A high gain steering controller to compensate for limitations in a handicapped driver's range of motion is employed when adapting vehicle to his use. A driver/vehicle system can become unstable as vehicle speed is increased, therefore it is desirable to use a computer simulation of the driver/vehicle combination as a design tool to investigate the system response prior to construction of a controller and road testing. Unknown driver parameters must be identified prior to use of the model for system analysis. A means to collect the data necessary for identification of these driver model parameters without extensive instrumentation of a vehicle to measure and record vehicle states is addressed. Initial tests of the procedure identified all of the driver parameters with errors of 6% or less

Mcdermott, M.

Mooring, B. W.

Su, J. M.

English

NASA Technical Reports Server

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b N82-13696 !,
A DATA COLLECTION SCHEME FOR IDENTIFICATION
OF PARAMETERS IN A DRIVER MODEL
'5
By B. W. Mooring, M. McDermott,
and Je-Meng Su
Texas A&M University
SUMMARY
When adapting a vehicle for use by a handicapped driver, it is often
necessary to employ a high gain steering controller to compensate for limit-
ations in the driver's range of motion. Because such a driver/vehicle system
can become unstable as vehicle speed is increased, it is desirable to use a
computer simulation of the driver/vehicle combination as a design tool to
investigate the system response prior to construction of a controller and
road testing. While there are a number of different driver models in exis-
tence, they all contain some unknown driver parameters which must be iden-
tified prior to use of the model for system analysis. This work addresses
a means to collect the data necessary for identification of these driver
model parameters without extensive instrumentation of a vehicle to measure
and record vehicle states.
The procedure consists of three steps. First, a road test is conducted
with the driver in a normal vehicle, during which only the steering wheel
T
angle and the vehicle speed is recorded. Next, the aata from the road test !
is input into a computer m_del of the vehicle which i_!,._rates the vehicle !
equations of motion with the given speed and steering _. its to yield the
vehicle states, some of which the driver senses. Finally, with the sensed
vehicle states as inputs and the recorded steering response as output, a
least squares parameter identification procedure is used to co,-ute the
parameters in the proposed driver model.
Initial tests of _he procedure identified all of the driver parameters
with errors of 6% or less.
1982005792-332
https://ntrs.nasa.gov/search.jsp?R=19820005823 2020-03-21T15:59:20+00:00Z
INTRODUCTION
The Rehabilitation Engineering Program at Texas A&M University is cur-
rently involved in the evaluation and design of low effort - high gain auto-
motive control devices for handicapped drivers. Experience has shown that
some vehicles with high gain steering are relatively easy to control at mod-
erate speeds and others require maximum driver effort to maintain control at
very low speeds. In order to better understand the causes of this wide vari-
ation in handling proterties and to quantify the eflects of changes in various
steering system parameters on vehicle response, development of a computer sim-
ulation of the driver-vehicle combination was begun.
At present, there are a number of vehicle models [3] and driver models
[1.5,6] that are available. Use of a typical vehicle simulation requires know-
ledge of the geometry, inertial properties, and tire characteristics of the
vehicle to be studied. Most of these can be obtained by direct measurement
or are easily estimated.
As with the vehicle models, most of the driver models were found to have
several coefficients whose magnitude is dependent on the characteristics of
the driver or his environment. In order to use a driver model, a means to
quickly and inexpensively identify these unknown parameters in a driver model
is required. Classically, this identification is accomplished by cunning a
road test and recording the driver inputs and all of the vehicle motion vari-
ables that the driver may respond to. As illustrated in Figure la, the
vehicle motion data is used as an input for the driver model and the driver
response data is compared to the results of the driver model to generate an
error. There are a number of parameter identification techniques available ""
[4] to determine the coefficients in the driver model that will minimize the
error in predicted and measured driver response. The difficulty in employing
this procedure lies in the instrumentation required to record the vehicle
motion variables. Variables such as heading angle or yaw rate require a
gyroscopic device which is expensive and bulky. The position of the vehicle
on the road may be obtained with an optical tracking device or by integrating
the output of accelerometers on an inertial platform. Either of these methods
