-5: Thread button cycle........................................................................................ 33

Figure 3-6: Moment arm for aligning moment ................................................................. 35

Figure 3-7: 2-D views to visualize the steering axis......................................................... 36

Figure 3-8: 3-D view for the steering axis alignment ....................................................... 37

Figure 3-9: (a) Vehicle Model without Suspension (10 DOF), (b) Vehicle Model with

Suspension (14 DOF) using Maple Softs DynaFlexPro/Tire toolbox..................... 41

Figure 3-10: Ackermann Geometric Requirement for a four wheeled vehicle ................ 42

Figure 3-11: Steering Column Concept ............................................................................ 44

Figure 3-12: Rack Force Estimation................................................................................. 45

Figure 3-13: Ackermanns Geometry Verification........................................................... 47

Figure 3-14: (a) Steering Input as a Square Wave, (b) Steering Torques......................... 47

Figure 3-15: (a) Vehicle Longitudinal Velocity, (b) Vehicle Trajectories ....................... 48

Figure 3-16: Shared Haptic Control between Human and Automation............................ 50

Figure 3-17: (a) Vehicle Trajectory, (b) Steering Angle Variation .................................. 51

Figure 3-18: Haptic collaborations ................................................................................... 52

Figure 3-19: (a) Indirect contact Mode (Mode I), Double Contact Mode (Mode II), Single

Contact Mode (Mode III).......................................................................................... 53

Figure 4-1: Simulink Block Implementation Overview ................................................... 57


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Figure 4-2: Single User Simulink Implementation........................................................... 57

Figure 4-3: Device Interface Block Parameters for (a) Omni Device, (b) Microsoft Side

Winder Joystick ........................................................................................................ 58

Figure 4-4: Vehicle Dynamics Model B Simulink Implementation................................. 59

Figure 4-5: Vehicle Dynamics Model C Simulink Implementation................................. 59

Figure 4-6: Collaborative Mode Simulink Implementation.............................................. 60

Figure 4-7: User and Automation Collaboration Simulink Implementation .................... 60

Figure 4-8: (a) Simulation Flowchart, (b) First Version of the Graphical User Interface

for Parameter Selection............................................................................................. 61

Figure 4-9: (a) Vehicle Motion displayed in Top View, (b) Vehicles Motion Displayed

in VRML Environment ............................................................................................. 62

Figure 5-1: (a) Experimental Setup (Side View), (b) Subject Driving in a Single User

Environment.............................................................................................................. 63

Figure 5-2: Error Value Parameter Computed as the Normalized Euclidean distance

between equal-arc-length correspondence points; (b) EVP between two curves v/s

the number of equal-arc0length segments ................................................................ 65

Figure 5-3: (a) User Trajectories with Various Vehicle Models, (b) EVP Evaluations with

Various Vehicle Models ........................................................................................... 66

Figure 5-4: Total EVP measure for all of the 16 tests for (a) Subject 1, (b) Subject 2, (c)

Subject 3, (d) Subject 4, (e) Subject 5 ...................................................................... 67

Figure 5-5: EVP Measure for (a) Single User Environment, (b) Collaborative Mode I, (c)

Collaborative Mode II, (d) Collaborative Mode III, with all Four Vehicle Models.68


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Figure 5-6: EVP Measure for all three Collaborative Modes with Vehicle (a) Model A, (b)

Model B, (c) Model C, (d) Model D......................................................................... 69

Figure 5-7: EVP Measure with User-Automation Collaboration Mode for (a) Subject 1,

(b) Subject 2.............................................................................................................. 70

Figure 5-8: Frequency Spectrum for Subjects 1 Steering Angle Signal........................... 72

Figure 5-9: Power Ratio Measure for (a) Single User Environment, (b) Collaborative

Mode I, (c) Collaborative Mode II, (d) Collaborative Mode III............................... 73

Figure 5-10: Power Ratio Measure with all Three Collaborative Modes with Vehicle (a)

Model A, (b) Model B, (c) Model C, (d) Model D................................................... 75

Figure 5-11: Power Ratio Measure with User-Automation Collaboration for (a) Subject 1,

(b) Subject 5.............................................................................................................. 76

Figure 5-12: Free Control Oscillation Comparison between Vehicle Models A, B, C and

D................................................................................................................................ 78

Figure 5-13: Free Control Oscillation Comparison for (a) Collaborative Mode-I, (b)

Collaborative Mode-II, (c) Collaborative Mode III.................................................. 79

Figure 5-14: Free Oscillation Behavior for all Three Collaborative Modes with Vehicle (a)

Model A, (b) Model B, (c) Model C, (d) Model D................................................... 80


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List of Tables

Table 3-1: Tire forces and moments ................................................................................. 31

Table 3-2: Vehicle and tire parameters............................................................................. 46

Table 4-1: Sampling Rates for different Vehicle Models while using Phantom Omni

Device ....................................................................................................................... 56

Table 4-2: GUI Vehicle Parameter Selection ................................................................... 62

Table 5-1: Design of Experiments I.................................................................................. 64

Table 5-2: Design of Experiments II ................................................................................ 64

Table 5-3: Vehicle Model User Performance Chart for EVP Measure ............................ 81

Table 5-4: Collaboration Mode User Preference Chart for EVP Measure ....................... 82

Table 5-5: Vehicle Model User Performance Chart for FFT (Power Ratio) Measure ..... 82

Table 5-6: Collaboration Mode User Preference Chart for FFT (Power Ratio) Measure 82


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1 Introduction

1.1 Motivation

In the past decade, technological developments in the areas of sensors, controllers,

wireless communication, and low-cost computers have made significant inroads into the

automobile with the potential for enhancing performance, safety etc. However the primary

operator of the automobile is the human driver. Hence there is a need for creating a

suitable human driving interface that can take advantage of these developments. This push

has led towards the ever increasing array of in-vehicle information systems (e.g. GPS) and

the increased use of automatic vehicle control systems (e.g., adaptive cruise control).

While useful individually, these technologies may distance drivers from the overall

driving situation and may delay their responses to unanticipated, high-demand situations.

It is in this scenario in which we believe haptic interfaces offer a promising alternative to

allow us to restore the intimacy of interactive control back to the driver.

