computer controlled steering system for vehicles having two independently driven wheels

Computer controlled steering system for vehicleshaving two independently driven wheels

B.C. Besselink

Agricultural Machinery Research and Design Centre, University of South Australia, Room J1-12, Mawson

Lakes, Adelaide 5095, Australia

Received 3 October 2002; received in revised form 22 January 2003; accepted 15 May 2003

Abstract

A computer controlled steering system for vehicles utilising two independent drive wheels

can be used to improve the ability of such vehicles to resist external side forces, such as that

which occur when traversing steep slopes. The objective is achieved by using an onboard

computer, utilising a specially-developed software algorithm, to positively control the steer

angles of the non-driven wheels (usually these are castors). The software algorithm uses the

mathematical relationship between the drive wheel speeds and the steer angles of the non-

driven wheels. The algorithm ensures that the turning radius produced by the drive wheel

speeds is the same as that produced by the steer angles. The vehicle motion includes

conventional turning but also rotation about the centre of the drive axle. The system provides

a non-conflicting secondary steering system able to assist the primary system when external

forces act on the vehicle. A vehicle using this system is able to have larger than usual non-

driven wheels, resulting in less design restriction and allowing such things as improved load

carrying and distribution of load compared to conventional vehicles of the type. The

integration of drive wheel speeds and steer angles of non-driven wheels maximises tractive

effort and minimises scuffing losses. The calculation intensive control system for a vehicle

described above is only feasible by the availability of relatively low cost microprocessors.

Vehicles of this type may be used in agriculture as tractors, harvesters, windrowers and

specialised off-road vehicles.

# 2003 Elsevier B.V. All rights reserved.

Keywords: Steering; Zero turn radius vehicle; Steer by wire system; Mechatronics; Computer control

E-mail address: [email protected] (B.C. Besselink).

Computers and Electronics in Agriculture 39 (2003) 209�/226

www.elsevier.com/locate/compag

0168-1699/03/$ - see front matter # 2003 Elsevier B.V. All rights reserved.

doi:10.1016/S0168-1699(03)00081-4

mailto:[email protected]

1. Introduction

In order to provide a high degree of manoeuvrability and traction, some wheeled

vehicles, such as garden tractors, windrowers and harvesters, drive left and right

drive wheels independently by means of continuously variable ratio transmissions

which allow both forward and reverse. The vehicle moves straight ahead when both

left and right drive wheels are driven forward at the same speed. Alternatively, thevehicle rotates about the centre of the drive axle when left and right drive wheels are

driven at equal and opposite speeds. However, the vehicle normally operates between

these two extremes. The absence of a differential means that if one drive wheel loses

traction, the other drive wheel is not affected and the vehicle is still able to move. In

these vehicles, the steering effect is provided solely by the drive wheels. Free-wheeling

castors at the front of the vehicle have no steering effect and only provide support for

the front section of the vehicle.

Castors are used on these types of vehicles because, as a result of their offset, theyturn under the action of sideways forces. On flat ground and shallow slopes, the side

force which turns a castor is a result of the action of the two independent drive

wheels. The castors turn to angles which provide minimum resistance to the motion

of the vehicle and correspond to the steer angles appropriate to the radius of

curvature produced by the two independent drive wheel speeds. This castor

arrangement is required, as there is no conventional system whereby an operator

can positively turn non-driven steerable wheels to the steer angles appropriate to the

radius of curvature produced by the two independent drive wheel speeds.However, when traversing steep slopes, castors present significant problems as

gravitational forces come into play. Since the castors cannot exert a side force, the

front of the vehicle tends to move down the slope due to the turning moment acting

on the vehicle. A counteracting moment is provided by a difference in traction

between the two drive wheels; but as the slope increases, traction is eventually lost.

To counter the problem with traversing steep slopes, the centre of gravity is often

moved towards the rear of the vehicle: however, this results in a tendency of the

vehicle to rear up when travelling straight up a steep hill. Castors can be locked inplace in these situations, but manoeuvrability and ease of use is reduced.

On flat ground, the use of castors also has disadvantages. Castors are typically

much smaller than the drive wheels. Hence, there is a limit to the load they are able

to carry. If higher loads are to be carried on castors, they need to be larger in order

to reduce the ground pressure. This presents design problems due to their offset.

