The validation of linear driver model

THE VALIDATION OF A LINEAR DRIVER MODEL TECHNISCHE HOGESCHOOL DElFT

lUCH .' T-HJ RUH~;tV:t/.lHT[Cn. lEK D21oUO UEE

Kluyv6(Weg 1 - DELFT

G7 JtiU 1980

by

L. D. Reid, W. O. Graf, A. M. Bi11ing

0"

i

THE VALIDATION OF A LINEAR DRIVER MODEL

by

L. D. Reid, W.

o.

Graf, A. M. Bi11ing

Submitted February, 1980

Mar eh , 1980

UTIAS Report No. 245 eN ISSN 0082-5255

Ac}mowledgement .

The authors wish to express their thanks to the driver subjects whose faithful participation made this project possible. Support for this work was provided ~y the Ontario Ministry of Transportation and Communications

J

Abstract

This report deals with the validation of a linear mathematical model of a driver developed by the Ontario Mïnistry of Transportation and Communica-tions •. The major portion of the investigation was devoted to the gathering of data on driver behaviour while controlling a car and a truck on a curved road-way. This was carried out in a fixed-base driving simulator employing a computer generated display of the driver' s forward view. The data were

analyzed and compared with those generated by the driver model. Driver model parrumeters were selected such that reasonable agreement with averaged subject driver response was achieved. The study also brought to light same interesting variations in driver behaviour.

'ol 1. 2. 3.

4.

5.

6.

Contents. Acknowledgement Abstract Notation INTRODUCTION

VEHICLE AND TASK SIMULATION

~.1 Vehicle ~quations of Motion

2.2 Display System

2.3

Work Station Details 2.4 Roadway Properties DRIVER IDDEL

EXPERIMENTAL PLAN DETAILS

ii iii v 1 2 2

4

5

6

8 9 4.1 Subjects 9 4.2 Training 9

4.3

Production Runs 10

4.4

Data Recording 11

4.5

Data Reduction

11

4.6

Data Analysis Including Driver Model Parameter Selection

13

DISCUSSION OF RESULTS

15

5.1

General Remarks on the Driving Behaviour of the Subjects

15

5.2

Subject Means and Standard Deviations

16

5.3

Driver Model Results

17

5.3.1

Time Histories

5.3.2

Means and Standard Deviations

5.3.3

RMS Differences

5.3.4

Extreme Offsets on Curves

5.3.5

Histograms

CONCLUSIONS REFERENCES TAB;LES FIGURES

APPENDIX A: VEHICLE EQUATIONS OF MOTION APPENDIX B: DISPLAY TRANSFORMA.TION APPENDIX C: PROGRAM DESCRIPTIONS APPENDIX D:. DISPLAY OPTICS

17

18

18

18

19

19

20

a A b bi C(i,j) 'w' Ccm. _~ C cmF C cmR dl d 2 F_B F_I F s F _v FYi g hl' h2 H

l1r

i Ixx' Iyy' I xy' I xz' kA

~

k_f k. ~ I _zz I yz Notation

distanee from mass centre to front axle

effective distanee from eye to viewing screen distanee frommass centre to rear axle

shock absorber damping constant, corner i' (see Fig. A.3) cubic spline coefficients

tire sideforce coefficient, i indicates the vehicle corner (see Fjg. A.3)

front tire sidefo~ce coefficient rear tire sideforce coefficient lens focal length

distanee fr<:>m eye to lens body-fixed reference frame

earth-fixed reference frame screen-fixed reference frame eye-fixed reference frame tire sideforce, corner i acceleration due to gravity image heights (see Fig. D.l) display screen height

Fresnel lens height

vehicle corner index (se~ Fig. A.3) vehicle moments of inertia in F

B vehicle produets of inert~a in F

B

acc~lerator effect parameter brake effect parameter

Coulomb friction effect parameter suspension compliances

!!BI

m M N p q r R s t

viscous friction effect parameter

driver model curvature gain

driver modellateral offset gain

driver model heading gain

image-to-eye distance

path length of spi ral transition curve

applied rolling moment about the vehicle mass centre, in F_B; or ~oad straight segment length (according to context) transformation matrix relating

Fr

and

F

_B

vehicle mass

applied pitching moment about the vehicle mass centre, in F

B

applied yawing moment about the vehicle mass centre, in

F B

tire nor.mal force, corner i

roll rate, in

F

_B pitch rate, in F

B

yaw or heading angle rate, in F B

coordinates of vehicle corner i in F B

radius of curvature of real road centre-line

radius of curvature of real road lane centre-line

distance along road; or Laplace variable (according to context)

half front wheel track

half rear wheel track

road lane semi-width

time from start of first road cycle; or student's t-statistic'

value (according to context)

driver model preview time

TL u u c v Vwo -, ~ w W ,; _W F (x,y)

(~

YD zD) (~ Y_{E ZE}} (xr Yr zr) (xo Yo zo) (xp Yp) (x_{s Ys )} (xt(i), yt(i)] X X A

XE

Xc

~i Y YTi Z

a.

_~

driver model lead time constant

forward speed with respect to Fr expressed as F

B x-component a nonlinear function of forward speed (see Eq.

A.99)

lateral speed with respect to Fr expressed, as F

B y-component resultant wheel velocity vector, cor.ner i

vertical speed with respect to Fr expressed as F

B z-compon~nt display scr.een width

Fresnel lens width

cubic spline road centre-line coordinates in Fr driver's eye coordinates in F

B

coordinates of the origin of F in Fr _{v .} vehicle mass centre coordinates in Fr

object point coordinates in 'Fr

vehicle position along road centre-line (see Fig .. 13) image point coordinates in F _s

segmented road coordinates in Fr

x-component of externally applied force in F

B (neglecting gravity)

component of X due to engine component of X due to brakes

component of X due to other effe cts x-component of tire sideforce in F

B

y-camponent of externally applied force in F

B (neglecting gravity)

y ... component of tire sideforce in FB' cOrner i z-camponent of externaliy applied force in F

B (neglecting gravity)

tire sideslip angle, corner i

---,.--...,.--- -~-a VF,

~F

~S' aLS " B BA

~

t)d Bi Bo Bos Bs Bss ~( ) ~tc ~ty ~t'l/l fiX ~ ~Bs ~ €

e

e

p( s) erc

vertical and lateral field of view as limited by the Fresnel lens

vertical and lateral field of view as limited by the

CRT screen

front road wheel angle

accelerator pedal deflection

brake pedal deflection

,

driver model desired front road wheel aQgle

road wheel angle, corner i

reference front road wheel angle (see Section

4.5)

reference steering wheel angle (see Section

4.5)

steering wheel angle

steady-state front road wheel angle

in the context of the linearized equations this represents a perturbation value

driver, model sampling interval for' curvature

driver model sampling interval for later al offset

driver model sampling interval for heading error

vehicle lateral offset from lane centre-line

the difference between actual and reference steering wheel angle (B - B ), called "steering offset"

s os

the difference between actual vehicle heading and road heading ('1/1 - 'I/IR)

di stance , CRT to lens focal plane

Euler elevation angle

road heading change

road centre-line curvature

standard deviation of the driver model curvature noise source

~

. .

