AU2004203063A1 - Improved off road vehicle - Google Patents

Description

IMPROVED OFF ROAD VEHICLE The invention describes means of manoeuvring wheeled vehicles such as conventional tractors, tractors with four wheel steering and gantry tractors so that errors in the path of these vehicles relative to the desired path of the vehicles is minimised by ensuring that rotation errors are eliminated simultaneously with translation errors. For conventional tractors and tractors with four wheel steering the driver can be aided by an on-board system which indicates the deviation of the steering wheel (or joy stick) from its optimum position.

Alternatively all the vehicles referred to above can be manoeuvred automatically using the techniques described. The manoeuvrability and tractive effort of these vehicles can be increased and the ground damage they inflict reduced if both the wheel angle steering effect and the wheel speed steering effect are enabled such that they both tend to produce the same centre of curvature. A method of automatically manoeuvring a gantry tractor through right angle turns, U turns and narrow gates is also described.

IMPROVED OFF ROAD VEHICLE Technical Field The invention relates to a means of increasing the tractability, stability, manoeuvrability and safety of wheeled vehicles while at the same time minimising fuel consumption and damage to the ground traversed.

Background There are two basic methods of manoeuvring a wheeled vehicle. One method is to turn one or more steerable wheels. The other method is to drive one or more left hand wheels independently of one or more right hand wheels. In general these two steering systems will conflict with one another when each tries to achieve a different centre of curvature for the path of the vehicle. This conflict causes a braking effect, which results in fuel wastage, scuffing of the ground traversed and associated tyre wear.

The traditional method of avoiding conflict between the two basic steering systems is to disable one system so that it cannot conflict with the remaining system. For example in a traditional road vehicle, the steering effect of driving the drive wheels at the same speed is eliminated by incorporating a differential into the drive train to the driving wheels. Conversely in a zero turn radius vehicle which is steered by driving the left hand drive wheel independently of the right hand drive wheel, the steering effect of one or more non driven wheels is eliminated by rendering the latter free to turn to any angle. That is, they are turned into castors.

The Problems to be solved Unfortunately, making one steering system compliant with the other leads to stability and traction problems when the vehicle is operated in difficult conditions. If the sideways, forwards or backwards force on the vehicle increases and/or the coefficient of friction between the tyres and the ground decreases, the system used to manoeuvre the vehicle will eventually fail. For example, the differential becomes the Achilles' Heel of the traditional tractor when working on steep terrain, and especially in slippery conditions. In this environment weight is transferred from the uphill drive wheel making it liable to spinning. Although the stability of the traditional tractor can be improved by the use of a limited slip differential or a lockable differential, it is somewhat illogical to provide a differential in the first instance along with a subsidiary system which either impedes its operation, or stops it altogether.

Similarly it can be seen that the Achilles' heel of the zero turn radius vehicle when traversing a steep slope are the non-driven castors. Because these castors cannot exert any sideways force on their end of the vehicle, the tendency for this end to swing down the hill can only be prevented by the two drive wheels applying opposing forces to the vehicle even though they may be driven at the same speed. As the steepness of the slope traversed increases, the uphill drive wheel eventually loses traction and the front of the vehicle swings down the hill. In short, the grip of the drive wheels on the ground is exhausted by the drive wheels fighting against each other in providing the torque necessary to stop the castored end of the vehicle swinging down the hill.

A method of overcoming the problems of traction and stability is to allow both steering systems to operate, but to allow one steering system to dominate the other. In this case the stability and traction problems are reduced at the expense of the introduction of a scuffing problem on turning.

For example the elimination of the differential from the rear axle of four wheeled motor bikes improves traction at the expense of introducing a scuffing problem.

A more extreme example of conflict between the two basic methods of manoeuvring a vehicle occurs in skid steer vehicles (both wheeled and tracked). In this case the dominant steering system is the independent drive to the right hand and left hand drive wheels or tracks. The second enabled but dominated steering system is the wheel or track angle which is usually fixed at zero degrees and tends to drive the vehicle straight ahead. The conflict between the two steering systems causes the vehicle to take a path which is a compromise between the paths that would be produced by each system alone. This method of manoeuvring causes extreme scuffing with associated ground damage, fuel wastage and tyre or track wear.

In traditional vehicles, rotation and translation are generally linked. Translation of the vehicle along a curved path usually involves rotation, and rotation of the vehicle always involves translation. As a consequence, rotation and translation in a confined space can be a problem.

Vehicles steered by independently driving the left and right hand wheels have improved manoeuvrability since they can be made to rotate about their own centre. This is pure rotation without translation). Manoeuvrability can be further increased by allowing translation in any direction without the need for rotation. This pure translation is sometimes referred to as crab steering.

The solution proposed previously

A

The essential feature of the invention previously proposed by Spark (Australian Provisional Application PR 0473 (03-10-2000) and Patent Cooperation Treaty Application PCTIAUI/01247 (03-10-2001)) is that both basic systems of manoeuvring a vehicle are to be used in unison so that they both try to produce the same centre of curvature for the path of the vehicle. With both systems reinforcing each other it will be possible to effectively manoeuvre the vehicle in much more difficult conditions than if only one system was used with the other system either disabled or dominated. Furthermore any centre of curvature can be selected by the driver, which further improves the manoeuvrability of the present invention. This enables the invented vehicle to execute either pure rotation or pure translation or any combination of translation and rotation.

The preferred means of driver control of the four wheel steering/four wheel drive variant of the previously proposed invention is by means of a rotatable joystick. This maximises the manoeuvrability of the vehicle by allowing independent translation and rotation of the vehicle. In this means of driver control, the direction of translation of the vehicle is determined by the direction of displacement of the joystick, whereas the rotation of the vehicle is determined by the degree of rotation of the joystick. The amount of displacement of the joystick determines the root mean square of the four wheel speeds. Pure translation occurs when the joystick is displaced but not rotated. Pure rotation occurs when the joystick is twisted as far as it will go.

Alternatively, two separate devices could be used for driver control. One joystick could be used to determine the radius of curvature of the path of the vehicle and the root mean square wheel speed, and the second joystick could be used to determine the direction of the centre of curvature.

Alternatively, a joystick, steering wheel, knob or lever could be used to determine the radius of curvature of the path of the vehicle, and a separate joystick could be used to determine the direction of the centre of curvature of the path of the vehicle and the root mean square wheel speed.

Deficiency of the previously proposed invention The patent applications cited above enumerate the control equations that must be satisfied if the steering effect of the wheel speeds is to be identical to the steering effect of the wheel angles.

However these applications do not take into account either the slip angles of the tyres or the longitudinal slip of these tyres. If these effects are ignored the effective centre of curvature of the path of the vehicle may be different the centre selected by the driver.

Drawings In order that the present invention may be more clearly understood, some preferred embodiments thereof will now be described with reference to the accompanying drawings. Although a four wheel steering/four wheel drive vehicle will be described, it will be appreciated that the principles invoked can be applied to any vehicle with more than one wheel.

Figure 1 shows the relationship between the actual wheel angle the effective wheel angle and the slip angle a.

Figure 2 shows the desired relationship between the effective wheel angles and the effective wheel speeds for a four wheel steering/four wheel drive vehicle.

Figure 3 shows a means of directly measuring the forces acting on any wheel and the means of driving and turning this wheel.

Figure 4 shows an alternative means of indirectly measuring the forces acting on any wheel and the means of driving and turning this wheel.

Figure 5 shows the relationship between the forces acting on the wheel when resolved in the wheel frame of reference and the vehicle frame of reference.

Figure 6 shows the relationship between the angle of front and rear castors, the radius of curvature of the path of each castor and the centre of curvature of the path of the vehicle.

Figure 6 also shows the relationship between angle of each castor and its velocity across the ground and the angles of the four wheels and the velocity of these wheels across the ground.

Figure 7(a) shows the initial castor angle and wheel angle configuration for a simplified vehicle.

Figure 7(b) shows the corrected wheel angle configuration when the measured slip angles have been taken into account.

Figure 8 shows the range of wheel angles required if turning centres close to the centre of the vehicles are not required.

Figure 9(a) is a plan view of the most.general four wheel steering/four wheel drive variant of the invention.

Figure 9(b) shows three alternative driver interfaces for this vehicle.

Figure 10O(a) depicts the special case where the centre of curvature of the path of the path of the vehicle lies on the transverse axis of the vehicle.

Figure 10(b) shows two alternative driver interfaces for this vehicle.