Larger castors require more swept volume in which to turn and protrusion of the

castors from the vehicle may present problems. A higher load on the castors

produces an increase in the force required to turn them to the appropriate angles.This may produce ground damage, tyre wear problems, reduced manoeuvrability

and reduced drive efficiency. As a result of these factors, there is a limitation on the

size of a vehicle using two independent drive wheels.

It would be desirable to have a vehicle with the tractive advantages of two

independent drive wheels but having non-driven wheels which are able to resist a side

force, have no offset, and able to be of similar size to the drive wheels. This would

B.C. Besselink / Computers and Electronics in Agriculture 39 (2003) 209�/226210

increase the design possibilities with respect to weight distribution and space

considerations, and improve tractability and safety on slopes and slippery surfaces.

The aim of the current research is to develop an improved vehicle which has two

independent drive wheels but has non-driven wheels which are not castors but which

have all the manoeuvrability advantages of castors. Such a vehicle may be adapted

for use in agricultural situations, for example, as a tractor. The current drive systems

for agricultural tractors include two-wheel-drive and four-wheel-drive. The im-proved vehicle of this paper may not be as costly as a four-wheel-drive to produce,

have greater manoeuvrability and have similar performance in most situations.

Speciality agricultural vehicles such as windrowers may be able to operate on steeper

terrain than is currently possible due to improved steering behaviour but also retain

their current manoeuvrability.

2. Background

A computer controlled steering system which can be used to improve the ability of

four-wheeled vehicles having two independent drive wheels to traverse steep slopes

has been reported in the literature (Spark and Besselink, 1994). The improvement isachieved by replacing the two free turning front castors with two steerable non-

driven wheels which are positively turned to steer angles appropriate to the radius of

curvature produced by the wheel speeds of the two independently driven rear wheels.

The appropriate steer angles are determined by a microprocessor using an

algorithm based on the mathematical relationship between the wheel speeds of the

two independently driven rear wheels and the appropriate steer angles of the two

front steerable wheels. Sensors are used to determine the speed and direction of the

two driven rear wheels and actuators, controlled by the microprocessor, are used toturn the non-driven wheels to the appropriate steer angles.

Although the mathematical relationships and some analysis of the motion of the

vehicle was presented in the above mentioned paper, the analysis for the

development of a practical program control logic was not presented. The presence

of the arctangent function presents some problems when transferring the abstract to

the concrete. Another related paper (Blair and Spark, 1996) highlights a problem

with flipping of a steerable wheel by 1808 due to the typical range of the arctangent

function being restricted to �/90 to �/908.Further work developed mathematical relationships for vehicles having more than

two driving wheels and more than four wheels (Spark et al., 1996; Lu et al., 1997;

Spark and Ibrahim, 2001).

3. Theory

The radius of the turning circle of a wheeled vehicle is a result of either or both of

the following two steering effects:

B.C. Besselink / Computers and Electronics in Agriculture 39 (2003) 209�/226 211

. the radius of curvature produced by the independent wheel speeds of the left drive

wheels and the right drive wheels; and/or,

. the radius of curvature produced by the direction of the wheels of the vehicle.

Where both effects are operational, there is usually conflict between the two

effects: one effect is usually dominant. An extreme example of this conflict is a skid-

steer vehicle, such as a four-wheeled skid loader. The vehicle’s wheels are always

directed straight ahead and hence give an infinite turn radius. This conflicts with the

dominant effect: the radius resulting from the different independent wheel speedsselected by the operator. The actual turn radius will be a compromise between the

two radii. The conflict results in extreme scuffing, ground damage, tyre wear and fuel

wastage.

At another extreme is the conventional motor vehicle. The operator turns the

steerable wheels to select the turning radius. The speeds of the driven wheels are

eliminated as an effect in steering by the inclusion of a differential. Hence, there is no

conflict between the two systems.

To illustrate the point further, it can be seen that four-wheeled motor bikes withno differential have the two conflicting steering effects. The two rear drive wheels

rotate at the same speed and, in the absence of other forces, would produce an

infinite radius. The front steerable wheels produce a radius from the wheel direction.

