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A Method to Estimate Friction and Slip Angle Using Steering Torque
Yung-Hsiang Judy Hsu
Shad LawsChristopher Gadda
J. Christian Gerdes
Stanford University
Judy HsuIMECE 2006
2 Dynamic Design LaboratoryStanford University
A Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering Torqueueueue
Motivationn Every day in the US, 10 teenagers are
killed in teen-driven vehicles in crashes1
¡ Loss of control accounts for 30% of these deaths
¡ Inexperienced drivers make more driving errors, exceed speed limits & run off roads at higher rates
n In 2003, motor vehicle traffic crashes were the leading cause of death for ages 5-33.2
To prevent loss of control, we need to understand what determines vehicle motion
1 USA Today. Study of deadly crashes involving 16-19 year old drivers (2003) 2 National Highway Traffic Safety Administration. Traffic safety facts (2003)
Judy HsuIMECE 2006
3 Dynamic Design LaboratoryStanford University
A Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering Torqueueueue
Motion of a Vehicle
n Motion of a vehicle is governed by tire forces
n Tire forces result from deformation in contact patch
n Lateral tire force is a function of tire slip
α
SIDE VIEW
Ground
BOTTOM VIEW
Contact Patch
Fy
Judy HsuIMECE 2006
4 Dynamic Design LaboratoryStanford University
A Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering Torqueueueue
Tire Curvemaximum tire grip
Linear Nonlinear Loss of control
Judy HsuIMECE 2006
5 Dynamic Design LaboratoryStanford University
A Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering Torqueueueue
Previous work with GPS
Global Positioning System (GPS)
With Inertial Navigation System (INS), have tire slip angle estimates [Ryu 2002]
Cornering stiffness in the linear region of handling [Bevly 2001]
Coefficient of friction estimated in real-time [Hahn
2002 & Hsu 2006]
à Need an online estimation process for friction and slip angle without GPS
Judy HsuIMECE 2006
6 Dynamic Design LaboratoryStanford University
A Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering Torqueueueue
Features of the Observer
n Uses measurements readily available on production vehicles
¡ Gyroscopes, accelerometers, steering encoder, steering torque (thru EPS or SBW)
n Takes advantage of total aligning torque
¡ Key piece of information for µ, α estimation
n Accuracy of µ, α estimates are comparable to GPS measurements up to limits of handling
Judy HsuIMECE 2006
7 Dynamic Design LaboratoryStanford University
A Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering Torqueueueue
Roadmap
n Derive overall observer scheme
1. Steering system model
2. Linear disturbance observer
3. Nonlinear µ,α-observer
n Experimental Results
¡ Ability to estimate µ and α up to the limits of handling
Judy HsuIMECE 2006
8 Dynamic Design LaboratoryStanford University
A Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering Torqueueueue
Observer Scheme
Steering System Model
Disturbance Observer
τd = τa + τj
Nonlinear µ,α-Observer
δ
i
ay, r
τa
Judy HsuIMECE 2006
9 Dynamic Design LaboratoryStanford University
A Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering Torqueueueue
1. Form Steering System Model
Steering System Model
Disturbance Observer
τd = τa + τj
Nonlinear µ,α-Observer
δ
i
ay, r
τa
Judy HsuIMECE 2006
10 Dynamic Design LaboratoryStanford University
A Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering Torqueueueue
We model the torque contributions around the steer axis:
Generated by steer-by-wire motor1. Motor torque à actuator torque
Generated by tire forces2. Vertical forces à jacking torque
3. Lateral forces à total aligning torque
Steering System Model
Steering System Model
Disturbance Observer
τd = τa + τj
Nonlinear µ,α-Observer
δ
i
ay, r
τa
Steering System Model
Disturbance Observer
τd = τa + τj
Nonlinear µ,α-Observer
δ
i
ay, r
τa
Judy HsuIMECE 2006
11 Dynamic Design LaboratoryStanford University
A Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering Torqueueueue
Total Aligning Torque
n Results from lateral tire forces acting at a distance known as total trail
Steering System Model
Disturbance Observer
τd = τa + τj
Nonlinear µ,α-Observer
δ
i
ay, r
τa
Steering System Model
Disturbance Observer
τd = τa + τj
Nonlinear µ,α-Observer
δ
i
ay, r
τa
tptm
αf
Fy,f
U
Judy HsuIMECE 2006
12 Dynamic Design LaboratoryStanford University
A Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering Torqueueueue
Steering System Model
Disturbance Observer
τd = τa + τj
Nonlinear µ,α-Observer
δ
i
ay, r
τa
Steering System Model
Disturbance Observer
τd = τa + τj
Nonlinear µ,α-Observer
δ
i
ay, r
τa
Total Aligning Torque
Varies with steer angle δü Know from ADAMS
Varies with slip angle α and friction coefficient µ
Also varies with slip angle α and friction coefficient µ
Judy HsuIMECE 2006
13 Dynamic Design LaboratoryStanford University
A Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering Torqueueueue
Steering System Model
Disturbance Observer
τd = τa + τj
Nonlinear µ,α-Observer
δ
i
ay, r
τa
Steering System Model
Disturbance Observer
τd = τa + τj
Nonlinear µ,α-Observer
δ
i
ay, r
τa
(Plot shown with tm = 0)
Simple τa model
Judy HsuIMECE 2006
14 Dynamic Design LaboratoryStanford University
A Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering Torqueueueue
Complete Steering Model
To form complete steering model
n Combine torque contributions
