LONGITUDINAL SLIP CONTROL FOR STEERED AXLES OF A VEHICLE

Abstract

A computer system and computer-implemented method for determining a longitudinal slip limit for a steered axle of a vehicle having two steered axles are disclosed. The computer system has processing circuitry to acquire a reference body slip for a steered axle of the vehicle; acquire a current body slip for the steered axle; determine a first difference between the reference body slip and the current body slip; acquire an initial longitudinal slip limit for the steered axle; and determine an adjusted longitudinal slip limit for the steered axle based on the first difference and the initial longitudinal slip limit for the steered axle.

Claims

1. A computer system for determining a longitudinal slip limit for a steered axle of a vehicle having two steered axles, the computer system comprising processing circuitry configured to: acquire a reference body slip for a steered axle of the vehicle; acquire a current body slip for the steered axle; determine a first difference between the reference body slip and the current body slip; acquire an initial longitudinal slip limit for the steered axle; and determine an adjusted longitudinal slip limit for the steered axle based on the first difference and the initial longitudinal slip limit for the steered axle.

2. The computer system of claim 1, wherein the steered axle is a front steered axle or a rear steered axle of the vehicle.

3. The computer system of claim 1, wherein the processing circuitry is configured to acquire the reference body slip for the steered axle by determining a reference body slip for the vehicle using a bicycle model.

4. The computer system of claim 1, wherein the processing circuitry is configured to acquire the reference body slip for a steered axle according to: ${}_{\mathrm{ref},f/r}={}_{ref}+\frac{L_{f/r}{}_z}{v_x}$ where .sub.ref, is the reference body slip for a front steered axle, .sub.ref,r is the reference body slip for a rear steered axle, .sub.ref is the reference body slip for the vehicle, L.sub. is the distance from the centre of gravity of the vehicle to the front steered axle, L.sub.r is the distance from the centre of gravity of the vehicle to the rear steered axle, .sub.z is the yaw rate of the vehicle, and .sub.x is the longitudinal velocity of the vehicle.

5. The computer system of claim 1, wherein the processing circuitry is configured to acquire the current body slip for the steered axle based on a current body slip for the vehicle, a distance from the centre of gravity of the vehicle to the steered axle, a current yaw rate of the vehicle, and a current longitudinal velocity of the vehicle.

6. The computer system of claim 1, wherein the initial longitudinal slip limit for the steered axle is based on a surface friction and/or one or more tyre properties of the steered axle.

7. The computer system of claim 1, wherein the processing circuitry is configured to determine the adjusted longitudinal slip limit for the steered axle based on a second difference between the initial longitudinal slip limit and a multiple of the magnitude of the first difference.

8. The computer system of claim 7, wherein the processing circuitry is configured to determine a maximum adjusted longitudinal slip limit for the steered axle based on a second difference between a maximum initial longitudinal slip limit and a multiple of the magnitude of the first difference.

9. The computer system of claim 7, wherein the processing circuitry is configured to determine a minimum adjusted longitudinal slip limit for the steered axle based on a second difference between a minimum initial longitudinal slip limit and a multiple of the magnitude of the first difference.

10. The computer system of claim 1, wherein the processing circuitry is configured to transmit the adjusted longitudinal slip limit to a controller of the vehicle for use in controlling one or more motion parameters of at least one steered axle of the vehicle, such that an implemented longitudinal slip adheres to the adjusted longitudinal slip limit.

11. The computer system of claim 10, wherein the one or more motion parameters of the steered axle comprise a torque, a force, a longitudinal slip, and/or a steering angle of the steered axle.

12. A vehicle comprising the computer system of claim 1.

13. A computer-implemented method for determining a longitudinal slip limit for a steered axle of a vehicle having two steered axles, the computer-implemented method comprising: acquiring, by processing circuitry of a computer system, a reference body slip for a steered axle of the vehicle; acquiring, by the processing circuitry, a current body slip for the steered axle; determining, by the processing circuitry, a first difference between the reference body slip and the current body slip; acquiring, by the processing circuitry, an initial longitudinal slip limit for the steered axle; and determining, by the processing circuitry, an adjusted longitudinal slip limit for the steered axle based on the first difference and the initial longitudinal slip limit for the steered axle.

14. The computer-implemented method of claim 13, wherein the steered axle is a front steered axle or a rear steered axle of the vehicle.

15. The computer-implemented method of claim 13, comprising acquiring, by the processing circuitry, the reference body slip for the steered axle by determining a reference body slip for the vehicle using a bicycle model.

16. The computer-implemented method of claim 13, comprising acquiring, by the processing circuitry, the reference body slip for a steered axle according to: ${}_{\mathrm{ref},f/r}={}_{ref}+\frac{L_{f/r}{}_z}{v_x}$ where .sub.ref, is the reference body slip for the front steered axle, .sub.ref,r is the reference body slip for the rear steered axle, .sub.ref is the reference body slip for the vehicle, L.sub. is the distance from the centre of gravity of the vehicle to the front steered axle, L.sub.r is the distance from the centre of gravity of the vehicle to the rear steered axle, .sub.z is the yaw rate of the vehicle, and .sub.x is the longitudinal velocity of the vehicle.

17. The computer-implemented method of claim 13, comprising acquiring, by the processing circuitry, the current body slip for the steered axle based on a current body slip for the vehicle, a distance from the centre of gravity of the vehicle to the steered axle, a current yaw rate of the vehicle, and a current longitudinal velocity of the vehicle.

18. The computer-implemented method of claim 13, comprising transmitting, by the processing circuitry, the adjusted longitudinal slip limit to a controller of the vehicle for use in controlling one or more motion parameters of at least one steered axle of the vehicle, such that an implemented longitudinal slip adheres to the adjusted longitudinal slip limit.

19. A computer program product comprising program code for performing, when executed by processing circuitry, the computer-implemented method of claim 13.