-cr

--f::;y ~à5s .O:bp

(jiJ!

T

.

x x(t) x(s) x

x

standard deviation of the driver modellateral offset noise source

standard deviation of the lateral offset standard deviation of the steering offset standard deviation of the heading error

standard deviation of the driver model heading noise source driver model time delay

Euler bank angle vehicle heading angle road heading angle dX/dt

average value of x(t) Laplace transform of x(t)

signal including noise and sampling effe cts equilibrium value

value at the driver's eye position column vector

matrix

transpose of X

ix.

1 . INTRODUCTION

The present project is aimed at the gathering of driving data for use in the validation and calibration of mathematical driver models. These'

models are currently under development for use in evaluating road safety and ground transportation performance under a variety of vehicle/roadway

co~ditions. As a first step towards this goal a fixed-base ground vehicle simulator has been developed and employed to generate the desired data. At a later stage it is anticipated that an instrumented road vehicle will be used to produce actual driving data.

There are a range of driving tasks of interest in this work and the form of the mathematical model best suited to each task may be somewhat different. A bibliography of recent research in this field is contained in Ref. 1. The task selected for study was the driving of a vehicle along a winding roadway. Once a suitable driver model for this situation has been determined, it is hoped th at a similar model can be applied 'in the future to more severe maneuvering tasks such as lane changing and obstacle avoidance . .

For the present study the equations of motion of the vehicle were

linearized about a fixed operating speed. Motion on a flat plane, with very small vehicle roll angles, and with no pitch or heave was assumed. This resulted in uncoupled longi tudinal and later al equations of motion . These were :i,mplemented on a combined analog-digital computer system. The analog

computer handled most of the dynamics, while the digital computer dealt with the kinematics and also generated the roadway display for viewing by

the driver of the simulator.

The display system consisted of a 20 x 25 cm CRT screen driven by the digital computer via a vector generator. A Fresnel lens between the driver and the screen increased the field of view and created a virtual image at a viewing distanee of about

5

meters. Masks were used on the aRT screen to simulate the hood of a car or the roof pillar and interior cab roof line of a truck.

The work station was set up in a booth to represent the driver'sseat, steering wheel, daShboard with instruments and foot pedals. The steering wheel had limited travel, but this was sufficient for the curves used in this study.

The roadway simulated had a variety of curves with different curva-turesand straight sections. The length of the basic róad cycle was

1783

m and this was repeated as required. Centre stripes and utility poles were used as addi tional motion cues. The scene on the CRT was made up from straight line segments and could be considered to be a night scene.

The driver model was provided by ~C and digital simulations were carried out to determine its response to the roadway geometry used in this study. These results were then campared with the driver's response obtained in thesimulator.

The study was run with 6 subjects, who, af ter some familiarization

at a time. The vehicle's position and state variables were recorded on digital magnetic tape for further analysis. The vehicles simulated were a full-size North American sedan and a cab-over-engine dump truck.

The data were reduced at MTC into a for.m where di stance along the road

was used as the independent váriable. The deviations .from areference

steering wheel angle, lateral offset from lane centre-line and heading angle error were computed and stored on magnetic tape. The data were processed to determine same statistical parameters which could be used to compare the model with the subjects.

2. VEHICLE AND TASK SIMULATION

In past driving studies involving fixed-base simulators it has been found that drivers perfor.m somewhat differently in the simulator when cam-pared to ac tual roadway dri ving. For example, system cros sover frequency is consistently higher in full-scale road tests than in the fixed-base simulator (Ref 2). It is relt that this is primarily due to the lack of motion cues in the simulator. With this in mind it is recognized that the present fixed-base simulation will not generate driving data identical to

those from a full-scale road test. The design of the simulator 'however

minimizes these differences and provides a starting point in the driver model study which at a later date can be expanded to employ data obtained from instrumented road vehicles.

The task to be simulated is the control of a road vehicle as it moves at constant forward speed along a specified curved roadway. The various aspects of the simulation system are described in detail below.

2.1 Vehicle Equations of Motion

The task under study involves the vehicle's lateral response under conditions of constant forward speed. With suitable assumptions, coupling

between the longitudinal and lateral degrees of freedom (at the test·

con-ditions) can be ignored, leading to simplified simulation requirements. Simplified lateral equations for a vehicle are developed in Appendix A. These apply when a vehicle is operated on a horizontal surface (i.e., no

road crown or bank). Vehicle pitch and heave have been taken to be

iden-tically zero and roll assumed to be very small because it was felt t~at they

play only a minor role in the present task. By restTicting the simulation to constant forward speed and small perturbations in lateral speed Cv),

yaw or heading angle rate (r), front rqad wheel steer angle .(5) and ti re

slip angles (ai) it was possible to reduce the set of equations to the form given in Table A.4 of Appendix A. The driver' s input is the front road wheel steer angle. (5) .

The value of forward speed employed was 50

km/ho

Table 1 lists the

values of the vehicle parameters employed. The car was representative of a full-size North American sedan (values from Ref. 3) and the truck represents

a cab-over-ergi..né. dump truck (va!ues from Ref. 4). The car had neutra! steël'ing while the . truck had oversteer* characteristics.

The equations of motion are solved in real time on a TR-48 analog computer and ·a HP 2l00A digi tal compute·r. The use of the digi tal coÏrrputer for this and the display generation introduces a series time delay of approxi-mately

55

ms into the simulation, a value considered to be insignificant in the present case. In order to minimize the use of the digital computer in the solution of the equations (because it was needed to perform other opera-tions reported in this document) it is only employed in the evaluation and integration of the Auxiliary Equations of Table A.4 in Appendix A. (Note that the present analog computer does not contain sine and cosine resolvers.) A rectangular integration scheme is employed with a time interval equal to the upd~te interval of approximatEüy 55 ms. The performance of the lateral simulation was verified by camparing step and frequency response measurement~ made on it against all digitai computer solutions performed on an IBM 370.