n Include effective steering system inertia and damping:
Total aligning moment Jacking torque Actuator torque
Steering System Model
Disturbance Observer
τd = τa + τj
Nonlinear µ,α-Observer
δ
i
ay, r
τa
Steering System Model
Disturbance Observer
τd = τa + τj
Nonlinear µ,α-Observer
δ
i
ay, r
τa
Judy HsuIMECE 2006
15 Dynamic Design LaboratoryStanford University
A Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering Torqueueueue
2: Describe Disturbance Observer
Steering System Model
Disturbance Observer
τd = τa + τj
Nonlinear µ,α-Observer
δ
i
ay, r
τa
Judy HsuIMECE 2006
16 Dynamic Design LaboratoryStanford University
A Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering Torqueueueue
Disturbance Observer
n Objective is to estimate total aligning
torque τa from available measurements
n Construct Luenberger observer
¡ Inputs motor current i and steer angle δ¡ Outputs total aligning moment τa
Steering System Model
Disturbance Observer
τd = τa + τj
Nonlinear µ,α-Observer
δ
i
ay, r
τa
Total aligning moment Jacking torque Actuator torque
Judy HsuIMECE 2006
17 Dynamic Design LaboratoryStanford University
A Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering Torqueueueue
3: Form Nonlinear µ,α-Observer
Steering System Model
Disturbance Observer
τd = τa + τj
Nonlinear µ,α-Observer
δ
i
ay, r
τa
Judy HsuIMECE 2006
18 Dynamic Design LaboratoryStanford University
A Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering Torqueueueue
A combination of total aligning torque with lateral force can be used to decode friction and slip angle information
Lateral Force Aligning Torque
0 0.02 0.04 0.06 0.08 0.10
5
10
15
20
25
30
35
40
α (rad)
τ a
µ = 0.3
µ = 0.7µ = 1
0 0.02 0.04 0.06 0.08 0.10
500
1000
1500
2000
2500
3000
3500
α (rad)
Fy
µ = 0.3
µ = 0.7µ = 1
Extracting (µ,α) from τa & Fyf
Judy HsuIMECE 2006
19 Dynamic Design LaboratoryStanford University
A Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering Torqueueueue
Nonlinear µ,α-Observer
Update Laws for
Steering System Model
Disturbance Observer
τd = τa + τj
Nonlinear µ,α-Observer
δ
i
ay, r
τa
Disturbance observer
Lateral accelerometer
Judy HsuIMECE 2006
20 Dynamic Design LaboratoryStanford University
A Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering Torqueueueue
Observer Summary
n Derived steering system dynamics (τa, τj, τact)
n From these dynamics, formed linear disturbance observer¡ Inputs motor current and steer angle
¡ Outputs total aligning moment measurements
n Based on simple models, we derived nonlinear µ,α-observer¡ Uses disturbance observer’s τa measurements to update µ,α
estimates
¡ Nonlinear gains based on current µ,α estimatesSteering System
Model
Disturbance Observer
τd = τa + τj
Nonlinear µ,α-Observer
δ
i
ay, r
τa
Judy HsuIMECE 2006
21 Dynamic Design LaboratoryStanford University
A Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering Torqueueueue
Experimental Results
n Apply overall observer to experimental maneuver on P1
Judy HsuIMECE 2006
22 Dynamic Design LaboratoryStanford University
A Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering Torqueueueue
Judy HsuIMECE 2006
23 Dynamic Design LaboratoryStanford University
A Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering Torqueueueue
Ramp: Friction Estimatesn µo = 0.6
n Relatively steady around µ = 1 (agrees with skidpad)
0 2 4 6 8 10 12 14 16
-0.3
-0.2-0.1
0Steering Angle
δ (r
ad
)
0 2 4 6 8 10 12 14 16
0.1
0.2
0.3
Front Slip Angle
α f (ra
d)
0 2 4 6 8 10 12 14 16-1
-0.5
0
Lateral Acceleration
a y (g
)
Time (s)
0 2 4 6 8 10 12 14 160
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2Friction coefficient
Est
ima
ted
µTime (s)
linear nonlinear saturation
Judy HsuIMECE 2006
24 Dynamic Design LaboratoryStanford University
A Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering Torqueueueue
0 2 4 6 8 10 12 14 160
0.1
0.2
0.3
Front slip angle
α f (ra
d)
GPS
NL Observer
0 2 4 6 8 10 12 14 16
0
0.05
0.1
Rear slip angle
Time (s)
α r (ra
d)
0 0.05 0.1 0.15 0.2 0.25 0.30
1000
2000
3000
4000
5000
6000
7000
8000Tire Curve
-La
tera
l Fro
nt T
ire F
orce
Fyf
(N
)
Slip angle αf (rad)
linear nonlinear saturation
Ramp: Slip Angle Estimates
Judy HsuIMECE 2006
25 Dynamic Design LaboratoryStanford University
A Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering Torqueueueue
Observer Performance
n Observer’s slip angle estimates match well with GPS-based measurements¡ Up to handling limits (peak Fyf)
n Friction estimates converge once observer has enough lateral dynamic information¡ On dry pavement, ~0.5 g
¡ Expected to converge faster on low-µsurfaces
Judy HsuIMECE 2006
26 Dynamic Design LaboratoryStanford University
A Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering Torqueueueue
Applications
n Observer uses measurements available in production vehicles
¡ can be integrated with GPS-based observers
¡ used during periods of GPS signal loss
n Provides two quantities (µ, α) very useful in vehicle dynamics control systems
¡ Enhance active safety systems
Judy HsuIMECE 2006
27 Dynamic Design LaboratoryStanford University
A Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering TorqA Method to Estimate Friction and Slip Angle Using Steering Torqueueueue
Current Work
n Experimentally validate observer on high-
µ surfaces
n Prove stability of nonlinear observer
n Integrate observer with control system that stabilizes vehicle at limits of handling
Racing tires