20. A non-transitory computer-readable storage medium comprising instructions, which when executed by processing circuitry, cause the processing circuitry to perform the computer-implemented method of claim 13.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Examples are described in more detail below with reference to the appended drawings.

[0026] FIG. 1 schematically shows a vehicle having two steered axles according to an example.

[0027] FIG. 2 is a plot of safe limits of longitudinal slip against a difference between current and reference body slips for a steered axle according to an example.

[0028] FIG. 3 is a flow chart of a computer-implemented method according to an example.

[0029] FIG. 4 is a schematic diagram of a computer system for implementing examples disclosed herein.

[0030] Like reference numerals refer to like elements throughout the description.

DETAILED DESCRIPTION

[0031] The detailed description set forth below provides information and examples of the disclosed technology with sufficient detail to enable those skilled in the art to practice the disclosure.

[0032] When controlling motion of vehicles with multiple steered axles, the steering between axles must be coordinated to ensure safe and correct manoeuvring of the vehicle. Current approaches to multi-axle steering are often quite rudimentary and can lead to instability at high speeds or on lower friction surfaces. This is particularly relevant when operating construction vehicles such as excavators, loaders, articulated haulers scenarios, and the like in such. Operation of such vehicles may therefore be unsafe when employing approaches known in the art, for example when cornering at high speed (relative for construction equipment, around 30 km/h) and/or in low friction scenarios.

[0033] To remedy this, systems, methods and other approaches are provided herein for determining a longitudinal slip limit for a steered axle of a vehicle having two steered axles. In particular, a difference is determined between a reference body slip and a current body slip for a steered axle. An initial longitudinal slip limit for the steered axle is acquired. Based on the determined difference and the initial longitudinal slip limit, an adjusted longitudinal slip limit for the steered axle is determined. The adjusted longitudinal slip limit can then be used in motion control of the vehicle. By determining longitudinal slip limits for the steered axles in this way, i.e. taking into account target body slips for the axles, it can be ensured that longitudinal slip is limited as body slip and/or path curvature increases. This means that lateral forces required for a particular manoeuvre can be achieved, which ensures that manoeuvres with lateral motion, such as cornering, can be performed more safely due to increased lateral traction. This is particularly advantageous at high speeds and offers an improved control strategy for autonomously controlled vehicles, but also offers benefits relating to non- or semi-autonomously controlled vehicles.

[0034] FIG. 1 schematically shows a vehicle 100 having two steered axles 102, 104. The front steered axle 102 has respective left and right wheels 106a, 106b. A steering angle of .sub. the front steered axle 102 and its wheels 106a, 106b is controlled by a front steering actuator 108. The rear steered axle 104 has respective left and right wheels 110a, 110b. A steering angle .sub.r of the rear steered axle 104 and its wheels 110a, 110b is controlled by a rear steering actuator 112. The vehicle 100 may be any suitable vehicle known in the art having two steered axles (each axle including any suitable number of wheels), including heavy-duty vehicles, such as trucks, and buses, among other vehicle types. In some examples, the vehicle 100 may be a construction vehicle, for example any vehicle suitable for transporting bulk material from one location to another. For example, the vehicle 100 may be an excavator, loader, articulated hauler, dump truck, or any other suitable construction vehicle known in the art. Whilst two steered axles 102, 104 are shown, it will be appreciated that further non-steered axles may be provided on the vehicle 100 as appropriate.

[0035] The vehicle 100 may also comprise one or more propulsion systems 114, 116 configured to drive, e.g. provide torque and/or steering to, one or more axles 102, 104 or individual wheels 106, 110 of the vehicle 100. The propulsion systems 114, 116 may include one or more electrical machines such as electric motors, which may be able to supply either a positive (propulsion) or negative (braking) force or torque. In the example of FIG. 1, each steered axle 102, 104 has a respective propulsion system 114, 116. As such, the steered axles 102, 104 are both driven axles. It will also be appreciated that any number of the steered axles 102, 104 and/or further axles may be driven axles. For example, in some implementations, only one of the steered axles 102, 104 may be driven. In some examples, a third axle (not shown) may be a driven axle while the steered axles 102, 104 are not driven. In some examples, the individual wheels 106, 110 may have respective propulsion systems. In some examples, the vehicle 100 may also include another source of propulsion, for example an internal combustion engine (ICE). The vehicle 100 also comprises a drivetrain (not shown) to deliver mechanical power from the propulsion source (the electrical machines or the ICE) to the wheels 106, 110.

[0036] The vehicle 100 may also comprise one or more brake systems 118, 120, for example one or more sets of service brakes, configured to supply a negative (braking) force. The service brakes may be, for example, frictional brakes such as pneumatic brakes. The steering actuators 108, 112, propulsion systems 114, 116, and brake systems 118, 120 may be collectively referred to as motions support devices (MSDs) of the vehicle 100.

[0037] In some examples, the vehicle 100 may be controlled (driven) by an on-board operator (driver). For example, the operator may provide an input to a steering wheel and/or accelerator/brake pedal of the vehicle 100 related to a manoeuvre, for example indicating a desired change of direction and/or speed of the vehicle 100. In other examples, the vehicle 100 may be an autonomous vehicle that is controlled by a vehicle motion management (VMM) unit 122 comprising processing circuitry 124 configured to control motion of the vehicle 100 via the MSDs of the vehicle 100. In some examples, the vehicle 100 may be capable of being controlled by an on-board or remote operator and/or the VMM unit 122, in what may be termed a semi-autonomous driving scenario.

[0038] The VMM unit 122 may be configured to provide control signals to each of the MSDs of the vehicle 100. To this end, the VMM unit 122 may be communicatively coupled to the steering actuators 108, 112, propulsion systems 114, 116, and/or brake systems 118, 120. In some examples, the VMM unit 122 may be configured to provide a force, torque, and or longitudinal slip request to one or more of the propulsion systems 114, 116 and/or brake systems 118, 120, and/or a steering angle request to one or more of the steering actuators 108, 112. In a common driving scenario, a steering angle request may involve simple counter-steering of the steered axles 102, 104, where a requested steering angle for the rear steered axle 104 is proportional (for example equal) but opposite to that of the front steered axle 102. FIG. 1 shows a single VMM unit 122 for all MSDs of the vehicle 100, however it will be appreciated that each MSD may comprise a dedicated controller. The VMM unit 122 may be a microcontroller.