Although the task under study involved only vehicle lateral response it was felt that in the interests of realism the simulation should be capable of represe~ting the acceleration up to test speed from a' standing start and the braking to a hält following a test run. In order to achieve this the uncoupled longitudinal equations developed in Appendix A (see Table A.5) were employed. Here the driver t s inputs are accelerator pedal and brake pedal deflections. The vehicle parameters employedare given in Table 2. Their, selection was somewhat arbitrary with the end result designed to match the vehicle performance criteria specified in Table 2.

This àpproach resulted in vehicles whose lateral respon~e was exactly correct only at the test speed. This is acceptable at low forward speeds when small steering inputs are employed. In the present simulator the

acc~lerator and brake pedals are representedby foot switches which produce outputs corresponding to constant pedal deflections. By closing the accelera-tor switch for. example the vehicle accelerates up to test speed and holds it until the switch is opened. The speed holding feature is similar to a

"cruise control" device. The effective pedal deflections were limited so as to produce the desired test speed of 50 km/h and resulted in an acceleration time of 60 seconds for 0-50 km/h and deceleration time for 50-0 kmjh of 7 seco:rids .

..

The implementation of the equations of motion on the analog computer is shown in Figs. 1 and 2. Two problems arose which were solved by employing digital algori thms. The firs t was caused by the uncoupled lateral equations. They ailowed the vehicle to be slewed (i.e., the generation of non-zero v~lue

of yaw rate) when it had no forward speed. This was preven ted by having the.

digital solutions to the auxiliary equations s'topped when the value of forward speed (u) was sensed to be below 2 km/ho The second problem involved heading angle (~) which was originally produced by the analog computer. The digital

*Oversteer implies that a decreased steady-state front road wheel angle 5_{ss is}

required to maintain the vehicle in a constant radius turn as the steady-state forward speed Ue employed.is increased. In the present simulation the

para-meter d5_s

s/dUe

has the same sign as (CaNR - CaNF) where (

h

and ( )R represent the front and rear wheels. Positive, zero, and negative values of this para-meter correspond to understeer, neutral steering, and oversteer respectively.

computer' s analog-to-digi tal converter has 10 bit resolution (one part in

1024) and if a wide range of ~ must be represented (± 1800

in the present case) this leads to a quantization level of 0.35°. Flickering of this least significant bit in the analog-to-digital converter caused

an.unaccep-table jitter on the display screen. This was corrected by having ~ (instead

of

-

'l/J)

fed to the analog- to-digi tal converter and in tegrating .. digi tally to

pr9duce~. With the present sealing .(10 V on the analog computer representing a'l/J of 28.6°/s) and an 18 sps update rate in the digital computer this

resulted in a steady display under operating conditions.

2.2 Display System

The display is generated on a CRT screen in the work station by the HP 2l0QA computer operating in conjunction with a hybrid vector generator.

It depiets in proper perspective the driver's view out the front window of the vehicle by drawing the scene using segments of straight lines. In the present task the picture represents (in real time) a winding two-lane highway lined with utility poles. Figure 3 shows a Photograph of the display (without the Fresnel lens) as the vehicle enters a left-hand turn. It is seen that the roadway is represented by its edges and a broken centre-line. The horizon line is also displayed.

The display is produced by storing in the computer all the necessary details concerning the simulated roadway. The vehicle's position andheading are computed from the equations of motion and the visual scene corresponding to these values is generated using the transformations outlined in Appendix B. The details of the software routines employed are contained in Appendix C.

In general there is a trade-off between the amount of detail in the displayed scene and the time delay introduced by the computer (and the resulting update rate). In generating the present display we achieved an update rate of

approximately 18 sps (a time delay of 55 ms) and also refreshed the display one additional time between each update to prevent flicker. These values produced a steady display on the CRT with an acceptably smooth display motion and sufficient detail for the present simulation.

The display CRT is a Hewlett Packard Model l43A Oscilloscope with a modified z-blanking circuit. This has a screen face measuring 20 cm x 25 cm. The vector generator employs an 8-bit digital-to-analog converter and thus

the display resolution is 1/256 of its outside screen dimensions. In order

to increase the field of view and to create a display image at a distanee where the driver's eye will be relaxed (as in a real driving situation) a

plastic rectangular Fresnel lens was placed in front of the CRT. The details

of this installation are given in Appendix D. In the present case the

following dimensions and lens parameters were selected:

lens focal length, dl (cm) 30.1

lens lines per cm 20

lens width,

WF

(cm) 25

lens height, HF (cm) 23

distanee, eye to lens, d2 (cm) 30

di stance , CRT to focal plane, E (cm) 1.9

Using Eq. D:4 of Appendix D the image-to-eye distance

Ct)

for this

, configuration is found to be 4.7 m. The lateral viewing angle is checked using Eqs. D.7 and D.9 of Appendix D and is found to be 450

for both expressions. It should be noted, however, that the Fresnel lens tends to be of imperfect optical quality and as aresult sorne crispness of the image is lost. In particular the display should be viewed through the centre of the lens. A picture of thè CRT/Fresnel lens combination is given in Fig. 4.

In order to place the hood of the car in the display as a point of reference for the driver the actual obstructed field of vision at ground level represented by the hood of a full-size North American sedan was

measured. The coordinates thus generated were used by the display software to drawan outline of the obstruction on the display. This outline was then used as a pattern for an illuminated cardboard temp late which was placed on the face of the CRT as shown in Fig. 3. In the case of the truck the limited field of view was created by a template representing the top edge of the window and the left hand roof pillar.

The displayed scene was limited in content in order to achieve the desired update rate. Since the roadway edges were approximated by straight line segments it was found that the displayed road scene became parallel to the horizon and showed little detail in the distance. As aresult the following approximations were made:

(i) The maximum distanee shown down the road was 300 meters. (ii) The right-hand road edge was developed for only 150 meters. (iii) The first four segments were shown in detail (see Section

2.4), then road picture lines were drawn using every second coordinate pair for another four segments, followed by lines joining every fourth coordinate pair up to 300 meters.

