anandnaik ms thesis
TRANSCRIPT
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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