Figure 11(a) depicts the special case where the centre of curvature of the path of the path of the vehicle lies on the axis of the rear wheels.

Figure 11(b) shows two alternative driver interfaces for this vehicle.

Figure 12(a) shows the three differentials and three steering differentials required to force all four wheels to rotate at the speeds where their steering effects are identical and identical to the steering effect of all the wheel angles.

Figure 12(b) shows the detailed structure of each differential and its associated steering differential.

Figure 13(a) shows that when the centre of curvature of the path of the vehicle lies on the transverse axis of the vehicle, the central differential and associated steering differential are not required.

Figure 13(b) shows that when the centre of curvature of the path of the vehicle lies on the axis of the rear wheels, three differentials and three associated steering differentials are required.

Figure 13(c) shows that when the centre of curvature of the path of the vehicle lies on the transverse axis of the vehicle, the front differential and associated steering differential can be replaced with two pair of right angle drives.

Figure 13(d) shows that when the centre of curvature of the path of the vehicle lies on the transverse axis of the vehicle, the rear differential and associated steering differential can be replaced with two pair of right angle drives.

Figure 14(a) shows a four wheel steering/four wheel drive vehicle where four steering differentials are integrated with four speed reduction gearboxes close coupled to the wheels.

Figure 14(b) shows the construction of an integrated speed reduction gearbox/steering differential.

Figure 15 shows the layout of the hydrostatic drives to the steering motors.

Figure 16(a) shows the layout of the hydrostatic drive to the steering motors close coupled to the four rear wheels where the steering effect of the speed of all four wheels is identical to the steering effect of the angles of all six wheels.

Figure 16(b) shows the construction of an integrated speed reduction gearbox/steering differential suitable for driving an inner drive wheel.

Figure 17 shows the layout of a simplified hydrostatic drive to the steering motors close coupled to the four rear wheels.

Overcoming the deficiencies of the previously proposed invention.

The essential feature of the present invention is that the slip angle of the tyres and the longitudinal slip of these tyres are taken into account so that the difference in the effects of the two basic steering systems is reduced, if not totally eliminated.

Reference to Figure 1 shows that the effective angle of any wheel is given by the equation: a Where is the actual wheel angle, a is the slip angle of the tyre, V is the velocity of the wheel across the ground, Fy is the Longitudinal force on the wheel (in the plane of the wheel) and Fx is the Lateral force on the wheel (parallel to the axis of the wheel) In this invention logarithmic slip is used as a measure of longitudinal slip i. It is defined by: i In('r/ V cos a) Where r, is the effective radius of the wheel, a is the slip angle and o' is the actual speed of rotation of the wheel. Note that the same equation can be used for both traction and braking, where i will be negative for the latter case.

Hence the effective speed of rotation of the wheel is given by: 0) V cos a re o' exp[- i] The preferred embodiment In the four wheel steering/four wheel drive variant of the invention depicted in Figure 2, an internal combustion engine I drives two right hand variable displacement hydraulic pumps 2 and 3 which in turn drive hydraulic motors 4 and 5 mounted in the steerable front and rear right hand wheels respectively. The internal combustion engine I also drives left hand variable displacement pumps 8 and 9 which in turn drive hydraulic motors 10 and 11 which are mounted in the steerable front and rear left hand wheels 12 and 13 respectively The effective angles of the wheels 6,12, 7 and 13 are shown as 01, 2, 03 and 4 respectively.

The effective rotational speed of the wheels 6, 12, 7 and 13 are ao, o 2 w 3 and 04 respectively.

The driver controls the vehicle by selecting the radius of curvature of the vehicle's path and the sense of rotation by rotating the joystick 24. If the joystick 24 is not turned the radius of curvature of the path of the vehicle will be infinity and the vehicle will move in a straight line parallel to the direction of displacement of the joystick 24. If the joystick 24 is twisted as far as it will go in a clockwise direction, the radius of curvature of the path of the vehicle will be zero and the vehicle will rotate clockwise about its own centre. Between these two extremes the radius of curvature of the path of the vehicle is given by: R cot(90 0 (Rx +R)I2/t t Where t is the track of the vehicle, 0 is the rotation of the joystick and 0, is the maximum rotation of the joystick 24.

If the driver displaces the rotatable joystick 24 at an angle yV to the straight ahead position, the direction of the of curvature of the path of the vehicle will by at right angles to the direction of joystick displacement and R x and R. will be given by the following equations:

R

x R/(tan 2 V 1 2 Rcos

T

and R Rtan /(tan 2 y 1 2 RsinW The driver selects the direction of the centre of curvature by displacing the joystick 24 at right angles to this direction. The centre of curvature of the path of the vehicle is now specified by the two components R. and Ry. He selects the root mean square of the four wheel speeds by the amount of displacement of the joystick 24.

The control system then rotates the four drive wheels to the following angles: tan&0 (b/2-Rr)I(R x tan (41' aI) tan 2 (b/2-Rr tan(4' a 2 tan 6 3 (b/2+Ry)/(R x tan( 43' a3) tan 4 (b/ 2 +Rr)/(Rx +t/ 2 tan 4 a4) Where b is the wheel base of the vehicle, R. is the displacement of the centre of curvature forward of the centre of the vehicle and R x is the displacement of the centre of curvature to the right of the centre of the vehicle.

The amount of displacement of the joystick d determines the root mean square of the four wheel speeds (RMSWS) according to the equation: RAtWS Kd (w c, +c) 2 where K is an appropriate constant.

The individual wheel speeds are given by the equations: o, KdR, RMSR coi'exp[- iI] where R 2 (b 2- R 2 -t/2) 2 a2= KdR 2 RMvSR w 2 'exp[- idi where J4 (bI/2 -Ry) 2 -it/2) 2 o3= KdR 3 I RMSR c 3 1 exp[-i 3 W where R32 =b2R 2+(R w04 KdR 4 /RMSR 04-exp(-isQ where R42.-(b2+Rr 2 +(RX-l-t/2) 2 Arnd RMSR is the root mean square radius, which is given by: RAM= 2 1 R 2 4+b Note that when the rotation of the joystick 0 is a maximum the radius of curvature will be zero and the direction of the displacement d of the joystick 24 will be immaterial. It will be natural for the driver to push the joystick 24 forward in this case to commence rotation. Pulling the joystick back will commence rotation in the opposite direction.

If the above equations for wheel angles and wheel speeds are satisfied then the two basic methods of steering the vehicle will reinforce each other. Such a vehicle would combine the traction and stability of skid steer vehicles with the non scuffing advantages of traditional road vehicles. However the vehicle described above has much greater manoeuvrability since it is capable of both pure rotation and pure translation (in any direction).

As slip angles and longitudinal slip are difficult to measure on a continuous basis, these parameters will be estimated from the measurement of lateral force on each wheel the longitudinal force on each wheel Fy, and the vertical force on each wheel F,.

These forces will be measured by means of load cells 24 attached to the support for each wheel.

In order to eliminate short-term transient) effects these forces will be averaged over a period of say 2 seconds for Fx and FY, and 5 seconds for F,.

In the present invention, only the linear component of the slip angle will be corrected for. This will lead to full compensation in the linear region of the lateral force versus slip angle curve and partial compensation outside this region. Full compensation for slip angle outside the linear region is not desirable as it could lead to instability in the angle control system. In the present invention the maximum slip angle compensation will be less than 10 degrees.

The slip angle correction a' is given by the equation: a' Fx/C, Where Ca is the cornering stiffness, which is given by the equation: C, (dF/ da),,o KnF z Kn' Where and n and constants which characterise the tyre. In general n will lie between and 0.8.

Thus a' Fx/( KnFz n In the present invention, only the linear component of the longitudinal slip will be corrected for.

This will lead to full compensation for longitudinal slip in the linear region of the Longitudinal force versus longitudinal slip curve and partial compensation outside this region. Full compensation for longitudinal slip outside the linear region is not desirable as this may lead to instability of the wheel speed control system at high longitudinal slips. In the present invention the maximum longitudinal slip compensated for will be 0.1.

The longitudinal slip compensated for is given by the equation: i F/C, Where C, is the gradient of the longitudinal force Fy versus longitudinal slip curve, and is given by: C, (dF/di)"o KmF m Km' Where Km, Km' and m are parameters which characterise the tyre.

Thus i' KmFz m Thus in order to compensate for slip angle Fx and Fz must be measured continuously and the constants Kn, Kn' and n determined for the tyres used.

Similarly in order to compensate for longitudinal slip i, F, and Fz must be measured continuously and the parameters K, Kin' and m determined for the tyres used.