In particular, the focus of this thesis is on the creation, implementation and testing of a

haptic enabled Steer-By-Wire (SBW) joystick for single, multi-user and user-automation

collaborative environment vehicle driving applications. SBW technology is characterized

by the absence of mechanical linkages between the output steered road wheels (tires) and

the input steering interfaces (usually a steering wheel or a joystick). Instead, the steering

interface and the steered wheels are electronically connected through a system of sensors

actuators, a communication network and an electronic controller [1, 2]. There are

numerous economic, safety and performance benefits accruing from SBW paradigm [1, 3]

that have driven the automotive industrys efforts to replace conventional steering systems

with intelligent mechatronic SBW solutions. For example, in addition to facilitating

mechanical isolation of steering wheel from the road wheels, SBW systems have

enormous safety benefits ranging from weight reduction in the steering system, relaxed

packaging constraints, to enabling advanced safety systems. Section 1.2.2 discusses some

of these advantages in greater detail. However, there is also the loss of proprioception


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(road feeling) associated with SBW systems. Road feeling can be one of the most

important and valuable information channel or modality facilitating vehicle control for the

human driver. Hence in recent times there exists considerable incentive for reincorporation

of force or haptic feedback to help restore the road feel. The challenge is to develop

mathematical models for hand-wheel torque feedback which would provide the requisite

tunable realistic steering feel in the absence of mechanical linkages [4]. In addition, such

haptic feedback also provides exciting opportunities for modulating (amplifying,

deamplifying, filtering and creating artificial feedback assists) force feedback presented to

the driver. In particular, sharing of control between multiple users or between user and

automation may now be easily incorporated within a haptic SBW paradigm. Ultimately,

our goal is to develop a haptic steer by wire simulator which is capable of simulating a

variety of vehicle and collaboration models.

1.2 Steer-By-Wire for Automotive Application

Research in the automotive systems is being proliferating with introduction of

integrated electronic sensors, actuators, microcomputers processing information for

systems like engine, drive train, suspension, and braking systems. In recent times

electronics have started to make their way into automotive steering systems in the form of

electronically controlled, variable and fully assistive steering systems.

Universal Joints

Steering Column

Rack and Pinion Assembly

Steering Wheel

(a) (b) (c)

Figure 1-1: (a) Conventional steering system; (b) Rack and Pinion Assembly; (c) Recirculation Ball

Bearing. [Courtesy: (b), (c)-www.howstuffworks.com]

The basic design of automotive steering system consists of steering wheel connected to

some type of gear reduction mechanism through a steering shaft (see Figure 1-1a). Two

commonly used gear reduction systems are rack and pinion system (Figure 1-1b.) and


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recirculation ball bearings system (Figure 1-1c). The drivers steering input is transmitted

through one of these gear reduction system which converts the rotational input from the

driver into a linear displacement required to turn the wheels.

1.2.1.1So, what is a Steer-By-Wire system?

Steer-by-Wire (SBW) indicates a steering system that replaces the rational mechanical

linkages as described above with direct electronic control between the steering wheel and

tires with careful design of distributed fault-tolerant systems [1]. To convert a

conventional steering system to a SBW system, the intermediate shaft is normally

disconnected as shown in Figure 1.2a.

Steering Wheel Position Sensor

Steering Column

Rack and Pinion Assembly

Steering Forc e

Feedback Motor

Steer-By-Wire

(a) (b) (c)

Figure 1-2: (a) Steer-By-Wire (SBW) Automotive Steering System; (b) General Motors Hy-Wire;

(c) BMWs concept SBW.

Most car producers are excited about this new technology and are putting much effort

into its development. The first examples of drive-by-wire vehicles are expected to be

completed and up for sale by BMW and Mercedes-Benz models by 2010. As a part of

fully integrated vehicle dynamics control, the first active steering system for a production

vehicle was recently introduced in the 2004 BMW 5-Series. While not yet a by-wire

system, this feature demonstrates the sort of handling improvements that can be made to a

vehicle equipped with a true steer-by-wire.

1.2.2 Advantages of a Steer-By-Wire System

While completely replacing a steering column with a Steer-By-Wire system is a very

intimidating concept but it has its advantages. The absence of a steering column greatly

simplifies the design of car interiors design and allows much better engine compartment


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space utilization. Furthermore, the entire steering mechanism can be designed and

installed as a modular unit for either left- or right- hand drive. In the absence of direct

mechanical connection between the steering wheel and the road wheels, the noise,

vibration and harness (NVH) from the road tire interaction can no longer propagate to the

drivers hands and arms. Safety is significantly improved because of reduced likelihood of

steering column intrusion into the drivers survival space in case of front impacts. Finally,

perhaps the greatest contributions to safety come about by the use of sensing and

automation to modulate the driver vehicle interactions. With SBW, previously fixed

characteristics like steering ratio is infinitely adjustable to optimize steering response and

feel. There is considerable research interest in developing adaptive steering system to

augment Adaptive Braking System (ABS) and Adaptive Cruise Control (ACC) for future

vehicles.

1.3 Haptics

Biomimetic systems development based research teams are attempting to copy the form

or the behavior of biological systems to create efficient machines and processes. To

advance in their research, scientists are learning from the greatest source of knowledge,

the nature. It would be very logical to approach the problem when designing machines and

processes since nature has had millions upon millions of years to perfect these systems.

These tools can also be used to design machines that specifically incorporate a human into

the system. These biologically-incorporated systems extend the abilities of humans with

the assistance of man-made devices.

Connecting human and machine systems together requires an interface which is

directly dependent on the human senses. Such an interface can truly be called bio-mimetic

system in that it is designed to respond to, or mimic, the reactions and sensations of a

biological system, namely the human operator. Various systems currently exist that

provide information to the human senses of sight and hearing. Video and audio systems

have been perfected over many decades so that it is now possible for a user to wear small

devices, such as goggles and earphones to enter or be a part of the virtual world. Systems

exist currently and others are being further developed that interface with a third human

sense, the sense of touch. These systems are called Haptic Systems or simply Haptics. [5]


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In the past decade there has been an enormous increase in interest in the science of

haptics. The quest for better understanding and use of haptic abilities (both human and

nonhuman) has manifested itself in heightened activity in disciplines ranging from

robotics and telerobotics; to psychophysics, cognitive science, and the neurosciences.

As a prelude to help readers understand the efforts invested in haptics research, we

would like to provide some background in the science of haptics.

So, what is haptics?Haptics: relating to or based on the sense of touch. Origin: Greek

haptesthai. [Webster]. Haptics refers to sensing and manipulating through touch. Since the

early twentieth century the term haptics has been used by psychologists for studies on

active touch of real objects by humans. In the late nineteen-eighties, when researchers

started investing time on developing novel machines pertaining to touch, it became

apparent that a new discipline was emerging that needed a name. Rather than concocting a

new term, researchers chose to redefine haptics by enlarging its scope to include machine

touch and human-machine touch interactions. [6]

Sense of touch is achieved through somatosensory system which is the sensory system

of somatic sensation. Somatic sensation consists of the various sensory receptors that

trigger the experiences labeled as touch or pressure, temperature (warm or cold), pain

(including itch and tickle), and the sensations of muscle movement and joint position

including posture, movement, and facial expression (collectively also called

proprioception).[5, 6]

The primary somatosensory area in the human cortex is located in the post central

gyrus. Areas of this part of the human brain map to certain areas of the body, dependant

on the amount or importance of somatosensory input from that area. For example, there is

a large area of cortex devoted to sensation in the hands, while the back has a much smaller

area [7].


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Figure 1-3: The Homunculus: Body parts sizes are proportional to the somatosensory cortex area

dedicated to it.