These two radii conflict to produce a compromise radius and consequential scuffing

and ground damage.

Zero turn radius vehicles do not have any steering conflict because the non-driven

wheels are made inoperative by turning them into castors. The steering is solely from

the independent drive wheel speeds.In the steering system of this paper, the non-driven wheels are pivoted about their

vertical centreline and comprise a secondary non-conflicting (integrated) steering

system. On a steep slope the non-driven wheels transmit turning forces to the vehicle

which assist the primary steering system and improve the steerability of the vehicle.

4. Further development of mathematical model

The equations for a vehicle with the track of the front and rear being equal were

presented in the paper by Spark and Besselink (1994). The mathematical relation-

ships between the speeds of the drive wheels and the steer angles found in this paper

are detailed as follows.

The steer angles are given by the two following equations:

fL�tan�1

�b

t

�1�

vR

vL

��(1)

where b , wheel base of vehicle; t , track of vehicle, when front and rear tracks are

equal; vL , rotational velocity of left drive wheel; vR, rotational velocity of right

drive wheel and fL , steer angle of left non-driven wheel.


fR�tan�1

�b

t

�vL

vR

�1

��(2)

where fR is the steer angle of right non-driven wheel.

An understanding of the terms used may be obtained from Fig. 1 which is for the

general case where the front and rear tracks are not equal.

However, the above equations are not for the general case. It is not uncommon to

have the track of the two non-driven wheels less than the track of the driven wheels.

Hence, the following result was derived for the general case where the track of the

front wheels is different to the track of the rear wheels. As well, the previous work

did not investigate the effect of longitudinal slip on the equations. The underlying

assumption in the previous work of no slip angles on any wheels will also be assumed

in this paper.

Fig. 1 depicts a vehicle with a primary steering system using two independently

driven wheels. fL and fR are the steer angles of the front left and front right wheels

of the secondary steering system, respectively. vL and vR are the rotational wheel

speeds of the rear left and rear right drive wheels, respectively. b is the wheel base. tB

is the track of the rear wheels. tF is the track of the front wheels. R is the radius of

the turning circle of the vehicle (or radius of curvature). Clockwise rotations are

regarded as positive and have a positive radius of curvature. Note that the drive

wheels may also be mounted on the front of the vehicle and the steerable wheels on

the rear.

The effect of longitudinal slip will now be considered. The rate of rotation of the

drive axle about the centre of curvature, u+; is given by

Fig. 1. Geometry of two-wheel-drive two-wheel steering vehicle with unequal track.


u

+

�VL

R �tB

2

�VR

R �tB

2

(3)

where, R is the radius of the turning circle of the vehicle (or radius of curvature), VL

is the translational velocity of the left drive wheel, VR is the translational velocity of

the right drive wheel.

If longitudinal slip is considered, this becomes

u

+

�rvL(1 � iL)

R �tB

2

�rvR(1 � iR)

R �tB

2

(4)

where r is the radius of a drive wheel, i is longitudinal slip.

When the longitudinal slips are equal for left and right drive wheels, as well as

equal radii for the drive wheels, we obtain the following:

vL

R �tB

2

�vR

R �tB

2

(5)

So a derivation based on the relationship between the steering geometry without

slip angles and the rotational drive wheel speeds may usefully be developed for equal

slip conditions. Equal longitudinal slips will occur where traction conditions are the

same and under these conditions slip angles will not be significant.

For the front left steerable wheel,

fL�tan�1

�2b(vL � vR)

vL(tB � tF ) � vR(tB � tF )

�(6)

We can see that if tB �/tF , the equation simplifies to the form of the equation

developed by Spark and Besselink (1994).

Similarly, for the front right steerable wheel,

fR�tan�1

�2b(vL � vR)

vL(tB � tF ) � vR(tB � tF )

�(7)

It may be desirable to have a vehicle using two independently driven wheels and

only one steerable wheel at the front. This corresponds to the case where tF �/0.

Hence, the equation for the steer angle is as follows:

f�tan�1

�2b(vL � vR)

tB(vL � vR)

�(8)

where f is the steer angle of a lone non-driven wheel.

