a method to estimate friction and slip angle using … method to estimate friction and slip angle...

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



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



Tire Curvemaximum tire grip

Linear Nonlinear Loss of control

Judy HsuIMECE 2006



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



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



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



Observer Scheme

Steering System Model

Disturbance Observer

τd = τa + τj

Nonlinear µ,α-Observer

δ

i

ay, r

τa

Judy HsuIMECE 2006



1. Form Steering System Model



τd = τa + τj


δ

i

ay, r

τa

Judy HsuIMECE 2006



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




τd = τa + τj


δ

i

ay, r

τa



τd = τa + τj


δ

i

ay, r

τa

Judy HsuIMECE 2006



Total Aligning Torque

n Results from lateral tire forces acting at a distance known as total trail



τd = τa + τj


δ

i

ay, r

τa



τd = τa + τj


δ

i

ay, r

τa

tptm

αf

Fy,f

U

Judy HsuIMECE 2006





τd = τa + τj


δ

i

ay, r

τa



τd = τa + τj


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





τd = τa + τj


δ

i

ay, r

τa



τd = τa + τj


δ

i

ay, r

τa

(Plot shown with tm = 0)

Simple τa model

Judy HsuIMECE 2006



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



τd = τa + τj


δ

i

ay, r

τa



τd = τa + τj


δ

i

ay, r

τa

Judy HsuIMECE 2006



2: Describe Disturbance Observer



τd = τa + τj


δ

i

ay, r

τa

Judy HsuIMECE 2006




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



τd = τa + τj


δ

i

ay, r

τa

Total aligning moment Jacking torque Actuator torque

Judy HsuIMECE 2006



3: Form Nonlinear µ,α-Observer



τd = τa + τj


δ

i

ay, r

τa

Judy HsuIMECE 2006



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




Update Laws for



τd = τa + τj


δ

i

ay, r

τa

Disturbance observer

Lateral accelerometer

Judy HsuIMECE 2006



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


τd = τa + τj


δ

i

ay, r

τa

Judy HsuIMECE 2006



Experimental Results

n Apply overall observer to experimental maneuver on P1

Judy HsuIMECE 2006



Judy HsuIMECE 2006



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



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



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



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



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

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a method to estimate friction and slip angle using … method to estimate friction and slip angle...

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