[0039] In some examples, the VMM unit 122 may determine the control signals itself, for example based on a predetermined mission plan or based on an input from an on-board operator. In some examples, the VMM unit 122 may receive control signals from a computer system 126 comprising processing circuitry 128. The computer system 126 is communicatively coupled to the VMM unit 122. The computer system 126 may be a vehicle control unit configured to perform various vehicle control functions, such as vehicle motion management. The computer system 126 may be local to the vehicle 100, or may be a remote system, implemented at a distance from the vehicle 100, e.g. a cloud server for remote control of the vehicle 100.

[0040] A communicative coupling as referred to above may be implemented in any suitable way, for example via a circuit or any other wired, wireless, or network connection known in the art. Furthermore, a communicative coupling may be implemented as a direct connection, e.g. between the VMM unit 122 and the computer system 126, or as a connection via one or more intermediate entities.

[0041] One function of the VMM unit 122 and the computer system 126 is to provide control inputs for the MSDs of the vehicle 100 to enable motion of the vehicle 100, for example including straight-line driving, cornering, braking and the like. The implemented motion should be safe, stable, and enable sufficient freedom of movement of the vehicle 100. To this end, a number of principles of motion for the vehicle 100 can be considered.

[0042] When the vehicle 100 is in motion, the wheels 106, 110 of the vehicle 100 experience slip. This can be considered in terms of body slip or slip angle. The body slip of the vehicle 100 is the angular difference between the direction the vehicle 100 is travelling and the direction that the body of the vehicle 100 is pointing, and may be defined as the ratio between the lateral velocity .sub.y and the longitudinal velocity .sub.x of the vehicle 100. Body slip can also be considered as the body slip on each of the steered axles 102, 104. As the steered axles 102, 104 may have different lateral velocities, they may have different values of body slip. The slip angle refers to an individual wheel 106, 110 and is the difference between the direction the wheel 106, 110 is travelling and the direction it is pointing. Slip can be divided into longitudinal and lateral slip. These parameters are known in the art, and not discussed in detail here. By considering the slip on the vehicle 100 as a whole as well as on the individual steered axles 102, 104, various slip limits can be determined that can be used when determining control inputs for the steered axles 102, 104.

[0043] The current rate of change of body slip {dot over ()} on the vehicle 100 as a whole can be given by a bicycle model defined as follows:

[00002]$\begin{array}{cc}\stackrel{.}{}=-\frac{C_f+C_r}{m.Math.v_x}+\left(\frac{-L_f.Math.C_{\mathrm{fa}}+L_r.Math.C_r}{m.Math.v_x^2}-1\right){}_z+\frac{C_f}{{\mathrm{mv}}_x}{}_f+\frac{C_r}{{\mathrm{mv}}_x}{}_r& \left(1\right)\end{array}$

where C.sub. is the cornering stiffness of the front steered axle 102, C.sub.r is the cornering stiffness of the rear steered axle 104, m is the mass of the vehicle 100, .sub.x is the longitudinal velocity of the vehicle 100, is the body slip on the vehicle 100, L.sub. is the distance from the centre of gravity (CoG) of the vehicle 100 to the front steered axle 102, L.sub.r is the distance from the centre of gravity (CoG) of the vehicle 100 to the rear steered axle 104, and .sub.z is the yaw rate of the vehicle 100. The cornering stiffnesses C.sub., C.sub.r may be determined from tyre properties of the steered axles 102, 104 as known in the art. The longitudinal velocity .sub.x of the vehicle 100 may be determined in any suitable manner known in the art, for example using speed sensors of the vehicle 100. The yaw rate .sub.z of the vehicle 100 may be determined in any suitable manner known in the art, for example using one or more yaw sensors and/or inertial measurement units (IMUs) of the vehicle 100.

[0044] The bicycle model defined in equation (1) gives the change in body slip per second {dot over ()}, and can be used to determine an expected body slip .sub.ref on the vehicle 100 as a whole for a desired value of the rate of change {dot over ()}. For example, for a steady state, the rate of change of body slip {dot over ()} will be zero. For a given yaw rate .sub.z, longitudinal velocity .sub.x, and front and rear steering angles .sub., .sub.r, an expected body slip .sub.ref on the vehicle 100 can be determined for the steady state based on equation (1).

[0045] This value can then be converted into an expected body slip .sub.ref, of the front steered axle 102 and an expected body slip .sub.ref,r of the rear steered axle 104. To determine the expected body slip .sub.ref, of the front steered axle 102, equation (2) can be used as follows:

[00003]$\begin{array}{cc}{}_{\mathrm{ref},f}={}_{\mathrm{ref}}+\frac{L_f{}_z}{v_x}& \left(2\right)\end{array}$

To determine the expected body slip .sub.ref,r of the rear steered axle 104, equation (3) can be used as follows:

[00004]$\begin{array}{cc}{}_{\mathrm{ref},r}={}_{\mathrm{ref}}+\frac{L_r{}_z}{v_x}& \left(3\right)\end{array}$

This provides respective expected body slip values .sub.ref,, .sub.ref,r for the steered axles 102, 104 for a given yaw rate .sub.z, longitudinal velocity .sub.x, and front and rear steering angles of .sub., .sub.r.