An onboard computer will calculate the slip angle compensation and longitudinal slip compensation i for each wheel. These two values will then be used in the actual wheel angle and actual wheel speed control equations.

Figure 3 shows one means of measuring Fx, Fy and Fz using a triaxial load 14 cell fixed to the shaft 15 used to turn each wheel about a vertical axis. The lower end of the vertical shaft 15 is supported by a roller bearing 16, which allows the shaft to rotate and slide freely (and tilt a small amount). The top of the load cell 14 is supported by the chassis via a self aligning bearing.

The laws of the lever can then be used to deduce the force exerted on the wheel 6 through the contact patch from the forces measured by the load cell 14.

The wheel angle is measured and the wheel turned to the correct angle by a steering motor 18, which is connected to the top of the vertical shaft 15 by means of an Oldham coupling 19. This coupling allows torque to be transmitted to the vertical shaft without any lateral, longitudinal or vertical force being transmitted to the vertical shaft Figure 4 shows an alternative configuration where the triaxial load cell 20 is connected to the vehicle chassis 22. In this case the load cell 20 measures Fx', Fy' and Fz' relative to the vehicle frame of reference. In this case the top of the vertical shaft is connected to the load cell by means of a ball joint 27. A disadvantage of this configuration is that it is more difficult to rotate the vertical shaft 23 by means of the steering motor 28. In this case the Oldham coupling 29 needs to surround the vertical shaft 23, such that the input to the coupling is supported by the chassis via a roller bearing 31 and rotated by the steering motor 28 by means of gears, sprockets 32 and chain 33 or toothed pulley 34 and toothed belt 35. The output of the Oldham coupling 29 is connected to the vertical shaft 23.

Figure 5 shows how the forces relative to the wheel frame of reference can be deduced from the forces relative to the vehicle frame of reference by means of the following equations.

Fy Fy' cos 4' Fx' sin4' Fx Fx' cos Fy' sin Fz Fz' where 4' is the actual wheel angle .As an alternative to deducing the linear portion of the slip angles and longitudinal slips of the wheels, the whole slip angles and whole longitudinal slips can be measured on a continuous basis.

In the present invention slip angles a and true longitudinal slip i are measured by means of two castors 36 and 37. These castors are pressed against the ground traversed by some form of spring (either mechanical or pneumatic). Each castor measures the direction and velocity of movement of the castors relative to the ground traversed. The angle and velocity of the castors allow the centre of curvature of the path of the vehicle and the velocity of the centre of the vehicle to be calculated. The slip angle and true longitudinal slip of each wheel can also be calculated.

Although the two castors can be located anywhere on the body of the vehicle, accuracy is increased if they are as widely separated as possible. In the derivation below the front castor 36 is located midway between the front wheels and the rear castor 37 is located midway between the rear wheels.

Reference to Fig 6 shows that +F and *R are the rotation of the front and rear castors from the straight ahead position in a clockwise and anti clockwise direction respectively. RF and RR are the radius of curvature of the path of the front and rear castors respectively.

The displacement of the centre of curvature of the path of the vehicle to the right of the vehicle R, is given by the equation: R, RR cos OR RF cOS OF RF/RR COS OR/COS OF VFNR where VF and VR are the velocity of the front and rear castors respectively.

The displacement of the centre of curvature of the path of the vehicle forward of the transverse axis of the vehicle Ry is given by the equation: b/2 Ry RF sin (F and b/2 Ry RR sin 4R Where b is the wheel base of the vehicle.

Adding the last two equations yields: b RpsinOF RRsinOR Substituting for RR where RR RF COS OF COs OR yields: RF b/(tan OR tan OF) COS p And R b/(tan *R tan 4F) COS OR Rx b/(tan OR tan 4F) and Ry b(tan OR tan +F)/2(tan OR tan Fp) The effective wheel angles and slip angles can now be calculated from the equations: tan 01 tan ai) tan OF/(1 t(tan R tan 4p)/2b) tan 2 tan (k a 2 tanF F/(1 t(tan 1R tan4 F)/2b) tan 03 tan (43' a 3 tan R /1(1 t(tan OR tan 4F)/2b) tan (4 tan (14' a 4 tan OR t(tan 4R tan OF)/2b) Fig 6 also shows the relationship between the castor speeds and angles and the wheel speeds and angles.

The rate of rotation of the vehicle 0 is given by: f VF/RF Vi/R 1 V2/R 2 V3/R V4IR 4

VR/RR

Where VF, VR, VI, V2, V3, and V 4 are the velocities of the front and rear castors and the front left wheel 12, the front right wheel 6, the rear left wheel 13 and the rear right wheel 7 respectively.

RF,

RR, RI, R 2 Z R3, and R 4 are the radii of curvature of the path of the front and rear castors and the front left wheel 12, the front right wheel 6, the rear left wheel 13 and the rear right wheel 7 respectively.

V VF(Rx t/ 2 cos F/Rx cos 11

V

2 VF(Rx t/2) cos *F/Rx coS 42

V

3 VR(Rx t/2) cos (R/Rx cos

V

4 VR(Rx t/ 2 Cos (R/Rx COS +4 The true longitudinal slips of the four wheels il, i 2 i3, and i4 are given by: ii In(oi're/Vicos al) i 2 In((0 2 'r/V2cos a 2 i3 ln()3're/V 3 cos a 3 i4 in(w 4 re/V 4 cos a 4 Where 03' and 04' are the angular velocities of each wheel where re is the effective wheel radius which in this case is assumed to be the same for all wheels.

To correct for slip angles and true longitudinal slip the following control strategy will be employed: The driver selects the desired Ry' and RMSWS. If a rotatable joystick is used q, 0, and d are selected.

The computer calculates the desired angles and speed for all four wheels.

As slip angles and longitudinal slip cannot be measured yet, the computer implements the above angles and speeds.

The castors now allow calculation of the effective wheel angles and wheel speeds. Slip angles and longitudinal slip are also calculated.

The slip angles are now added to the actual front wheel angles and subtracted from the actual rear wheel angles in order to achieve the desired effective wheel angles. This step assumes the slip angles will not be changed by a small change in each wheel angle.

The castor angles and speeds are remeasured. Note that the desired castor angles are given by the equations: tan F (b/2 Ry')/Rx' and tan R (b/2 Ry')/Rx' In an attempt to correct the effective wheel speeds to the desired wheel speed, the wheel speed error is added to the actual wheel speed. Once again it is assumed that the speed error will not be changed by this process.

If the desired centre of vehicle is still not achieved, steps 4 to 7 can be repeated.

It is expected that the energy required to move or rotate the vehicle will be a minimum when the root mean square of all the slip angles and the root mean square of all the longitudinal slips are also minimum. An intelligent control system could fine tune the actual wheel angles and wheel speeds in an attempt to find these minimums. The accuracy of this assumption may be increased if the individual slip angles and longitudinal slips are divided by the vertical loads applied to the respective wheels.

In principle the general vehicle described above can be simplified by restricting the desired centre of curvature of the path of the vehicle to the transverse axis of the vehicle. In this case the front and rear effective wheel speeds for each side of the vehicle will be the same as will the effective wheel angles.

However when slip angles are taken into account, each of the four actual wheel angles will be different. Similarly when longitudinal slip is taken into account, each of the four actual wheel speeds may also be different. If four wheel speed control systems and four wheel angle control systems are required no simplification is possible. However it will be shown below that simplification is still possible if the effective centre of curvature of the vehicle is manipulated to the transverse axis of the vehicle. In this case only one speed control is required for each side of the vehicle.

Fig 7(a) shows a vehicle where the speed of both left hand vehicles is identical 02 04), and the speed of both right hand wheels is identical w, o 3 The driver selects the desired centre of rotation C' on the transverse axis of the vehicle and the root mean square wheel speed.

As slip angles cannot be measured until the vehicle is moving, the computer implements the desired wheel angles and wheel speeds on the assumption that all slip angles and true longitudinal slips are zero. Once the vehicle is moving the front and rear castors (36 and 37 respectively) can be used to determine the actual centre of rotation of the vehicle C. From the latter the slip angles of all four wheels can be calculated by the on-board computer. These slip angles are now added to or subtracted from the original wheel angles and implemented by the computer so that the actual centre of rotation C is moved to the transverse axis of the vehicle.

This situation is shown in Fig Note that this last step assumes the slip angles are not changed by the small change of wheel angles.

