Oral presentation

Experimental Validation of a Multibody
Model for a Vehicle Prototype and its
Application to State Observers

Roland Pastorino

A thesis submitted for the degree of Doctor Ingeniero Industrial

June 25, 2012, Ferrol, Spain

Mechanical Engineering Laboratory, University of La Coruña

0 Outline

1 Motivations

2 Vehicle eld testing

3 Vehicle modeling and simulation environment

4 Validation results

5 State observers

6 Conclusions

Mechanical Engineering Laboratory, University of La Coruña 2/48

1 Outline

1 Motivations




5 State observers

6 Conclusions


1 Motivations

Laboratorio de Ingeniería Mecánica (LIM).
Specialized in realtime simulations of rigid and exible multibody systems

Fig. 1 Realtime simulations of Fig. 2 Realtime simulations of
vehicles excavators

Fig. 3 Realtime simulations of Fig. 4 HumanInTheLoop
container cranes simulators of excavators

1 Motivations

Multibody dynamics analysis in the automotive eld.
comfort

ride
accuracy
analysis noise
vibration highly
durability
detailed
analysis
models
crash
worthiness
crash ease
ANALYSIS
analysis of use MB MODELS
TYPES
nonlinear
vehicle
handling dynamics special
analysis formu.

design
realtime eciency
tuning of reduced
app required
controllers models

HIL
HITL


1 Motivations

Objectives.

Without validation of the vehicle dynamics there is only speculation that a
given model accurately predicts a vehicle response

A.H. Hoskins and M. El-Gindy, Technical report: Literature survey on driving simulator validation studies,
International Journal of Heavy Vehicle Systems, vol. 13 (3), pp. 241252, (2006)

reliability and validity of the
modeling procedure and
MB formulation to simulate
new insigths into comprehensive vehicle models
the automotive re-
search line of the LIM
state estimation using
MB models applied
to vehicle dynamics


2 Outline

1 Motivations




5 State observers

6 Conclusions



Validation methodology.
based on the validation methodology developed by the VRTC (Vehicle Research and
Test Center) for the NADS (National Advanced Driving Simulator)
composed of 3 main phases

1 experimental 2 vehicle parameter 3 simulation predictions
data collection measurement vs experimental data

vehicle eld testing parameter simulations using the same
maneuvers → broad range of measurements for the control inputs that were
vehicle operating conditions MB model and the measured at the 1st phase
subsystem models comparisons between the
repetitive maneuvers to
determine the random simulation experimental
uncertainty results

experimental postprocessing

Fig. 5 NADS bay



Diagram of the iterative validation methodology.

vehicle
reference
maneuver brake model tire model

maneuver MB formu.
repetitions + integrator

sensor outputs

vehicle model



test track topo. survey

virtual en-
vironment

vehicle
reference

maneuver benchmark MB formu.
repetitions input data + integrator

sensor outputs

vehicle model

vehicle parameter measurement



test track topo. survey

virtual en-
vironment

vehicle
reference

maneuver benchmark MB formu.
repetitions input data + integrator

sensor outputs sensor outputs

comparisons

vehicle model

vehicle parameter measurement



The XBW vehicle prototype.
selfdeveloped from scratch

onboard digital acquisition system

longitudinal and lateral maneuver repetition
capability

Mechanical characteristics.
Fig. 6 Design and manufacturing
tubular frame

internal combustion engine (4 cylinders, 2barrel
carburator)

automatic gearbox transmission

front suspension → double wishbone

rear suspension → MacPherson

tyres → Michelin E3B1 Energy 155/80 R13 Fig. 7 XBW vehicle prototype


Steering wheel

Encoder B

The bywire systems of the prototype.
Precision gearbox

Encoders A Coreless DC motor

SBW → steerbywire Precision gearbox
Torque sensor

TBW → throttlebywire
Rack and pinion gear system

BBW → brakebywire
Fig. 8 Steerbywire system
Extra sensors.
Measured magnitudes Sensors
vehicle accelerations (X,Y,Z) accelerometers (m/s2 )
vehicle angular rates (X,Y,Z) gyroscopes (rad/s)
vehicle orientation angles inclinometers (rad)
wheel rotation angles halleect sensor (rad) Fig. 9 Throttlebywire
brake line pressure pressure sensor (kP a) system
steering wheel and steer angles encoders (rad)
engine speed halleect sensors (rad/s)
steering torque inline torque sensor (N m)
throttle pedal angle encoder (rad)
rear wheel torque wheel torque sensor (N m)
Fig. 10 Brakebywire system