This somatosensory map is termed the homunculus. The classical representation of this

is the homunculus (Figure 1.3), where body parts sizes correspond to the proportion ofsomatosensory cortex dedicated to it. This shows how some body parts like hands, feet

and lips are very important for sensation and perception.

1.3.1 Haptic Systems Architecture

Touch allows us to explore and manipulate the world with tactile exploration,

assessment of textures and feedback from object manipulation. Touch is also critical to our

social and emotional lives.

Haptics has been a part of virtual reality research for many years, but the costs of

building devices and learning the control algorithms has greatly limited its application.

Virtual environments or virtual reality are computer created environments with which

humans can interact to do various activities. Typically a virtual reality system may have a

helmet (head mounted display) which projects computer generated images and sounds

when a user interacts or commands the virtual environment to do different tasks.

Unfortunately, no matter how good the visual and auditory rendering may be, all pretenses

to reality are crushed the moment you pass through an object without feeling it. This can

definitely not be achieved by merely changing object colors or triggering audio tones. The

ability to feel the environment (provided by implementing haptics) can greatly enhance

the quality of the experience. [7]


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Haptic interfaces are devices that enable manual interactions with virtual environments

or in our case stimulating. They are employed for tasks that are usually performed using

hands in the real world, such as manual exploration and manipulation of objects.

VirtualEnvironment

User Haptic Device

VisualandA

udiosignal

Simulation

Engine

Haptic

Rendering

Figure 1-3: Architecture of Haptic Interface

The basic structure of a haptic feedback simulation is as follows (Figure 1-3): Human

Operator (User) typically holds the haptic device while interacting with the virtual

environment. The interaction is processed by the simulation engine with haptic rendering

algorithms. The transducers convert visual, audio and force signals from computer into a

form that the operator will perceive. The key feature here is that the audio and visual

channels carry information unidirectional whereas the haptic modality exchanges

information and energy in two directions (from and towards the user). These receive

motor action commands from the human user and display appropriate tactual images to the

user. Such haptic interactions may or may not be accompanied by the stimulation of other

sensory modalities such as vision and audition. [7]

As seen in Figure 1-4, a human being needs to engage all five of its sensory modalities

to interact and understand a real environment completely. Virtual environment makes use

of many of these same modalities. Along with the visual and auditory modalities a

substantial research and development in haptics is being pursued around the world today

in order to create information rich virtual worlds.


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Figure 1-4: Haptic modality can be implemented to enhance the Human Environment Interaction

1.3.2 Classification of Haptic Devices and Haptic Applications

The haptic sensory information can be distinguished as either tactile or kinesthetic

information; haptic devices are broadly classified under the following two categories:

A. Tactile interfaces: Tactile sense plays an important role in object discrimination and

manipulation. Imagine running your finger over a surface. The initial sense of contact in

this case will be provided by the receptors in the skin. These receptors can also provide

information such as surface geometry, texture. It can also provide information on surface

compliance, elasticity, viscosity and electrical conductivity. These sensations can be

achieved in number of different ways. The technologies currently being used for these

include mechanical pins activated by solenoid, piezoelectric crystal, and shape memory

alloy technologies [5].

B. Kinesthetic interfaces: Suppose we apply more force on the finger while running it

over a surface. Kinesthetic information comes in play by providing us details about

position, forces acting, surface compliance and resistance or weight. As we can see tactile

and kinesthetic information or sensing occur simultaneously. As discussed earlier, haptic

interfaces are devices that stimulate the sense of touch such as the sensory capabilities

within our hands. The surge to exploit computer capability and the desire for better ways

Virtual

EnvironmeHaptic (Touch)

Visual (See)

Auditory (Hear)

Real

Environment

Haptic (Touch)

Visual (See)

Auditory (Hear)

Olfactory (Smell)

Gustatory (Taste)


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to connect to computer-generated virtual worlds has driven the creation and development

of practical devices for haptic interaction.

Until recently haptic systems comprised a small part of engineering society mostly used

for demonstrations in research facilities. However, while research is still continuing,consumer-level off the shelf haptic systems are continuously been introduced. For

example, force feedback gaming devices, such as joysticks and computer mice, have

become available, while in the medical field, surgeon directed robotic surgery

(telesurgery) has been gaining recognition. Haptic devices can be further classified as

shown in Figure 1-5.

a. CyberGlove [8]; b. PhantomOmni [9]; c. Master Arm [10]; d. Haptic Walker[11]

Figure 1-5: Classification of Haptic Devices

There are wide ranges of possibilities in implementing these haptic devices. In the field

of medical surgery, from virtual surgical training, teleoperated haptic surgery, to local

haptic assisted surgery. Figure 1-6a shows one such commercially available haptic device

for surgery.

Haptic

Devices

Gloves And

Wearable

Ground Based,

Point Source

Exoskeleton

Devices

Locomotion or

Full Body


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(a) The da Vinci S

Surgical System from

Intuitive Surgical Inc.

(b) MITs Biomechanics Lab

Stroke Rehabilitation.(c). Gearbox Design (d)Nano Manipulation

Figure 1-6: Haptic Applications

Recent technological advances including the use of interactive virtual reality

environments promise to advance movement rehabilitation. Professor Hogan and Kerbs at

MITs Biomechanics Laboratory are developing methods to retain stroke patients while

measuring their progress as shown in Figure 1-6 b. In manufacturing, many opportunities

exist for haptics application. For example, haptics can assist design for assembly, in terms

of reducing the need for prototyping, as well as for rapid prototyping. Based in United

Kingdom, the Virtalis Group is recognized as one of the foremost interactive visualization

organizations in the world. Figure 1-6 c shows a few industry level applications they have

developed. The HapticMaster is used to render interaction forces in gearbox design.Nanotechnology has emerged as a new frontier in science and technology. The essence of

nanotechnology is the ability to work at the molecular level, atom by atom, to create large

structures or devices with fundamentally new molecular organization. Researchers at

Carnegie Mellon University are currently working on developing one degree of freedom

haptic interface to interact and manipulate nano particles (Figure 1-6 c).

1.4 Research Issues

The multitude of challenges to successful implementation of haptic assist in SBW

system can be broadly categorized into three main areas: User, Haptic User Interface

(HUI) and Virtual Environment as shown in Figure 1-7.


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Physiological

Psychological

Ergonomics

User

AnalyticalModel

SimulationAlgorithm

Softwares

Virtual Environment

Human User Interface

StabilityVSTransparency

Realtime

rates,Resolution,Bandwidth

ControlMethods

Figure 1-7: Challenges faced in implementing Haptics

Along the User Axis the biomechanical, sensorimotor and cognitive abilities of

humans play a vital role in governing the overall interaction performance. Our work will

not focus much on this aspect but a broad overview of research challenges entailed here

can be seen in [12]. On the HUI Axis the underlying mechanical properties of the

hardware (viscosity, friction, mass) together with the selection of control methods

(impedance, admittance) serve to modulate the interaction between the human user and the

virtual environment. Haptic rendering algorithms operate in discrete time where as users

operate in continuous time. While moving into and out of virtual object (in our case, if the

car goes over a bump), the sampled avatar position will always lag behind the avatars

actual continuous time position. For example, a tire going over a bump on the road should

be instantaneously felt by the driver. This is where sensor latency could cause a

considerable lag between the input and output signals as shown in Figure 1-8. In general

this interaction may create unwanted energy. The area of the curve shown in Figure 1-8

represents this amount of energy generated. This extra energy can cause an unstable

response from the haptic devices. Transparency and stability are used as metrics of

performance of HUIs but these tend to place conflicting requirements. Thus one of the


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challenges is selection of suitable tradeoff between the stability and transparency via

selection of device and control characteristics, real-time rates, instrumentation

requirements [13-15].