(iv) Only the nearest six centre stripes were generated. (v) Only the nearest five utility poles were generated for

each side of the road.

See Appendix C for an outline of the display generation program and associated subroutines.

2.3 Work station Details

The work station booth has been configured to represent the driver's station in a road vehicle (see Fig. 4). The booth is air-conditioned and soundproofed in order to isolate the driver from the laboratory environment. The light level is controlled by a dimmer switch. The booth is linked to the computers by trunk lines and to the experimenter by an intercom. The display system is fixed in position directly in line with the driver's eyes and a second display is generated at the experimenter's station to allow

him to monitor the progress of the tests. The driver sits in a seat that can be adjusted vertically and fore and aft in order to place the driver's eyes at the desired location with respect to the display.

In the case of the North American sedan the steering wheel is 38 cm in diameter and mounted such that i t can be adjusted fore 'at:J.d aft. The steering colUllll'l is mounted on roller bearings and connected'to a torsionaJ,.,spring to provide centering. The spring constant was selected to give reasonably representative wheel forces for small deflections. Steering wheel motion is limited to

±

90°. The spring has a stiffness of 0.08 niN/deg, corresponding to a sedan with power steering (for small wheel deflections). A steering ratio of 17:1 is employed between the steering wheel and the front road wheels. A potentiometer is geared to the steering colUllll'l to act as a wheel position sensor.

The same layout of controls was used in the case of the truck ,simulation. Here the steering ratio was taken to be 23:1. The road layout and vehicle size were such that steering wheel deflections to

70°

were required. Since none of the subj ects were truck drivers, the Unchar,acteri s tic steering wheel

tilt angle was considered not to be obj,ectionable. '

The accelerator and brake foot switches are mounted on a sloping surface which can be moved fore and aft to accommodate a range of sitting positions.

An illuminated speedometer (in km/h) is located on the instrument panel. In order to improve somewhat on the sterile environment associated

with fixed-base simulation some audio and tactile stimuli have been included. A vibrating shaker (a panel shaker from an aircraft simulator) is fixed to

the foot switch board. This provides both tactile and audio inputs whose frequency is coupled to the forward speed of the vehicle. In addi tion, the cooling fan in the CRTdisplay and the circulating fan in the air-conditioning unit provide a reasonable representation of the aerodynamic hiss heard inside a vehicle. A radio is also provided to produce a common-place audio masking signal.

2.4 Roadway Properties

The simulated roadway was made up of straight and circular arc sections with spiral transitions . The spirals had curvatures which changed linearly with distanee along the curve. Four straight sections and six curved sections were combined to make up one "cycle" of the roadway 1783 m long. The roadway was extended indefinitely by joining successive cycles together. A test run comprised two complete cycles.

The roadway geometry was chosen to meet Ontario standards for a design speed of 50 km/h, the test speed. The only exception was the absence of superelevation on the curves; the road was flat throughout its length. Ontario standards (Ref. 5) limit the minimum horizontal radius of turn to 85 m and set a lane width of 3.25 m.

Radii R of the six circular arcs were selected to span the range between the mininrum and maximum allowable, and the lengths },S of the spiral transi-tions were determined from Ref.

5.

The tot al' angle between curve entry and exit

e

'

,

and straight segment length L, were 'selected at random to yield the roadway ás defined in Table 3. In the remainder of this report the roadway represented by Table 3 will be referred to as the "real road".

In order to produce a display of the roadway using the .digital computer to generate a picture based on straight 1ine segments i t was necessary to form a "segmented road" based on the real road data. To achieve this a computer program was written to generate coordinates a10ng the road centre-1ine in 1 m steps. In this process the spiral segments were each approximated by .10 circular arcs. This defined too lIla.Ily ségments for display purposes

so the number of points was greatly reduced by choosing the fewest number of points such that chords drawn between the se1ected points were never more than 0.1 m from the centre-1ine. This provided many points on sharp curves but onlya few on straight sections. In this way a segmented road represented by 136 straight segments joining 137 points on the rea1 road centre-1ine was produced and used for display purposes. The program emp10yed, ABROAD, is described in Appendix C.

Data reduction of the driver test ·results as we11 as the imp1ementati.on of the driver model required the calculation of vehic1e lateral ·offset from the 1ane centre-1ine at rahdom·10cations·a1ong the road. This necessitated interpo1ation between points at which the roadway geometry data were avai1ab1e in the digital computer. Use was made of a cubic sp1ine interpo1ation routine along with the segmented road data. A set of 136 cubic equations resulted, each defining a curve between two adjacent points. The cubic sp1ine approxi-mation to the road centre-1ine had the fo110wing properties:

y(x) :;: C(i; 1) + C(i,

2)~

+ C(i, 3)bc2 + C(i, 4)bc3 (2.1) where

(2.2)

1 ~ i ~ 136 (2.4)

The [xt(i), yt(i)] are the 137 coordinate pairs giving the segment end-points for the segmented road. The four coefficients C(i, 1) to C(i, 4) for each of the 136 segments were se1ected so that the cubic curves passed through their respective end points and the slopes of successive curves were identi-cal at their cammon meeting point. Thus each curve satisfied two conditions at each end point, unique1y determining the four coefficients.

In addition a tab1e of 2000 va1ues for road curvature p(s) was generated as a·function of distance (s) (at uniform intervals) along the road by using the segmented road coordinate data and the rea1 road curvature va1ues. Road heading at the same 2000 points was obtained from

'1fJ

Values of p and '1/IR at arbi trary points along the road can then be found by applying linear interpolation to these data.

The road defined by the cubic spline fit and the above tables of curva~

ture and heading is called the "hybrid road" in the present report. Plots,'

of these data for the hybrid road are given in Fig.

5.

3 •

DRIVER IDDEL

The model used for the driver of the car and the truck is fully des-cribed in Ref. 1. It was developed by the MrC and provided for use in this project. Figure

7

shows the logic of the model. The driver contröls the vehicle via the front road wheel angle in response to external and internal

stimuli. He is assumed to generate front road wheel angle inputs based on three variables derived fram his view of the road and the vehicle' s position on

ft.

The first input is the road curvature p previewed at the point on the road ahead of the car that i t will reach in time

!1>.