Note that this equation also applies to four-wheeled vehicles with two steerable

wheels on a rigid axle which is rotated.


Further relationships may be determined for steerable wheels which do not turn

about their vertical axis but an axis parallel to it (much as in a conventional motor

vehicle). However, in this paper the discussion is limited to the motion of a steerable

wheel turning about its vertical axis.

5. Motion analysis

The mathematical relationship developed requires careful analysis along with that

of the real world motion of the vehicle in order to develop the program logic for the

steering system.

The analysis will be for the case where steering control is by the operator varying

the wheel speeds of each of the two independent drive wheels and where there are

two steerable non-driven wheels. For simplicity, it will be taken that tB �/tF . The

analysis for the general case where tB "/tF and for the specific case where tF �/0 is

similar.

The aim is to emulate or improve upon the motion of a vehicle with real castors by

using a computer controlled steering system. Essentially, real castors have unrest-

ricted turning. When a vehicle is moving straight forward the castor is trailing the

axis of turning: and when moving straight backwards, it is in front of the axis of

turning. When the vehicle movement changes from forward to reverse, and vice

versa, castors will flip through 1808.The basic motions of the vehicle are defined as follows. Rotation is defined to

occur when the centre of the turning circle lies on or between the centres of the rear

drive wheels. Turning is defined to occur when the centre lies outside this region,

when translational motion also occurs.

5.1. Forward mode

If vL �/0 and vR �/0, the vehicle is travelling in a forward direction, either

turning or moving in a straight line (Fig. 2). Under these conditions, equations (1)

and (2) produce raw angles which need no modification by the program logic.

Fig. 2. Forward mode.


5.2. Backward mode

If vL B/0 and vR B/0, the vehicle is travelling in a backward direction, either

turning or moving in a straight line (Fig. 3). A backward right turn occurs when

vL B/vR B/0 (taking sign into consideration) (Fig. 3a). A backward left turn occurs

when vR B/vL B/0 (Fig. 3b). In the backward mode, unmodified equations (1) and

(2) produce raw angles which need modification by the program logic.For a backward right turn, the equations produce raw angles between 0 and 908:

the raw angles need the subtraction of 1808.For a backward left turn, the equations produce raw angles between 0 and �/908:

the raw angles need the addition of 1808.However, for straight backward (Fig. 3c), the program logic needs to give either

180 or �/1808 so that the vehicle can move from a backward turn to straight

backward. If the program logic does not alter the raw angle (which is 08), a

‘‘flipping’’ of the non-driven wheels will occur.A modified steer angle of �/1808 has been arbitrarily chosen for the straight

backwards mode since there can only be one actual value for angular position. This

result is achieved if the logic for the backward left turn is used.

5.3. Rotation modes

Clockwise rotation occurs when vL ]/0 and vR 5/0 where vL "/vR . Equations(1) and (2) produce raw angles which need modification by the control program

logic; otherwise, when using raw angles, one of the non-driven wheels will ‘‘flip over’’

(rotate 1808) when transitioning from a turn (Fig. 4a) to a rotation (Fig. 4c).

In order to produce the desired configurations for the steerable wheels for

clockwise rotation about a centre between the drive wheels (as in Fig. 5a), when

vL �/0 and vR B/0, the raw angle for the right steerable wheel needs the addition of

1808.A singularity occurs in the transition from turning to clockwise rotation when

vL �/0 or vR �/0. Mathematically, this results in one steer angle being undefined;

and, in reality, corresponds to rotation about the vertical axis of one rear drive

Fig. 3. Backward mode.


wheel. Clearly, fL needs to be 908 when vL �/0 (Fig. 5b); and fR needs to be 908when vR �/0 (Fig. 5c).

The analysis is similar for anticlockwise rotation (Fig. 6).

5.4. Modified steer angles

The flowcharts of the logic for modifying the raw steer angles, fL and fR , fromthe basic equations to left modified steer angle, fLM , and right modified steer angle,

fRM , are shown in Figs. 7�/9. These flowcharts represent modules in the overall

flowchart for the steering system in Fig. 10.

The modifications to the raw angles from equations (1) and (2) which result from

this analysis are shown in Table 1.

