WO2005101945A2 - Off road vehicle steering systems - Google Patents

Abstract

A six wheeled vehicle with two front steerable wheels and four rear coaxial non-steerable left and right wheels pair driven by separate longitudinal shafts fitted with bevel gears of unequal diameter driving each wheel via an integral speed reduction/correction gearbox further driven by speed correcting hydraulic motors. The rear wheels are driven a speed which produces the same centre of curvature for the path of the vehicle as the driver-selected angles of the front wheels. A vehicle with individually driven wheels at least one of which is steerable where the speed of driven wheels and wheels angles are integrally controlled to produce a single centre of curvature for the path of the vehicle and where steerable wheels are driven by a gear train including a substantially vertical shaft allowing the wheel to be turned at least 180°. A gantry tractor consisting of plurality of four wheeled modules hitched together where the hitch angle can be controlled by a pair of actuators linking together the corners of the modules.

Description

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 AND PRIOR ART

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 ofthe 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 ofthe 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. In other words, 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 ofthe 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 ofthe 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 ofthe 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 ofthe slope traversed increases, the uphill drive wheel eventually loses traction and the front ofthe vehicle swings down the hill. In short, the grip ofthe 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 ofthe 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 ofthe introduction of a scuffing problem on turning. For example the elimination ofthe 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 ofthe vehicle along a curved path usually involves rotation, and rotation ofthe 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 (i.e. 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 The essential feature of the invention previously proposed by Spark (Australian Provisional Application PR 0473 (03-10-2000) and Patent Cooperation Treaty Application PCT/AU01/01247 (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 ofthe 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 previous 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 ofthe 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 ofthe path of the vehicle and the root mean square wheel speed, and the second joystick could be used to determine the direction ofthe 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 ofthe path of the vehicle and the root mean square wheel speed.

Deficiency of the previously proposed inventions (PCT7AU01/01247 and PCT/AU03/00035)

The first patent application cited above enumerates the control equations that must be satisfied if the steering effect ofthe wheel speeds is to be identical to the steering effect ofthe 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. Two means of accounting for longitudinal slip and slip angle are described in PCT/AU03/00035. Longitudinal slip is defined as logarithmic slip i, which is given by the equation: i = ln(ω'r_e/V cos α)

Where V is the velocity ofthe centre of the wheel across the ground, r_e is the effective radius of the wheel, is the slip angle and ω' is the actual speed of rotation ofthe wheel. Note that the same equation can be used for both traction and braking, where i will be negative for the latter case. For wheel spinning and wheel skidding i will be positive and negative respectively.

Note that it is only feasible to correct for the linear portion of slip angle α and longitudinal slip i. For the remainder of this document the effects of slip angle and longitudinal slip will be assumed to be negligible.

Whereas the vehicles described in PCT/AU01/01247 can best be driven by means of hydrostatic drives, the vehicles described in PCT/AU03/00035 can best be driven by means of shafts and gears. The latter mechanical drives are capable of higher efficiencies.

DRAWINGS

In order that prior art and 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(a) is a plan view of the most.general four wheel steering/four wheel drive variant ofthe invention.

Figure 1 (b) shows three alternative driver interfaces for this vehicle.

Figure 2(a) depicts the special case where the centre of curvature of the path of the path ofthe vehicle lies on the transverse axis ofthe vehicle.

Figure 2(b) shows two alternative driver interfaces for this vehicle.

Figure 3(a) depicts the special case where the centre of curvature of the path of the path ofthe vehicle lies on the axis ofthe rear wheels.

Figure 3(b) shows two alternative driver interfaces for this vehicle.

Figure 4(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 4(b) shows the detailed structure of each differential and its associated steering differential.

Figure 5(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 5(b) shows that when the centre of curvature ofthe path ofthe vehicle lies on the axis of the rear wheels, three differentials and three associated steering differentials are required.

Figure 5(c) shows that when the centre of curvature ofthe path of the vehicle lies on the transverse axis ofthe vehicle, the front differential and associated steering differential can be replaced with two pair of right angle drives.

Figure 5(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 6(a) shows a four wheel steering/four wheel drive vehicle where four speed-correcting differentials are integrated with four speed reduction gearboxes close coupled to the wheels.

Figure 6(b) shows the construction of a combined speed reduction gearbox/ speed-correcting differential.

Figure 7 shows the layout ofthe hydrostatic drives to the speed-correcting motors.

Figure 8(a) shows the layout ofthe hydrostatic drive to the speed-correcting motors close coupled to the four rear wheels where the steering effect ofthe speed of all four wheels is identical to the steering effect ofthe angles of all six wheels.

Figure 8(b) shows the construction of a combined speed reduction gearbox/ speed-correcting differential suitable for driving an inner drive wheel.

Figure 9 shows the layout of a simplified hydrostatic drive to the speed-correcting motors close coupled to the four rear wheels.

Figure 10 shows the layout of an improved simplified hydrostatic drive to the speed-correcting motors close coupled to the four rear wheels.

Figure 11 shows the power train to a driven wheel which can be turned through 180 ° .

Figure 12 shows the power train to a driven wheel which can be turned through 180 °where the wheel rolls around the axis of turning.

Figure 13 shows the power train to a driven wheel which can be turned through 180 ° where a turn-correcting differential is mounted above the wheel.

Figure 14 shows the power train to a driven wheel which can be turned through 180 ° where a combined speed-correcting/tum-correcting differential is mounted above the wheel.

Figure 15 shows the power train to a driven wheel which can be turned through 180 ° where a steering differential also corrects for turning ofthe wheel. Figure 16 shows the power train to a driven wheel which can be turned through 180 ° where a combined speed-reducing gearbox/speed-correcting differential also corrects for turning of the wheel.

Figure 17 shows the five possible error states of a guided vehicle.

Figure 18 shows the ideal path for eliminating errors.

Figure 19 shows the simultaneous correction of both translation and rotation errors.

Figure 20 shows a gantry tractor made by latching four modules together.

Figure 21 shows the unlatched gantry tractor manoeuvring around obstacles.

Figure 22 shows the relationship between the desired path of the module and its centre of curvature.

Figure 23 shows an alternative path through a gate.

Figure 24 shows one means of latching the modules together.

Figure 25 shows a second means of latching the modules together.

Figure 26 shows the relationship between the hitch angle and length of actuators.

Figure 27 shows telescoping hydraulic actuators.

Figure 28 shows an alternative driver interface.

Figure 29 shows the relationship between the position of driver controls and the centre of curvature of the path ofthe vehicle.

Figure 30 shows the operation of a second alternative driver interface.

Some relevant embodiments of previous inventions

In the four wheel steering/four wheel drive variant ofthe invention depicted in Figure 1, an internal combustion engine 1 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 1 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 ofthe wheels 6,12, 7 and 13 are shown as φ_x ,φ₂ ,φ_s and φ₄ respectively.

The effective rotational speed of the wheels 6, 12, 7 and 13 are ω_λ , ω₂ , ω₃ and ω respectively.

The driver controls the vehicle by selecting the radius of curvature ofthe vehicle's path and the sense of rotation by rotating the joystick 14. If the joystick 14 is not turned the radius of curvature of the path ofthe vehicle will be infinity and the vehicle will move in a straight line parallel to the direction of displacement of the joystick 14. If the joystick 14 is twisted as far as it will go in a clockwise direction, the radius of curvature ofthe path ofthe 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 ofthe vehicle is given by:

^ = coi(90⁰θ f θ_m = (R_x ² +R²)^m /t

Where t is the track ofthe vehicle, θ is the rotation ofthe joystick and θ_msx is the maximum rotation of the joystick 14.