is expensive and the equipment is not easily moved from one vehicle to another.
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1982005792-333
PREDICTED
DRIVER RESPONSE
VEHIC LE DRIVER × ERROR
MOTION MODEL
MEASURED
DRIVER
RESPONSE
Figure la. Typical Parameter Identification
Procedure
MEASURED PREDICTED PREDICTED
DRIVER VEHICLE DRIVER
RESPONSE RESPONSE RESPONSE
MODEL MODEL '
Figure lb. Proposed Procedure
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1982005792-334
I:
l-
In order to minimize the instrumentation necessary to obtain the required Iifdata, an alternate procedure was examined. As illustrated in Figure lb, the
measured variables are driver inputs (steering wheel angle and vehicle {I_
only
forward velocity). Thes_ inputs are then used with a vehicle simulation to
determine what the motion must have been during the test. In this manner the
required data for driver model i_entification is obtained with a minimum of
instrumentation.
VEHICLE MODEL
The vehicle model used in this procedure was chosen because it was co**-
sidered to be the simplest model available that exhibited the handling pro- ,:
perties under study. Figure 2a is an illustration of the vehicle model. This
vehicle has three degrees of freedom including the forward and lateral posi-
tion of the mass center P, (rpx and rpy) and the heading angle (@). Two
coordinate systems are employed. The X, Y, Z system is fixed to the roadway
and has the associated unit vectors I, J, and K. The x, y, z system is fixed
to the car and has unit vectors i, j, and k.
Using these definitions, the acceleration of the mass center, P, may be
shown to be
= ['" cos _ + "" sin _] i + ['" cos _ "" sin _] J (I)
P rpx rpy rpy - rpx
The free body diagram for the vehicle is illustrated in Figure 2b. In
order to simplify the analysis, secondary forces such as tire rolling resis-
tance, self aligning torque, aerodynamic drag, and gyroscopic moment are con-
sidered negligible. Applying Newton's Laws to the free body diagram results "
in the following equations of motion.
FfL cos 6L + FfR cos 6R + FRL + FRR = mrpy cos _ - mrpx sin _ (2)
-a[(FRL + FRR) + al(FfL cos 6L + FfR cos 6R) - (a2 + a4) FfL sin 6L
°.
+ (a2 - a_) FfR sin 6R = I, (3)
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1982005792-335
Q2
Figure 2a. Vehicle Model
FfL FeR
_Y
Figure 2b. Vehlcle Free Body
Diagram
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1982005792-336
A third equation may be obtained by recalling that the vehicle forward
velocity is known. The x component of a , therefore, may be expressed as
P
rex cos _ + rpy sin _ = V (4)
Equations (2), (3), and (4) represent the three equations of motion for
the vehicle. Unfortunately, the tire forces (FfL, FfR , FRL, FRR) are unknown
and must be related to the vehicle motion parameters. It is well documented
[2] that a rolling pneumatic tire under the influence of a lateral load
exhibits a viscoelastic deformation of the tread surface. This deformation
results in a deviation of the wheel center velocity fzom its expected direc-
tion. This deviation is termed the slip angle and may be expressed in terms
of the vehicle motion variables. Using the defined coordinates, (rpx , rpy,
and _) the slip angle at each wheel may be shown to be:
alL 6L tan-l_-'PY c°s * - rpx sln * + al_-]
= - v + _ ¥ a_)_ (s)
alL 6R tan-l[#PY c°s * - rpx sln * +al!]-_ _
= - V - (a2 - _-_3$ (6)
E " '1aRL tan-I py cos _ - rpx sin _ - a5
= - V + (a_ _ a_)_ (7)
py cos 0 rpx sin 0 a 5 (8)
aRR v - (a3 - a_)_
where 6L and 6R are left and right steering angles as defined in Figure 2a.
Once the slip angle at a given wheel is specified, the tire lateral force
may be determined. For this work, the tire used is a Goodyear FR70-14.
Figure 3 illustrates the relationship between slip angle and lateral force for
various normal loads on the tread surface.
Given the equations of motion (2-4), the slip angle e_pressions (5-8)
and the tire force function illustrated in Figure 3, the motion of the vehicle
may be determined if the forward velocity V, and the front wheel angles, 6L
and 6R are known. Assuming Ackermann Steering, 6L and 6 R may be related to
the steering wheel angle by the following relationships
L
x = (9)
tan (KsT6)
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1982005792-337
1400 NORMAL FORCE--F n= 16_
,°°°
_ y F_.9.._
.la
I1:
0
<: 600 _--
O:
IJJ
I--
,¢
,_1
400
200
0 , , , j,
o , _ ,_ ,6
SLIP ANGLE (Oeg)
Figure 3. Tire Lateral Force vs.
S11p Angle
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1982005792-338
!L
6R = tan -I _-_ _) (i0)
t (ll)
6L = tan-I (x - _)
where KST represents the steering gain, _ is steering wheel angle, and L is
wheelbase.
Now, given the driver inputs of steering wheel angle, 6, and forward
ve]ocity, V, the motion of the vehicle may be determined. Because of the non-
linearity of th .otion and constraint equations, the most expedient means of
obtaining a so]ution is by utilizing a numerical integration procedure on a
digital computer. The computer that was used in the following example was a
PRIME 750 minicomputer. The program was written in FORTRAN and utilized a