Note also for the symmetrical vehicle shown in Fig 7 the actual centre of rotation will lie on the transverse axis of the vehicle when the angle of the front and rear castors are equal.

Front and rear castor speeds VF and VR can also be measured and effective wheel velocities

V,

to V 4 can be calculated. Ideally V, cos a/w0 1

V

2 cos ac2/0 2 V3 cos a3/ 3 and V 4 cos 0a4W should all be the same. If not the same and o 2

(=W

4 can be adjusted to minimise the difference.

The last three steps can be repeated to fine tune the process as required.

In the simplified vehicle considered above where the selected value of Ry equals zero, and the wheelbase b and track t are equal, if all radii of curvature of the path of the vehicle from oo to oo are to be possible, then the effective wheel angles must be able to be varied from +45° to -135° for the left wheels and -45° to +1350 for the right wheels. In short, each wheel must be able to turn a total of 180°. The latter is the case even when the wheelbase and track are not equal.

Although being able to rotate the vehicle about its centre is very desirable, being able to rotate the vehicle about centres close to its centre are not very useful. If the ability to rotate the vehicle about non-zero radii of curvature on its transverse axis between +t and -t are sacrificed, then the wheels only have to turn Fig 8 gives examples of possible wheel configurations for this simplified vehicle.

Fig 8(a) shows the vehicle rotating about its centre in an anti clockwise direction Rx In this case the right wheels are turned -450 and run forward, whereas the left wheels are turned +450 and run in reverse. The magnitude of all wheel speeds is the same.

Fig 8(b) shows the vehicle turning anti-clockwise about a centre given by Rx The angles of the left and right hand wheels are -450 and -18° respectively. The speed of the right wheels will be 2.19 times the speed of the left wheels.

Fig 8© shows the vehicle moving straight ahead. Rx oo and all wheel angles are zero.

Fig 8(d) shows the vehicle turning clockwise about a centre given by Rx The angles of the left and right wheels are +180 and +45° Fig 8(e) shows the vehicle rotating about its centre in a clockwise direction Rx In this case the left wheels turn +450 and run forward, whereas the right wheels turn -450 and run in reverse. The magnitude of all wheel speeds is the same.

'e Note that all values of Rx between -t and infinity and +t and infinity are possible. All other radii are not possible with the exception of Rx 0.

Note that the technique of making the steering effect of wheel speeds identical to the steering effect of the wheel angles can also be applied to braking wheeled vehicles. In the vehicles described above the drive train consists of a motor driving two or more variable displacement hydraulic pumps, which in turn drive four hydraulic wheel motors. These vehicles are decelerated by the driver reducing the strokes of the (usually dclosed circuit) variable displacement pumps.

However the computer integrated steering/drive system ensures that the instantaneous wheel speeds, as well as the wheel angles, tend to rotate the vehicle about the centre selected by the driver. This system will function regardless of whether the vehicle is accelerating, travelling at constant speed or braking. The advantage of this cooperative redundant system is that as one steering system fails (as it inevitably must as operating conditions worsen) it is backed-up (or reinforced) by the other system. This cooperative redundancy will have a stabilising effect on a braking vehicle.

By way of comparison, let us now consider the traditional braking system used by road vehicles.

For the sake of simplicity, the engine braking effect and the moment inertia of the wheels will be neglected. Traditionally equal dclamping forces are applied to the front wheels and equal dclamping forces are applied to the rear wheels. However the frictional torque applied to any wheel cannot exceed the opposing torque applied to the wheel by the ground traversed. When the frictional braking torque equals the maximum torque that can be applied by the ground the wheel will lock.

When the wheel locks the torque exerted by the ground generally decreases. Furthermore the ability of the ground to exert sideways forces on the wheel will also decrease. Since there is no direct control of the speed of each wheel, there is no driver selected steering effect applied by the braking process. Only the wheel angle steering effect is under the control of the driver, and the effectiveness of this will decrease if wheel locking occurs.

Various electronic means have been proposed or implemented to overcome the problems outlined above. One example is a valve to reduce the clamping force applied to the rear wheels to compensate for the weight transfer to the front wheels. Another is an anti-skid braking system which momentarily reduces the dclamping force applied to all wheels if one or more wheels stop turning. This enables the locked wheels to turn and re-establish their grip on the road and their steering effect.

However, these add-on systems are an attempt to fix an inherently flawed system. It would be much better if the braking system was based on a system of wheel speed control rather than a system based on clamping force control where secondary systems are added in an attempt to overcome inherent instability problems.

Although it is not feasible to use hydrostatic wheel motors in a high speed road vehicle, a computer integrated steering/ braking system is possible if the braking system focuses on controlling individual wheel speeds rather than wheel clamping forces. The control strategy to be used is as follows: 1. The driver selects the desired radius of curvature with the steering wheel (or joystick) and root mean square wheel speed or rate of acceleration with the accelerator (or joystick).

2. When deceleration is required the driver selects the desired rate by the force on(or position of) the brake pedal.

3. The on-board computer calculates the speed-time program for each wheel, so that these wheel speeds produce the same steering effect as the wheel angles.

4. To implement the desired speed-time program for each wheel, the clamping force acting on each wheel is modulated. If any wheel speed is too high the clamping force acting on this wheel will be increased. If any wheel speed is too low the clamping force acting on this wheel will be decreased. This can be achieved by means of four high speed valves, similar to Moog valves. Alternatively the wheel clamping force can be controlled by high speed electric motors.

Ideally the vehicle should stop when all the wheels simultaneously stop turning. However if the rate of wheel deceleration selected by the driver is in excess of that that can be produced by the ground/wheel interaction, all wheels will simultaneously stop turning before the vehicle comes to rest.

This problem can be eliminated if an accelerometer on the vehicle detects when the average wheel deceleration exceeds the vehicle deceleration and reduces the individual wheel decelerations accordingly. This system would come into operation into operation in panic braking situations.

Note that a separate anti-lock braking system is not required if the above computer integrated steering/braking system is employed.

Note that in the above derivations neutral steering is assumed so that the centre of rotation of the vehicle will be identical to the centre of curvature of the path of the vehicle.

The general embodiment of the invention The general embodiment of the invention is shown in Fig Alternative means of driver control are shown in Fig The Preferred means of driver control is by means of a rotatable joystick 41.

Alternatively, one joystick 42 could be used to determine the radius of curvature of the path of the vehicle and the root mean square wheel speed, and a second joystick 45 could be used to determine the direction of the centre of curvature.

Alternatively a steering wheel 43 (or steering knob or lever) could be used to determine the radius of curvature of the path of the vehicle and the root mean square wheel speed, and a second joystick 45 could be used to determine the direction of the centre of curvature.

A disadvantage of the variant of the invention described above is that four independent steering systems and four independent drive systems are required. It will be shown below that under special conditions the number of systems required can be reduced.

The first special case Figure I10(a) shows that if 14. 0, the eight general control equations become: tan 01 (b t2) taflg 3 -t12) =tanA, tait 4 (bI2)I(Rx t12) =tant 2 and w, 1 KdR 1 RAMI whereR,2 =b 2 /4 +(Rx -t/2)2 W2 KdP2 RAISR 61 where Rq b 2 A (Ri-i 03 KdR3 /RMSR 04 KdR4/ RISR where

R

2 b 2 /4 (R x -t/2) 2

=R

where 2 b 2 /4 (Rx t/2

=R

Where RMSR (Rx' +b 2 /4 t 2 /4)1/2 In this case only two wheel angle control systems are required since 01 03 and 02 =04.

Similarly only two wheel speed control systems are required since 0 03 and w2 wo 4 In this case the rotatable joystick only needs to rotate and move forward and backwards in a single plane. In this case the rotatable joystick 41 can be replaced with a normal joystick 42 where the forward displacement d determines the root mean square wheel speed and the lateral displacement determines the radius of curvature of the path of the vehicle where moving the joystick 42 as far as it will go to the right will reduce the radius of curvature to zero and the vehicle will rotate about its own centre in a clockwise direction, Alternatively a steering wheel 43 can be used by the driver to select the radius of curvature of the path of the vehicle. The root mean square wheel speed can be selected with a speed control lever or pedal 44. See Figure 2(b) The second special case Figure 11 shows that if R b 2, then the eight control equations become: tan41 b/(Rx -t12) tan2 bI(R x +t/2) tan$ 3 tan4 4 0 C0 KdR,/ RMSR W2 KdR 2

RMSR

where R, b 2

+(R

x -t/2) 2 where R] b 2

(R

x t 2) 2 a' 3 KdR 3 /R SR where R3 (R x -t/2) 2 04 KdR 4 RAMSR where R 2 (R +t 2) 2 where RMASR (Rx 2 +b2 /2 t 2 /4)1/2 In this case no steering system is required for the rear wheels since 03 and 04 are zero. See Figure 11 The vehicle is further simplified if either the front or rear wheels are not driven that is are free wheels) so that only two speed control systems are required. See Figures 11 and 13(b).