If the driver displaces the rotatable joystick 14 at an angle ψ to the straight ahead position, the direction ofthe of curvature of the path ofthe vehicle will by at right angles to the direction of joystick displacement and R_x and R_y will be given by the following equations:

R = R/(tanV + l)^1/2

and R_γ = R tan ψ /(tan² ψ +1)^1/2

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 ofthe path ofthe vehicle is now specified by the two components R_x and R₇ . He selects the root mean square ofthe four wheel speeds by the amount of displacement of the joystick 14.

The control system then rotates the four drive wheels to the following angles:

t φ_λ = (b/2-R_r)/(R_x -t/2) tanφ₂ = (b/2-R_r)/(R_x +t/2) tanφ₃ = b /2+R_r)/(R_x -t/2) tanφ₄ = (b/2+R_r)/(R_x +t/2)

Where b is the wheel base of the vehicle, R_r is the displacement of the centre of curvature forward ofthe centre of the vehicle and R_x is the displacement ofthe centre of curvature to the right of the centre ofthe vehicle. The amount of displacement ofthe joystick d determines the root mean square ofthe four wheel speeds (RMSWS) according to the equation:

RMSWS = Kd = (ω²+ω² +ω² +ω²)^{1 2} 12

where K is an appropriate constant.

The individual wheel speeds are given by the equations:

ω = KdR_x IRMSR where R² = (bl2-R_Y f +(R_X -tl2) ²

ω₂ = KdR, IRMSR where R₂ ² = (bl2-R_Y +(R +t/2)²

fi>₃ = KdR₃ /RMSR] where R² = (b/2+R_r)² +(R_X -tl2f

ω₄ = KdR₄ IRMSR] where R² = (b/2+R_yf +(R_x +t/2)²

And RMSR is the root mean square radius, which is given by:

RMSR = (R² +R₂ ² +R₃ ² +R²)^1/2 12 = (R² +R² +t² /4+b² /4)^1/2

Note that when the rotation of the joystick θ is a maximum the radius of curvature will be zero and the direction of the displacement d of the joystick 14 will be immaterial. It will be natural for the driver to push the joystick 14 forward in this case to commence forward rotation.

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).

Note that the technique of making the steering effect of wheel speeds identical to the steering effect ofthe 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 ofthe (usually closed 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 clamping forces are applied to the front wheels and equal clamping 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 clamping 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 ofthe ground to exert sideways forces on the wheel will also decrease. Since there is no direct control ofthe 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 ofthe 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 clamping force applied to all wheels if one or more wheels stop turning. This enables the locked wheels to turη 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.

In vehicles with hydrostatic drives, engine braking is usually provided by engaging a lower drive ratio. 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 (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 ofthe vehicle will be identical to the centre of curvature ofthe path ofthe vehicle.

The general embodiment ofthe previous inventions

The general embodiment of the invention is shown in Fig 1(a). Alternative means of driver control are shown in Fig 1(b). The preferred means of driver control is by means of a rotatable joystick 14. Alternatively, one joystick 15 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 16 could be used to determine the direction of the centre of curvature.

Alternatively a steering wheel 17 (or steering knob or lever) could be used to determine the radius of curvature ofthe path of the vehicle and the root mean square wheel speed, and a second joystick 18 could be used to determine the direction of the centre of curvature.

A disadvantage of the variant ofthe 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 2(a) shows that if R₇ = 0, the eight general control equations become:

tan^ = (b/2)/(R_x -t/2)

tanφ₂ = (bl2)l(R_x +tl2)

tan ₃ = (bl2)l(R_x -tl2) = tan^

tan^₄ = (bl2)l(R_x + tl2) = tanφ₂

and ω = KdR_λ IRMSR where R² = b²1 + (R_x -t/2)²

ω₂ = KdR₂ IRMSR where = b² IA + (R_x + t/2)²

ω₃ = KdR₃ IRMSR where R² = b²1 + (R_x -t/2)² = R²

ω₄ = KdR₄ IRMSR where R² = b²1 + (R_x + t/2)² = R

Where RMSR = (R_x +b² 1 A + f I A)¹¹² In this case only two wheel angle control systems are required since φ_λ =φ₃ and φ₂ =φ₄. .

Similarly only two wheel speed control systems are required since -y. -ω₃ and ω₂ =ω₄.

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 14 can be replaced with a normal joystick 15 where the forward displacement d determines the root mean square wheel speed and the lateral displacement determines the radius of curvature ofthe path of the vehicle where moving the joystick 15 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 17 can be used by the driver to select the radius of curvature ofthe path of the vehicle. The root mean square wheel speed can be selected with a speed control lever or pedal 18. See Figure 2(b)

The second special case

Figure 3(a) shows that if R_r = - b 12 , then the eight control equations become:

tan^ = bl(R_x -tl2)

tanφ₂ = bl(R_x +tl2)

tanφ₃ = tan^₄ = 0

ω_x = KdR, I RMSR where R² = b² + (R_x - 112f

ω₂ = KdR, IRMSR where R = b² +(R_X +tl2)

ω₃ = KdR₃ 1 RMSR where R₃ ² = (R_x -tl 2)²

ω₄ = KdR₄1 RMSR where R² = (R_x +tl2)²

where RMSR = (R_x +b²12 + t² In this case no steering system is required for the rear wheels since φ₃ and φ₄ are zero. See

Figure 11 (a). 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 3(b) and 5(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:

R SR = (R² +t² /4)^{1 2}

If the rear wheels are free wheels the RMSR for the front driven wheels is given by:

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 θ and ψ . 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 θ , ψ 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 1 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 ofthe wheels to be varied from maximum forward to zero to maximum in reverse. The on board computer is used to alter the displacement ofthe pumps to produce the desired wheel speeds.

In smaller vehicles, such as wheel chairs, the wheels could be conveniently driven by electric motors. Similariy 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 ofthe invention, higher wheel speeds and smaller wheel angles are required. Furthermore the displacement ofthe centre of curvature in the longitudinal direction is constant. In the four wheel steering/four wheel drive vehicle described in Figures 2(a) and 5(a) R_r = 0. In the two wheel steering/ four wheel drive or two wheel steering/ two wheel drive vehicles described in Figures 3(a) and 5(b) R_γ =- 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 ofthe 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 ofthe steerable wheels. Speed can be controlled with a speed control lever or pedal. See Figures 2(b) and 3(b).

Figure 4(a) shows the general arrangement of components required for computer integrated steering/drive system utilising a mechanical drive. An internal combustion engine 19 drives a gearbox 20 which in turn drives a central differential 21, which in turn drives both a front "tail" shaft 22 and a rear tail shaft 23. The front "tail" shaft 22 is linked to a steering differential 24 by a pair of gears 25 and 26 The rear tail shaft 23 is linked to the steering differential 24 by means of a pair of gears 27 and 28 with the same speed ratio as gears 27 and 28, where gears 27 and 28 do not mesh, but are linked by means of an idler gear 29. The input to the steering differential is driven as required by means of a hydraulic motor 30. Note that when the vehicle is proceeding straight ahead (i.e R_x = infinity), the speed of the two tail shafts should be identical. This is positively achieved if the hydraulic motor 30 is stationary.

When the vehicle turns it may be necessary for the speed of the front tail shaft 22 to be greater than the speed of the rear tail shaft 23 if wind up is to be avoided. This can be achieved by driving the hydraulic motor 30 at the right speed (in the right direction).

A steering differential 31 is also linked in parallel with the front differential 32. This is driven at the appropriate speed by a hydraulic motor 36. A steering differential 34 is also linked in parallel with the rear differential 35. This steering differential 34 is also driven at the appropriate speed by a hydraulic motor 36. Note that the front and rear differentials are driven by front and rear tail shafts 22 and 23 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 4(b) shows the detailed layout ofthe rear differential 35 and the associated steering differential 34. The casings (or housings) have been omitted in the interests of clarity. Although bevel gear differentials 34 and 35 have been shown here, differentials using over lapping straight cut planetary gears can also be used.