Figure 1-8: Sensor Latency

The third axis pertains to the Virtual Environment that computes motion/force

interaction in response to user inputs and disturbances. In our case, it corresponds to themathematical model of vehicle dynamics and the computation of steering feel

(torques/motions) in response to driver/road inputs.

HUIHuman

A/D

HapticModel

Graphic

Rendering

Vehicle

Dynamics

HumanUser

Interface(HUI)

Forces(F

)

Torques = J' F

Virtual Environment

Digital WorldAnalog World

Haptics Loop > 1000Hz

VisualizationLoop 30 Hz

Figure 1-9: Challenges faced due to high refresh rates

Virtual Environment (VE) requires high frame rates and fast response because of its

inherently interactive nature. The concept of frame rate comes from motion picture

technology. In a motion picture presentation, each frame is really a still photograph. If a


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new photograph replaces the older images in quick succession, the illusion of motion in

engendered. The update rate is defined to be the rate at which display changes are made

and shown on the screen. In case of visual information a system needs to have an update

rate of 30Hz or more in order to create a smooth motion picture. This means that after

receiving a command from the user the VE simulator which includes the device and the

math models need to compute information and relay it back to the user within 0.0333

seconds. If this is possible then the illusion of virtual environment is successfully created.

The same update rate concept is equally important in a haptic or touch modality based

VE. Except in this case the tactile information should be generated with an update rate of

1000 Hz or more (Figure 1-9). This means that all the computations and processing should

be achieved and relayed back to the user with in 0.001 seconds. The fidelity with which

the tactual images have to be displayed and the motor actions have to be sensed by the

interface should strike the right balance. As one can clearly see that the computational

speed of the software has to immensely high and the math modeling has to be creatively

optimized in order to match these high real time computation rate requirements.

1.4.1 Principal Issues and Thesis Contribution

From the above discussion we see that a careful selection of complexity of the

underlying dynamic model as well as good matching of haptic model-device capabilities iscritical and this serves to focus our research efforts. The principal issues can be separated

in two major categories, posed in the form of the following principal research questions.

Research Question 1: How does complexity (fidelity) in vehicle dynamics modeling relate

to providing a realistic steering feel to the user in Steer by Wire automotive systems?

It is well understood that real time operations at high sample rates are easier to achieve

with lower fidelity models. However, to the best of our knowledge there is little or no

prior work examining the role of modeling fidelity or user control. Hence in this work we

first focus on creating analytical models at four fidelity (Vehicle Model A, B, C and D).

We will first study the effects of use of varied fidelity of vehicle dynamics models on a

users performance of driving in a single user environment. These models will range from


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a simple torsional-spring-mass damper (no slip) model to a complex 14 degree of freedom

full-car-ride model.

Research Question 2: How does collaborative driving (user-automation and multi-user

environment) affect user control in SBW application? Is there globally preferredcollaborative mode?

The development and application of methodologies for sharing of an interactive haptic

experience with a common virtual object have numerous possibilities ranging from

sharing of control between multiple individual users [16] to sharing of control between

user and automation technology [17, 18]. Hence the results/effects of collaboration

between multiple users or between user and automation need to be evaluated.

To answer these questions, we beginby first developing and implementing

varying fidelity vehicle models which were then extended to encompass the various

collaborative modes. A GUI tool was developed for easy selection of vehicle models,

collaborative modes and two different haptic devices for real time simulations. This tool

also incorporated easy access for changing some of the vehicle parameters such as mass,

yaw inertia, and steering ratio of a particular vehicle model and automatic creation of

user defined parametric surface (road) generation in VRML Environment. Experimental

Analysis was conducted to understand the role of vehicle dynamics modeling fidelity for

haptic SBW tasks along with the evaluation of 3 modes of shared control, user

automation control vs. individual control. Particularly, preliminary experimental analyses

with five subjects using three performance metrics (Error Value Parameter, FFT Power

Ratio and Free Control Oscillations) were evaluated to quantify vehicle models and

collaboration modes performance.


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1.5 Thesis Organization

The rest of this thesis is organized as follows:

Chapter 2 presents a relevant overview of research literature in the field of Steer-By-

Wire automotive applications. Within the SBW application we will also introduce prior

research work conducted in the field of haptic collaboration between individual users and

between user automation.

Chapter 3 discusses vehicle dynamics model development as well as validation.

Chapter 3.1.6 presents details of the analytical modeling of multi-user and human-

automation collaboration modes.

Chapter 4 provides an overview of the implementation framework. The hardware

issues such as real time sampling rates are further investigated. The development of

Graphical User Interface along with the simulation process flowchart is discussed.

Chapter 5 discusses critical aspects of the experimental setup. This is then followed by

analysis of the results using three different performance measures.

Chapter 6 concludes this research effort and discusses and provides some direction for

our future work.


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2 Literature Survey

The steering linkages transmit forces/moments from the road wheels to the hand wheel

in a conventional steering system. However as explained earlier, in a drive by wire system

these linkages are absent and are replaced by electronic control. Such a situation

necessitates the development of two main control schemes. First scheme is necessary to

ensure that driver steering angle commands are accurately followed and second scheme is

essential to provide the driver with a realistic road feel.

Bertacchini et.all [19] pursued their research in validating their control strategies of

determination of the position of the drive shaft of a brushless motor and that of a DC

motor is particularly suitable as force feedback actuators in steer-by-wire applications.

Amberkar et.all (Delphi, Inc) [20], Yao (Visenteon Corp) [21] discuss control

methodologies, variable steering ratios for a SBW systems using direct instrumental pick-

up from sensors to monitor the tire forces and moments from an actual test vehicle. Cesiel

and Gaunt (General Motors, Corp) present the complete development of GMs SBW

vehicle in [22]. Lui and Chang [23], Ryu and Kim [24] established stationary hardwares

and conducted experiments to show that their proposed virtual environment can be used as

a tool to study electronic steering systems. A high precision, cost effective, experimental

hardware-in the-loop steer-by-wire test environment are presented and discussed to

support engineering and psychology studies in [25].

Researchers at Stanford University have built one such vehicle where the steering

torque feel is based on actuators and sensors placed at critical location. The vehicle

considered in this study is a production model 1997 Chevrolet Corvette.