Driver's force feedback of the SBW.
objective → accurate torque feedback to the
driver

problem → exibility, backlash friction

solution → highly accurate model of the
assembly ampliermotorgearbox
future work → model based torque controller

Fig. 12 Steering wheel system

4 1
3 2

4 Quadrant Linear
PMDC Motor Gearbox Steering Wheel
Servoamplifier

Fig. 11 Scheme of the modeling Fig. 13 CAD model of the steering wheel
system



7 repetitions of a low speed straightline maneuver.
total distance = 63.5 m
max speed = 23 km/h



6 repetitions of a lowspeed Jturn maneuver.
total distance = 59.6 m
max speed = 18 km/h


3 Outline

1 Motivations




5 State observers

6 Conclusions



Vehicle modeling.
Type of coordinates : natural + some relative coordinates (angles distances)

MB formulation : index3 augmented Lagrangian formulation with
massdampingstinessorthogonal projections

Bodies / Variables : 18 → all the vehicle bodies / 168 → points and vectors

Steering : kinematically guided

Forces : gravity forces, tire forces, engine torque, brake torques

Degrees of freedom : 14 → suspension systems (4)
chassis (6)
wheels (4)

Fig. 14 CAD model of the prototype Fig. 15 Points vectors of the MB model


Ecient MB formulation developed and used at LIM.
index3 augmented Lagrangian formulation with massdampingstinessorthogonal
projections
integration → the trapezoidal rule and the NewtonRaphson method
eq. of motion→
2 rst order trap. rule
predictor → ∆t
f = (Mq +
¨ approx. →
q, q, q
˙ ¨ 4
ΦT αΦ + ΦT λ − Q) fq ∆q = −f λ = λ + αΦ
q q

tangent matrix → eq. of motion→ tangent matrix →
∆t ∆t
fq = M + C+ ∆t 2
fq = M + C+
2 f = (Mq +
¨ 2
∆t2 T 4 ∆t2 T
(Φq αΦq + K) ΦT αΦ + ΦT λ − Q)
q q (Φq αΦq + K)
4 4

no
error
min
→
projections in velocities
t = t + ∆t ∆t ∆t2∆t2 T
fq q =
˙ M+ C+ K q −
˙ ∗
Φq αΦt yes
2 4 4
projections in accelerations →
∆t ∆t2 ∆t2 T
fq q = M +
¨ C+ K q −
¨∗
Φq α(Φq q + Φt )
˙ ˙ ˙
2 4 4



Tire model.
part of the empirical and physical
TMeasy model

rstorder dynamics → longitudinal
and lateral deections

transition to standstill → stickslip
behavior

tire curves → linearized model
Fig. 17 Longitudinal deformation of the tire

Fig. 16 Points vectors for the tire modeling Fig. 18 Lateral deformation of the tire



Road prole.
topographical survey of the test track with a total station

300 points for a track of 80 meters long

interpolation of the scattered points

Delaunay triangulation → mesh of triangles for the collision detection

1
Height (m)

0.5

0
0
80 −10
60
40 −20
20 −30
Length (m) 0 Width (m)

Fig. 19 Total station used for Fig. 20 3D scattered points Fig. 21 3D model of the test
the topographical survey track



Collision detection.
tire normal force → function of the
interpenetration of the stepped
triangles of the ground mesh

4 spheres for the collision geometry of
Fig. 22 3D model of the test track
the tires

Simulation environment.
realistic graphical environment of the
campus
selfdeveloped 3D environment
opensource 3D graphics toolkit (C++)
inclusion of the topographical survey of
the test track


4 Outline

1 Motivations




5 State observers

6 Conclusions



MB model inputs.
averaging of the experimental data
100 100
Torque (Nm)

0

Torque (Nm)
0

−100 −100

−200 −200
0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20
Time (s) Time (s)

Fig. 23 Repetitions (wheel torque) Fig. 24 Mean and CI (wheel torque)