Figure 5(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 5(b) shows that when the centre of curvature of the path of the vehicle lies on the axis of the rear wheels, three differentials 21, 32 and 35 and their associated steering differentials 24, 31 and 34 are required. Figure 5(c) shows that when the centre of curvature ofthe path ofthe vehicle lies on the transverse axis of the vehicle the front differential 32 and associated steering differential 33 can be replaced with a pair of left hand right angle drives 37 and a pair of right hand right angle drives 38

Figure 5(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 35 and associated steering differential 34 can be replaced with a pair of left hand right angle drives 39 and a pair of right hand right angle drives 40

Figure 6(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 speed-correcting differentials integrated into speed reduction gear boxes close coupled to each wheel. In this case engine 19 drives gear box 20 which in turn drives an integrated front and rear tail shaft 44 by means of right angle drive 45 which in turn drives front and rear drive shafts 46 and 47 by means of right angle drives 48 and 49. The front and rear drive shafts 48 and 49 drive combined speed reduction gearboxes/speed-correcting differentials 50, 51 , 52 and 53. Each combined speed reduction gearbox/speed-correcting differential is also driven by wheel speed correcting hydraulic motors 54, 55, 56 and 57. 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 6(b) shows the detailed layout of the combined speed reduction gearbox/speed-correcting differential. This is a three stage compound epicyclic gearbox where the speed-correcting differential is incorporated into the first stage. Power is transmitted to the combined speed reduction gearbox/speed-correcting differential by means of drive shaft 58 which drives sun gear 59. Sun gear 59 drives planet gear 60, which is also driven by annular gear 61. Annular gear 61 is driven by the speed correcting hydraulic motor 62 as required. Planet gear 61 is supported by arm (or cage) 63, which drives the sun gear of stage two 64. Stage two 64 and stage three 65 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) 65 ofthe last stage is connected to the drive wheel 66. 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 ofthe 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 ofthe speed correcting hydraulic motor will have little effect on the overall drive efficiency since only a small fraction ofthe output power is provided by the hydraulic motor.

Note that whereas steering differentials have one input and two outputs, speed-correcting differentials have two inputs and one output. Whereas the single input to a steering differential is the speed of the steering motor, the two outputs are the equal but opposite speed corrections to the left hand and right hand wheels. Whereas the two inputs to a speed-correcting differential are the speed of the primary drive shaft and the speed ofthe speed-correcting motor, the single output is the speed of the driven wheel.

Figure 7 shows a hydraulic circuit which would allow the wheel speed correcting hydraulic motors 54, 55, 56 and 57 to rotate at appropriate speeds. Each hydraulic motor is driven by a variable displacement pump. These pumps 67, 68, 69 and 70 are driven by a common shaft 85 at a speed proportional to the tail shaft speed by means of gears 86 and 87. 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 6 and 7 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 root mean wheel speed RMSWS. The on board computer then calculates the angle and speed of each wheel that ensures that the steering effect ofthe wheel angles is identical to the steering effect of the wheel speeds. The on board computer then turns the wheels 88, 89, 90 and 91 to the calculated angles. The computer also calculates the appropriate speed for each wheel speed correcting hydraulic motors 54, 55, 56 and 57, and implements these speeds by adjusting the squash plate angles of the respective variable displacement hydraulic pumps 67, 68, 69 and 70. Figure 8(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 ofthe angles of all six wheels (i.e. the four coaxial drive wheels, and the two steerable non driven wheels).

In this vehicle engine 19 drives gearbox 20, which in turn drives a tail shaft 23 via right angle drive 45. The tail shaft 23 drives a drive shaft 71 via a second right angle drive 72. The drive shaft 71 drives four combined speed reduction gearboxes/speed-correcting differentials 73, 74, 75 and 76. The speed correcting differentials 73, 74, 75 and 76 are also driven as required by four wheel speed correcting hydraulic motors 77, 78, 79 and 80. These hydraulic motors 77, 78, 79 and 80 are driven by variable displacement hydraulic pumps 81 , 82, 83 and 84 respectively. These hydraulic pumps are driven by a common shaft 85, which is driven at a speed proportional to the tail shaft speed by means of gears 86 and 87. The advantage of this arrangement is that it enables all four driven wheels to be positively driven at slightly different speeds on turning. The outer wheels 88 and 91 may be slowed down and speeded up more than the inner wheels 89 and 90.

Figure 8(b) shows the detailed layout of a combined speed reduction gear box/speed-correcting differential suitable for driving an inner wheel. In this case the drive shaft 71 must pass through the combined speed reduction gearbox/speed-correcting differential so that it can also drive the outer wheel 91.

Figure 9 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 92 is used to drive all four speed correcting hydraulic motors 77, 78, 79 and 80 which are now connected in series. The displacement ofthe inner and outer speed correcting hydraulic motors is inversely proportional to the distance ofthe respective wheels from the centre line ofthe vehicle.

In the vehicles depicted in Figures 8 and 9 the computer integrated steering drive system can be implemented as follows:

The driver selects the radius of curvature ofthe path ofthe vehicle with a steering wheel and the root mean square wheel speed with a speed control lever or pedal. The on board computer calculates the appropriate angles ofthe front wheels and the individual speeds of the four rear drive wheels, and the required speed ofthe four wheel speed correcting hydraulic motors 77, 78, 79 and 80. 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 81, 82, 83 and 84 or the single variable displacement pump 92.

It should be noted that if the speed ofthe 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).

IMPROVEMENTS TO THE COMPUTER INTEGRATED STEERING/DRIVE SYSTEM OUTLINED ABOVE: DISCLOSURE OF THE PRESENT INVENTION

Improvements to the Application ofthe Computer integrated Steering/Drive System to Large Dump Trucks:

PCT/AU03/00035 describes large dump trucks with two steerable non-driven wheels at the front and four coaxial driven wheels at the rear where the speed of each driven wheel is positively controlled so that they tend to produce a radius of curvature for the path ofthe vehicle which is identical to the radius of curvature which is produced by the angles of the front wheels. A disadvantage of this configuration, which is depicted in Figures 8 and 9, is that it would be difficult to remove the inner rear wheels, since such removal would require the removal of the outer rear wheel, the outer combined speed reduction gear box/speed correcting differential, the horizontal drive shaft and the arm that connects the combined speed reduction gear box/speed correcting differential to the chassis of the vehicle.

An improved configuration is shown in Figure 10. In this configuration the inner supporting arms are deleted and the inner combined speed reduction gear box/speed correcting differentials 74 and 75 are connected to the inside ofthe two remaining arms 93 and 94. The inner and outer combined speed reduction gear box/speed correcting differentials 73, 74, 75 and 76 are driven by means of longitudinal shafts 95 and 96 located inside or adjacent to the left hand and right hand arms. The rear end ofthe longitudinal shafts are fitted with two bevel gears 97 and 98 of different diameters. These bevel gears drive the inner and outer combined speed reduction gear box/speed correcting differentials 73 and 74 respectively. The second input to each combined speed reduction gear box/speed-correcting differential is provided by hydraulic (or electric) motors 77, 78, 79 and 80.

This configuration will allow the inner drive wheels to be simply removed inwards. A further improvement would be to extend the main gear box output shaft 99 forward so that it could drive the two front wheels 100 and 101 via a pair of bevel gears 102, four universal joints 103, two splines 104 and left and right hand combined speed-reducing gearbox/speed-correcting differentials 105 and 106, where the secondary input to the integrated speed reduction/speed- correcting gearbox is provided by left and right speed-correcting hydraulic (or electric) motors 107 and 108 which are driven via flexible hoses (which are not shown) by two separate variable displacement pumps 109 and 110. These pumps are driven at a speed proportional to the speed of the longitudinal drive shafts 95 and 96, and the squash plate angle of the pumps is controlled to produce the optimum speed ofthe front wheels, so that the steering effect of the speed of each front wheel is identical to the steering effect of all the wheel angles.