'Th1s permits anticipa-tory open-loop control that reduces errors requiring closed-loop con trol '

to manageable levels, requiring little or no further lead generation . Two feedback loops are p~ovided to control the vehicle lateral offset ~ and heading angle error ~ relative to the lane centre-line. In this instance

~ is the difference between the vehicle heading angle and the roadway

, heading angle at a point where a line drawn fram the driver's eye meets the road centre-line at a right angle. ~ is the distance from the vehicle's centre-line at a point adjacent to the driver's eye to the above same point on the road centre-line. In both cases deviations to the right are repre-sented by positive values.

Each of the variables is distorted by two factors. Random noise is added and the result is sampled at a specified rate. The rate may differ for each variable. The distorted variables p', ~ and

4rÈ

are cambined linearly to provide the desired front road wheel angle 0d'

5 :;: K

d c P ' + K 7jJ • ~E /lnlt' + K Y !Jg.' E which has astaircase form in the time domain.

(3.1)

5d is the input to the driver characteristics of a time delay T, ànd a first order lag and lead to provide the 'front road wheel angle 5. This is represented by the transfer function:

(3.2)

The front road wheel angle 5 is fed ~nto the vehicle equations of mot ion described in Appendix A to generate the vehicle response.

4 .

EXPERIMENTAL PLAN DErAILS

4.1 . Subjects

Six subjects were selected from 8 male volunteers from the staff and students of UTIAS. Table

4

summarizes their charac~eristics.

4.2 Training

On the first day of training the subjects were seated in the work station

with the display showing the view corresponding to the sedan positioned in

the centre of the right-hand lane of a straight road. The functions of the various wor~ station components were explained (brake pedal, accelerator pedal, steering wheel, speedometer, radio, intercom, Fresnel lens). The

seat was adjusted to set the subject' s eyes at the proper level about 30 cm from the lens, and this seat position was no,ted and used for all further tests. The properties of the displayed view were pointed out to the subjects with the aid of a scale drawing of the straight roadway (see Fig.

8).

It was emphasized that the hooq-line represented that of a full-size North American sedan as did the vehicle under control. The subjects were told that the first phase of the training was to familiarize them with the dis-play and in particulap with how the hood line appeared against the roadway display when the vehicle was centred in the right-hand lane. To demonstrate this the vehicle was driven down the centre of the right-hand lane by having the subject depress the accelerator pedal to accelerate up to speed while the computer was set to keep the car heading down the centre of the lane

(the steering wheel output was disconnected). This lasted for

3

min. The next step was to allow thesubjects to familiarize themselves with the con-trol of the vehicle. These runs were made wi th the vehicle fully operational and employed the same straight road. The subjects were told that the study tests were concerned with the lateral control of the vehicle and that the accelerator pedal would normally be held down throughout each test and that this would activate a form of "cruise control" that would accelerate the car up to speed and then maintain it. In a similar fashion the brake pedal represented a preset braking effort. The subjects were cautioned not to carry out any severe maneuvers until travelling faster than 40 km/h due to simUlator limitations; Two 3 min. runs were performed with a 1 min. rest between them. During these runs the subjects were encouraged to perform lane changes and other maneuvers which would familiarize them with both the vehicle dynamics and thedisplay. In all cases the vehicle was accelerated from rest up to 50 km/h and th en following the constant speed run, braked to a halt.

The next set of training runs consisted of having the subjects drive the vehicle down the right-hand lane of the same straight road in their normal manner. No disturbances were present in the system. They were told that we were trying to learn their usual lane position from these tests. Each run

l~sted

3-lj2

min. and was separated from the next run by a 1 min. rest during which the display was shut off. In all cases the vehicle was accelerated from rest' up to 50 km/h and then following the constant speed run, braked to a halt. Three of these runs were performed as part of the first day's training, to be followed by

3

more during the next training period several days later.

Their tracking records for the last

2.4

min. of eacn run were recorded on

the HP 2100 9-track magnetic tape unit (see Section

4.4)

and their mean

lateral offset and the standard deviation of lateral offset were computed.

In order to avoid encouraging the subjects to drive in an unnatural lane

position the only feedback on performance that they were given was a warning if they deviated on the average more than 40 cm from the centre of the

lane; otherwise they were told that everything, was fine. In only one case

did a subject have to be warned of the 40 cm deviation. The subjects were not aware of this feedback scheme. The mean lateral offset and its standard

deviation for the subjects are given in Table

5.

In the present case it is

not possible to tell whether the display actually resulted in the subjects driving in their normal lane position. However it can be seen that each subject was quite consistent in his driving habits. Only the last run by Subject 2 obviously differs from his other runs.

The .second day of tr.aining consisted of completing 3 more straight

road driving runs followed by three training runs on the curved roadway. On the curved roadway runs the subjects were tbld to drive in their normal

manner under the assumption that there was oncoming traffic,. They were told

that the road curves conformed to standard MTC practice for a 50 km/h road-way. Each curved roadway run lasted 5-1/2 minutes and was followed by a 2

min. rest p~iod during which the display was turned off. They were told.to

keep their foot on the accelerator during the complete run. In all cases

the vehicle was accelerated from rest up to 50 km/h and then f.ollowing the

constant speed run (2 roadway cycles', each 1783 m in length) braked to a

halt. Data were recorded for the last

4.3

min. of the run (2 full cycles)

and their tracking performance computed from this. In order to provide some motivation for the subjects they were told the standard deviation of their lateral offset at the end of each run and encouraged to minimize this. The resulting mean offsets and standard deviations are plotted in

Figs. 9 and 10. These figures include all curved roadway runs for the,

car. It is seen that driver perforÏnance has settled down in less. than six

runs. Asa result training for the car was considered to be complete af ter six runs. Mean lateral offset is similar to the straight-road value for each subject.

Af ter production runs for the car were complete (see Section

4.3)

the

simulator was converted to represent a truck:. For this vehicle subject

familiarization time was shorter than for the car .as the subjects were now'

experienced with the simulator and the task. The truck was described to the subjects and they were shown how it differed from the car in the driver

position, vèhicle.width, and in having no hood. Computer-controlled driving

down the lane'centre-line and vehicle handling familiarization on the

straight roadway we re identical to the Car' However, only three 'runs of

driving normally along the straight road were felt to be necessary as subjects were adapting very rapidly to this task. Based on the results of Figs. 9 and 11 all curved road runs for the truck were considered to be production runs.