Although the same equations apply to the two wheel steering/two wheel drive vehicle as apply to the two wheel steering/four wheel drive vehicle, there is no control imposed on the speed of the free wheels. In this case the speed of these free wheels could be ignored for the purpose of calculating the root mean square wheel speed. If the front wheels are free wheels the RMSR for the rear driving wheels is: RMSR (R +t 2 /4)12 If the rear wheels are free wheels the RMSR for the front driven wheels is given by: RMR (Rx +b 2 +t2 /4) 2 The system used to control the wheel angles may work as follows: The angle of a particular wheel will be measured. An on board computer will calculate (or approximate from a look up table) the correct angle from the driver's inputs of 0 and y. If an error exists between the actual angle and the desired angle an actuator will be energised so as to eliminate this error. The on board computer will adjust the angles of all the other steerable wheels before repeating the cycle.

A similar system will be used to control the wheel speeds. The wheel speed of a particular wheel will be measured. The on board computer will calculate (or approximate from a look up table) the correct wheel speed from the driver's inputs of 0, V and d (the latter determining the root mean square wheel speed). If an error exists between the actual speed and the desired speed the drive to the wheel be adjusted so as to eliminate the error. The on board computer will adjust the speed of all other wheel speeds before repeating the cycle.

In large vehicles the actuators used to turn the wheels could be rotary hydraulic actuators.

Alternatively double acting cylinders connected to rack and pinions could be used. In this case the engine I would also drive an auxiliary hydraulic pump (not shown in Figure 1) which would drive the actuators via control valves activated by the on board computer.

In large vehicles the wheels could be driven by in built hydraulic motors which are powered by variable displacement hydraulic pumps. These pumps are driven by an internal combustion engine, which is governed to run at a constant speed. The speed of the wheels is controlled by varying the displacement of the pumps from a maximum flow in one direction to zero to maximum flow in the reverse direction. This allows the speed of the wheels to be varied from maximum forward to zero to maximum in reverse. The on board computer is used to alter the displacement of the pumps to produce the desired wheel speeds.

In smaller vehicles, such as wheel chairs, the wheels could be conveniently driven by electric motors. Similarly the wheels could be turned by electrically powered actuators. Storage batteries could be used to power the motors and the actuators. The motors and actuators would be controlled by an on board computer as indicated above.

Alternatively, the wheels could be driven by an internal combustion engine, via variable ratio friction drives. The wheels could be conveniently be turned by electric actuators. The friction drives and actuators would be controlled with the aid of an on board computer.

In an on road variant of the invention, higher wheel speeds and smaller wheel angles are required. Furthermore the displacement of the centre of curvature in the longitudinal direction is constant. In the four wheel steering/four wheel drive vehicle described in Figures 10(a) and

R

r 0. In the two wheel steering/ four wheel drive or two wheel steering/two wheel drive vehicles described in Figures 11(a) and 13(b) Ry b 2. In these cases the wheel angles could be set by a steering wheel. The on board computer would positively control the wheel speeds to match the wheel angles selected. In this case the drive wheels would be driven mechanically by an internal combustion engine via a gear box and one or more traditional differentials where the wheel speeds are positively controlled by means of one or more steering differentials working in parallel with the one or more of the traditional differentials, where the speed of the electrically or hydraulically driven steering differentials are controlled by the on board computer.

Let us consider applying the invention to large dump trucks. In this application fuel efficiency is important and it is known that mechanical drives are more efficient than electrical drives and much more efficient than hydrostatic drives. In this application a zero turn radius is not required, so that the wheels are not required to turn through large angles. The maximum angle required is likely to be less than 30 degrees. In many cases only the front wheels are turned. These limitations make mechanical drives feasible. The preferred driver interface is a steering wheel, where the maximum angle of the steering wheel produces the maximum turn angle of the steerable wheels. Speed can be controlled with a speed control lever or pedal. See Figures and 11(b).

Figure 12(a) shows the general arrangement of components required for computer integrated steering/drive system utilising a mechanical drive. An internal combustion engine 114 drives a gearbox 115 which in turn drives a central differential 116, which in turn drives both a front "tail" shaft 117 and a rear tail shaft 118. The front "tail" shaft 117 is linked to a steering differential 119 by a pair of gears 120 and 121. The rear tail shaft 118 is linked to the steering differential 119 by means of a pair of gears 122 and 123 with the same speed ratio as gears 120 and 121, where gears 122 and 123 do not mesh, but are linked by means of an idler gear 124. The input to the steering differential is driven as required by means of a hydraulic motor 125. Note that when the vehicle is proceeding straight ahead (i.e infinity), the speed of the two tail shafts should be identical. This is positively achieved if the hydraulic motor 125 is stationary.

When the vehicle turns it may be necessary for the speed of the front tail shaft 117 to be greater than the speed of the rear tail shaft 118 if wind up is to be avoided. This can be achieved by driving the hydraulic motor 125 at the right speed (in the right direction).

A steering differential 126 is also linked in parallel with the front differential 127. This is driven at the appropriate speed by a hydraulic motor 128. A steering differential 129 is also linked in parallel with the rear differential 130. This steering differential 129 is also driven at the appropriate speed by a hydraulic motor 131. Note that the front and rear differentials are driven by front and rear tail shafts 117 and 118 respectively. The appropriate speeds are those where the steering effect of all the wheel speeds is identical to the steering effect of all the wheel angles.

Figure 12(b) shows the detailed layout of the rear differential 130 and the associated steering differential 129. The casings (or housings) have been omitted in the interests of clarity. Although bevel gear differentials 132 have been shown here, differentials using over lapping straight cut planetary gears can also be used.

Figure 13(a) shows the layout for the mechanical drive when the centre of curvature of the path of the path of the vehicle lies on its transverse axis. In this case the central differential and its associated steering differential can both be dispensed with.

Figure 13@ shows that when the centre of curvature of the path of the vehicle lies on the transverse axis of the vehicle the front differential 126 and associated steering differential 127 can be replaced with a pair of left hand right angle drives 51 and a pair of right hand right angle drives 52.

Figure 13(d) shows that when the centre of curvature of the path of the vehicle lies on the transverse axis of the vehicle the rear differential 130 and associated steering differential 129 can be replaced with a pair of left hand right angle drives 53 and a pair of right hand right angle drives 54.

Figure 13(b) shows that when the centre of curvature of the path of the vehicle lies on the axis of the rear wheels, three differentials 116, 127 and 130 and their associated steering differentials 119, 126 and 129 are required.

Figure 14(a) shows the layout of a vehicle incorporating a computer integrated steering/drive system where the differentials and associated steering differentials have been replaced with steering differentials integrated into speed reduction gear boxes close coupled to each wheel. In this case engine 133 drives gear box 134 which in turn drives an integrated front and wheel tail shaft 135 by means of right angle drive 199 which in turn drives front and rear drive shafts 136 and 137 by means of right angle drives 138 and 139. The front and rear drive shafts 136 and 137 drive integrated speed reduction gearbox/steering differentials 140, 141, 142 and 143. Each integrated speed reduction gearbox/steering differential is also driven by wheel speed correcting hydraulic motors 144, 145, 146 and 147. The wheel speed correcting hydraulic motors ensure that the steering effect of all wheel speeds is identical to the steering effect of all the wheel angles.

Figure 14(b) shows the detailed layout of the integrated speed reduction gearbox/steering differential. This is a three stage compound epicyclic gearbox where the steering differential is incorporated into the first stage. Power is transmitted to the integrated gearbox/differential by means of drive shaft 149, which drives sun gear 150. Sun gear 150 drives planet gear 151, which is also driven by annular gear 152. Annular gear 152 is driven by the speed correcting hydraulic motor 153 as required. Planet gear 151 is supported by arm (or cage) 154, which drives the sun gear of stage two 155. Stage two 155 and stage three 156 are similar to stage one, except that the annular gears in the latter two stages are fixed to the housing and are thereby stationary. The arm (or cage) 157 of the last stage is connected to the drive wheel 158. For the sake of simplicity only one planet gear is shown in each stage. In practice more planet gears would be used to both balance the rotating parts and share the load.