Although in principle only five combined speed reduction gear box/speed correcting differentials would be required to independently control the speed of the six drive wheels, the provision of six speed correcting hydraulic motors would enable the average speed of the speed correcting motors to be minimised. The driver would control the speed of the vehicle by selecting the root mean square wheel speed (RMSWS). The on board computer then calculates the desired individual wheel speeds. The speed of each wheel is determined by the common speed of the drive shafts and the speed of each speed correcting hydraulic motor. If the speed of the shaft is made to correspond to the algebraic average of the desired wheel speeds then the average of the magnitude of the desired speeds of the six hydraulic motors will be minimised.

For a given desired wheel speed there is an infinite number of ways of splitting the inputs to combined speed-reducing gear box/speed-correcting differential between the speed of the common drive shaft and the speed of the speed correcting hydraulic motor. The speed ofthe nth wheel will be given by the following equation:

ω_n = K_sω_s + K_cω_c

where ω_n is the speed of the nth wheel, ω_s and ω_c are the speeds of the common drive shaft and the nth speed-correcting hydraulic motor respectively, and Ks and K_c are the ratios ofthe wheel speed to ω_s and ω_c when ω_c = 0 and ω_s = 0 respectively.

If the driver-selected root mean square wheel js chosen for the speed of the common drive shaft, the equations for the speed of the speed-correcting hydraulic motors will be simplified, but the average of the magnitude of the speeds of the speed-correcting hydraulic motors will not be minimised. Such minimisation is achieved if the speed of the common shaft ω_s is the algebraic mean of all the required wheel speeds.

A third option is to choose the algebraic average of the desired speed of the wheels on one axle for the speed of the common drive shaft ω_s. The advantage of this arrangement is that the desired speed ofthe left hand speed-correcting hydraulic motor will always be equal but opposite that of the corresponding right hand hydraulic motor. This means that a single variable displacement hydraulic motor can be used to drive both motors in series.

Similarly, the four rear speed correcting hydraulic motors shown in Figure 10 could be connected in series to a single variable displacement pump driven at a speed proportion to the common drive shaft speed, if this drive shaft speed corresponds to the average of the desired speed ofthe four rear wheels. In this case the displacement of the inner hydraulic pumps would have to be greater than the displacement of the outer pumps, in proportion to the distance from the centre line ofthe vehicle of the outer and inner tyre contact patches.

An alternative arrangement would be to make the capacity of the hydraulic motors constant, but to drive the outer hydraulic motors with a larger (or faster) variable displacement pump than that used to drive the inner hydraulic motors.

Separate variable pumps would be required to drive the front speed correcting hydraulic motors, since the outer front wheel will need to be speeded up more than the inner front wheel will need to be slowed down.

The control protocol will be as follows:

1. Driver selects RMSWS, R _x and R _y.

2. On-board computer calculates all desired wheel speeds and angles.

3. Computer calculates desired speed of common drive shaft and desired speed of each speed- correcting hydraulic motors.

4.Control system implements the speed of common drive shaft, al! speed-correcting hydraulic motors and angles of all steerable wheels.

Application of the Computer Integrated Steering/Drive System to Vehicles Capable of Zero Radius of Curvature with Mechanical Drives to All Wheels.

PCT/AU03/00035 describes wheeled vehicles where the driven wheels are rotated about substantially horizontal axes by means of hydraulic wheel motors, electric wheel motors, or by means of drive shafts which connect the wheels to a prime mover (such as an internal combustion engine) via a gear box.

The advantage of hydraulic and electric wheel motors is that they allow the wheels to be turned (about substantially vertical axes) through large angles. Zero radius of curvature can be achieved if all or some of the wheels can turned through a total angle of 180 degrees. The disadvantage of the mechanical shaft drives depicted in PCT/AU03/00035 is that constant velocity joints are required to transmit power to the turned wheels. Unfortunately constant velocity joints experience very large forces if power is transferred between axes mutually inclined by more than 45 degrees. If constant velocity joints are used, an angle range of 180 degrees is not feasible.

The advantage of mechanical drives is that they are more efficient than electric drives, which in turn are more efficient than hydraulic (i.e. hydrostatic) drives.

A system is first described here where mechanical drives to the wheels are employed, but where the drive wheels can be turned through 180 degree (or more). In the system proposed power is transmitted from a horizontal drive shaft to the driven wheels via a substantially vertical shaft, which corresponds (or is close) to the turning axis ofthe driven wheel (sometimes referred to as the kingpin axis). The basis of this system is shown in Figure 11.

In this system the horizontal drive shaft 107 can be located well above the driven wheels so that the drive shaft 107 does not interfere with the turning ofthe driven wheels 108 about substantially vertical axes. Reference to Figure 11 shows that power is transmitted from the horizontal shaft 107 to the vertical shaft 109 by means of a pair of bevel gears 100 and 101. Power is transmitted from the vertical shaft 109 to the horizontal axis of the wheel 112 by means of a second pair of bevel gears 113 and 114. The two pairs of bevel gears can be used to form a two-stage reduction gearbox.

A potential problem with the basic arrangement described above is that the turning and rotation of the driven wheels are interlinked. If both the vehicle and the horizontal drive shaft 107 are stationary, turning ofthe wheel 108 (about a vertical axis) must be accompanied by rotation ofthe wheel 108 "on the spot" (about its horizontal axis). If the left and right hand driven wheels are turned the same amount in the same direction, they will rotate "on the spot" in opposite directions.

The drive system above is used for the front wheel drive of some four wheel drive tractors and off-road trucks. In this case the "rotation on the spot" problem is eliminated by the presence of a differential 115 between the left and right horizontal drive shafts. This differential allows the driven wheels be turned without on the spot rotation by allowing the left and right drive shafts to rotate equal amounts in opposite directions.

A key feature ofthe computer integrated steering drive system described here is that the speed of each driven wheel is always positively controlled. If differentials are used they are always linked in parallel to matching steering differentials. See Figures 4 and 5.

The alternative method of positively controlling the speed of the driven wheels is to use speed- correcting "differentials" close coupled to the driven wheels. The output of these speed-correcting differentials is the desired wheel speed, while the inputs are the drive shaft speed and the necessary speed correction by means of a hydraulic or electric speed-correcting motor.

In the absence of unrestrained differentials, three methods of counteracting the troublesome linkage between the rotation of a driven wheel about vertical and horizontal axes will now be described

One method depicted in Figure 12 is to offset the centre of the tyre contact patch a distance r ^ from the vertical turning axis. If the ratio of the effective radius of the driven wheel r _β to the said offset r ι is equal to the ratio ofthe number of teeth N ₂ on the gear attached to the wheel and the number of teeth N ^ on the pinion gear which engages the afore mentioned gear, then the turning driven wheel will roll over the ground with minimal scuffing.

A second method of overcoming the linkage between the rotation ofthe driven wheels about vertical and horizontal axes depicted in Figure 13 is to mechanically link the rotation ofthe wheel about its vertical axis to the rotation ofthe secondary input shaft of a turn-correcting differential. In this case the horizontal drive shaft is rotated at the correct speed and the turn-correcting differential merely counteracts the tendency of the driven wheel to rotate when it is turned.

A third and much more elegant method of overcoming the troublesome linkage between the rotation ofthe driven wheel about vertical and horizontal axes is to take advantage of the presence of a steering differential or wheel mounted speed-correcting differentials.