Fig. 4. ‘‘Flipping’’ of non-driven wheel when using raw angles.

Fig. 5. Clockwise rotation.

Fig. 6. Anticlockwise rotation.


5.5. Stationary mode

When vL �/0 and vR �/0, there is no mathematical solution for both the steer

angles. This situation may occur prior to moving, or when the operator stops the

vehicle during the course of its motion (but does not shut the vehicle down). The

most suitable solution is for the program to use the previous steer angles. In effect,

algorithm returns to the start to read the wheel speeds.

This logic may be combined with a shutdown sequence which sets the steer angles

to 08.

Fig. 7. Module: calculate modified angles for rotation about right drive wheel.

Fig. 8. Module: calculate modified angles for rotation about left drive wheel.


5.6. Turning limits

Although the problems of the mathematical solutions to the steer angles have been

overcome in the above explanation of segments of the control program logic, the

next set of problems relate to the requirement for unlimited turning of the non-

driven wheels. If the non-driven wheels are to at least emulate castors, there must be

no restriction on the turning of the non-driven wheels.

As the system currently stands, the possible steer angles able to be outputted from

the program for the non-driven wheels range from �/180B/fL 5/180 and �/180B/

fR 5/180. This corresponds to the angular positions able to be measured by a

position sensor mounted on a non-driven steerable wheel.However, this system is not satisfactory if unrestricted turning is required. The

control logic must provide information to enable the actuators to turn the non-

driven wheels in the correct direction. This is possible, as the system now stands, for

transitions from left to right turns, and vice versa, in the forward direction and for

rotations. For example, for fL �/�/208 to fR �/208, we obtain a difference (final

minus initial) of �/408; and so the positive sign indicates a clockwise turning of the

left non-driven wheel and an amount of turning of 408 For fL �/208 to fL �/�/208,we obtain a difference of �/408 However, when transitioning from a backward left

turn to a backward right turn, and vice versa, this is not possible. For example,

fL �/1608 to �/1608, we obtain a difference of �/3208 when �/408 is required (a

clockwise turn of 408 of magnitude 408).

Fig. 9. Module: calculate modified angles (for all other cases).


Fig. 10. Flowchart of steering system.


Table 1

Modified steer angles for various modes of motion

Mode of motion Wheel speed conditions Modified steer angles Figures

Left, fLM Right, fRM

Stationary vL �/0 vR �/0 PreviousfLa PreviousfR

b None

Forward vL �/0 vR �/0 fL fR Fig. 2

Backward Backward right turn vL B/0 vR B/0 vL B/vR fL�/180 fR�/180 Fig. 3a

Backward left turn vL B/0 vR B/0 vL �/vR fL�/180 fR�/180 Fig. 3b

Straight backward vL B/0 vR B/0 vL �/vR fL�/180 (or 180) fR�/180 (or 180) Fig. 3c

Clockwise rotation About a centre between drive wheels vL �/0 vR B/0 fL fR�/180 Fig. 5a

About left drive wheel vL �/0 vR B/0 90 /tan�1 �b

t

� �/�/180 Fig. 5b

About right drive wheel vL �/0 vR �/0 /tan�1b

t

� �90 Fig. 5c

Anticlockwise rotation About a centre between drive wheels vL B/0 vR �/0 fL�/180 fR Fig. 6a

About left drive wheel vL �/0 vR �/0 �/90 /tan�1 �b

t

� �Fig. 6b

About right drive wheel vL B/0 vR �/0 /tan�1 �b

t

� �/�/180 �/90 Fig. 6c

a fL is left steer angle (raw).b fR is right steer angle (raw).

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5.7. Virtual angles

To overcome this problem, a set of virtual angles, fV , will be calculated by the

control program. These virtual angles can extend outside the physical angle range of

the steerable wheels. The effect of the program logic will be to give a range of

possible virtual steer angles of 9/1808 with respect to the previous steer angle. The

modified steer angles will also become virtual angles even if they are within the rangeof physical angles. This is to facilitate program decisions with reversals of direction

later.