In principle the hydraulic speed correcting motor could drive any one of the three annular gears.

However if the first stage annular gear is driven, a more convenient higher speed low torque hydraulic motor can be used. Note that the hydraulic motor could be replaced by an electric motor with appropriate speed control.

Note that the lower efficiency of the speed correcting hydraulic motor will have little effect on the overall drive efficiency since only a small fraction of the output power is provided by the hydraulic motor.

Figure 15 shows a hydraulic circuit which would allow the wheel speed correcting motors 144, 146, 146 and 147 to rotate at appropriate speeds. Each hydraulic motor is driven by a variable displacement pump. These pumps 161,162, 163 and 164 are driven by a common shaft 165 at a speed proportional to the tail shaft speed by means of gears 159 and 160. This arrangement automatically compensates the speed of the pumps for the overall speed of the vehicle. When the vehicle is turning to the right, the right hand pumps slow the right hand wheels and the left hand pumps speed up the left hand wheels. The amount of speeding up and slowing down is determined by the displacement of each of the variable displacement pumps. These displacements are determined by the squash plate angle of each pump.

In the vehicles depicted in Figures 12 and 13 the computer integrated steering/drive system can be implemented as follows: The driver selects the centre of curvature of the path of the vehicle and the average wheel speed.

The on board computer then calculates the angle and speed of each wheel that ensures that the steering effect of the wheel angles is identical to the steering effect of the wheel speeds. The on board computer then turns the wheels 166, 167, 168 and 169 to the calculated angles. The computer also calculates the appropriate speed for each wheel speed correcting hydraulic motors 144, 145, 146 and 147, and implements these speeds by adjusting the squash plate angles of the respective variable displacement hydraulic pumps 161,162, 163 and 164.

Figure 16(a) depicts a vehicle where the four rear drive wheels are driven independently so that the wheel speed steering effect of all four wheels is identical to the steering effect of the angles of all six wheels the four coaxial drive wheels, and the two steerable non driven wheels).

In this vehicle engine 170 drives gearbox 171, which in turn drives a tail shaft 172 via right angle drive 173. The tail shaft 173 drives a drive shaft 174 via a second right angle drive 175. The drive shaft 174 drives four integrated speed reduction gearbox/speed correcting differentials 176, 177, 178 and 179. The speed correcting differentials 176, 177, 178 and 179 are also driven as required by four wheel speed correcting hydraulic motors 180, 181,182 and 183. These hydraulic motors 180, 181,182 and 183 are driven by variable displacement hydraulic pumps 184, 185, 186 and 187 respectively. These hydraulic pumps are driven by a common shaft 188, which is rotated at a speed proportional to the tail shaft speed by means of gears 197 and 198. The advantage of this arrangement is that it enables all four drive wheels to be driven at slightly different speeds on turning. The outer wheels 176 and 179 may be slowed down and speeded up more than the inner wheels 177 and 178.

Figure 16(b) shows the detailed layout of an integrated speed reduction gear box/speed correcting differential suitable for driving an inner wheel. In this case the drive shaft 194 must pass through the integrated speed reduction gearbox/speed correcting differential so that it can also drive the outer wheel 179.

Figure 17 shows a simplified version of a vehicle where the four rear drive wheels are driven at four different speeds on turning. In this case a single variable displacement hydraulic pump 189 is used to drive all four speed correcting hydraulic motors 190, 191,192 and 193, which are now connected in series. The displacement of the inner and outer speed correcting hydraulic motors is inversely proportional to the distance of the respective wheels from the centre line of the vehicle.

In the vehicles depicted in Figures 16 and 17 the computer integrated steering drive system can be implemented as follows: The driver selects the radius of curvature of the path of the vehicle with a steering wheel and the average wheel speed with a speed control lever or pedal. The on board computer calculates the appropriate angles of the front wheels and the individual speeds of the four rear drive wheels, and the required speed of the four wheel speed correcting hydraulic motors 180, 181, 182 and 183 or 190, 191,192 and 193. The computer implements the calculated front wheel angles and calculated hydraulic motor speeds. The required hydraulic motor speeds are achieved by adjusting the squash plate angles of the four variable displacement pumps 184, 185, 186 and 187 or the single variable displacement pump 189.

It should be noted that if the speed of the drive wheels is positively controlled by any of the methods outlined above, the wheel speed steering effect applies when the vehicle is being braked (or decelerated) as well as when the vehicle is being driven (or accelerated).

APPLICATION OF THE CONCEPT OF COMPUTER INTREGRATION OF THE STEERING SYSTEM AND THE DRIVE SYSTEM TO VEHICLES WITH AUTOMATIC OR COMPUTER ASSISTED

STEERING:

Vehicles with two wheel steering: In controlled traffic farming, it is important that the vehicle keeps to the desired path with the minimum of error. Minimisation of error can become an onerous task for the driver. There are two types of error. The first is translation error For convenience this is defined as the distance of the centre of the non-steered axle (the vehicle reference point in this case) from the desired path (measured perpendicular to the desired path, where errors to the right of the desired path are considered positive). The second is rotation error This is defined as the rotation of the vehicle relative to the direction of the desired path, where clockwise rotation is considered positive.

Although the primary objective of an automatic steering system is to keep the translation error as small as possible, the rotational error is also important because the vehicle cannot maintain the translation error at zero unless the rotational error is also zero.

The essential feature of the error minimisation system proposed here is that corrective action should ensure that when the translation error is zero the rotation error should also be zero. This means that the corrective path of the vehicle must be tangential to the desired path of the vehicle.

Figure 18 shows there are five possible vehicle states.

Figure 18(a) shows a vehicle where both the translation and rotation error are zero. In this case no corrective action is required.

Figure 18(b) shows a vehicle where the translation error is positive but the rotation error is negative. If no corrective action is taken the path of the vehicle will cross the desired path and the translation error will become increasingly negative.

Figure 18(c) shows a vehicle where both the translation error and the rotation error are positive. If no corrective action is taken the path of the vehicle will diverge from the desired path and the translation error will become increasingly positive.

Figure 18(d) shows a vehicle where the translation error is positive and the rotation error is zero.

If no corrective action is taken the path of the vehicle will be parallel to the desired path, so that the translation error will remain constant.

Figure 18(e) shows a vehicle where the translation error is zero the rotation error is positive. If no corrective action is taken the path of the vehicle will diverge from the desired path, so that the translation error will become increasingly positive.

For the vehicle shown in figure 18(b) the simultaneous elimination of both the translation and rotation errors can be achieved if the centre of the non-steered axle follows a curved path which is tangential to the desired path. If the desired path is a straight line and a circular correction path is used (see Figure 19(a)) then the radius of curvature (ROC) of the circular path required is given by the equation: ROC TE/(1 cos RE) The vehicles shown in Figures 18 18(d) and 18(e) must first be brought to the state shown in Figure 18(b). This can quickly be achieved by turning the steerable wheels towards the desired path.

In the control strategy described above the radius of curvature needs to suddenly decrease to the calculated value. It is then held constant until both the translation error and the rotation error become zero. The radius of curvature is then suddenly increased to infinity. This means that the steering wheel angle is suddenly increased, held constant, then suddenly decreased to zero.

If the position of the vehicle reference point (in this case the midpoint of the non-steerable axle) and the vehicle heading are continuously monitored, then new radii of curvature and steering wheel angles can calculated continuously. A control system can be used to implement these steering wheel angles.

If the initial radius of curvature is set at a value slightly smaller than the ideal, (so that the steering wheel is initially set at a value slightly greater than the ideal value), continuous monitoring of the position and heading of the vehicle, and correction of the steering wheel angle will mean that the latter will decrease continuously as the translation and rotation errors decrease. This "Increasing radius of curvature" control strategy will mean the control system will not have to respond as rapidly as for the previously described "Constant radius of curvature" strategy.

Although the steering wheel angle can best be controlled automatically with a control system, the cost could be reduced if the automatic control system is replaced with a system that assists the driver to turn the steering wheel to the correct angle. In this case the correct steering wheel angle is calculated from the translation and rotation errors. If the driver has to turn the steering wheel to the right a laser dot will be projected on the windscreen to the left of one or more aiming marks, and vice versa. When the steering wheel is at the correct angle the laser dot will be centred with respect to one or more aiming marks.

If the driver prefers the first described "constant radius of curvature" strategy, his task would be aided by a strong steering wheel self-centring effect and a strong indication when the translation error is zero. The zero error state could be indicated by an audible tone. Conversely the size of the translation error could be indicated by the tone so that the zero error state would be indicated by silence.