In this case the speed ω ₀ of the steering motor 116 or speed-correcting motor 117 will be a function of both the necessary speed correction and the rate of change of wheel angle ω _a (about the vertical axis) according to the equation:

ω_c = con /K_c- K_sω_s /K_c - K_aω_a /K_c Where ω_n, ω_s, ω_c and ω_a are the angular speeds of the tumable driven wheel about its horizontal axis, the drive shaft, the speed and turn correcting hydraulic motor and the turnable driven wheel about its turn axis, and where Kg = ω_n /ω_s when ω_c and ω_a are zero Kc = ω_n /ω_c when ω_s and ω_a are zero, and Ka = ω_n /ω_a when ω_s and ω_c are zero

In this case the rate of change of each wheel angle ω_a will be measured and the speed of the steering motor or speed correcting motor ω_c will be corrected accordingly.

Figure 14 depicts the case where speed-correcting differentials are close coupled to each turning driven wheel.

Figure 15 depicts the case where a steering differential is used to correct the speed of the turning driven wheels.

Figure 16 depicts the case where a combined speed-reducing gearbox/speed-correcting differential is mounted inside the turning driven wheel.

Application of the Concept of the Computer Integrated Steering/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 (TE). 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 (RE). This is defined as the rotation of the vehicle relative to the direction ofthe desired path, where clockwise rotation is considered positive. Although the ultimate 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 ofthe 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 ofthe vehicle.

Figure 17 shows there are five possible vehicle states.

Figure 17(a) shows a vehicle where both the translation and rotation error are zero. In this case no corrective action is required.

Figure 17(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 17(c) shows a vehicle where both the translation error and the rotation error are positive. If no corrective action is taken the path ofthe vehicle will diverge from the desired path and the translation error will become increasingly positive.

Figure 17(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 remain parallel to the desired path, so that the translation error will remain constant.

Figure 17(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 17(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 18(a)) then the radius of curvature (ROC) ofthe circular path required is given by the equation:

ROC = TE/(1 - cos RE) The vehicles shown in Figures 17 (c), 17(d) and 17(e) must first be brought to the state shown in Figure 17(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 ofthe vehicle reference point (in this case the midpoint ofthe 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 of say 2/3 ofthe calculated value, (so that the steering wheel angle is initially set at 1.5 of the calculated value), continuous monitoring of the position and heading of the vehicle, and correction ofthe 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 ofthe rear wheels is the mirror image ofthe effective angle ofthe front wheels about a plane which contains the transverse axis ofthe vehicle, the centre of curvature ofthe path of the vehicle will always lie on the transverse axis of the vehicle. In this case the speed ofthe right front wheel should be the same as the speed of the right rear wheel, and the speed ofthe 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 in PCT/AU03/00035. 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 ofthe vehicle from the desired path ofthe vehicle, measured perpendicular to the desired path (as shown in Figure 18(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 (i.e. without translation) and pure translation (i.e. 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 (i.e. consecutively). A major advantage is that vehicles in states depicted in Figures 17(c), 17(d) and 17(e) can be corrected without first changing to the condition depicted in Figure 17(b).

If the translation and rotation error have the same sign (see Figure 17(c) 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 17(c) 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 ofthe yehicle 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 19(a).

If the centre ofthe 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 ofthe vehicle Ro is given by the equation:

Ro = TE/(1 - cos θa)

The position ofthe desired centre of curvature ofthe path of the vehicle relative to the vehicle frame of reference is given by the equations:

Rx = R₀ COS (R_E + θa)

And R_γ = Ro sin (R_E + θ_a)

The effective wheel angles required to correct the translation error (but not the rotation error) are given by the equations: tanφ_λ = (b/2-R_Y)/(R_x -t/2) tanφ₂ = (bl2-R_Y )l R_x +t!2) ta φ₃ = (b!2+R_Y)/(R_x -t/2)

and tan^₄ = bl2+R_Y)/(R_x +t/2)

The time required to correct the translation error is given by the equation:

Time = θ_aRo/V₀

where V_o is the velocity ofthe centre of the vehicle.

The required rate of rotation Ω ofthe vehicle about its own frame of reference is given by the equation: Ω = (RE + θ_a)/time = V₀(RE + θa)/θ_aR₀

The rate of rotation Ω of the vehicle about its own frame of reference is also given by:

Ω = 2V₀sinΔφ/(b² + 1²)^1/2 = V₀(RE + ΘJ/θaRo

Therefore sinΔφ = (RE + θ_a) (b² + t²)^{1 2}/2θ_aR₀ = (RE + θ_a) (b² + 1²)^{1 2}(1 - cosθ_a)/ 2θ_aTE

Where Δφ is the increase in the basic wheel angles necessary to eliminate the rotation error.

Although the desired radius of curvature R₀ should remain unchanged, the components R_x 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 17(d)), 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 θ_a This strategy is shown in Figure 19(b).

If the translation error is zero but the rotation error is positive (as shown in Figure 17(e)), 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, φi and φ₂ will be - RE and φ₃ and φ 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 sjnce 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 19(c).

Application of the Concept of Computer Integration 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 ofthe 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 20, 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 between +90 degrees and -90 degrees.

Working mode: Figure 20 shows the proposed gantry tractor is working mode. In this mode the modules are latched together to form a rigid truss. The position ofthe 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) ofthe gantry can be monitored by some form of compass, or it can be deduced from the position ofthe two said hitch points. The operating procedure is as follows:

1. The gantry will start from the non-worked (e.g. 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 ofthe 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

5. At the end ofthe 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 21 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 (e.g. 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 ofthe 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 ofthe path of the centre ofthe module Ro begins to reduce from infinity. The centre of rotation ofthe module is given by the intersection ofthe normal to the path of the front hitch point and the normal to the path of the rear hitch point. See Figure 22.

5. 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 ofthe centre of the module can be expressed as the speed of a notional castor located at the centre ofthe module. The relation between ω₀ and the root mean sqgare wheel speed RMSWS is given by the equation: ω₀ = RMSWS/(1 + (t²/4R₀ ²+ b²/4R₀ ²)^1/2) = RMSWS/(1 + (t² +b )^1/2/2R₀) 6. The individual effective wheel angles ofthe module are given by the equations:

tanφ₂ = (bl2-R_Y )/(R_x +t/2) tanφ₃ = (b/2+R_Y)/(R_x -t/2)

and tan^₄ = bl2+R_Y)l R_x +t/2)

The individual effective wheel speeds are given by the equations:

on = ωoFVRo where R² = (b 12 - R₇ )² + (R_x - 112) ²

ω₂ = ω₀R₂/R₀ where R² = (b!2-R_Y )² +(R_x +t/2)²

ω₃ = ω₀Rs/Ro where R² = (b 12 + R₇ f + (R_x - 112)²

ω = ωoR^Ro where R² = (b/2+R_Y)² +(R_x +t/2)²

where ω₀ = KdRo/ RMSR where R₀ ² = R_x ² + R_γ ²

and RMSR = (R_x ² + R_γ ² + t²/4 + b²/4)^1/2 = (R₀ ² + t²/4 + b²/4)^1/2

Note that as the front or rear hitch points move along a circular path both the centre of curvature ofthe path ofthe module and the radius of curvature ofthe path ofthe module will change constantly.

8. The velocity of the rear hitch point can be calculated from the angular velocity Ω of the module and its radius of curvature R₀. This must be identical to the velocity ofthe 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.

10. 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. Any 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 ofthe 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 23 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 steeper angle.

Extension of the Concept of Computer Integration of the Steering System and the Drive System to Articulated Vehicles with Active Hitch Points

A gantry tractor has been described above where a plurality of four-wheeled modules 118 are hitched together. In working mode the modules 118 are latched together, by means of struts 119 , to form a rigid truss. In transport mode the modules are unlatched by effectively disconnecting one end ofthe struts 119 that latch the modules together. Figure 24 shows one method of disconnecting one end of the strut 119 by lifting it vertically so that a vertical pin 120 on the end of the strut 119 no longer engages a vertical hole 121 at the corner of the adjacent module. Figure 25 shows an alternative method of unlatching the modules where a pin 122 latching one end of the strut 124 to a rotatable sleeve 123 attached to the corner of the adjacent module is withdrawn. The other end of the strut is connected to the first module by means of a vertical hinge 125.