[0046] The relationship between body slip and longitudinal slip is important to stability of the vehicle 100. Since there are two steered axles 102, 104, the current body slip is a direct measurement of how the vehicle 100 moves. FIG. 2 is a plot 200 of the safe limits of longitudinal slip for the front steered axle 102 of the vehicle 100 on the y-axis against a difference between a current body slip .sub. of the front steered axle 102 and the reference (expected) body slip .sub.ref, for the front steered axle 102 on the x-axis. A similar plot could be produced for the rear steered axle 104. In general, the negative x-axis indicates that the current body slip for the axle 102, 104 is lower than expected, while the positive x-axis indicates that the current body slip for the axle 102, 104 is higher than expected. The line 202 on the plot 200 indicates the maximum positive longitudinal slip .sub.max for a given difference in body slip to ensure safe vehicle operation and may apply to a propulsion scenario. The line 204 on the plot 200 indicates the maximum negative longitudinal slip .sub.min for a given difference in body slip to ensure safe vehicle operation and may apply to a braking scenario. The larger the difference between current and expected body slip, the more the longitudinal slip should be limited.

[0047] When considering the front steered axle 102, as in FIG. 2, the negative x-axis (where the current body slip .sub. for the front steered axle 102 is lower than expected, i.e. .sub.<.sub.ref,) indicates understeer. This occurs when the yaw rate .sub.z of the vehicle 100 is lower than expected, for example when the front steered axle 102 does not rotate into the curve being travelled by the vehicle 100 (its body slip .sub. is not increasing as much as expected). In this case, the front wheels 106 have less grip than they need, and the lateral velocity .sub.y of the front steered axle 102 is lower than expected. To remedy this, the magnitude of the longitudinal slip of the front steered axle 102 can be limited. As discussed above, the magnitude of the longitudinal slip of (the wheels of) the front steered axle 102 should be limited more strictly as the magnitude of the difference between the current body slip .sub. and the reference (expected) body slip .sub.ref, for the front steered axle 102 increases.

[0048] When considering the rear steered axle 104, the positive x-axis (where the current body slip P, for the rear steered axle 104 is higher than expected, i.e. .sub.r>.sub.ref,r) indicates oversteer. This may occur when the rear steered axle 104 rotates out of the curve being travelled by the vehicle 100 (its body slip .sub.r is increasing more than expected). In this case, the rear wheels 110 have less grip than they need. To remedy this, the magnitude of the longitudinal slip of the rear steered axle 104 can be limited. As discussed above, the magnitude of the longitudinal slip of (the wheels of) the rear steered axle 104 should be limited more strictly as the magnitude of the difference between the current body slip .sub.r and the reference (expected) body slip .sub.ref,r for the rear steered axle 104 increases.

[0049] Based on these behaviours, longitudinal slip limits .sub.max/min can be determined for (the wheels of) the steered axles 102, 104 of the vehicle 100, which allows corresponding control inputs, such as force, torque, longitudinal slip, and/or steering angle, to be determined that provide safe motion of the vehicle 100.

[0050] FIG. 3 is a flow chart of a computer-implemented method 300 according to an example. The method 300 is for determining a longitudinal slip limit for a steered axle of a vehicle having two steered axles, such as the vehicle 100. The method 300 enables longitudinal slip to be limited as body slip and/or path curvature increases, meaning that lateral forces required for a particular manoeuvre can be achieved. This ensures that manoeuvres with lateral motion, such as cornering, can be performed more safely due to increased lateral traction. The method 300 may be implemented by processing circuitry of a computer system (e.g., the processing circuitry 124 of the VMM unit 122, or the processing circuitry 128 of the computer system 126 described in relation to FIG. 1). Since the front steered axle 102 and the rear steered axle 104 will have different lateral velocities, they will have different amounts of body slip. Therefore, longitudinal slip limits for the steered axles 102, 104 can be set separately.

[0051] At 302, a reference (target) body slip for a steered axle 102, 104 is acquired. For example, a reference (target) body slip .sub.ref, for the front steered axle 102 may be acquired. In particular, a bicycle model such as that of equation (1) may be used to determine a reference body slip .sub.ref for the vehicle 100, from which the reference body slip .sub.ref, for the front steered axle 102 may be derived, for example using equation (2). The reference body slip .sub.ref for the vehicle 100 and/or the reference body slip .sub.ref, for the front steered axle 102 may be determined in advance and stored in a memory associated with the vehicle 100, for example associated with the VMM unit 122 or the computer system 126.

[0052] Additionally or alternatively at 302, a reference (target) body slip .sub.ref,r for the rear steered axle 104 may be acquired. In particular, a bicycle model such as that of equation (1) may be used to determine a reference body slip .sub.ref for the vehicle 100, from which the reference body slip .sub.ref,r for the rear steered axle 104 may be derived, for example using equation (3). The reference body slip .sub.ref for the vehicle 100 and/or the reference body slip .sub.ref,r for the rear steered axle 104 may be determined in advance and stored in a memory associated with the vehicle 100, for example associated with the VMM unit 122 or the computer system 126.

[0053] At 304, a current body slip for the steered axle 102, 104 is acquired. For example, a current body slip .sub. for the front steered axle 102 is acquired. This may be acquired in any suitable manner known in the art, for example using radar, IMU or laser measurements. In one example, the current body slip .sub. for the front steered axle 102 can be acquired based on the current body slip for the vehicle 100, the distance L.sub. from the centre of gravity of the vehicle 100 to the front steered axle 102, a yaw rate .sub.z of the vehicle 100, and a longitudinal velocity .sub.x of the vehicle 100. In particular, the current body slip .sub. for the front steered axle 102 may be determined in a similar manner to equation (2), as follows:

[00005]$\begin{array}{cc}{}_f=+\frac{L_f{}_z}{v_x}& \left(4\right)\end{array}$

The current body slip for the vehicle 100 may be acquired in any suitable manner known in the art, for example by determining the ratio between the lateral velocity .sub.y and the longitudinal velocity .sub.x using sensor or state estimation measurements, or by using inverse tyre models. The yaw rate .sub.z and longitudinal velocity .sub.x of the vehicle 100 may be determined in any suitable manner known in the art, as discussed above.