If the driver prefers the second described" increasing radius of curvature strategy, the effect of driver reaction time will be reduced.

Vehicles with four wheel steering and symmetry about their transverse axis For vehicles with four wheel steering where the effective angle of the rear wheels is the mirror image of the effective angle of the front wheels about a plane which contains the transverse axis of the vehicle, the centre of curvature of the path of the vehicle will always lie on the transverse axis of the vehicle. In this case the speed of the right front wheel should be the same as the speed of the right rear wheel, and the speed of the left front wheel should be the same as the speed of the left rear wheel. Methods of compensating for slip angles and longitudinal slip have been described above. In this case the error-correction strategy advocated above for two wheel steering vehicles, can also be used for vehicles with a transverse axis of symmetry. In this case the translation error is the distance of the centre of the vehicle from the desired path of the vehicle, measured perpendicular to the desired path (as shown in Figure 19(b)).

Vehicles with independent four wheel steering For vehicles with four wheel steering and two wheel or four wheel drive, where all wheels can be turned independently about substantially vertical axes, and where all the driven wheels can be driven independently about substantially horizontal axes, much more flexibility is available since these vehicles can be rotated about any centre of curvature. These vehicles are capable of both pure rotation without translation) and pure translation without rotation). The latter is often referred to as crab steering.

The main advantage of vehicles with independent steering of all four wheels is greater manoeuvrability, and this makes correction of translation and rotation errors easier. In principle the two errors can be corrected separately consecutively). A major advantage is that vehicles in states depicted in Figures 18@, 18(d) and 18(e) can be corrected without first changing to the condition depicted in Figure 18(b).

If the translation and rotation error have the same sign (see Figure 18@ where they are both positive), then they can both be reduced simultaneously. This contrasts with vehicles which don't have independent four wheel steering, where the translation error must be increased before both errors can be eliminated.

For the vehicle shown in Figure 18@ the translation error could be eliminated followed by the rotation error or vice versa. However the control system need not respond as rapidly if both are eliminated simultaneously. If the centre of the vehicle is driven along a circular path which is tangential to the desired path, the vehicle can be simultaneously rotated so that the rotation error becomes zero at the same time as the translation error. See Figure If the centre of the vehicle is to be initially driven towards the desired path with an angle of attack of say 10 degrees, then the radius of curvature for the path of the vehicle Ro is given by the equation: Ro TE/(1 cos 0,) The position of the desired centre of curvature of the path of the vehicle relative to the vehicle frame of reference is given by the equations: Rx Ro cos OJ And Ry Ro sin (RE 8,) The effective wheel angles required to correct the translation error (but not the rotation error) are given by the equations; tan 1 t 2) tan 2 (b/2-Rr)/(Rx+t/2) tan 3 (b/2+Ry)/(Rx -t12) and tan 4 (b/2+Ry)/(R x +t/2) The time required to correct the translation error is given by the equation: Time ORoVo where Vo is the velocity of the centre of the vehicle.

The required rate of rotation of the vehicle about its own frame of reference Q is given by the equation: 0 (RE 6a)/time Vo(RE 0,)/eaRo The rate of rotation of the vehicle about its own frame of reference is also given by: Q 2VosinA/(b 2 t 2 12 Vo(RE Oa)/ORo Therefore sinA (RE (b 2 t 2 )2/2OaRo (RE (b 2 t2)f2(l cos.)/ 2aTE Where A+ is the increase in the basic wheel angles necessary to eliminate the rotation error.

Although the desired radius of curvature Ro should remain unchanged, the components Rx and Ry will change as the rotation error is reduced. This will necessitate constant change in the basic wheel angles as the translation and rotation errors are simultaneously eliminated.

If only the translation error is corrected, the final position and path of the vehicle wheels are shown by the dashed lines. If the rotation error is simultaneously corrected the final position of the vehicle is shown by the solid lines. The path of the wheels in this case is shown by the dotted lines.

If the rotation error is zero but the translational error is positive (as shown in Figure then the latter error can be eliminated by crab steering the vehicle on to the correct path. If the vehicle is crab steered along a circular path which is tangential to the correct path, the wheel angles will gradually decrease to zero from the initial angle of attack 0. This strategy is shown in Figure If the translation error is zero but the rotation error is positive (as shown in Figure the translation error can be maintained at zero by turning the wheels so they are initially parallel to the desired path. In the sign convention used here, 4j and +2 will be RE and 43 and 4 will be RE. The rotation error can be simultaneously be eliminated by rotating the vehicle as it proceeds along the desired path. This can be achieved by turning the front and rear wheels slightly less than the rotation error respectively. Note that since the basic wheel angles of the front and rear wheels are negative and positive respectively, the modulus of the front and rear wheel angles will increase and decrease respectively. This strategy is shown in Figure APPLICATION OF THE CONCEPT OF COMPUTER INTREGRATION OF THE STEERING SYSTEM AND THE DRIVE SYSTEM TO GANTRY TRACTORS In order to increase their productivity agricultural implements are becoming wider and wider.

These implements require heavier and more powerful tractors to pull them. As these heavy tractors tend to compact the soil under their wheels, there has been a move to controlled traffic farming, where the tractor wheels always move on the same path, thus reducing the area of the field compacted to a series of narrow strips.

Gantry tractors have several advantages over traditional tractors. The essential feature of a gantry tractor is that it is slightly wider than the implements it "pulls". These implements are located between the front and rear wheels of the gantry tractor. Generally many pairs of wheels are used in order to distribute the weight between all wheels and the tractive force between the driving wheels. Usually all wheels are driving wheels.

The main disadvantages of gantry tractors are as follows: 1. They are clearly ungainly and difficult to manoeuvre. In order to keep them on the correct path some form of automatic guidance system is almost inevitable.

2. At the end of a pass (usually a straight line) the gantry tractor must be shifted sideways to face fresh ground. Since it is not generally feasible to rotate the gantry tractor 180 degrees, the implements themselves must be effectively rotated (or reversed).

3. The biggest problem is transporting the gantry tractor from one field to another along narrow lanes of compacted soil. These unproductive lanes are generally adjacent to fences. The ideal gantry tractor would be able to move parallel to fence lines and "snake" through gates in these fence lines.

The application of computer integration of the steering system and the driving system of an advanced gantry tractor will now be described. The essential feature of this gantry tractor is that is consists of a series of four wheel modules that are hitched together. In working configuration, the modules are also latched together to form a single rigid frame. Although four modules are shown in Figure 21, any number of modules can be employed.

All wheels can be driven independently at any desired speed between maximum forward and maximum reverse. All wheels can be independently turned more than +90 degrees and degrees.

Working mode: Figure 21 shows the proposed gantry tractor in working mode. In this mode the modules are latched together to form a rigid truss. The position of the two uncoupled hitch points at either end will be monitored continuously by means of a geographic information system or some other positioning system. The orientation (or heading) of the gantry can be monitored by some form of compass, or it can be deduced from the position of the two said hitch points. The operating procedure is as follows: 1. The gantry will start from the non-worked unploughed) compacted lane probably adjacent to a fence. The implements will already be disengaged from the ground.

2. The gantry will be positioned so that the translation error is zero. This can be done with the wheels at 90 degrees. The rotation error will be eliminated by turning the wheels to 0 degrees, and driving the wheels at the opposite ends of the gantry in opposite directions until the rotation error is zero. The speed of the intervening wheels will be a linear interpolation between the speed of the end wheels. It is also possible to eliminate the translation and rotation errors simultaneously using the techniques described above for conventional tractors.

3. The gantry will be driven forward onto the ground to be worked and the implements engaged with the soil.

4. The gantry will be driven forward to work the soil. Translation and rotation errors will be continuously monitored. Translation errors can best be corrected by turning all wheels in unison and crab steering the gantry along a circular path that is tangential to the desired path.

Since all wheel angles are identical, all wheels will be driven at the same speed. Small rotation errors are less important, but these can be corrected by speeding up the lagging wheels. If the speed up of the leading wheels is zero, the speed up of the intervening wheels will be proportional to their distance from the leading wheels. Ideally the wheels should be turned so their centre of curvature is the same as that caused by the wheel speed differences. However if the rotation errors are small the scuffing caused by not turning the wheels will be negligible.

Side Shift Mode At the end of the pass the implements will be disengaged from the ground and the gantry driven on to the non-worked but compacted lane. The implements are then rotated (or reversed) 6. All wheels are turned 90 degrees and the gantry driven sideways until the translation error relative to the new desired path is zero.