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Figure 2-1: Experimental Steer-By-Wire Vehicle (Courtesy Dynamic Design Lab Stanford University)

Two rotary position sensors one on the steering column and the other on the pinion

provide absolute measurements of rotation angles, which are used in steering feel real time

estimation [26]. The above studies have presented solution to the problem of mimicking

the steering feel of a conventional vehicle using state of the art control schemes to provide

force feedback information exerted by the road-wheel actuator(s) to the hand wheel

system by direct instrumental pickups from sensors. However, measurement of road-

wheel actuator force/torque may usually turn out to be prohibitively expensive. Therefore,

in some cases the steering torque prediction schemes that have been proposed have used

mathematical models of tire-road dynamics and/or the dynamics of power steering

systems in conjunction with real-time measurements of easy-to-measure variables of

interest.

Lorincz [27], constructed second order steering system models and developed a control

scheme based on ARMAX system identification method to provide force feedback to the

user. Yih and Gerdes [28], represent first application of GPS-based state estimation and

SBW to modify vehicle handling characteristics based on the bicycle model to model the

vehicle dynamics. Setlur et.all [29], presents a nonlinear tracking controller for haptic

interface in SBW where the vehicle model is modeled using the bicycle model.

Specifically, this controller ensures that the steering mechanism follows the operatorcommanded maneuvers. Coundon et.all [30] propose two control algorithms to meet

specific transient behavior and stability margins for the bicycle model used in a SBW

paradigm and aims at imposing a particular steering behavior to improve vehicle handling

characteristics. Bajcinca et.all [31] developed a force feedback actuation loop for SBW

vehicle and improved its performance by introduction of a torque sensor. Similar study


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with an experimental cabin (Mohellebi et.all [32]) which sits on a six degree of freedom

platform along with a motorized steering wheel simulates steering feel. The steering forces

are calculated using simple second order system in conjunction with measuring human

applied steering torques using torque sensors. As seen from most of the cases from the

above literature review, the steering torques are usually based on development a linear

combination of the following second order model, a b c

= + + , where,

and

is the steering angle, steering velocity and acceleration respectively. Researchers have

developed many strategies to determine the values of a, b and c. One of such strategy was

applied in an experiment conducted at the Renault Technical Center for simulation in

France [33]. As we can see from Figure 2-2 K1, K2 and K3 are three ways to estimate the

constant a that we defined earlier.

Figure 2-2: Three different laws used to provide steering feel [20]

Many researchers and educational practitioners believe that virtual reality simulation

systems offer strong benefits that can support education through their experiential and

intuitive characteristics in which learners can share contexts and interact [34] and

especially facilitate constructivist and situated learning [35]. As mentioned in the Chapter

1, SBW also allows us to explore exiting opportunities in the field of shared/collaborative

control (steering) of the underlying mechanical system (vehicle). Possibilities range from

sharing of control between user and automation technology or between multiple individual

users.


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In the case of studying the possibility, where the system/device manipulation control

may be shared by multiple users Gillespie et. all [16] introduce the concept of a virtual

teacher. The virtual teacher is an agent that supplements the user action in order to

facilitate and accomplish the manual task. Gillespie et.all proposes that, there are three

major ways in which a virtual teacher could be designed. As shown in Figure 2-3 the three

basic arrangements of mechanical contact between a pupils hand, a teachers hand and the

device used to perform the task are a. Indirect Contact b. Double Contact, c. Single

Contact.

a. Indirect Contact b. Double Contact c. Single Contact [Courtesy: [28]]

Figure 2-3: The Virtual Teacher [16]

The author describes the case of indirect contact as the teacher and pupil both hold the

device at different location. The teacher wields control and hopes that the pupil will be

able to mimic the action. Case b is where the teacher grasps the pupils hand which in turn

grasps the device. Here the pupil acts as the force and motion sensor monitoring the

teachers actions. Pupil explores two distinct contact one with the device and other with

the teacher. Case c arrangement allows teacher to manipulate the device allowing the pupil

to feel the forces and motions through a single contact [16].

The virtual teacher can also be in form of an automatic controller or in the form of

virtual fixtures [36] that may be used by the operator as mechanical guides for controlling

force or motion direction. In the case of studying various control schemes by which a

human and automatic controller may share control, Griffiths and Gillespie [17] present a

control strategy to assist user with an automatic controller to drive along a prescribed path.

The vehicle model used in this case is derived assuming no slip between the tires and the


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road and the steering torque is calculated based on steering angle, k = , where the

proportionality constant k can be tuned for the desired steering feel. Switkes et.all [18]

work with the bicycle model for vehicle dynamics simulation to construct a lane keeping

controller using a potential field approach. In their work, the user is provided with a force

feedback based on vehicles lateral and heading error.

Needless to say that during the development of vehicle dynamic models and steering

feel, tire modeling should not be overlooked as it is a very important field which needs

paramount attention. Improper or poor tire modeling may lead to misleading results. One

of the many ways to classify tire models is by the internal structure of the model. With

respect to such classification there are three main groups of tire models: finite element

models, simplified mechanical models and semi-empirical models (e.g. Pacejka Tire

Models) [37].

Figure 2-4: Cornering Stiffness: Lateral Force vs. Slip Angle Curve [Courtesy: [38] [37]]


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Because of the exceedingly complicated calculation while using finite element models

and the fact that these give more detailed information than is typically needed in vehicle

dynamics such models are usually not preferred in real time processing given the high

requirements over the haptic refresh rates. Simplified physical models can also be easily

built using mechanical analogies and lumped parameters (such as lateral stiffness,

longitudinal stiffness, damping etc) [37]. Many researchers conducted thorough testing on

the pneumatic tires to establish fundamental relationships between operating variables and

tire outputs. The well known linear tire model is defined from the fact that for small slip

angles the tire behaves linearly, producing a lateral force proportional slip angle in an

amount defined as the cornering stiffness (as shown in Figure 2-4) [37].

However, availability of a complete numerical tire parameters model will be the best

way to generate tire forces [39]. Hsu et.all [40] utilize available vehicle information to

identify these tire parameters in real-time. Another simple way of accessing the tire forces

and moments is by using packages such as CARSIM or DynaFlexPro. CARSIM [41]

animates simulated tests and generates about 600 output variables to plot and analyze, or

export to other software such as MATLAB, Excel, or other optimization tools.


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Figure 2-5: CARSIM simulating car handling characteristics [Courtesy: Mechanical Simulation]

As seen in Figure 2-3, CarSim is built on decades of research in characterizing vehicles

and reproducing their behavior with mathematical models [41].

Figure 2-6: DynaFlexPro-Tire: Latest pneumatic tire models incorporated for building system

equations [Courtesy: Maple Soft/DynaflexPro-Tire]

As mentioned earlier another similar package is DynaFlex Pro/Tire[42], which is an

add on toolbox thats available to the user from the developers of Maple Soft.