[0054] Additionally or alternatively at 304, a current body slip .sub.r for the rear steered axle 104 may be acquired. This may be acquired in any suitable manner known in the art, for example using radar, IMU or laser measurements. It will be appreciated that the current body slip .sub.r for the rear steered axle 104 can be determined in a similar manner to equation (3), using the current body slip for the vehicle 100 instead of the expected body slip .sub.ref,r. In particular, the current body slip .sub.r for the rear steered axle 104 can be determined in a similar manner to equation (4), but using the distance L.sub.r from the CoG of the vehicle 100 to the rear steered axle 104 instead of the distance L.sub. from the CoG of the vehicle 100 to the front steered axle 102.

[0055] At 306, a difference between the reference body slip acquired at 302 and the current body slip acquired at 304 is determined for the steered axle 102, 104. As discussed above, for the front steered axle 102, this difference may indicate that the vehicle 100 is understeering, and for the rear steered axle 104 the difference may indicate that the vehicle 100 is oversteering. As such, the difference, in particular the magnitude of the difference, is indicative of a safe level of longitudinal slip.

[0056] At 308, an initial longitudinal slip limit for (the wheels of) the steered axle 102, 104 is acquired. This may include a maximum initial longitudinal slip limit .sub.max,in and a minimum initial longitudinal slip limit .sub.min,in. It should be noted that the minimum initial longitudinal slip limit .sub.min,in is in fact a maximum negative value and may apply to a braking scenario. These values may be set based on tyre parameters associated with the steered axle. As known in the art, the maximum tyre force provided by a tyre occurs in a certain band of longitudinal slip (for example between 0.20 and 0.25). The exact values of optimal slip are dependent on various tyre parameters, such as tyre material, tyre tread shape, tyre size, and the like. They are also dependent on surface friction, which can be affected by weather conditions and the type of surface on which the vehicle is travelling (e.g. dry asphalt, wet asphalt, ice, snow, etc.). Other factors can be taken into account when setting these limits, for example an acceleration of the vehicle or an ABS trigger criteria.

[0057] At 310, an adjusted longitudinal slip limit for (the wheels of) the steered axle 102, 104 is determined. This may include an adjusted maximum longitudinal slip limit .sub.max and/or an adjusted minimum longitudinal slip limit .sub.min. Again, it should be noted that the adjusted minimum longitudinal slip limit .sub.min is in fact a maximum negative value and may apply to a braking scenario. The adjusted longitudinal slip limit(s) can be determined based on the initial longitudinal slip limit acquired at 308 and the magnitude of the difference determined at 306. In particular, each adjusted longitudinal slip limit can be determined based on the respective initial longitudinal slip limit acquired at 308 and a multiple of the magnitude of the difference acquired at 306

[0058] For the front steered axle 102, these can be determined as follows:

[00006]$\begin{array}{cc}{}_{\max ,f}={}_{\max ,\mathrm{in},f}-.Math.K\left({}_f-{}_{\mathrm{ref},f}\right).Math.& \left(5\right)\end{array}$$\begin{array}{cc}{}_{\min ,f}={}_{\min ,\mathrm{in},f}+.Math.K\left({}_f-{}_{\mathrm{ref},f}\right).Math.& \left(6\right)\end{array}$

where .sub.max, is the adjusted maximum longitudinal slip limit for the front steered axle 102, .sub.max,in, is the maximum initial longitudinal slip limit for the front steered axle 102, .sub.min, is the adjusted minimum longitudinal slip limit for the front steered axle 102, .sub.min,in, is the minimum initial longitudinal slip limit for the front steered axle 102, and K is a constant that may be a tuning parameter set accordingly by an operator.

[0059] Similar relations for the rear steered axle 104 can be expressed as follows:

[00007]$\begin{array}{cc}{}_{\max ,r}={}_{\max ,\mathrm{in},r}-.Math.K\left({}_r-{}_{\mathrm{ref},r}\right).Math.& \left(7\right)\end{array}$$\begin{array}{cc}{}_{\min ,r}={}_{\min ,\mathrm{in},r}+.Math.K\left({}_r-{}_{\mathrm{ref},r}\right).Math.& \left(8\right)\end{array}$

where .sub.max,r is the adjusted maximum longitudinal slip limit for the rear steered axle 104, .sub.max,in,r is the maximum initial longitudinal slip limit for the rear steered axle 104, .sub.min,r is the adjusted minimum longitudinal slip limit for the rear steered axle 104, and .sub.min,in,r is the minimum initial longitudinal slip limit for the rear steered axle 104.

[0060] By determining longitudinal slip limits for (the wheels of) the steered axles 102, 104 in this way, i.e. taking into account target body slips for the axles 102, 104, it can be ensured that longitudinal slip is limited as body slip and/or path curvature increases. This can be achieved by limiting the torque and/or force on the axle to adhere to the adjusted longitudinal slip limit. In this way, in situations where lateral force is not as high as required (i.e. high body slip), less force is applied longitudinally. Indeed, the more the current body slip on a steered axle 102, 104 deviates from a target body slip, the more aggressively the longitudinal slip limit of that axle is limited. This means that lateral forces required for a particular manoeuvre can be achieved, which ensures that manoeuvres with lateral motion, such as cornering, can be performed more safely due to increased lateral traction. This is particularly advantageous at high speeds and offers an improved control strategy for autonomously controlled vehicles, but also offers benefits relating to non- or semi-autonomously controlled vehicles.

[0061] Taking the understeer example discussed above, there is a difference between the current body slip .sub. and the reference (expected) body slip .sub.ref, for the front steered axle 102. Therefore, the magnitudes of the adjusted longitudinal slip limits .sub.max,, .sub.min, for (the wheels of) the front steered axle 102 are decreased with respect to the initial longitudinal slip limits .sub.max,in,, .sub.min,in,. Taking the oversteer example discussed above, there is a difference between the current body slip pr and the reference (expected) body slip .sub.ref,r for the rear steered axle 104. Therefore, the magnitudes of the adjusted longitudinal slip limits .sub.max,r, .sub.min,r for (the wheels of) the rear steered axle 104 are decreased with respect to the initial longitudinal slip limits .sub.max,in,r, .sub.min,in,r.