If the current steer angle, fC , is zero or positive, the modified raw angles in the

range �/180B/modified angleB/f�/180 will have 3608 added to them, shown as the

shaded area in Fig. 11a.

So, for the example of the transition of a backward left turn to a backward right

turn, from 1608 to �/1608 (modified angles), the second angle of �/160 becomes �/

2008. Hence, the difference is �/408: the required value to provide the requiredinformation.

Similarly, if the current steer angle, fC , is negative, then the modified raw angles

in the range �/180B/modified angleB/f�/180 will have 3608 subtracted (Fig. 11b).

A flowchart illustrating the logic for the front right steerable wheel (producing

fRV ) is shown in Fig. 12. The logic for the left steerable wheel is the same.

5.8. Reversal of direction

The algorithm developed, so far, emulates the behaviour of castors. As a result,

when reversing the vehicle in a straight line, the non-driven wheels turn 1808 from theprevious positions. Since the non-driven wheels do not have a castor offset, they are

stable in both directions of rolling rotation. Hence, it is not necessary that they flip

around. The advantage not flipping around is the reduction in time for the actuators

to position the non-driven wheels. Where the change in motion is an exact mirror

image, the time is reduced to zero. It is not uncommon for an operator to move a

vehicle backwards and forwards repeatedly. With the algorithm as it now stands, the

non-driven wheels would be flipping constantly.

Fig. 11. Representation of the correction of modified angles to virtual angles.


A reversal of direction is usually considered to be a change in the direction of

rotation of both drive wheels. However, it is not particularly useful to think in terms

of changes in the direction of rotation of drive wheels. It is more useful to look at

reversals in terms of steer angles. The solution to all reversals of direction is to

consider that each wheel speed ratio has two possible steer angles instead of one:

these are 1808 apart. The correct steer angle is the steer angle closest to the previoussteer angle (within 908 of the previous steer angle). However, if each non-driven

wheel is considered individually, it can result in the non-driven wheels turning in

opposing directions (e.g. one clockwise and the other anticlockwise).

With the algorithm developed, the appropriate pair of steer angles is selected by

checking the combined change in steer angle: if the magnitude of the combined

change is greater than 1808, subtract or add 1808 depending on whether the new steer

angle is greater than the last steer angle or not. This method stops contrary turning

of the steerable wheels.A flowchart illustrating the logic is shown in Fig. 13. Since both steer angles

always have the same sign and increase or decrease together, only one wheel needs to

be tested for reversal (in this case the left steerable wheel).

6. Experimental

The experimentation is to be conducted in three phases. The first phase was a

computer simulation of the steering control program. The algorithms described in

this paper were used to produce a program in Visual Basic. The graphical display of

the simulation uses two slide controls as wheel speed inputs and shows the track and

Fig. 12. Module: calculate virtual angles (for front right steerable wheel).


wheel base to scale in plan view, as well as the steerable wheels. Lines representing

the turning radii are drawn by the program and show by their intersection on the

centreline of the drive wheels that the result is correct (a geometric fact). This

simulation visually verifies that the logic of the system is correct.

The second phase was a benchtop simulation using the hardware sensors to be

used in the final test vehicle. The software for the benchtop simulation combined the

programming from the computer simulation with additional code for the actuators

and sensors. A front steerable wheel steering actuator was emulated by a 3 V electric

motor with a worm drive gearbox. The output shaft of the gearbox has a pointer

indicating the direction of motion of the steerable wheel. Also connected to the shaft

is an absolute optical encoder, used to obtain the current steer angle. The steer angle

was changed using relays to switch the direction of the electric motor. A rear drive

wheel was emulated using a 3 V electric motor, and the wheel speeds and direction

were obtained from an attached 2-channel rotary pulse generator. The encoders,

pulse generators and relays were interfaced with a laptop computer via a data

acquisition card. The timers of data acquisition card were used to obtain the drive

wheel speeds from the pulse frequencies. The benchtop simulation verified that the

above mentioned hardware was suitable for a test vehicle in order to implement the

algorithms developed in the analysis.