DynaFlexPro can be used for modeling and simulating the dynamics of mechanical

multibody systems. A graphical user interface, DynaFlexPro/ModelBuilder, facilitates the

rapid creation of system models using block diagrams. These softwares combine graph

theory with engineering mechanics in algorithms that automatically generate the system

equations from the system model. Thus no errors are introduced while formulation which

is one of the prominent threat while trying to derive these complex equation by hand and

plus it is much less time consuming. As shown in Figure 2-4, with DynaFlexPro/Tire,

users can incorporate the latest pneumatic tire models into simulations of vehicle systems

[42].

Computers through information technology and data mining have dramatically changed

many aspects of daily life. It is only a matter of time that these improvements may as

dramatically change automotive driving too [43]. There are a large number of in vehicle

information systems that are now available at the drivers disposal (such as speech based

email, voice activated navigation systems, inbuilt computers with internet browsing


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technology etc). However would such systems add to drivers distraction? Lee et.all [43]

propose one way to address this issue is to provide the driver with additional information

with haptic interfaces. Their work describes techniques adapted from Ecological Interface

Design which might help identify suitability with in different types of haptic interfaces

might to best convey driving-related information.


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3 Mathematical Model Development

3.1 Vehicle Dynamics

Vehicle dynamics is the science that studies the kinetics of wheeled land vehicles

operating on regular or an irregular terrain. Kinetics encompasses the motion and forces

encountered during dynamic interaction of the articulated multibody vehicle system with

its surrounding environment.

An articulated multibody (AMB) vehicle is comprised of groups of tires, links, joints

springs, dampers and actuators that form the various subsystems of a vehicle. The driver

provides the principle control inputs in the form of acceleration, breaking, and the steering

motion (via a suitable driver interface). The road surface with various parameters such as,

surface roughness, stiffness, slope, curvature act as disturbance inputs to the vehicle.

Careful articulated multibody system modeling now presents opportunities for numerical

simulation and analysis. Outputs such as hand wheel torque can be fed back to the

user/driver to evaluate the vehicle dynamic models performance, in response to the

steering motion as inputs.

It is noteworthy that the driver interface may have mechanical, hydraulic, electrical or

electronic subsystem components. However, control loops for these inner subsystems have

much faster closed loop time constants than the mechanical components and can be

replaced by corresponding zeroth order models i.e. as constant gains. Thus we will only

focus on developing vehicle dynamic models based only on the articulated mechanical

subsystems.

As discussed earlier in Chapter 2 are several different strategies employed in the

research community to mimic the steering feel. These range from direct instrumented-

pickup and feedback of road-wheel interactions (using accelerometers/ force-sensors) to

steering torque prediction schemes based on mathematical dynamics models of tire-road,

suspension, power steering systems in conjunction with selected real-time measurements.


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While the latter sets of approaches offer the greatest promise from the view point of

accuracy and fidelity, real-time implementations at high sampling rates in noisy

environments pose challenges. Hence in this chapter we first focus on creating analytical

vehicle dynamics models at four fidelity (Models A, B, C and D).

3.1.1 Model A: Spring-Mass-Damper Analogy (No Slip Model)

Vehicleand Tires

2k

Steering

1k

2b

1b

b

a

X

Y

x

y

Figure 3-1: (a) Steering System modeled with rotational spring mass damper analogy, (b) simple

bicycle kinematics model (no slip)

Model A (Figure 3-1a) is comprised of two rotational bodies, viz steering wheel, and

vehicle-tire connected via a rotational spring and damper , 1,2i ik b i = as shown above

whose values should be appropriately selected to provide the requisite steering feel. Note

that in this case we have lumped vehicle and tire bodies as one single inertia body. The

human is allowed to apply a prescribed motion profile at the steering wheel, which in the

case translates to providing and

, the steering angle and steering velocity respectively.The governing system equations can be written as follows,

1 1 2 2( ) ( ) ( ) ( )J k b k b = + (3.1)


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WhereJ, represent the moment of inertia of the steering wheel, and vehicle-tires

subsystems. Thus the steering torque felt by the user is given by Equation (3.1) and can

be re written as,

1 1( ) ( )A k b = +

(3.2)

Additionally, it is also important to derive the kinematics of the vehicle which would

help describes how the vehicles position would evolve through time. With the assumption

of no slip between tires and the road the following sets of equations can be written,

sin sin cos cos( )

u bx u

a b

= +

+ (3.3)

sin cos cos sin( )

u b

y ua b

= ++ (3.4)

sin( )

u

a b =

+ (3.5)

Vehicle is shown in Figure 3-1 (b) with ,x ybeing the coordinates for the center of mass

while is the yaw angle about the z axis.


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3.1.2 Model B: The Bicycle Model with Linear Tire Model

CG

xy

Body

Fram

e{B}

Earth Fixed Frame {N}

X

Y

Figure 3-2: Bicycle Model State Description

Many vehicle dynamics books outline the equations of motions for a vehicle derived

from a bicycle model.[38, 44-46] In this section we will re-derive this well studied

Bicycle Model.

We will consider a motor vehicle as a rigid body moving on a surface, in this case the XY

plane as shown in figure 3.1. This rigid body will have three degrees of freedom. By

considering the inertial frame XY we can have X and Y of the center of mass CG of the

vehicle and the yaw angle between the body based frame {B} xy and inertial frame

{N} XY as the generalized coordinates. Thus the equations of motions are:

XmX F= (3.6)

YmY F= (3.7)

Z ZI M = (3.8)


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Where, Fx, Fy and Mz are longitudinal forces, lateral forces and yawing moment

respectively. From Figure 3-2, we can construct the rotation matrix between the fixed and

the body frame as,

cos sin 0sin cos 0

0 0 1

N

BR

=

(3.9)

We now develop the equation of motions using the Lagrange formulation.

Kinetic Energy (K.E) =2 2 21 1( )

2 2Zm X Y I + +

Generalized coordinates ,,YXqi =

( . )K EmX

X

=

,( . )K E

mY

Y

=

,( . )K E

I

=

(3.10)

Using the rotation matrix from equation(3.9), we transform

cos sin

sin cos

xX

yY

=

(3.11)

For consistency in representing velocities we convert our longitudinal and lateral velocity

symbols as, x u

= andy v

= (3.11).

sin( ). . cos( ). cos( ). . sin( ).X u u v v

= + (3.12)

( . ) cos( ) ( . )sin( )u v v u

= + (3.13)

cos( ). . sin( ). sin( ). . cos( ).Y u u v v

= + +

( . ).cos( ) ( . )sin( )v u u v

= + + (3.14)

.[( . )cos( ) ( . ) sin( )] X

d K Em X m u v v u F

dtX

= = + =

(3.15)


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.[( . ).cos( ) ( . ) sin( )] Y

d K EmY m v u u v F

dtY

= = + + =

(3.16)

As we can see equations (3.15) and (3.16) are in inertial frame of reference. Hence we

transform them into the body fixed frame by pre-multiplying by 1)( BFR

1 1[( . )cos( ) ( . ) sin( )]

( ) ( )

[( . ).cos( ) ( . ) sin( )]

XB B

F F

Y

Fm u v v uR R

Fm v u u v

+ = + +

(3.17)