4.3

Production Runs

Production testing on the curved road was undertaken on one day .. each

week. Each subject drove three runs each day in asession lasting 30-40

minutes. Eight good runs per subject were required for data analysis. A total of fifteen runs on the car were completed byeach subject.

Af ter training was complete for the truck, curved road runs commenced on a similar basis. However the plots of vehicle lateral offset mean and standard deviation (Figs. 9 and 11) showed no signs of adaptation, presumably because the task was similar enough to car dri ving. Thus only 9 runs per

subject were recorded to provide the 8 needed for analysis.

In some cases (both for car and truck) runs were not available for analysis due to data gathering problems and extra runs were required. Figure 12 shows the rtms campleted and those analysed. It also shows vehicle speed (mean and standard deviation) for the eight runs selected.

Obviously they may all. be taken as constant speed runs at 50 km./h (13.89

mis) .

4.4

Data Recording

For each run the-following variables were sampled at about 18 samples/

second starting at the beginning of cycle one and continuing to the end of cycle two and recorded on a 9-track digital magnetic tape:

t Elapsed time since start of first cycle (ms)

XI Vehicle C.G. location in x-direction of F_{I Cm)}

YI Vehicle C.G. location in y-direction ofFi (m) See Fig. 13

1/J Vehicle he ading angle (rad)

5_s Steering wheel angle (rad)

The sample time was not -~ixed, as data sampling had less priority in

the computer program than dispJ,.ay updating and refreshing. Wi th the roadway used for this work, the period between samples was about 55 milliseconds.

Each run recorded on tape constituted one tape :file. The dynamic data were preceded by a he ader record listing the parameters of the run, listed

in Table

6,

and followed by an end-of-file mark. A total of 229 runs (both

familiarization and test) were recorded on I I data tapes.

These data were read immediately af ter each run and the vehicle lateral

offse'j; (from thelane centre-line) ;.:. mean and standard deviation calculated.

Several runs were plotted each day to check that the data were reasonable. All selected run data were also reduced for later analysis.

4.5

Data Reduction

Data reduction to a form suitable for analysis was performed using the

MrC IBM 370 computer. This was made possible by first converting the data

for each run from the HP word format to that used by IBM using the program

It was decided to base the data analysis on the vehicle and driver perf'ormance relative to the roadway. The independent variable selected was

distance along the roa.d.way s, which ran f'rom 0 to 1782.9 m. Using

inter-polation the measured variables were determined at 2000 points equally spaced along the roadway. Vehicle speed, which was essentially constant, was then no longer a factor in synchronizing the different runs.

The variables recorded were:

6y - lateral offset of' vehicle centre of' gravity f'rom lane centre-line (m) along anormal to the hybrid road; distance from

(xI, YI) to (~, yp) less lane semi-width sw (see Fig. 13);

a pos i tive value represents of'f'set to the right,

~ - heading angle of' vehicle relative to that of' the hybrid

road at (Xp' yp) (deg) (see Fig. 13); a positive value

represents a heading to the right,

b.B _s - steering wheel angle relative to the ref'erence steering

wheel angle Bos (see paragraph below) at (~, yp) (deg);

given by (Bs - Bos) and also ref'erred to as "steering of'f'-set"; posi tive to the right,

Bs - steering wheel angle (deg); positive to the right.

The equations of motion given in Table A.4 of Appendix A can be solv~d

f'or the front road wheel angle Bo required to produce a steady turning radius

RL.

This is a steady-state case with

and all the time

Bo The corresponding deri va ti ve s u e

&=11,

set to zero. 2 The resUlt u _ .. =l-{a +b + :

(C~F

-

C~R

)} RL is

reference steering wheel angle is given by B _os

=

G.B

l. 0

(4.1)

(4.2)

(4.3) where Gi is the appropriatè steering ratio. The reference steering wheel

angle Bos is plotted against distance along the road s in Fig .. 14 f'or the

car and the truck (based on the hybrid road) with RL set equal to the lane centre-line radius of curvature.

The use of' b.Bs in the present context removes the large scale features f'rom the steering wheel data and allows a better study of' the small scale driver activity.

Thése caJ..culations were performed by program TCSR .ABUTIAS (DSCONV), producing a data set for the two roadway cycles (plus a header). These were converted back into HP word format using HPIBM and stored on two

tapes, UTIASl for

ear

runs and UTIAS2 for truck runs, f'or data analysis.

Program DSCONV is described in Appendix C.

4.6

Data Analysis Including Driver MOdel Parameter Selection

As part of the data analysis process the time history of each subject '.s

last run was plotted. S8mple plots for Subject 1 are given in Figs. 15 to 18 (based on one roadway cycle) for the car and the truck. The means and standard deviations (based on tpe data contained in the 8 production runs)

of the reduced data (~, ~, ~s) and 5_{s were computed for each subject as}

well as for all the subjects lumped tcgether. These values are given in

Table 7 and Fig. 29. (Nbte th at in Tables7, 8, 12 and 13 and Figs. 29 and

30 the entry corresponding to "ALL" was based on a record formed by joining

the appropriate time histories from each subject :end to end to form one long

record. )

To reduce same of the noise in the individual subject driver time histories (introduced by the drivers themselves) in order to allow a better

camparison with the driver model (which, as described later in this section, did not include noise sources) each subject's eight runs of two cycles each were averaged together on a point-by-point basis to produce one road cycle of "the averaged run" per subject. The results of this procedure when applied to Subject 1 are shown in Figs. 19 and 20. Comparison of these figures with Figs. 17 and 18 indicates the resulting reduction in the high

frequency noise present in the individual time histories. (Note that this

so-called noise is the result of steering wheel activity of a random nature injected into the system by the driver.) The means and standard deviations for these averaged runs (bäsed on the data contained in the single averaged run) are given in Table 8 and Fig. 29. As expected, the means are identical to those based on eight individual runs (see Table 7) and the standard devia-tions of the averagedruns are less than those based oneight individual runs (see Table 7 and Fig. 29). Figures 21 and 22 summarize the average driving time histories for all six subjects based on the averaged runs with

their means removed. These plots were obtained by taking the averaged run

for each subject and subtracting out its mean vaJ..ue. The resulting six

records (for each variable) were",ti,hen used to compute a mean valueand a

standard deviation at each point along the roadway.

Once the subject data has been gathered it is then possible to select the driver model parameters. The driver model described in Section 3 requires the 13 parameters listed in Table 9 to fully de fine it. While no detailed parameter identification process was attempted, accepted ranges for many of them were available fram the open literature. Their selection is described below.