predictor-corrector numerical integration scheme.
VALIDATION OF VEHICLE MODEL
In order to verify the accuracy of the vehicle simulation, a series of
test runs was made with a vehicle that was instrumented to record several of
the vehicle motion parameters as well as the driver responses. The driver
responses were used as input data for the vehicle simulation The results of
the vehicle simulation were then compared to the vehicle motions recorded
during the test. Several test runs were made at different vehicle speeds and
over different courses. Figure 4 illustrates the comparison between predicted
and measured heading angle, yaw rate, and lateral acceleration as the vehicle
passed through an offset alley. As shown in Figure 4, the vehicle simulation
provides a good estimation of the vehicle motion. The large difference in
measured and predicted heading angle is due to a difference in reference
position. The simulation automatically sets the vehicle's initial heading to
zero deBrees while the measured heading depends on the vehicle orientation
when the gyroscope unit is switched on. When this bias is removed, the
results compare quite well.
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1982005792-339
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1982005792-340
VALIDATION OF IDENTIFICATION PROCEDURE
The driver model used to validate the parameter identification procedure
assumes that the driver can be represented as a two part cascade of a brain
r_,sponse and _ neuromuscular lag. Reaction time delay and precognition or
prevlew are not included since they tend to cancel and, at any rate, the par-
tlcular form of the driver model is not crltlcal to the identiflc_tlon pro-
ced.,re at this stage. The inputs to the driver model are the lane position
_.rror, e , and tile handing angle error, eq/ For a straight roadway c = rY Y PY
and c_, = _. The output of the brain is the co_L_anded nteerlng wheel angle _"
•md is modeled as
_" - K (rpy + _) (12)
where K is the brain gain and n is a weighting factor. The brain output is
the input to the neuromuscular system which is modeled as
_ ! (6-- ¢) (13)
T
where x is the neuromuscular time constant. Thus, the parameter Sdentlfl-
cation procedure must compute values of K, _, and _ for which the computer
model output best fits the measured data in a least squares sense.
Since the driver parameters K, n, and x are not available from an actual
driver/vehicle test a computer simulation was used to generate test data that
allows direct comparison of computed parameter values to true parameter
value_. The test data was generated using the same driver model as the
identification code, but a different vehicle model. The vehicle model used
was more complete aad had been thoroughly checked out.
The test maneuver was lane tracking on a straight road at a nominal speed
of 55 mph with an initial lane error of five feel. As shown in Tabl_ 1 the
largest error between the true and =omputed parameter values is 6%.
£arameter True Value identified Value Percent Error
: 0.I 0.I00 O_
K -0.I -O.094 -6_
n 1OO 94.40 -5.6_
Table I Errors in Identified Values
of the Driver Model Parameters
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1982005792-341
CONCLI _IONS
A_ shown in Figure 4, the computer model provides a very accurate simu-
lation of the actual vehicle states. This is a critical result, since the
data collection scheme proposed in this paper is based on the premise that
vehicle states, which are inputs to the _r[ver, can be accurately constructed
from simulation, thu_ eliminating the need to instrument each vehicle to oe
tested with an inertial platform. Also, assuming that an appropriate driver
model is used, the identification procedure accurately coTuputes the driver
model parameters as indicated by the data in Table 1. Thus, each part of
.he overall procedure has been independently validated.
The final test of th_ procedure will be identification of driver model
parameters from an actual road test and comparison of computed vehicle states
and driver outputs to actual measured v'tues. This testing is currently in
progress.
REFERENCES
1. Sexier, J., Harrison, d. Y., "A Nonlinear Model Describing Driver Behavior
on Straight Roads," Human factors, 1979, 21(1), 87-97.
2. Clark, S. K., Mechanics of Pneumatic Tires, MBS Monograph 122, U.S.
Go,,_rnment Printing Office, November i9_i.
3. Ellis, d. R., Vehicle Dynamics, Business Books Ltd., London, 1973.
&. Craupe, D., Identification of Systems, New York, Robert E. Krieger Pub-
lishing Company, 1976.
5. qcRuer, D. T., Allen, R. W., Weir, D. H,, K1eln, R, H., "Ne_ Results
_n Driver Steering Control Models," Human Factors, 1977, 19(4), 381-397.
6. Phatak, A. V., "Formulation and Validation of Optimal Control Theoretic
Models of the Humat_ tS,ecator," Machine S_.stems Review, 1976, _, 11-12.
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1982005792-342


A data collection scheme for identification of parameters in a driver model

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