Condence intervals.
assumption → the uncertainty follows a normal distribution
small number of samples → Student's t distribution

S
C.I. bounds: x ± tn−1
¯ (1−α/2) · √
n
n n
1 1
sample mean → x =
¯ xi sample variance → S 2 = 2
(xi − x)
¯
n i=1
(n − 1) i=1

(1 − α/2) critical value for the t
distribution with (n − 1) degrees of freedom


Simulation of the low speed straightline maneuver.
MB model inputs → averaged experimental data

road prole → topographical survey



Validation results for the low speed straightline maneuver.
25 3

Angular velocity ( °/s)
20 2
Speed (km/h)

15 1

10 0

5 −1

0 −2

−5 −3
0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20
Time (s) Time (s)
Fig. 25 Left front wheel speed Fig. 26 Roll rate of the chassis

1
Acceleration (m/s2)

0

−1

−2

0 2 4 6 8 10 12 14 16 18 20
Time (s)
Fig. 27 Longitudinal acceleration of the chassis


Simulation of the lowspeed Jturn maneuver.
MB model inputs → averaged experimental data

road prole → topographical survey



Validation results for the low speed Jturn maneuver.
5 3

0

Acceleration (m/s2)
2
−5

−10 1

−15
0
−20

−25 −1
0 2 4 6 8 10 12 14 16 18 20 22 0 2 4 6 8 10 12 14 16 18 20 22
Time (s) Time (s)
Fig. 28 Yaw rate of the chassis Fig. 29 Lateral acceleration of the chassis

1
2

Acceleration (m/s2)
0
0
−1

−2
−2

−4 −3
0 2 4 6 8 10 12 14 16 18 20 22 0 2 4 6 8 10 12 14 16 18 20 22
Time (s) Time (s)
Fig. 30 Roll rate of the chassis Fig. 31 Longitudinal acceleration of the
chassis

5 Outline

1 Motivations




5 State observers

6 Conclusions


5 State observers

Model running in realtime with the same inputs

DISTURBANCES
unknown
forces, etc

OUTPUTS
sensors set of
sensors
INPUTS
forces, Real Mechanism
torques, etc
CONTROLLERS

MODEL OUTPUTS
variables of model variables =
the model numerous avail-
Realtime model able magnitudes


5 State observers

Model running in realtime with the same inputs

DISTURBANCES
unknown
forces, etc

OUTPUTS
sensors set of
sensors
INPUTS
torques, etc
CONTROLLERS

DRIFT OF THE MODEL
disturbances,unmodeled
dynamics, param-
eters of the model
MODEL OUTPUTS
variables of model variables =
the model numerous avail-
Realtime model able magnitudes


5 State observers

State observers for mechanical systems based on Kalman lters

DISTURBANCES
unknown
forces, etc

OUTPUTS
sensors set of
sensors
INPUTS
torques, etc
CONTROLLERS

+
Kalman
corrections -

sensors of
the model
MODEL OUTPUTS
variables of
model variables
the model
= virtual sensors
Realtime model

State observer based on Kalman lters


5 State observers

State observers for mechanical systems based on Kalman lters

DISTURBANCES
unknown
forces, etc

OUTPUTS
sensors minimum set
of sensors
INPUTS
torques, etc
CONTROLLERS

+
Kalman
the model follows the
corrections -
motion of the mechanism
with sensors of delay
minimum
the model
MODEL OUTPUTS
variables of
model variables
the model
= virtual sensors
Realtime model

State observer based on Kalman lters


5 State observers

State estimation in mechanical systems.
Advantages

minimum set
new sensors virtual sensors
of sensors

ubiquitous reduced
reduced costs
magnitude failure rate

The more detailed the model is,
the more it provides information about the motion of the mechanism

Past researches

Kalman lter + linear mechanical systems  lack of generality
linearized Kalman lter + nonlinear mechanical  linear models
systems simple nonlinear models


5 State observers

First implementations using a 4bar linkage and a VW Passat.
Recent researches at the LIM
extended Kalman lter + realtime MB general approach
models complex nonlinear models

A

D

B

C
s

Fig. 32 4bar linkage Fig. 33 VW passat model state observer w/
MB model


5 State observers

Description.
simple mechanism: 5bar linkage → 2 DOFs

mechanism parameters → experimental
measurements

parameters of the sensors → characteristics from
otheshelf sensors

MB Modeling.
Fig. 34 5bar linkage image
natural coordinates (8 variables, 6 constraints, 2
DOFs)
MB formulations
independent coordinates → projection matrixR
method
dependent coordinates → penalty formulation
simulation of the real mechanism for
Fig. 35 5bar linkage modeling scheme
comprehensive comparisons

known errors between the real mechanism and
its MB model → lengths, masses, inertias. . .