[0062] At 312, the adjusted longitudinal slip limit(s) may be transmitted to a controller of the vehicle 100 configured to control one or more motion parameters of the steered axle 102, 104. For example, if the method 300 is performed at the computer system 126, the adjusted longitudinal slip limit(s) may be transmitted to the VMM unit 122. The adjusted longitudinal slip limit(s) may then be used in controlling one or more motion parameters of the steered axle to ensure that the implemented (e.g. experienced and/or measured) longitudinal slip of (the wheels of) the steered axle adheres to the determined limit(s). In particular, it is ensured that the implemented longitudinal slip of the steered axle is below the adjusted maximum longitudinal slip limit .sub.max and above the adjusted minimum longitudinal slip limit .sub.min.

[0063] The motion parameters include a force, torque, and/or longitudinal slip (in the case of a driven axle), and/or a steering angle to be implemented at the steered axle. In the case that the individual wheels 106, 110 have respective propulsion systems, the wheels 106, 110 can operate with different forces or torques until the slip limits per wheel. This may be beneficial for torque vectoring, since an outer wheel will have better traction in a curve, which allows higher torque before a slip limit is reached. In some embodiments, the slip limits are the same for both wheels on a single axle. This can be implemented in a simple manner using existing control interfaces of the vehicle 100. For example, electric motors that operate based on speed control have an internal controller that reduces the torque if the motor spins too fast. In this case, the speed of the motor can be limited.

[0064] FIG. 4 is a schematic diagram of a computer system 400 for implementing examples disclosed herein. The computer system 400 is adapted to execute instructions from a computer-readable medium to perform these and/or any of the functions or processing described herein. The computer system 400 may be connected (e.g., networked) to other machines in a LAN, an intranet, an extranet, or the Internet. While only a single device is illustrated, the computer system 400 may include any collection of devices that individually or jointly execute a set (or multiple sets) of instructions to perform any one or more of the methodologies discussed herein. Accordingly, any reference in the disclosure and/or claims to a computer system, computing system, computer device, computing device, control system, control unit, electronic control unit (ECU), processor device, processing circuitry, etc., includes reference to one or more such devices to individually or jointly execute a set (or multiple sets) of instructions to perform any one or more of the methodologies discussed herein. For example, control system may include a single control unit or a plurality of control units connected or otherwise communicatively coupled to each other, such that any performed function may be distributed between the control units as desired. Further, such devices may communicate with each other or other devices by various system architectures, such as directly or via a Controller Area Network (CAN) bus, etc.

[0065] The computer system 400 may comprise at least one computing device or electronic device capable of including firmware, hardware, and/or executing software instructions to implement the functionality described herein. The computer system 400 may include processing circuitry 402 (e.g., processing circuitry including one or more processor devices or control units), a memory 404, and a system bus 406. The computer system 400 may include at least one computing device having the processing circuitry 402. The system bus 406 provides an interface for system components including, but not limited to, the memory 404 and the processing circuitry 402. The processing circuitry 402 may include any number of hardware components for conducting data or signal processing or for executing computer code stored in memory 404. The processing circuitry 402 may, for example, include a general-purpose processor, an application specific processor, a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field Programmable Gate Array (FPGA), a circuit containing processing components, a group of distributed processing components, a group of distributed computers configured for processing, or other programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. The processing circuitry 402 may further include computer executable code that controls operation of the programmable device.

[0066] The system bus 406 may be any of several types of bus structures that may further interconnect to a memory bus (with or without a memory controller), a peripheral bus, and/or a local bus using any of a variety of bus architectures. The memory 404 may be one or more devices for storing data and/or computer code for completing or facilitating methods described herein. The memory 404 may include database components, object code components, script components, or other types of information structure for supporting the various activities herein. Any distributed or local memory device may be utilized with the systems and methods of this description. The memory 404 may be communicably connected to the processing circuitry 402 (e.g., via a circuit or any other wired, wireless, or network connection) and may include computer code for executing one or more processes described herein. The memory 404 may include non-volatile memory 408 (e.g., read-only memory (ROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), etc.), and volatile memory 410 (e.g., random-access memory (RAM)), or any other medium which can be used to carry or store desired program code in the form of machine-executable instructions or data structures and which can be accessed by a computer or other machine with processing circuitry 402. A basic input/output system (BIOS) 412 may be stored in the non-volatile memory 408 and can include the basic routines that help to transfer information between elements within the computer system 400.

[0067] The computer system 400 may further include or be coupled to a non-transitory computer-readable storage medium such as the storage device 414, which may comprise, for example, an internal or external hard disk drive (HDD) (e.g., enhanced integrated drive electronics (EIDE) or serial advanced technology attachment (SATA)), HDD (e.g., EIDE or SATA) for storage, flash memory, or the like. The storage device 414 and other drives associated with computer-readable media and computer-usable media may provide non-volatile storage of data, data structures, computer-executable instructions, and the like.

[0068] Computer-code which is hard or soft coded may be provided in the form of one or more modules. The module(s) can be implemented as software and/or hard-coded in circuitry to implement the functionality described herein in whole or in part. The modules may be stored in the storage device 414 and/or in the volatile memory 410, which may include an operating system 416 and/or one or more program modules 418. All or a portion of the examples disclosed herein may be implemented as a computer program 420 stored on a transitory or non-transitory computer-usable or computer-readable storage medium (e.g., single medium or multiple media), such as the storage device 414, which includes complex programming instructions (e.g., complex computer-readable program code) to cause the processing circuitry 402 to carry out actions described herein. Thus, the computer-readable program code of the computer program 420 can comprise software instructions for implementing the functionality of the examples described herein when executed by the processing circuitry 402. In some examples, the storage device 414 may be a computer program product (e.g., readable storage medium) storing the computer program 420 thereon, where at least a portion of a computer program 420 may be loadable (e.g., into a processor) for implementing the functionality of the examples described herein when executed by the processing circuitry 402. The processing circuitry 402 may serve as a controller or control system for the computer system 400 that is to implement the functionality described herein.