The third phase is a test vehicle. A zero turn radius mower has been modified by

replacing the two front castors with computer controlled non-driven steerable front

wheels. The vehicle is steered by means of left and right steering levers which in turn

control the speed of the left and right drive wheels, respectively, by means of

continuously variable ratio drives. The front steerable wheels are turned by means of

Fig. 13. Module: adjust virtual angles for reversal of motion (using left steerable wheel).


12 V DC motors. The control software is in the early stages of assessment using this

hardware.

The tractive performance of the test vehicle using the computer integrated steering

drive system is to be measured in order to quantify the improvements and when these

are significant. This may also lead to further refinements of the steering system.

7. Discussion

The feasibility of replacing the conventional castors of a zero turn radius vehicle

with computer controlled non-driven steerable wheels has been demonstrated by the

development of a computer simulation and benchtop simulation. In the simulations,

the entire behaviour of castors in terms of manoeuvrability has been emulated and

improved upon. By positively controlling the steerable wheels using an onboard

computer with the steering control system developed, the secondary steering system

is able to assist the primary steering system of the independent drive wheels. Thedevelopment of the software so that reversals of vehicle direction do not result in the

excessive turning of the non-driven wheels is a further improvement over vehicles

using conventional castors.

Further enhancements could include replacing the mechanical levers with joysticks

so that the software can become aware of the operator’s intentions rather than only

using the actual wheel speeds. With some further development of the software, and

with the appropriate hardware, the driver interface can be changed to a steering

wheel instead of two levers. In this case, the operator selects the turning radius andthe average speed, and the computer must also control the wheel speeds as well as the

steerable wheel angles. A steering wheel would remove the problem which occurs at

zero wheel speed, that is, determining the direction in which the operator would

desire to move the vehicle.

A hydraulic/hydrostatic drive system is considered to be the best system to use to

provide the independent drive for the two drive wheels. However, electric motors or

controlled differentials may also be used.

An underlying assumption of the control algorithm is that the radius of the drivewheels is always constant and that the wheels do not sink into the surface on which

the vehicle is moving. A change in wheel radius (for example, from lower inflation)

leads to the algorithm using an incorrect wheel speed (as it is determined from the

revolutions of the wheel). With under-inflation, the algorithm uses a speed which is

too high. The effect of slip angles and unequal longitudinal slip has also not yet been

accounted for and needs further development.

Various feedback loops may be incorporated into the steering system. For

example, linking the rate of change of wheel speed to the rate of change of steerangle, so that an error margin for scuffing and skidding may be set at an appropriate

value.

Further sensitivity analysis needs to be conducted at an experimental level on the

effect of error in reading wheel speed on error in steer angle. It is anticipated that

maximum error will occur at low speeds and at around 08 steer angle.


8. Conclusion

The research outlined in this paper has demonstrated the feasibility of an

improved vehicle which utilises two independent drive wheels for motion and

steering, and a computer steering system controlling steerable non-driven wheels.

Such a vehicle is not only feasible but practical, due to the availability of low cost

microprocessor technology. This vehicle will have all the tractive advantages of twoindependent drive wheels with none of the disadvantages. The computer-controlled

non-driven wheels provide a non-conflicting secondary steering system to assist the

primary system when side forces act on the vehicle. The major advantages of a

vehicle using this system are the ability to traverse steep slopes, and the ability to

have larger wheels and improved load carrying and distribution of load compared to

conventional vehicles of the type.

Acknowledgements

The author would like to thank Dr Ian Spark for his past assistance.

References

Blair, D.B., Spark, I.J., 1996. Computer controlled integrated steering/drive system for vehicles. ASME

Computers in Engineering Conference, California, USA.

Lu, J., Spark, I.J., Vains, G.G., Spriggs, K.R., 1997. Computer integrated steering/drive systems with

steering wheel control. Proceedings on I.E. Aust. Conference on Control Engineering, Sydney,

Australia, p. 236�/241.

Spark, I.J., Besselink, B.C., 1994. Zero turn radius vehicle incorporating computer-controlled ‘intelligent

castors’. ASME Computers in Engineering Conference, Minneapolis, USA, Book No. G0875B, p.

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Spark, I.J., Ibrahim, M.Y., 2001. Integrated mechatronics solution to maximise tractability and efficiency

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computer controlled steering system for vehicles having two independently driven wheels

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