5 State observers

Free motion simulation.
Drift of the model due to errors in the parameters of the model

real mechanism
(matrixR, trap. rule)

model


5 State observers

Comparison of NL Kalman lters. SPKF

EKF ,UKF ,SSUKF

What is it? de facto NL Kalman lter recent NL Kalman lters

Why to use it ? eciency accuracy and easy implementation

Which form ? continuous discrete

How does it state estimates → propaga- state estimates → propagation
work ? tion through NL system. through NL system.
mean and state estimation mean and state estimation uncer-
uncertainty → propagation tainty → propagation of sigma
through linearization points through the NL system

Assumptions additive white Gaussian noises

rst order dierential equations
x(t) = f(x(t)) + w (t)
˙
with independent states
System
dynamics
nonlinear dierence equations
xk+1 = φk (xk ) + w k


5 State observers

The extended Kalman lter EKF.
rst order ODEs rst order DAEs

Mq + ΦT λ = Q
¨ q
x(t) = f(x(t))
˙ =
Φ=0


5 State observers

rst order ODEs rst order DAEs

Mq + ΦT λ = Q
¨ q
x(t) = f(x(t))
˙ =
Φ=0 independent coordinates

duplication of variables state space reduction

(positions velocities) method matrix R

z(t)
x= ¨ = (RT MR)−1 [RT (Q − MRz)]
z ˙˙
w(t)

z(t)
˙ w
= =
w(t)
˙ (RT MR)−1 [RT (Q − MRz)]
˙˙

integration
implicit integrator
trapezoidal rule


5 State observers


state estimates ˆ(t) = f(ˆ(t), t) + K[y(t) − ˆ(t)]
x
˙ x ¯ y

Kalman gain K(t) = P(t)H[1]T (t)R(t)
¯

Riccati equation P(t) = F[1] P(t) + P(T)F[1]T + GQ(t)GT − KR(t)K
˙ ¯ ¯

∂ f(x, t) ∂ h(x, t)
linear approximations F[1] (t) H[1] (t)
∂x ∂x

0 I
 
0 I
F[1] (t) =  ∂(M−1 Q)
¯ ¯ ¯ −1 ¯
∂(M Q)  −1 −1
−M
¯ RT (KR + 2MRq Rw)
˙ −M
¯ RT (CR + MR)
˙
∂z ∂w


5 State observers

The unscented Kalman lter UKF.
nonlinear recurrences
rst order DAEs

Mq + Φ T λ = Q
¨ q
xk+1 = φk (xk ) =
Φ=0


5 State observers

rst order DAEs

Mq + Φ T λ = Q
¨ q
xk+1 = φk (xk ) =
Φ=0
independent coordinates
state space reduction
method matrix R

¨ = (RT MR)−1 [RT (Q − MRz)]
z ˙˙

= integration


5 State observers

rst order DAEs

Mq + Φ T λ = Q
¨ q
xk+1 = φk (xk ) =
Φ=0
independent coordinates
dependent coordinates state space reduction
penalty formulation method matrix R

q = (M + ΦT αΦ)−1 [Q − ΦT α(Φq q + 2ζω Φ + ω 2 Φ)]
¨ q q
˙ ˙ ˙

¨ = (RT MR)−1 [RT (Q − MRz)]
z ˙˙
= integration

= integration


5 State observers

The unscented Kalman lter UKF.measurementupdate equations (executed if
timeupdate equations (always executed) information from the sensors is available)

