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Vehicle
Dynamics Estimation
using Kalman Filtering
Experimental Validation
Moustapha
Doumiati
Ali Charara
Alessandro Victorino
Daniel Lechner
Series Editor
Bernard Dubuisson
©WILEY
Table of Contents
Preface
xiii
Introduction
xvii
1.1. Needs of ADAS systems
xvii
1.2. Limitation of available ADAS systems
xix
1.3. This book
xix
1.4.
versus
Laboratory
existing
studies
vehicle
xx
1.5. Outline
xxi
Chapter 1. Modeling of Tire
and Vehicle
1
Dynamics
1.1. Introduction
1.2. Tire
dynamics
1
2
.
1.2.1. Tire forces and moments
2
1.2.1.1. Vertical/normal forces
1.2.1.2.
Longitudinal forces and
1.2.1.3. Lateral forces and
1.2.1.4.
1.2.1.5.
2
longitudinal slip ratio
5
Aligning
Coupling
effects between
longitudinal
1.2.2. Tire-road friction coefficient
longitudinal
7
traction force
1.2.2.2. Normalized lateral traction force
Quasi-static tire model
1.2.3.1.
1.2.3.2.
Pacejka's magic tire
Dugoff's tire model
1.2.3.3. Linear model
1.2.4. Transient tire model
1.3. Wheel rotational
and lateral
6
tire forces
1.2.3.
4
sideslip angle
moment
1.2.2.1. Normalized
3
dynamics
9
9
10
model
11
17
18
18
19
viii
Vehicle
Dynamics
Estimation using Kalman Filtering
1.3.1. Static tire radius
20
1.3.2. Effective tire radius
20
1.4. Vehicle
21
body dynamics
1.4.1. Vehicle's vertical
1.4.1.1.
Suspension
22
dynamics
23
functions
23
1.4.1.2. Quarter-car vehicle model
1.4.2. Vehicle
25
planar dynamics
25
1.4.2.1. Four-wheel vehicle model
1.4.2.2.
Wheel-ground
Bicycle model
1.4.2.3.
1.4.3. Roll
dynamics
27
vertical forces calculation
30
and lateral load transfer evaluation
34
1.5. Summary
Chapter
2. Estimation Methods Based on Kalman
Filtering
37
37
2.1. Introduction
2.2.
31
State-space representation
and system
38
observability
39
2.2.1. Linear system
39
2.2.2. Nonlinear system
40
2.3. Estimation method: why stochastic models?
Closed-loop observer
41
2.3.2. Choice of the observer type
42
2.3.1.
2.4. The linear Kalman filter
43
2.5. Extension to the nonlinear case
44
2.6. The unscented Kalman filter
46
46
2.6.1. Unscented transformation
2.6.2. UKF
48
algorithm
2.7. Illustration of
a
linear Kalman filter application: road
profile
50
estimation
50
2.7.1. Motivation
51
2.7.2. Observer design
2.7.3.
Experimental
2.7.3.1.
2.7.3.2.
2.8.
results: observer evaluation
53
53
signal
Comparison
with LPA
Comparison
with GMP
56
signal
59
Summary
Chapter
61
3. Estimation of the Vertical Tire Forces
61
3.1. Introduction
62
3.1.1. Related works
62
3.2.
Algorithm description
3.3. Techniques for lateral load
scheme
transfer calculation in
an
open-loop
64
Table of Contents
ix
3.3.1. Lateral acceleration calculation
65
3.3.2. Roll
65
angle
calculation
3.3.3. Limitation of the
open-loop
66
model
3.4. Observer design for vertical forces estimation
67
3.5. Vertical forces estimation
69
3.5.1. Observer
Ofze design
3.5.2. Observer
Opzl
3.6.
3.7.
3.8.
70
formulation
the
Analysis concerning
two-part
Models observability analysis
Determining the vehicle's mass
3.8.1. Experimental validation of
72
estimation
73
strategy
74
74
the vehicle's
weight
identification
method
75
3.9. Detection of rollover avoidance: LTR evaluation
76
3.10.
78
Experimental
validation
3.10.1. Regulation of observers
80
3.10.2. Evaluation of observers
81
3.10.3. Road
results
experimental
Starting-slalom-braking test
82
3.10.3.1.
3.10.3.2.
Circle-braking
86
82
test
87
3.10.3.3. Turn test
3.10.3.4.
Concluding
remarks
Comparison between
Ofzl versus Ofze
3.10.5. Observability results
3.10.4.
93
linear and nonlinear observers:
93
94
3.10.6. LTR evaluation
94
3.10.7. Road geometry effects
97
3.11.
99
Summary
Chapter 4. Estimation of the Lateral Tire
Forces
101
101
4.1. Introduction
4.2.
Background
on
lateral force parameters calculation
104
4.2.1.2. Tire-road friction estimation
105
4.2.1.3.
106
Cornering
stiffness estimation
4.2.1.4. Effect of camber
106
angle
4.3. Lateral force reconstruction in
an
open-loop
scheme
4.3.1. Test at low lateral acceleration level
4.3.2. Test
4.4.
102
103
4.2.1. Lateral force parameters evaluation
4.2.1.1. Sideslip angle estimation
at
Techniques
107
108
high lateral acceleration level
112
for lateral tire force evaluation
112
4.5. Estimation process for
force estimation
sideslip angle
and individual lateral tire
115
x
Vehicle
Dynamics
Estimation using Kalman Filtering
4.5.1. Estimation
116
algorithm
4.5.2. Vehicle model
117
4.5.3.
118
Dynamic tire model representation
4.5.4. Reference lateral tire force model
119
4.5.5. Further consideration for the cornering stiffness Ca
120
4.5.6. Lateral force observers:
121
4.5.7.
4.5.8. Estimation
4.5.9.
4.6.
Experimental
4.7.2.
124
methodologies
Sensitivity analysis
4.7. Pavement
4.7.1.
state-space representation
Observability analysis
of the
124
sideslip angle
estimation
validation
125
results
128
bend combination test
128
experimental
Left-right
Single left bend
test
132
4.7.3. Slalom test
4.7.4. Circle
4.7.5.
137
141
test
Longitudinal
forces estimation
4.7.6. Concluding remarks
4.7.7.
4.7.8.
4.8.
Ofve
versus
Tuning
Analysis
on
143
experimental
results
Ofvu
153
and observations
154
respect to road friction variation
Summary
Chapter
156
158
5. Embedded Real-Time
Experimental
152
153
of observers
4.8.1. Robustness with
4.9.
125
System
Results
for Vehicle State Estimation:
159
5.1. Introduction
159
5.2.
159
Laboratory
vehicle
5.2.1. Embedded
sensors
160
5.2.2. Software modules
164
5.2.3. DLL configuration
164
5.3. Estimation process: VSO system
165
5.4. Test tracks
167
5.5. Test results
168
5.5.1. Bourbriac test
169
5.5.2. Callac
179
test
5.5.3. Rostrenen
5.5.4.
5.6.
test
Concluding
Summary
remarks
185
199
200
Appendices
201
Appendix
203
1
Table of Contents
xi
Appendix 2
207
Appendix
3
209
Appendix
4
Appendix
5
221
Appendix 6
225
Bibliography
227
Index
237
217