Let, ( )u v A

= and ( . )v u B

+ =

1

2 2

cos( ) sin( )1

( ) sin( ) cos( )cos ( ) sin ( )

B

NR

= + (3.18)

2 2

cos( ) sin( ) [ cos( ) sin( )]1.

sin( ) cos( ) [ .cos( ) sin( )]cos ( ) sin ( )

x

y

Fm A B

Fm B A

= ++

2 2

2 2cos ( ) sin( )cos( ) sin( )cos( ) sin ( )cos ( ) sin( )cos( ) sin( )cos( ) sin ( )x

y

FA B B Am

FB A A B

+ += + +

( . )

( . )

X

Y

FA u vm m

FBv u

= = +

.X

Fx u v

m

= = + (3.19)

.YF

y v um

= = (3.20)


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CG

r

u

v

V

F

R

a

b

FyF

FyR

p

g

Y

X

Figure 3-3: The Bicycle Model

.Z

d K EI M

dt

= =

. .yF yRZ

Z Z

a F b F Mr

I I

= = = (3.21)

Equations(3.19), (3.20) and (3.21) are the equations of motion for the vehicle. Lateral

velocity and the side slip angle of the vehicle can be represented as,

cos( )

uV u

= (3.22)

:F Front Slip Angle

:R Rear Slip Angle

:u Longitudinal Velocity

:v Lateral Velocity

r: Yaw Rate

: Heading Angle

:yFF Front Lateral Force

:yRF Rear Lateral Force

: Side Slip Angle


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1tanv v

u u

=

(3.23)

Now we move on to calculate the front and the rear slip angles,

. . ( )CGVp V rk ai u i v j rk ai u i v ar j= + = + + = + +

1tan ( ) ( )Fv ar v ar v ar

u u u u

+ + = = + (3.24)

F

ar

V = + (3.25)

R

br

V = (3.26)

This completes the bicycle model formulation. Next we look at constructing a model for

the steering torque. The steering torque is a function of forces and moments produced at

the road tire interface. However, before we dwell into steering torque formulation it is

imperative to understand what exactly happens at the road-tire interface. In this section we

will visualize how forces and moments are developed at the road tire interaction. Details

of this literature can be found in many vehicle dynamics text books and in [37].

Road Tire Interaction:

The ground reaction on the tire is described by three forces and moments, as shown in

Table 3-2. Figure 3-4 represents these forces and their location on the tire.

Table 3-1: Tire forces and moments

Forces Moments

Normal Force -- Fz Aligning Torque Mz

Tractive Force -- Fx Rolling resistance Moment My

Lateral Force -- Fy Overturning Moment Mx


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Tire Forces:

Normal force (Fz) is the vertical load on the wheel. This force acts upwards and is

considered to be positive as shown in Figure 3-4. Since the bicycle model has only one

front wheel and one rear wheel we will not experience the phenomenon of load transfer.

Hence we only consider the weight of the tire and the vehicle to calculate the normal force

generated at the road tire interface.

Tractive forces (Fx) arise due to acceleration or braking of the wheels. This model has

been developed with the assumption of constant longitudinal velocity (no longitudinal

acceleration). Hence due to this assumption effects of these forces will be eliminated from

the steering torque formulation.

Lateral forces (Fy) arise due to two main physical processes elastic deformation and

sliding friction happening at the same point. We will consider the effects of this force

while formulating our steering torque. Figure 3-5 shows the thread button cycle which

generates the lateral force and aligning moment.

Fy: Lateral Forces

Fz: Lateral Forces

Fx: Tractive Forces

{A}: Tire Axis System

Mz: Aligning Moment

My: Rolling

Resistance Moment

Mx: Overturning

Moment

Figure 3-4: Tire Forces and Moments


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The generation of lateral force and consequently aligning moment is carried out through

5 distinctive phases. Each of the phase is also numbered and displayed on Figure 3-5

The thread button cycle:

1. First the thread button on a tire approaches the ground.

2. Button sticks to the ground.

3. Deformation of the button increases as tire rotates because of side slip angle.

4. Button continues to deform until Fy exceeds Fz.

5. After this the button starts slide until it reaches back to the wheel centerline

undeflected position and lifts off the ground.

Wheel Axis

CG of ForceGenerated

Heading (x)Actual

Lateral Force

Pneumatic Trail

Side Slip Angle

4

1

2,3

5

b

a

X

Y

Aligning Moment

Figure 3-5: Thread button cycle


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Assuming that the tire or wheel is rolling then the process of lateral force generation

occurs through two processes,0

. . tan( ) ( )

tp b

y

tp

F k x dx q x dx= + . Where the first integral is

the elastic deformation and second comes from sliding friction ( )q x is the lateral force

capability, k is the tire stiffness. Moment caused due to the centroidal location of the

generated force around the Z axis is called the aligning moment.

As one can see from figure 3-5, the lateral force is dependent on the slip angle and

cornering stiffness [37, 38]. This can be represented as,

.yF F F F C= (3.27)

.yR R R

F C= (3.28)

Where,F

C andR

C represent the cornering stiffness of front and rear tire. ,F R is the

slip angle generated at the front and the rear wheel.

Thus to summarize we will consider the normal force Fz and the lateral force Fy during

the formulation of the steering torque. Tractive force Fx is zero since the vehicle will be

running at a constant velocity and there will also be no breaking or deceleration. Now let

us discuss the moments that are generated at the road tire interaction and discuss which of

these will play a role in the development of the steering torque equation.

Tire Moments:

Aligning Moment: Self-aligning torque, also known as self-aligning moment, is the

resultant of the lateral force and the moment arm known as pneumatic trail, tp (Figure 3-6)

[39] [28] [40]. It is a restoring moment that attempts to return the wheels to a zero slip

angle state. Essentially, the presence of the self aligning torque exposes the fact that a tire

likes to head in the direction it is presently running. It may be important to note that the

self-aligning torque may be influenced by a mechanical trail induced from suspension

geometry. For example, more mechanical trail and therefore more self-aligning torque can

be induced with the presence of caster and kingpin offset. Trail may also be affected by

camber, which can induce a small destabilizing force. However, this is also small and

hence we have neglected the effects induced due to mechanical trail.


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CG of

Generated Force

tpPneumatic Trail

tmMechanicalTrail

Steering Axis

Figure 3-6: Moment arm for aligning moment

In Figure 3-5 and Figure 3-6, Fy is the lateral force acting on the tire, is the tire slip

angle, tp is the pneumatic trail, the distance between the application of lateral force and

the center of the tire. tm is the mechanical trail, the distance between the tire center and

the point on the ground about which the tire pivots as a result of the wheel caster angle.

Thus the total aligning moment is given by [40],

Mz = (tp + tm) Fy (3.29)

As discussed earlier we are not going to consider the effect of mechanical trail and hence

tm = 0. The portion of aligning moment due to the tire pneumatic trail may be directly

approximated as an empirical function of tire slip angle and from the foundation stiffness

model [39]. The model predicts that this distance tp (pneumatic trail) is equal to;

2tp c I = (3.30)

Where, c is the foundation stiffness of the road, I is the length of the tire patch. To

summarize, for the purpose of the formulation of steering torque we will only consider the

effects of the aligning torque as describe above. Rolling resistance and overturning


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moment effects are small and will be neglected in the analysis of steering system

torques[44].