2L
x xk
ˆk = ˆ− + Kk (yk − ˆ− )
¯ yk
xk
ˆ− = wim χi,k|k−1
i=0

χk|k−1 = φk−1 (χk−1 ) Kk = Pxk yk P˜k
¯ −1
y

2L
 x

 ˆk−1
yk
ˆ− = ωim Y i,k|k−1
x Pk−1

χi,k−1 = ˆk−1 + γ i=0
i
x Pk−1

 ˆk−1 − γ

i

Y k|k−1 = hk (χk|k−1 )
2L
Pxk =
−
ωic (χk|k−1 − xk
ˆ− )(χk|k−1 − xk
ˆ− )T
T
i=0 Pxk = P− − Kk P˜k Kk
xk
¯ y ¯


5 State observers

timeupdate equations (always executed)

zk+1 , zk+1
˙
2L
xk
ˆ− = wim χi,k|k−1
integ.
i=0

χk|k−1 = φk−1 (χk−1 ) z
¨k+1

 x

 ˆk−1 zk+1
¨1 zk+1
¨2 zk+1
¨3 zk+1
¨4 zk+1
¨5
x Pk−1

χi,k−1 = ˆk−1 + γ
i
x Pk−1

 ˆk−1 − γ

φk φk φk φk φk
i

z
¨k z
¨k z
¨k z
¨k z
¨k
zk
˙ zk
˙ zk
˙ zk
˙ zk
˙
z1
k z2
k z3
k z4
k z5
k

Fig. 36 Set of sigmapoints (2 dim. GR variable) ¨k , zk , zk
z ˙

5 State observers

The spherical simplex UKF.
same equations as for the UKF
reduced set of sigmapoints
UKF → (2L+1) sigmapoints
SSUKF → (L+2) sigmapoints
equations of the reduced set of sigmapoints

χj−1

 0 for i = 0
  0



χj−1

 


 i
  1 for i = 1, . . . , j
χj = −

i
  j(j + 1)w1
0j−1




Fig. 37 Reduced set of sigmapoints (2

 
 1 for i = j + 1
dim. GR variable

 

j(j + 1)w1


5 State observers

Free motion simulation.
Drift of the model due to errors in the parameters of the model

The observers estimate correctly the motion of the real mechanism

real mechanism
model
EKF
UKF
SSUKF
SSUKF
(matrixR, RK2)
SSUKF
(penal, RK2)


5 State observers

Performance comparisons of the lters → eciency vs RMSE.

non multirate
10
∆tinteg = 2ms
9 ∆tsensors = 2ms
multirate
8
∆tinteg = 2ms
7 ∆tsensors = 6ms
multirate
case
6
EKF (matrixR, trap.
rule)
RMSE

5
UKF (matrixR, trap.
4 rule)
3 SSUKF (matrixR, trap.
rule)
non multi
2 SSUKF (matrixR, RK2)
rate case

1 Simulation SSUKF (penal, RK2)
100 125 150 175 200 225 250 time (%)


5 State observers

Data
acquisition EKF
system
param-
eters UKF

NL
mechanism Kalman SPKF SSUKF
STATE OB- lters
SERVERS
sensors NL Kalman lters
with MB models
indepen-
dent
coord.

MB
matrix
implicit integrators R
formulation
method
depen-
TR dent
coord.
explicit
penalty-
formu.

RK2


5 State observers

Pros Cons.
EKF
Pros → most ecient lter with independent coordinates
Cons → involved and errorprone calculation of the Jacobian, not suitable to employ
with dependent coordinates, not multirate

SPKFs
Pros → easiest implementation, possible use of dependent coordinates, highest
accuracy
Cons → high computational cost due to the sigmapoints


6 Outline

1 Motivations




5 State observers

6 Conclusions


6 Conclusions

Vehicle eld testing.
1 X-by-wire vehicle prototype from scratch
2 highly detailed model of the driver's force feedback system
3 repetitions of 2 reference manoeuvres in the campus

Vehicle modeling and simulation environment.
1 real-time 14 DOFs MB model
2 modelling of subsystems → tire, brake
3 topographical survey of the test track
4 realistic 3D simulation environment


6 Conclusions

Validation results.
1 condence intervals for the experimental data
2 simulation of the test manoeuvres using the experimental data
3 evaluation of the accuracy of the MB model

State observers.
1 use of MB models with the extended Kalman lter
2 application to a 4bar linkage and a VW Passat
3 use of MB models with SPKFs lters
4 implementation using a 5bar linkage