(1)

Kc;

curvature gain:

Logically,

Kc

must be selected close to that value which would result

parameters ~ and Ky were set to zero. This depends upon wheelbase,

under-steer/oversteer characteristics, and ,speed. At 50 km/h the required values

of'

Kc

we re 180 deg m for the car and 245 deg m for'the truck. It was

veri-f'ied by digital simulation that 10% changes' in these parameter values were

not signif'icant. . .

(2)

K,p

and

Ky;

:lle ading ana -of'f' set gain s :

These gains are determined by the need for stability and well-damped steering behaviour. While they dep end strongly on vehicle geometry, values f'ound in the literature provided guidance in the case of' the car (Ref's. 7-10).

These values 'are listed in Table 10. In applying them to the present car

they have been scaled based en the gain of' the transf'er f'unction relating

heading angle rate to front road wheel angle. The values actually. used in

i:his.L,study~ were selected f'or their ability to provide stable, accurate tracking.

, A range of' values for the truck was obtained by scaling' up the car

values based on the

Kc

values used in (1) above.

(3) botc , öt7f! and öty; sampling in tervals :

In Ref'. 11, Kreifeldt f'ound that in 'a pursuit tracking task a human

operator samples the display every 0.2 seconds. This value was used in the present model f'or all three sampling intervals . Crossman and Szostak in

Ref'. 12 f'elt that the three sampling intervals would not be the same, wi th

botc very short, öt'IÛ about 0.5 to 1. O. _{s and öty about 0.5 s. In the presen t}

study trials quickly showed that sampling intervals greaterthan 0.4 s f'ot

~~ _{and öty resulted in poor tracking accuracy with the driver mddel of'}

Section

3.

.

(4)

T, TL and TI; time delay, lead and lag time constants:

Published values for these parameters are listed in Table 11. TL and

TI values close to those of' Ref's. 8 and 9 were selected f'or both vehicles.

The values of' time delay T shown in the table represent values employed in

models having continuous input signals and processing. However, thepresent

driver model contains a f'irst order sample and hold with a 0.2 s s'ampling

interval. It can be shown that to a f'irst approximation this first order sample and hold is equivalent to a time delay of' 0.1 s. Hence it was decided

to set ~

=

0 in the model so as not to introduce unrealistically excessive

time delays.

(5) _{t p ; preview time:}

It was shown in Ref. 1 that driver model perf'ormance in a limited task

was insensitive to

tp

in the range 0.4 - 1.0 s. In the present case a value

of' 1.0 s (equiValent to 13.9 m of preview at 50 km/h) was selected f'or both vehicles.

(6) _{rrc ,} rr7f!' and rry; noise levels:

Since a suitable noise model has not yet been developed f'or the present driver model, all noise levels were set to zero. The selection of noise source characteristics will be left to future studies.

The final model parameter selection was carried out by visually comparing the run time histories produced by the driver model against the same data

generated by the driver subjects (e.g. Figs.

15-22).

Fourteen cambinations

of driver mod,el parameters were examined. The values finally selecte'd are

listed in Table

9.

The corresponding run time histories are given in,Figs.

23

to

26

for the car and truck cases. Figures

27

and

28

give an expanded

plot of the, same data at two locations on the roadway along with averaged

runs for Subject 1.

The model output used for comparisons with subject data was generated

using program DRSIM described in Appendix C. Data were recorded in the same

form and reduced using the same procedures employed wi th thè human drivers. A single run comprising two cycles of the hybrid road was used for each vehicle.

The means and standard deviations for the driver model data were camputed

and these can oe foun~ in Tables

7

and

8

and Fig.

29.

Computations were also carried out to deter.mine the RMS of the difference

between the subjects' and the driver models' responses. In order to eliminate

any contribution due to constant offsets in the data, each run employed first

had its mean value removed. The results are presented in Tables

12

and

13

and

Fig.

30.

Because excursions away fram the lane centre represent a potential driving hazard an analysis was performed to determine the extremes in the

lateral offset 6Y for the 9 curves identified in Fig. 5 and Table

14.

Since

the subjects' data were to be campared with the driver model results it was decided to remove the meao lateral offset corresponding to the local road

segment (as defined in Table

14)

fram each set of data before processing.

The subjects' averaged runs were employed with the extremes for each curve

from each of the

6

data sets averaged together to produce the results given

in Figs

31

and

j2

for the car and truck respectively, along with the driver

model results The outcome of at-test (with

5

degrees of freedam) performed

on the same data set comparing the subjects' mean'values with the models'

:mean values :is also shown on the same figures.

In order to provide à qualitative means for comparing the amplitude

distributions of the driver model and subject data, histograms were generated based on the appropriate data records with their means removed. These have

been plotted in Figs.

33

to

42

as the percent of all data samples contained

in the specified cells. These distributions all have zero means and their

spreads (± lrr) are indicated in the figures. Figures

33, 34, 37

and

38

give

histograms for Subject

1.

Figures

35, 36, 39

and

40

give histograms for all

subjects combined. Figures

41

and

42

give the histograms for the driver

models.

5.

DISCUSSION OF RESULTS

5.1

General Remarks on the Driving Behav:iour of the Subjects

Subjects were instructed to driv~ in a consistent manner and were not

required to follow the centre-line of the lane. While driving with a

consis-tent offset for a particular vehicle, Subjects

3

and

6

showed a shift from

truck -(see Table

7).

For most subjects the truck was driven closer to the centre-line of the lane than the car, although the average offset of all

drivers wàs almost zero for the car and 10 cm to' the right for the truck.

The standard deviation of the lateral offset based on all drivers was

sub-stantially the same for the car and the tru.ek (22 cm vs 24 cm, see Table 7

and Fig.

29).

.

When plotting the mean of all subjects' runs (Figs. 21 and 22) ~t is

seen that the lateral offset is increased upon c~e entry, tending to cut

the corner, with a slight recovery towards the mean track once the curve is

being negotiated. The car shows a much greater tendency to be drivEm 011 the

inside of ·curves than the truck.

From the sample plots of Figs',

17

and

.