[0069] The computer system 400 may include an input device interface 422 configured to receive input and selections to be communicated to the computer system 400 when executing instructions, such as from a keyboard, mouse, touch-sensitive surface, etc. Such input devices may be connected to the processing circuitry 402 through the input device interface 422 coupled to the system bus 406 but can be connected through other interfaces, such as a parallel port, an Institute of Electrical and Electronic Engineers (IEEE) 1394 serial port, a Universal Serial Bus (USB) port, an IR interface, and the like. The computer system 400 may include an output device interface 424 configured to forward output, such as to a display, a video display unit (e.g., a liquid crystal display (LCD) or a cathode ray tube (CRT)). The computer system 400 may include a communications interface 426 suitable for communicating with a network as appropriate or desired.

[0070] The operational actions described in any of the exemplary aspects herein are described to provide examples and discussion. The actions may be performed by hardware components, may be embodied in machine-executable instructions to cause a processor to perform the actions, or may be performed by a combination of hardware and software. Although a specific order of method actions may be shown or described, the order of the actions may differ. In addition, two or more actions may be performed concurrently or with partial concurrence.

[0071] According to certain examples, there is also disclosed: [0072] Example 1: A computer system (122, 126, 400) for determining a longitudinal slip limit for a steered axle (102, 104) of a vehicle (100) having two steered axles (102, 104), the computer system (122, 126, 400) comprising processing circuitry (124, 128, 402) configured to: acquire a reference body slip for a steered axle (102, 104) of the vehicle (100); acquire a current body slip for the steered axle (102, 104); determine a first difference between the reference body slip and the current body slip; acquire an initial longitudinal slip limit for the steered axle (102, 104); and determine an adjusted longitudinal slip limit for the steered axle (102, 104) based on the first difference and the initial longitudinal slip limit for the steered axle (102, 104). [0073] Example 2: The computer system (122, 126, 400) of example 1, wherein the steered axle (102, 104) is a front steered axle (102) or a rear steered axle (104) of the vehicle (100). [0074] Example 3: The computer system (122, 126, 400) of example 1 or 2, wherein the processing circuitry (124, 128, 402) is configured to acquire the reference body slip for the steered axle (102, 104) by determining a reference body slip for the vehicle (100) using a bicycle model. [0075] Example 4: The computer system (122, 126, 400) of any preceding example, wherein the processing circuitry (124, 128, 402) is configured to acquire the reference body slip for a steered axle (102, 104) according to:

[00008]${}_{\mathrm{ref},f/r}={}_{\mathrm{ref}}+\frac{L_{f/r}{}_z}{v_x}$

where .sub.ref, is the reference body slip for the front steered axle (102), .sub.ref,r is the reference body slip for the rear steered axle (104), .sub.ref is the reference body slip for the vehicle (100), L.sub. is the distance from the centre of gravity of the vehicle (100) to the front steered axle (102), L.sub.r is the distance from the centre of gravity of the vehicle (100) to the rear steered axle (104), .sub.z is the yaw rate of the vehicle (100), and .sub.x is the longitudinal velocity of the vehicle (100). [0076] Example 5: The computer system (122, 126, 400) of any preceding example, wherein the processing circuitry (124, 128, 402) is configured to acquire the current body slip for the steered axle (102, 104) based on a current body slip for the vehicle (100), a distance from the centre of gravity of the vehicle (100) to the steered axle (102, 104), a current yaw rate of the vehicle (100), and a current longitudinal velocity of the vehicle (100). [0077] Example 6: The computer system (122, 126, 400) of any preceding example, wherein the initial longitudinal slip limit for the steered axle (102, 104) is based on a surface friction and/or one or more tyre properties of the steered axle (102, 104). [0078] Example 7: The computer system (122, 126, 400) of any preceding example, wherein the processing circuitry (124, 128, 402) is configured to determine the adjusted longitudinal slip limit for the steered axle (102, 104) based on a second difference between the initial longitudinal slip limit and a multiple of the magnitude of the first difference. [0079] Example 8: The computer system (122, 126, 400) of example 7, wherein the processing circuitry (124, 128, 402) is configured to determine a maximum adjusted longitudinal slip limit for the steered axle (102, 104) based on a second difference between a maximum initial longitudinal slip limit and a multiple of the magnitude of the first difference. [0080] Example 9: The computer system (122, 126, 400) of example 7 or 8, wherein the processing circuitry (124, 128, 402) is configured to determine a minimum adjusted longitudinal slip limit for the steered axle (102, 104) based on a second difference between a minimum initial longitudinal slip limit and a multiple of the magnitude of the first difference. [0081] Example 10: The computer system (122, 126, 400) of any preceding example, wherein the processing circuitry (124, 128, 402) is configured to transmit the adjusted longitudinal slip limit to a controller (122, 126) of the vehicle (100) for use in controlling one or more motion parameters of at least one steered axle (102, 104) of the vehicle (100), such that an implemented longitudinal slip adheres to the adjusted longitudinal slip limit. [0082] Example 11: The computer system (122, 126, 400) of example 10, wherein the one or more motion parameters of the steered axle (102, 104) comprise a torque, a force, a longitudinal slip, and/or a steering angle of the steered axle (102, 104). [0083] Example 12: A vehicle (100) comprising the computer system (122, 126, 400) of any preceding example. [0084] Example 13: A computer-implemented method (300) for determining a longitudinal slip limit for a steered axle (102, 104) of a vehicle (100) having two steered axles (102, 104), the computer-implemented method (300) comprising: acquiring (302), by processing circuitry (124, 128, 402) of a computer system (122, 126, 400), a reference body slip for a steered axle (102, 104) of the vehicle (100); acquiring (304), by the processing circuitry (124, 128, 402), a current body slip for the steered axle (102, 104); determining (306), by the processing circuitry (124, 128, 402), a first difference between the reference body slip and the current body slip; acquiring (308), by the processing circuitry (124, 128, 402), an initial longitudinal slip limit for the steered axle (102, 104); and determining (310), by the processing circuitry (124, 128, 402), an adjusted longitudinal slip limit for the steered axle (102, 104) based on the first difference and the initial longitudinal slip limit for the steered axle (102, 104). [0085] Example 14: The computer-implemented method (300) of example 13, wherein the steered axle (102, 104) is a front steered axle (102) or a rear steered axle (104) of the vehicle (100). [0086] Example 15: The computer-implemented method (300) of example 13 or 14, comprising acquiring (302), by the processing circuitry (124, 128, 402), the reference body slip for the steered axle (102, 104) by determining a reference body slip for the vehicle (100) using a bicycle model. [0087] Example 16: The computer-implemented method (300) of any of examples 13 to 15, comprising acquiring (302), by the processing circuitry (124, 128, 402), the reference body slip for a steered axle (102, 104) according to:

[00009]${}_{\mathrm{ref},f/r}={}_{ref}+\frac{L_{f/r}{}_z}{v_x}$

where .sub.ref, is the reference body slip for the front steered axle (102), .sub.ref,r is the reference body slip for the rear steered axle (104), .sub.ref is the reference body slip for the vehicle (100), L.sub. is the distance from the centre of gravity of the vehicle (100) to the front steered axle (102), L.sub.r is the distance from the centre of gravity of the vehicle (100) to the rear steered axle (104), .sub.z is the yaw rate of the vehicle (100), and .sub.x is the longitudinal velocity of the vehicle (100). [0088] Example 17: The computer-implemented method (300) of any of examples 13 to 16, comprising acquiring (304), by the processing circuitry (124, 128, 402), the current body slip for the steered axle (102, 104) based on a current body slip for the vehicle (100), a distance from the centre of gravity of the vehicle (100) to the steered axle (102, 104), a current yaw rate of the vehicle (100), and a current longitudinal velocity of the vehicle (100). [0089] Example 18: The computer-implemented method (300) of any of examples 13 to 17, wherein the initial longitudinal slip limit for the steered axle (102, 104) is based on a surface friction and/or one or more tyre properties of the steered axle (102, 104). [0090] Example 19: The computer-implemented method (300) of any of examples 13 to 18, comprising determining (310), by the processing circuitry (124, 128, 402), the adjusted longitudinal slip limit for the steered axle (102, 104) based on a second difference between the initial longitudinal slip limit and a multiple of the magnitude of the first difference. [0091] Example 20: The computer-implemented method (300) of example 19, comprising determining, by the processing circuitry (124, 128, 402), a maximum adjusted longitudinal slip limit for the steered axle (102, 104) based on a second difference between a maximum initial longitudinal slip limit and a multiple of the magnitude of the first difference. [0092] Example 21: The computer-implemented method (300) of example 19 or 20, comprising determining, by the processing circuitry (124, 128, 402), a minimum adjusted longitudinal slip limit for the steered axle (102, 104) based on a second difference between a minimum initial longitudinal slip limit and a multiple of the magnitude of the first difference. [0093] Example 22: The computer-implemented method (300) of any of examples 13 to 21, comprising transmitting (312), by the processing circuitry (124, 128, 402), the adjusted longitudinal slip limit to a controller (122, 126) of the vehicle (100) for use in controlling one or more motion parameters of at least one steered axle (102, 104) of the vehicle (100), such that an implemented longitudinal slip adheres to the adjusted longitudinal slip limit. [0094] Example 23: The computer-implemented method (300) of example 22, wherein the one or more motion parameters of the steered axle (102, 104) comprise a torque, a force, a longitudinal slip, and/or a steering angle of the steered axle (102, 104). [0095] Example 24: A computer program product comprising program code for performing, when executed by processing circuitry (124, 128, 402), the computer-implemented method (300) of any of examples 13 to 23. [0096] Example 25: A non-transitory computer-readable storage medium comprising instructions, which when executed by processing circuitry (124, 128, 402), cause the processing circuitry to perform the computer-implemented method (300) of any of examples 13 to 23.

[0097] Terminology used herein is for the purpose of describing particular aspects only and is not intended to be limiting of the disclosure. As used herein, the singular forms a, an, and the are intended to include the plural forms as well, unless the context clearly indicates otherwise. As used herein, the term and/or includes any and all combinations of one or more of the associated listed items. It will be further understood that the terms comprises, comprising, includes, and/or including when used herein specify the presence of stated features, integers, actions, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, actions, steps, operations, elements, components, and/or groups thereof.

[0098] It will be understood that, although the terms first, second, etc., may be used herein to describe various elements, these elements should not be limited by these terms. These terms are only used to distinguish one element from another. For example, a first element could be termed a second element, and, similarly, a second element could be termed a first element without departing from the scope of the present disclosure.

[0099] Relative terms such as below or above or upper or lower or horizontal or vertical may be used herein to describe a relationship of one element to another element as illustrated in the Figures. It will be understood that these terms and those discussed above are intended to encompass different orientations of the device in addition to the orientation depicted in the Figures. It will be understood that when an element is referred to as being connected or coupled to another element, it can be directly connected or coupled to the other element, or intervening elements may be present. In contrast, when an element is referred to as being directly connected or directly coupled to another element, there are no intervening elements present.

[0100] Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs. It will be further understood that terms used herein should be interpreted as having a meaning consistent with their meaning in the context of this specification and the relevant art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.

[0101] It is to be understood that the present disclosure is not limited to the aspects described above and illustrated in the drawings; rather, the skilled person will recognize that many changes and modifications may be made within the scope of the present disclosure and appended claims. In the drawings and specification, there have been disclosed aspects for purposes of illustration only and not for purposes of limitation, the scope of the disclosure being set forth in the following claims.