6 Conclusions

Future research.
1 eld testing
manoeuvres at higher speeds → new test track
GPS RTK for realtime positioning of the vehicle

2 vehicle modelling and simulation environment
better characterization of the tire curves
HumanInTheLoop simulation using experimental inputs

3 state observers
EKF in discrete form
research on the observability of MB models
tests of the UKF/SSUKF with more complex mechanisms
implementation using the MB model of the XBW prototype


6 Conclusions

Congress papers.
[1] J. Cuadrado, D. Dopico, J. A. Pérez, and R. Pastorino. Inuence of the sensored magnitude in the performance of
observers based on multibody models and the extended Kalman lter. In Proceedings of the Multibody Dynamics
ECCOMAS Thematic Conference, Warsaw, Poland, June 2009.

[2] R. Pastorino, M. A. Naya, J. A. Pérez, and J. Cuadrado. Xbywire vehicle prototype: a steerbywire system with geared
PM coreless motors. In Proceedings of the 7th EUROMECH Solid Mechanics Conference, Lisbon, Portugal, September
2009.

[3] J. Cuadrado, D. Dopico, M. A. Naya, and R. Pastorino. Automotive observers based on multibody models and the extended
Kalman lter. In The 1st Joint International Conference on Multibody System Dynamics, Lappeenranta, Finland, May 2010.

[4] R. Pastorino, M. A. Naya, A. Luaces, and J. Cuadrado. Xbywire vehicle prototype: automatic driving maneuver
implementation for realtime MBS model validation. In Proceedings of the 515th EUROMECH Colloquium, Blagoevgrad,
Bulgaria, 2010.

[5] R. Pastorino. La simulation des systèmes multicorps dans l'automobile. Interface, revue des ingénieurs des INSA de Lyon,
Rennes, Rouen, Toulouse, (111):22, 3ème et 4ème trimestre 2011.

[6] R. Pastorino, D. Dopico, E. Sanjurjo, and M. A. Naya. Validation of a multibody model for an xbywire vehicle prototype
through eld testing. In Proceedings of the ECCOMAS Thematic Conference Multibody Dynamics 2011, Brussels,
Belgium, 2011.

[7] R. Pastorino, M. A. Naya, A. Luaces, and J. Cuadrado. Xbywire vehicle prototype : a tool for research on realtime
vehicle multibody models. In Proceedings of the 13th EAEC European Automotive Congress, Valencia, Spain, June 2011.

[8] R. Pastorino, D. Richiedei, J. Cuadrado, and A. Trevisani. State estimation using multibody models and nonlinear Kalman
lters. In The 2nd Joint International Conference on Multibody Systems Dynamics, Stuttgart, Germany, May 2012.

[9] R. Pastorino, D. Richiedei, J. Cuadrado, and A. Trevisani. State estimation using multibody models and unscented Kalman
lters. In Proceedings of the 524th EUROMECH Colloquium, Enschede, Netherlands, 2012.

[10] E. Sanjurjo, R. Pastorino, D. Dopico, and M. A. Naya. Validación experimental de un modelo multicuerpo de un prototipo
de vehículo automatizado. In XIX Congreso Nacional de Ingeniería Mecánica (to be presented), Castellón, Spain, Nov. 2012.


6 Conclusions

Journal papers.
[1] J. Cuadrado, D. Dopico, J. A. Pérez, and R. Pastorino. Automotive observers based on multibody models and
the Extended Kalman Filter. Multibody System Dynamics, 27(1):319, 2011.
[2] R. Pastorino, M. A. Naya, J. A . Pérez, and J. Cuadrado. Geared PM coreless motor modelling for driver's force
feedback in steerbywire systems. Mechatronics, 21(6):10431054, 2011.

Journal papers in preparation.
[1] R. Pastorino, M.A. Naya, and J. Cuadrado. Experimental validation of a multibody model for a vehicle prototype.
Vehicle System Dynamics, 2012.
[2] R. Pastorino, D. Richiedei, J. Cuadrado, and A. Trevisani. State estimation using multibody models and nonlinear
kalman lters. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multibody Dynamics,
2012.

Acknowledgments.
Spanish Ministry of Science and Innovation Grant TRA200909314 (ERDF funds)


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