Steering System Model:

Now that we have constructed our vehicle model and discussed tire forces and

moments we need to incorporate geometric effects of the steering system which will

influence our steering torque model. The forces and moments imposed on the steering

geometry arise from those generated at the tire-road interface [44]. As seen from the

section describing the road tire interaction, these forces are measured at the center of the

contact with the ground Frame {A} in Figure 3-4. To provide the requisite steering feel we

need to represent these forces and moments in the frame where the steering wheel

connects and is aligned with the steering axis. But before we begin our analysis it is

crucial to understand the location of the steering axis. Figure 3-7 and Figure 3-8, shows

the steering axis alignment.

d

Z

Y

Z

X

Caster Angle

a. Front View b. Side View

Figure 3-7: 2-D views to visualize the steering axis

As you can see from Figure 3-8 the inclination angle and the caster angle orient the

steering axis. The addition of the translational offset d as seen from Figure 3-8a

completely determines the exact location of the steering axis. This offset as can be seen


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depends completely on the car manufactures specification of the caster, inclination and tie

rod assembly.

{A}Z

XY

R

Tire Radius

{C}

1

2

d

King Pin Offset

{B}

Steering Axis

Z'

X'Y'

Z''

X'' Y''

Steering Torque

Figure 3-8: 3-D view for the steering axis alignment

As stated earlier we now have to transfer tire force and moments generated in frame

{A} the tire axis system, through the steering system geometry to frame {C} where the

steering wheel is mounted along the steering axis ''Z . The tire forces considered in this

analysis are, (i) Moment due to the normal force Fz : Because the steering axis is inclined,

Fz has a component acting to produce a moment attempting to steer the wheel. This

moment arises from both the caster and lateral inclination angle. Note that we do not

consider the effects on the normal force due the load transfer phenomenon during the

turning of the vehicle. Hence we consider a constant force Fz acting at the tire center

patch. (ii) Moment due to lateral force Fy: This force produces a moment through the

longitudinal offset resulting from the caster angle. (iii) Component of aligning moment

acting on the steering axis


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The preceding discussion will determine the influence of the above three elements on

the steering torque experienced about ''Z (Figure 3-8) using screw theoretic frame work.

Screw coordinates are extensively used in both velocity and force analysis problems.

Forces can be represented using the underlying screw vector and screw coordinates as a

wrench,

^

$o

W

n

F

M

=

(3.31)

whereo

F is the force applied at a point on the body in terms of the reference frame in

which the screws are expressed and nM

is the moment created byo

F at the origin of the

same reference frame. It is important to note that multiple twists or wrenches can be

combined and represented as a single twist or wrench acting on a body. For greater details

on screw theory and such screw based motion and force descriptions see [47] and [48]. In

our case we want to transfer forces and moments from frame {A} to frame {C} as see in

Figure 3-8. The transformation from frame {A} to {C} can be written as,

'

'

A A B C

C B C C A A A A= (3.32)

Where,

0 1

1 0 0

0 cos( ) sin( )

0 sin( ) cos( )

0

0

A A

A BB

A

B

A

R sA

R

s d

=

=

=


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''

'

0 1

cos( ) 0 sin( )

0 1 0

sin( ) 0 cos( )

0

0

B B

B C

C

B

C

B

R sA

R

s

R

=

=

=

Finally, the steering angle rotation about Z axis in frame A gives us,

' ''

'

'

0 1

cos sin 0

sin cos 0

0 0 1

0

0

0

C C

C C

C

C

C

C

R SA

R

s

=

=

=

Finally using the screw theoretic frame work we can write,

0AA CCA A AA C

C C

RF F

D R RM M =

, but since we know AF and AM we find,

1

0AC ACA A AC A

C C

RF F

D R RM M

=

(3.33)

Where CF and CM are forces and moments in the steering axis frame. However the

steering joystick or device is constrained in ''X and ''Y . Thus for this model (Model B),

the steering torque feedback to the driver will only be the ''Z component of CM .

" sin( )cos( ) cos( ) cos( )

cos( ) cos( ) sin( )

VB Z Z y

Z y

T M d F F d

M F R

= = + +

+(3.34)


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3.1.3 Model C, D: Vehicle Model (With and Without Suspension)

Using DynaFlexPro

It is readily apparent that developing complex articulated multi-body system equations

can be very arduous and subject to human coding errors. For example, the development

of governing system equations even for small DOF models (such as Model A & B)

requires careful formulation and meticulous coding. To alleviate, we employed

DynaFlexPro, an add-on toolbox for Maple that can be used for developing the analytical

equations of motion and subsequently simulating mechanical multi-body systems.

Equations of motion of large degree of freedom (DOF) mechanical systems can be

symbolically derived without the expense of time and hand coding. DynaFlexPro allows

the users to also incorporate various latest pneumatic tire models into simulations of

vehicle systems [42]. Figure 3-9 (a), (b) shows the models which have 10 and 14 degree

of freedom respectively. The base model in this car is the full 14 DOF model including

the four independent vertical motions at each of the tires which we will refer to as Model

D. Alternately the suspension effects from this 14 DOF can be eliminated to create a 10

DOF Model that we will refer to as Model C. As discussed earlier DynaFlexPro can be

used for modeling and simulating the dynamics of mechanical multibody systems. A

graphical user interface, DynaFlexPro/ModelBuilder, facilitates the rapid creation of

system models using block diagrams. This software combines graph theory with

engineering mechanics in algorithms that automatically generate the system equations

from the system model. Procedure for generation of code in Maple and its Simulink

diagram construction is shown in Appendix A. For this model we have used the Pajama

tire model. It is based upon fitting experimental data to the well-known magic tire

formula. The resulting Pacejka tire model represents the state-of-the-art for high-fidelity

vehicle dynamics modeling. Complex expressions for all tire forces and moments are

computed, taking into account a wide range of physical phenomena. Due to the presence

of advanced tire models we can easily access all the three force components, including

the load transfer on the wheels while the vehicle maneuvers.


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6 Chassis Degree of freedom

X

Z

Y

4 Tire RotationDegree of freedom

(a)

X

Z

Y

6 Chassis Degree of freedom

4 T ire RotationDegree of freedom

4 Suspension TranslationDegree of freedom

(b)

Figure 3-9: (a) Vehicle Model without Suspension (10 DOF), (b) Vehicle Model with Suspension (14

DOF) using Maple Softs DynaFlexPro/Tire toolbox.


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Note that the assumption of constant velocity is still carried over to Model C and D by

proving constant wheel spin velocity at each of the two rear wheel revolute joints (for

further details see Appendix A). Next we will discuss the Ackermann steering angles and

the way we implemented Ackermanns steering geometry in this model. Ackermann

anandnaik ms thesis

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