A further improvement will now be described

To reiterate, the essential feature ofthe computer integrated steering/drive system described above is that the steering effect ofthe positively controlled individual wheel angles is made identical to the steering effect ofthe positively controlled individual drive wheel speeds. This is a cooperative redundant system since conflict between the two steering systems has been eliminated. The advantage of this system is that if one steering system begins to fail it is backed up by the other system.

It should be borne in mind that almost all pre-existing wheeled vehicles utilise either non- redundant steering systems (such as road cars and zero turn radius mowers) or conflicting redundant steering systems (such as skid steer loaders or vehicles with no (or locked) differentials).

The traditional philosophy has been that redundancy in the steering system is bad as it leads to conflict.

The philosophy espoused here is that redundancy is good - providing it is cooperative redundancy, which leads to mutual reinforcement of the two (or more) enabled steering systems.

In articulated vehicles, the concept of cooperative redundancy can be further extended, by employing active hitch points. Normal hitch points are passive in so far as they can transmit forces but not torque between the two (or more) connected modules.

The control strategy advocated for the gantry tractor (in transport mode) described above would result in zero forces transferred through the hitch points if the control system was free of errors. However the fact that the hitch points are connected produces a level of redundancy with respect to the path ofthe centres of the modules. For example, if the trajectory of one module is in error, the trajectory ofthe leading and trailing modules must also be in error, by virtue of the connection of the hitch points.

When the modules are on the correct path, the correct angle for the hitch points can be calculated. See Figure 26. When the leading and trailing hitch points of any module are both on a circle of radius R , the radius of curvature R _m of the centre of the module will be related to R _m by the equation R _m = R _h cos β where β = sin ^"1(b/R _h). In this case the hitch angle is 2β, where β is the angle between the longitudinal axis ofthe module and the tangent to the desired circular path. This special case is shown in Figure 26.

In general the total angle ofthe hitch points is the sum ofthe angle ofthe longitudinal axes of the leading and trailing modules to the desired path of the vehicle

If the desired angle of the hitch points is positively controlled, then an extra level of redundancy is imposed on the control ofthe path ofthe vehicle. In this case the wheel speed control, the wheel angle control, and the hitch angle control are all causing the vehicle to follow the desired path. Two levels of redundancy are now operative.

Positive control ofthe hitch angles can be readily achieved by replacing the latching struts referred to above with telescopic struts 126, which could be activated by either hydraulic rams or mechanical screw actuators. See Figure 27

The relationship between the length of the left and right hand telescopic struts and the hitch angle 2 β is shown in Figure 26. In this case:

b_L = 2d₀cos(δ₀+ β) and b_R = 2d₀cos(δ₀ - β)

where do = (t² + b²)^1/2/2 and δ₀ = tan^"1(t/b)

where b_R and b_L are the required lengths ofthe right and left hand actuators respectively, 2β is the hitch angle, δ₀ is the angle subtended at the hitch point by the nearest wheel relative to the longitudinal axis ofthe module, d₀ is the distance between the hitch point and the adjacent wheels and t and b are the track and wheel base of each module respectively.

Note that when (δ₀ + β) = 90°, b_L = 0 and b_R = 2d₀cos(2δ₀ - 90)

A strategy for controlling the path ofthe articulated vehicle is now as follows:

1. The articulated vehicle is lined up at the beginning ofthe path so that all the hitch points lie on the correct position as indicated by means of a geographic positioning system (or some other navigation system). The driver selects the speed ofthe centre ofthe lead module.

2. The on board computer calculates required linear and angular velocities ofthe first module. The computer then calculates the correct individual wheel speeds and wheel angles. It also calculates the correct rear hitch angle.

3. The on board computer calculates the desired linear and angular velocities for the second module to keep it on the desired trajectory. The computer then calculates the correct individual wheel speeds and wheel angles and the rear hitch angle for the second module.

4. Steps,2 and 3 are repeated for all modules in the train. 5. The control computer then proceeds to implement all individual wheel speeds and wheel angles and hitch angles.

6. Errors detected in the path ofthe modules should be corrected in the cooperative manner described above in order to avoid conflict between the modules. Most errors will be due to small amounts of skidding ofthe driven wheels and scuffing of all wheels (where wheel spinning is regarded as negative skidding).

Alternative Driver Interface for Vehicles capable of Achieving Zero Radius of Curvature

In PCT/AU03/00035 three driver interfaces were described for four wheeled vehicles incorporating computer integrated steering/drive systems. The object of the driver interface is to enable the driver to select the desired centre of curvature of the path of the vehicle and the root mean square wheel speed (RMSWS).

The first driver interface described previously is a rotatable joystick where the direction ofthe centre of curvature is at right angles to the direction of displacement of the joystick and the root mean square wheel speed is determined by the magnitude of this displacement. The reciprocal of the radius of curvature is determined by the rotation of the joystick. If the joystick is rotated as far as it will go, the reciprocal ofthe radius of curvature will be infinity so that the radius of curvature will be zero.

The second driver interface described previously employs two joysticks where the forward movement of one joystick determines the root mean square wheel speed and the sideways movement determines the reciprocal of the radius of curvature. The second joystick is used to determine the direction of the centre of curvature ofthe path ofthe vehicle where the latter is at right angles to the displacement ofthe second joystick.

The third driver interface described previously employs a steering wheel, knob or lever, and a joystick. Here the reciprocal ofthe radius of curvature ofthe path ofthe vehicle is determined by the rotation of the said steering wheel, knob or lever, and the direction of displacement ofthe joystick will be at right angles to the direction of the centre of curvature. The magnitude of this displacement determines the root mean square wheel speed.

An alternative driver interface is first described here consisting of one joystick 127 and one speed control lever or pedal 128. See Figure 28. In this case the forward movement of the joystick 127 determines the distance of the centre of curvature of the path of the vehicle forward of the transverse axis through the centre of the vehicle (i.e. the midpoint ofthe vehicle wheelbase). The sideways movement of the joystick determines the reciprocal ofthe transverse component of the radius of curvature.

In this case R _y = K _y y

and t/R _x = tan(90 ° x/x _max )

and RMSWS = K d

The advantage of this driver interface is that the driver can easily select how far the centre of curvature ofthe path ofthe vehicle will be forward ofthe centre of the vehicle. It is suggested that the forward movement ofthe joystick 127 will have at least four detent positions. In the null detent position depicted in Figure 29(a) the centre of curvature will always lie on the transverse axis through the centre ofthe vehicle. In the backwards detent position depicted in Figure 29(b) the centre of curvature will always lie on the axis of the rear wheels. In the first forward detent position depicted in Figure 29(c) the centre of curvature will always lie on the axis ofthe front wheels. In the second forward detent position depicted in Figure 29(d) the centre curvature will always lie on a transverse axis passing through the front edge of any forward mounted tools 129 (such as a bucket or fork). The advantage ofthe last arrangement is that the orientation ofthe tool about a vertical axis can be adjusted by the driver without altering the transverse position of the tool (i.e. without moving it sideways).

A second alternative driver interface depicted in Figure 30 consists of a joystick 130 and a lever or switch 131. In this case the lever or switch 131 controls how far the centre of curvature ofthe path of the vehicle is forward of the centre of the vehicle. The forward displacement of the joystick 130 determines the root mean square wheel speed and the sideways displacement of the joystick 130 determines the reciprocal ofthe transverse component ofthe radius of curvature of the path of the vehicle.