18

the small scale steering

motions can be seen. These tend to obscure the trends since a subject does

not reproduce exactly the-same movements fram cycle tO.cycle. By taking the

average over all stibjects' car runs the trends shown in Fig. 21 are revealed. There are over-reactions in steering wheel angle to the left on left-hand

turns ·(e.g., curve 2 at s = 0.2 x

1783

m), over-steering to the right on

right-hand turns (e.g. curve

9

at s

=

0.92

x

1783

m), and a gener al

oscilla-tory behaviour when en tering all curves. Similar but mer e exaggerated

behaviour is seen for the truck in Fig. 22., ,These results seem to indicate

a tendency for drivers to' over-react to,-:curves.

It was also noted that at curve

6

(s

=

0.6

x

1783

m), where a gentle

curve was entered, the subjects veered off into the curve before it was '

actually reached, thus tending to anticipate the step change in curvature

(see Fig. 5) and smooth it out.

5.2

Subject Means and Standard Deviations

The means and standard deviations of the reduced data

(ÄY,

~, ~5s)

and 5s are given in Tables

7

and

8.

The standard deviations are shown in

Fig. 29 for the individual runs and the averaged runs. The following obser-vations can be made concerning the reduction in the standard deviation in going from results based on individual runs to those based on the averaged runs.

~ - For the car Sub~ect 1 shows the'least reduction, hence one would

assume that he tended to be quite consistent from run to run.

Subject

5

had the greatest reduction and also had the lowest standard

deviations. For the truck Subject 6 had the greatest reduction"

I

~ - The reduction for the car data was about the same for all subjects.

With the truck data there were same inter-subject differences.

~ - The greatest reduction was for Subject 1 (both car and truck) .

s Subject 3 showed the least reduction for car and truck. The overall

effect of averaging runs was to::ré.duce the steering offset deviation'

to about the same level for all subj ects .

From the above it is seen that no consistent trends with subject number can be claimed for the orerall set of standard deviation results . In general

theaveraged run data tend to have both lower standard deviations and reduced (in same cases only slightly however) inter-subject differences than the individual run data. If a single driver mode1. is sought for each vehicle type, it is seen that although it might be possible to select a model that

would represent t::,5_{s for all subjects, it would} IlO t be possible to achieve

the same result for the ~ data (see Fig. 29). This suggests that in the

model parameter selection process the use of the data set with all stibjects averaged together might be the best course of action.

5.3 Driver Model Results

As outlined in Section 4.6 the model parameters selected and listed in

Table 9 represent a first attempt at choosing reasonable values. The extent

to which the resulting models (one ·for the car drive~fartd one for the. truck

driver) are representative of the driver subjects participating in the present study can be judged by eroploYing several measures:

(1)

(2)

(4)

5.3.1

a visual inspection of the time histories produced by the stibjects and the driver models (Figs. 15-28),

a comparison of the means and standard deviations of the run data

generated by the subjects and the driver models (Tables

7

and

8

and

Fig. 29),

an examination of the RMS of the differences between the subject and

driver model run data (Tables 12 and 13 and Fig. 39);,

a comparison of the extreme lateral offsets generated on the curves by the subjects and the driver models (Figs. 31 and 32),

à comparison of the histograms of the sUbject and driver model data

(Figs. 33-42).

Time Histories

A comparison of the driver model data of Figs. 23 and 24 with the

corresponding Subject 1 data of Figs. 15 and 16 shows that the ~ _{and 5s}

time histories have the same gener al features with the model results for

5s lacking in high frequency content due to the absence of noise sourc~s

wi thin the driver model. The lateral offset results (fSr) are not

unreason-able in the case of the truck but for the car the agreement is poorer. As stated earlier it should not be expected that the model would match a single driver's response and thus a better set of data to examine would be the one

averaged across all subjects (contained in Figs. 21 and 22) o' These sho1.Üd

be campared with the driver model results of Figs. 25 and 26. (Note that

since the means of ~, ~ and t::,5_s for the driver model are quite small, as

indicated in Table 8, the comparison is valid. It is assumed that lOOM

off-sets in the model data could be set to match those of the averaged subject data by making some minor adjustments.) It is seen that in gener al the

agreement is quite good except for two features. The driver model t::,5_{s is}

of a greater amplitude than the subject data and slightly more oscillatory

corner-cutting characteristics as the subject data. In Figs. 27 and 28 an expanded plot for two roadway curves is given to show that the driver model can come close to duplicating the detailed features of the averaged subject data.

5.3.2 Means and standard Deviations

Here we compare the means and standard deviations of the driver models with the subject data lumped together under the title "ALL" in Tables 7 and 8 and Fig. 29. The means for ~ and ~ show reasonable agreement except for the ~ truck value for which the driver model result (approximately zero) does not match the·9.6 .cm offset seen in the subject data. This modest difference however may not be of significanee in many applic.ations. Inthe case of the means for 60s and Os (steering wheel data) the driver models uhderestimate the subject means. Here again all the magnitudes are quite small and hence this may not be an important effect.

The comparison of the standard deviations is best made using Fig. 29. It is seen that the driver models'

tz

results are smaJJer than those of the 'subjects indicating superior lane tracking performance. In the case of ~

and Ms better agreement is evident, with model results closest to'&the

~ . ihdividual subject run data in the case of the truck. In all caset!' the magnitudes of the differences between the driver models and the subjects may not be of significance wlien the driver models are applied to real world

situa-tions.

5.3.3 RMS Differences

The RMS of the ~ifferences between the driver model and subject time

histor~es (with their mean values removed) are presented in Tables 12 and 13 and Fig. 30. For the present study the lumped subject data reported under the heading "ALL" is of interest. It is seen that the results based on the averaged runs show bet ter agreement for all variables than those based on individual runs. The agreement for the variables

tz

and ~ was similar for bath the car and the truck. In the case of the steering wheel variables

(60s and os) the agreement was much better in the case of the car . .... Again, the practical implication- àf these differences will depend upon th~ situations in which the driver models are applied.

5.3.4 Extreme Offsets on Curves

In general the data presented in Figs. 31 and 32 indicate a qualitative similarity between the extreme offsets in

tz

generated by the driver models and the subjects. The greatest differences between the 'model and subject data are found for positive offsets with the car. As a general trend it is seen that the extremes for the car are greater than those for the truck. With the driver model the same trends with curve number are observed for both the car and the truck results while the subject data 'show less similarÏ'ty.

The t-test results shown in Figs. 31 and 32 are based on 5 degrees of freedom and repres,ent a two-sided test wi th the corresponding level of