7. Steps 2 to 7 are now repeated until the field is completely worked.

If steps 5 and 6 are combined, say by driving and turning all wheels in unison so they move along a circular arc which is tangential to the desired side shift path, the problem of turning stationary wheels through 90 degrees is avoided.

Transport Mode Figure 22 shows a gantry tractor passing through a gate. This is the most difficult manoeuvre. U turns and right angle turns (also shown in Figure 22 are easier to achieve. The control strategy to be used is as follows: 1. The gantry tractor is moved along a lane adjacent to a fence. Translation errors can best be corrected by turning all the wheels in unison. Rotation errors can best be corrected by turning the leading and trailing wheels slightly in opposite directions. The wheels in between will be turned by amounts proportional to their distance along the gantry (by a process of linear interpolation).

2. Prior to the gantry approaching the gate, the desired path of the reference points the GPS sensors) must be stored in the on board computer. In this case the reference points will be all the hitch points of the four-wheel modules. In this example the path of the hitch points through to gate will be circular arcs. In principle any path could be used, including straight lines. The disadvantage of the latter is they require sudden changes in the radius of curvature of the centre of the modules.

3. As each module approaches the gate it is unlatched from the following module so that the modules can articulate around the hitch points. The leading module will have already been unlatched.

4. When the front hitch point of the first module reaches the start of the desired circular arc the desired radius of curvature of the path of the centre of the module Ro begins to reduce from infinity. The centre of rotation of the module is given by the intersection of the normal to the path of the front hitch point and the normal to the path of the rear hitch point. See Figure 23.

Once the speed of the centre of the module has been selected, the angular velocity of the module about its instant centre can be calculated. The speed of the centre of the module can be expressed as the speed of a dummy castor located at the centre of the module. The relation between mo and the root mean square wheel speed RMSWS is given by the equation: eo RMSWS/(1 (t 2 /4Ro 2 b 2 /4Ro2) 2 RMSWS/(1 (t +b 2 )/2R o 6. The individual effective wheel angles of the module are given by the equations: tanA (b/2-Rr)/(Rx t/2) tanq -t/2) and tan, 4 (b +t/2) The individual effective wheel speeds are given by the equations: W1 O)OR/Ro where R 2 (b/2-R) 2 +(Rx 2 =0 touR 2

/R

0 where R (Iu/2-I4)2 +t/2) (03 =)ORg/R 0 where R.2 (b/2+R 7 92 -t/2/2 04 coR 4

/R

0 where R 2 (b /2 Ry)2 (R +t/2) 2 where wD, KdRW1 RMSR where R 0 2 Rx2+ RY and RMSR (RX 2 RY2+ te14 b 2 /4) 1 /2 t 2 /4 b 2 /1491,1 Note that as the front or rear hitch points move along a circular path both the centre of curvature of the path of the module and the radius of curvature of the path of the module will change constantly.

8. The velocity of the rear hitch point can be calculated from the angular velocity f) of the module and its radius of curvature R 0 This must be identical to the velocity of the front hitch of the second module. The centre of curvature, radius Of curvature and velocity of the second module can now be deduced.

9. Steps 4 to 8 are repeated until the appropriate wheel angles and wheel speeds for all modules are calculated.

The control system implements the above wheel speeds and angles.

11 The calculations are repeated as the gantry tractor snakes its way through the gate.

If translation or rotation errors are detected they can de Corrected by means of the strategies outlined above for vehicles with independent four wheel steering. However errors in the path of the modules must be corrected in a cooperative fashion so that there is no conflict between Modules. Conflict is avoided by calculating the corrective path required by the first module. The desired path and velocity of the first rear hitch point becomes the desired path and velocity for the second front hitch point. Mny further correction of the second module must be achieved by adjusting the path of its rear hitch point. To avoid instability (such as oscillation) the errors in the positions of the front and rear hitch points should become zero at the same time. The errors of the following modules must be corrected in a similar cooperative fashion.

Figure 24 shows a slightly more complicated path through a gate, which allows narrower gates to be negotiated. In this case the modules turn away from the fence slightly before they turn through the gate at a deeper angle.

Claims (4)

1. A wheeled vehicle which is driven along a path as close as possible to a desired path by correcting errors in the path in such a way that the rotation error of the vehicle becomes zero at the same time as the translation error becomes zero.

2 A vehicle according to claim 1 where the heading of the vehicle will cross the desired path, where the steerable wheels are turned so that the path of the vehicle will be tangential to the desired path.

3 A vehicle according to claim 2 where the steerable wheels are turned such that the ideal radius of curvature of the path of the vehicle ROC 0 is given by the equation: ROCo TE/(1 cos RE) Where TE is the translation error and RE is the rotation error.

4 A vehicle whose heading is parallel to or diverging from the desired path where the steerable wheels are turned towards the desired path and held at this angle until the vehicle heading crosses the desired path at a distance ahead of the vehicle set by the operator The steerable wheels are then reset to achieve the condition specified in claims 2 or 3. A vehicle according to claims 1 or 2 where the ideal ROCo is calculated according to the equation given in claim 3, but where the actual ROC set by the steerable wheels is slightly less than the ideal value by a factor selected by the operator. In this case the ROC will have to increase continuously until it becomes infinity when both TE and RE become zero. 6 A vehicle according to any one of claims 1 to 5 where the ROC is controlled by controlling the angle of one or more steerable wheels. 7 A vehicle according to any one of claims 1 to 5 where the ROC is controlled by positively and independently controlling the speeds of the left hand and right drive wheels instead of the angle of one or more steerable wheels. 8 A vehicle according to any one of claims 1 to 5 where the ROC is controlled by simultaneously controlling both the angle of one or more steerable wheels and positively and independently controlling the speeds of the left hand and right drive wheels. 9 A vehicle according to any one of claims 1 to 8 where the ROC and speed of the vehicle is controlled automatically. A vehicle according to any one of claims 1 to 8 where the ROC and speed of the vehicle is controlled by the driver with the aid of an instrument display which indicates the deviation of the steering wheel or joystick from the position which produces the correct ROC. 11 A vehicle according to claim 10 where the primary display is supplemented by a secondary display or audible signal which indicates when the translation error TE is zero. 12 A vehicle according to claim 1 with four wheel steering where a translation error TE and a rotation error RE can be eliminated simultaneously regardless of the heading of the vehicle. 13 A vehicle according to claim 12 where the speed of each drive wheel is automatically controlled to achieve the same instantaneous radius of curvature as the wheel angles. 14 A gantry tractor consisting of two or more modules hitched together so that each module can rotate relative to its neighbour or neighbours about substantially vertical axes through the hitch points, where each module has four wheels all or some of which will be driven where all wheels can rotate about a substantially vertical axis plus or minus an angle greater than degrees, where the modules can be latched together with struts which connect the front left corner of one module with the front right corner of the neighbouring module and the rear left corner of the first mentioned module with the rear right corner of the second mentioned module, so that when all the modules are latched together they form a rigid truss in the horizontal plane. A gantry tractor according to claim 14 where the modules are latched together where all wheels are turned through 90 degrees to allow the gantry tractor to move in a direction parallel to a straight line through all the hitch points. 16 A gantry tractor according to claim 14 where the modules are latched together where all the wheels are oriented substantially at right angles to the long axis of the truss where the path of the tractor, when its tools are engaged with the ground, is controlled by continuously monitoring the location of two or more hitch points and correcting the translation error relative to the desired path by turning all the wheels through a small angle and driving the tractor forward until the translation error is eliminated. 17 A gantry tractor according to claim 14 where the modules are latched together where all the wheels are oriented substantially at right angles to the long axis of the truss where the path of the tractor, when its tools are engaged with the ground, is controlled by continuously monitoring the location of two or more hitch points and correcting the rotation error relative to the desired path by speeding up the lagging wheels where the amount of speed up is proportional to the lateral distance of each wheel from the leading pair of wheels. 18 A gantry tractor according to claim 14 which can be manoeuvred along a curved path by unlatching the modules so they can rotate relative to each other about their common hitch points and then controlling the angle of all wheels and the speed of all driven wheels so that all wheels follow the desired path. 19 A gantry tractor according to claim 18 where the desired trajectory of the leading and trailing hitch points of each module is converted to a desired centre of curvature and rate of rotation about this centre for each module. The instantaneous wheel speeds and wheel angles can then be calculated and implemented by an appropriate control system.