In this case R _y = K _d d

and t/R _x = tan(90 ° x /x _max )

and RMSWS = K' y It should be noted that in all five driver interfaces described there are two ways of reversing the sense of rotation ofthe vehicle about a vertical axis when the radius of curvature ofthe path of the vehicle approaches zero.

One method is to displace the driver interface element that controls the radius of curvature ofthe path of the vehicle in the opposite direction. The second method is to displace the driver interface element that controls the root mean wheel speed in the opposite direction.

The disadvantage ofthe first method of reversing the sense of rotation ofthe vehicle is that all or some of the wheels must be turned through 180 degrees while they are not rotating. This turning will require a large torque and will cause scuffing ofthe ground and wear of the tyres.

The scuffing produced by the first method can be avoided if the second method of reversing the sense of rotation ofthe vehicle is used where the wheels are driven in reverse but not turned.

Claims

The claims defining the invention are as follows:

1. A six wheeled vehicle with two steerable wheels at the front and four coaxial non-steerable driven wheels at the rear, where the inner and outer left hand rear wheels are driven by a longitudinal shaft which runs between the left hand rear wheels, where the rear end of this longitudinal shaft is fitted with two bevel gears of unequal diameter, where one bevel gear meshes with a bevel gear which drives an outer integrated speed reduction/speed correction gearbox, the output shaft of which is fixed to the hub of the left hand outer wheel. The other bevel gear meshes with a bevel gear which drives an inner integrated speed reduction/speed correction gearbox, the output shaft of which is fixed to the hub of the left hand inner wheel. The secondary input shafts of the inner and outer integrated speed reduction/speed correction gearboxes are driven by inner and outer speed correcting hydraulic motors respectively. A right hand longitudinal shaft drives the outer and inner right rear wheels in an identical fashion to that described for the left rear wheels. He left and right longitudinal shafts are driven by the engine via the gear box and a gear train consisting ofthe gearbox output gear, left and right hand idler gears and gears fixed to the front end ofthe left and right longitudinal shafts. Each ofthe rear wheels is positively driven at a speed which tends to produce the same centre of curvature for the path of the vehicle as the driver-selected angles ofthe front wheels.

2 A vehicle according to claim 1 where the speed of the rear drive wheels and the angles of the steerable front wheels are given by the equations:

tanφ₁ = b/(R_x -t/2)

tanφ₂ = b/(R_x + 1/2)

And tanφ₃ = tanφ₄ = tanφ₅ = tanφ₆ = 0

Where t/R = t/(R_x + b²/4)^1/2 = tan( 90° θ/θ_max)

Where: fa and φ₂ are the angles of the front left and right wheels (where clockwise turns are positive) b and t are the wheel base and track of the vehicle respectively

R_x is the distance ofthe centre of curvature to the right ofthe centre line of the vehicle φ₃to φ₆ are the angles of wheels 3 to 6 θ is the angle ofthe driver's steering wheel θm-ix is the (hypothetical) angle of the steering wheel when R_x = 0

The driver selects the root mean square wheel speed (RMSWS) for all 6 wheels with a speed control pedal or lever.

The speed ofthe rear wheels are given by the equations:

ω₃ = (RMSWS/RMSR)(R_x - t/2)

ω₄ = (RMSWS RMSR)(R_x + t/2)

ω₅ = (ΕMSWS/RMSR)(R_x - ti/2)

ω₆ = (RMSWS/RMSR)(R_x + ti/2)

Where Root mean square radius (RMSR) = (R_x ² + b²/2 + 1²/4)1/2

Where the speed of wheel n is given by the equation:

Where K_s is the ratio of wheel speed to shaft speed when ω₀ = 0

And K_o is the ratio of wheel speed to hydraulic motor speed when ω_s = 0

3 A vehicle according to claim 2 where the speed of the longitudinal drive shafts are driven at the algebraic average ofthe desired speeds ofthe four rear wheels, so that the required speed ofthe left hand outer and inner speed correcting hydraulic motors will be equal but opposite that ofthe right hand outer and inner speed correcting hydraulic motors respectively, where the hydraulic motors can be connected in series with a single variable displacement pump which is driven at a speed proportional to the speed ofthe longitudinal drive shafts, where the angle ofthe squash plate is controlled to produce the desired rear wheel speeds, where the displacement ofthe inner and outer speed correcting hydraulic pumps is inversely .proportional to the distance of the centre of the inner and outer tyre contact patches from the centre line of the vehicle.

4. A vehicle according to claim 1 where the front wheels are also driven by means of a gear train consisting ofthe output shaft ofthe gearbox, a right angle bevel gear drive, left and right inner universal joints, left and right drive shafts, left and right outer universal joints, left and right integrated speed reduction/speed correcting gear boxes and left and right front wheels, where the secondary input to the integrated speed reduction/speed correcting gear boxes is provided by left and right speed correcting hydraulic motors which are driven by two separate variable displacement pumps which are driven at a speed proportional to the speed of the longitudinal drive shafts, where the squash plates of the variable displacement pumps is controlled to produce the desired speed ofthe front wheels, where the centre of curvature of the path ofthe vehicle produced by these speeds is identical is identical to that produced by the driver selected front wheel angles.

5. A vehicle according to claim 4 where the desired speeds of the steerable driven front wheels are given by the equations: co_! = (RMSWS/RMSR)R-, = Kd(b² + (R_x ² - t/2)²)/(R_x ² + b²/2 + t²/4)

ω₂ = (RMSWS/RMSR)R₂ = Kd(b² + (R_x ² + t/2)²)/(R_x ² + b²/2 + t²/4)

ω-i = K_sω_s + KoCOoi and ω₂ = K_sω_s + Koco_c2

where ω_s = (ω₃ + ω )/2 K_s

6. A vehicle consisting of two or more wheels, at two of which are driven wheels and at least one of which is steerable, where the axes of all wheels lie in a substantially in the same horizontal plane and where the steerable wheels turn about substantially vertical axes, where the driven wheels are positively and independently driven so that they tend to produce a single centre of curvature for the path ofthe vehicle, and where all the wheel angles are positively controlled so they tend to produce a single driver-selected centre of curvature for the path ofthe vehicle, and where the speeds of the driven wheels and the angles of all wheels are integrated so that the first said centre of curvature is identical to the second said centre of curvature, where at least one of the steerable driven wheels is driven by a gear train which includes a substantially vertical shaft which is driven by a substantially horizontal drive shaft via a pair of meshing bevel gears, where the undesirable linkage between the turning ofthe driven wheel and its rotation is either accommodated or cancelled out without the use of an unrestrained differential.

7. A vehicle according to claim 6 where the undesirable linkage between the turning of each of the steerable driven wheels and their rotation is accommodated by displacing the centre of the contact patch outwards from the turning axis of each steerable driven wheel, so that, when the horizontal drive shaft is stationary, turning of each steerable driven wheel causes it to be driven around a circular path without longitudinal skidding ofthe wheel on the ground.

8. A vehicle according to claim 7 where the displacement ofthe centre of the contact patch from the turning axis ofthe wheel ri, the effective radius of the wheel r_e, the number of teeth on the gear connected to the wheel N₂ and the number of teeth on the meshing gear fixed to the vertical shaft Ni are related by the equation:

9. A vehicle according to claim 6 where the undesirable linkage between the turning of a driven wheel and its rotation is cancelled out by counter rotation ofthe driven wheel by means of a turn-correcting differential located above the tumable driven wheel where the axis ofthe two sun gears is coincident with the turning axis ofthe wheel, where the cage of this differential is driven by a horizontal drive shaft via a pair of meshing bevel gears, where the first sun gear drives the tumable wheel via a gear train which includes a vertical shaft, and the second sun gear is caused to turn by the turning ofthe wheel so that the first sun gear is rotated in the opposite direction so as to cancel out the undesirable rotation ofthe wheel which would otherwise result from its turning.

10. A vehicle according to claim 6 where a speed and turn-correcting differential is mounted above the wheel, where the axes of the sun gears coincides with the turning axis ofthe wheel, where the output ofthe differential drives the tumable driven wheel via a gear train which includes a vertical shaft and where one input to the differential is provided by a horizontal drive shaft and the second input is provided by a speed and turn correcting hydraulic motor, the speed of which is controlled to produce both the desired speed of the wheel but also cancel out the undesirable linkage between the turning of the wheel and its rotation.

11. A vehicle according to claim 10 where the speed of the speed and turn correcting hydraulic motor is given by the equation:

ω₀ = ω_n Kc- K_sω_s /K. - K_aω_a Kc

Where ω_n, ω₀, ω_s and ω_a are the angular speeds of the tumable driven wheel about its horizontal axis, the drive shaft, the speed and turn correcting hydraulic motor and the tumable driven wheel about its turn axis, and where

K_s = ω_n /cos when ω₀ and ω_a are zero

K_c = ω_n /ω₀ when ω_s and ω_a are zero, and

K_a = co_n /ω_a when ω_s and ω_c are zero

12. A vehicle according to claim 6 where a steering differential is connected in parallel to a power differential that drives left and right steerable driven wheels via gear trains which include vertical left and right vertical shafts, where the cage of the steering differential is driven by a hydraulic steering motor the speed of which is controlled to produce the desired speed for the left and right steerable wheels while cancelling out the undesirable linkage between the turning of the wheels and their rotation.

13. A vehicle according to claim 12 where the speed ofthe steering hydraulic motor is given by the equation: ω_c = ω_n /Ko- K_sω_s Kc - K_aω_a /Kc

Where ω_n, ω₀, ω_s and ω_a are the angular speeds of the tumable driven wheel about its horizontal axis, the drive shaft to the power differential, the steering hydraulic motor and the tumable driven wheel about its turn axis, and where

K_s = ω_n /ω_s when ω_c and ω_a are zero

K_o = ω_n /ω₀ when ω_s and co_a are zero, and

K_a = ω_n /ω_a when ω_s and ω_c are zero

14. A vehicle according to claim 6 where a combined speed-reducing gearbox/ speed correcting differential is mounted inside each steerable driven wheel, the output of which drives the wheel, and where the primary input is provided by a gear train which includes a vertical shaft, and the secondary input is provided by a hydraulic motor mounted on the said gearbox, where the speed of the hydraulic motor is controlled to produce both the desired speed of the wheel but also cancel out the undesirable linkage between the turning of the wheel and its rotation.

15. A vehicle according to claim 14 where the speed of the hydraulic motor is given by the equation: ω₀ = co_n /Ko— K_sω_s /Ko — K_aω_a /Ko

Where ω_n, ω_c, ω_s and ω_a are the angular speeds of the turnable driven wheel about its horizontal axis, the drive shaft to the combined speed-reduction gearbox/speed-correcting differential, the speed-correcting hydraulic motor and the turnable driven wheel about its turn axis, and where

K_s = ω_n /co_s when ω₀ and ω_a are zero

Ko = ω_n /ω_c when ω_s and ω_a are zero, and

K_a = ω_n /ω_a when ω_s and ω₀ are zero

16. 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 ofthe vehicle becomes zero at the same time as the translation error becomes zero.

17. A vehicle according to claim 16 where the heading ofthe vehicle will cross the desired path, where the steerable wheels are turned so that the path ofthe vehicle will be tangential to the desired path.

18. A vehicle according to claim 17 where the steerable wheels are turned such that the ideal radius of curvature ofthe path of the vehicle ROC₀ is given by the equation:

ROCo = TE/(1 - cos RE)

Where TE is the translation error and RE is the rotation error.

19. 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 17 or 18.

20. A vehicle according to claims 16 or 17 where the ideal ROC₀ is calculated according to the equation given in claim 3, but where the actual ROC set by the steerable wheels is greater 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.

21. A vehicle according to any one of claims 16 to 20 where the ROC is controlled by controlling the angle of one or more steerable wheels.

22. A vehicle according to any one of claims 16 to 20 where the ROC is controlled by positively and independently controlling the speeds of the left hand and right hand drive wheels instead of the angle of one or more steerable wheels.

23. A vehicle according to any one of claims 16 to 20 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.

24. A vehicle according to any one of claims 16 to 23 where the ROC and speed of the vehicle is controlled automatically.

25. A vehicle according to any one of claims 16 to 23 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.

26. A vehicle according to claim 25 where the primary display is supplemented by a secondary display or audible signal which indicates when the translation error TE is zero.

27. A vehicle according to claim 16 with four wheel steering where a translation error TE and a rotation error RE can be eliminated simultaneously regardless of the heading ofthe vehicle.

28. A vehicle according to claim 27 where the speed of each drive wheel is automatically controlled to achieve the same instantaneous radius of curvature as the wheel angles.

29. A gantry tractor consisting of two or more modules hitched together so that each module can rotate relative to its neighbour or neighbours about a substantially vertical axis 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 90 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 ofthe second mentioned module, so that when all the modules are latched together they form a rigid truss in the horizontal plane.

30. A gantry tractor according to claim 29 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.

31. A gantry tractor according to claim 29 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.

32. A gantry tractor according to claim 29 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.

33. A gantry tractor according to claim 29 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.

34. A gantry tractor according to claim 33 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.

35. A gantry tractor consisting of a plurality of four wheeled modules that are hitched together where the hitch angle can be positively controlled by a pair of hydraulic rams or screw actuators which link the rear left corner of one module to the front left corner of the module that follows, and the rear right corner of one module to the front right corner ofthe module that follows when the gantry tractor is operating in transport mode, where the controlled hitch angle will produce the same path for each module as that which would be produced by both the controlled wheel angles and controlled wheel speeds of each module.

36. A gantry tractor according to claim 35 where the lengths ofthe left hand and right hand actuators are given by the equations:

b_L = 2d₀cos(δ₀+ β) and b_R = 2d₀cos(δ - β)

where d₀ = (t² + b²)^1/2/2 and δ₀ = tan^_1(t/b)

where b_R and b_L are the required lengths ofthe right and left hand actuators respectively, 2β is the hitch angle, δ₀ is the angle subtended at the hitch point by the nearest wheel relative to the longitudinal axis ofthe module, d₀ is the distance between the hitch point and the adjacent wheels and t and b are the track and wheel base of each module respectively.

37. A vehicle according to claim 6 where the driver determines the path ofthe vehicle with a single joystick and the speed ofthe vehicle with a speed control lever or pedal, where the forward displacement ofthe joystick y is proportional to the distance of the centre of curvature of the path ofthe vehicle forward of the transverse axis ofthe vehicle, R_y, and the sideways displacement of the joystick x determines the ratio of the track t to the displacement ofthe centre of curvature ofthe path ofthe vehicle to the right of the longitudinal axis of the vehicle R_x according to the equation :

and the root mean square wheel speed RMSWS is proportional to the forward displacement ofthe speed lever or pedal, where backwards displacement reverses the rotation ofthe wheels.

38. A vehicle according to claim 6 where the driver determines the path and speed of the vehicle with a single joystick and a lever or switch, where the forward displacement of the joystick y determines the root mean square wheel speed RMSWS, and the sideways displacement of the joystick x determines the ratio of the track t to the displacement of the centre of curvature ofthe path ofthe vehicle to the right ofthe longitudinal axis ofthe vehicle R_x according to the equation : t/R_x = tan(90° x/x _max) and the position of the lever or switch forward of the null point is proportional to the distance of the centre of curvature of the path of the vehicle forward of the transverse axis of the vehicle, R_y