Wheel slip control

Abstract

A computer system comprising processing circuitry configured to receive a normal load, Fz, associated with a wheel of a vehicle, receive a side slip angle, α, associated with the wheel, determine a longitudinal force, Fx, associated with the wheel for a range of values of longitudinal slip based on the normal load, Fz, and the side slip angle, α, determine a lateral force, Fy, associated with the wheel for a range of values of longitudinal slip based on the normal load, Fz, and the side slip angle, α, determine a total force, Ft, associated with the wheel for a range of values of longitudinal slip based on the determined longitudinal force, Fx, and the determined lateral force, Fy, and determine a longitudinal slip value for the wheel corresponding to the peak value of the total force, Ft. A computer-implemented method, computer program product, and non-transitory computer-readable storage medium are disclosed.

Description

WHEEL SLIP CONTROLTECHNICAL FIELD

[0001] The disclosure relates generally to vehicle control. In particular aspects, the disclosure relates to wheel slip control. The disclosure can be applied to heavy-duty vehicles, such as trucks, buses, and construction equipment, among other vehicle types. Although the disclosure may be described with respect to a particular vehicle, the disclosure is not restricted to any particular vehicle.BACKGROUND

[0002] Many modem vehicles are provided with stability systems such as electronic stability control (ESC), dynamic stability control (DSC), roll stability control (RSC), traction control systems (TCS), and / or anti-slip regulation (ASR). These systems aim to improve a vehicle's stability by detecting and reducing loss of traction (wheel slip). One approach to this is to prevent the wheels from locking while braking, whilst another is to maintain a predefined safe range of longitudinal wheel slip. Existing wheel slip stability systems tend to perform well in straight line braking manoeuvres, but their performance deteriorates during inturn manoeuvres.

[0003] There is therefore a need for alternative approaches to electrical machine identification that aim to solve, mitigate, alleviate, or eliminate at least some of the above or other disadvantages.SUMMARY

[0004] This disclosure provides systems, methods and other approaches for determining a reference longitudinal slip value for use in vehicle control. In particular, a reference longitudinal slip value is determined by taking into account both longitudinal and lateral forces on the wheels of the vehicle. This is achieved by determining a total force made up of longitudinal and lateral forces for a range of values of longitudinal slip. A longitudinal slip value for the maximum total force is then determined.

[0005] According to a first aspect of the disclosure, there is provided a computer system comprising processing circuitry configured to receive a normal load Fzassociated with a wheel of a vehicle, receive a side slip angle a associated with the wheel, determine a longitudinal force Fxassociated with the wheel for a range of values of longitudinal slip based on the normalIload Fzand the side slip angle a, determine a lateral force Fyassociated with the wheel for a range of values of longitudinal slip based on the normal load Fzand the side slip angle a, determine a total force Ft associated with the wheel for a range of values of longitudinal slip based on the determined longitudinal force Fxand the determined lateral force Fy, and determine a longitudinal slip value for the wheel corresponding to the peak value of the total force Ft.

[0006] The first aspect of the disclosure may seek to provide a reference longitudinal slip value for use in vehicle control that takes into account both longitudinal and lateral dynamics. By determining the longitudinal slip value based on a maximum total force, rather than simply a longitudinal force, longitudinal braking and acceleration can be improved by providing sufficient lateral capacity for a vehicle to perform manoeuvres with lateral dynamics. In particular, a large increase in lateral force can be provided for a relative small reduction in longitudinal force. This can reduce the deviation from an intended path and, in braking, reduce the stopping distance of the vehicle. The disclosed approaches are simple, robust, flexible, and practical to implement in real-life scenarios.

[0007] Optionally in some examples, including in at least one preferred example, the processing circuitry is configured to determine the longitudinal force . and / or the lateral force Fyusing a tyre model. A technical benefit may include providing accurate estimations of the longitudinal force Fxand / or the lateral force Fyin a robust manner.

[0008] Optionally in some examples, including in at least one preferred example, the processing circuitry is configured to determine the longitudinal force,x, and / or the lateral force, Fy, using the magic formula tyre model. A technical benefit may include the accurate and efficient provision of curves for the tyre forces at issue.

[0009] Optionally in some examples, including in at least one preferred example, the longitudinal force Fxcomprises a pure longitudinal force Fxpure and / or wherein the lateral force Fycomprises a pure lateral force Fypure. A technical benefit may include the simple and efficient provision of a representation of the forces.

[0010] Optionally in some examples, including in at least one preferred example, the longitudinal force Fxcomprises a combined longitudinal force Fxcombined, the processing circuitry is configured to determine the combined longitudinal force Fxcombined by applying a first weight Ga to the pure longitudinal force, Fxpure, and the first weight Ga is dependent on the side slip angle a. A technical benefit may include the provision of a more robust representation of the longitudinal force Fxthat captures the effect of lateral dynamics.

[0011] Optionally in some examples, including in at least one preferred example, the lateral force Fycomprises a combined lateral force Fycombined, the processing circuitry is configured to determine the combined lateral force Fycombined by applying a second weight GKto the pure lateral force Fy pUre, and the second weight GKis dependent on longitudinal slip. A technical benefit may include the provision of a more robust representation of the lateral force Fythat captures the effect of longitudinal dynamics.

[0012] Optionally in some examples, including in at least one preferred example, the processing circuitry is configured to determine the total force Ft according to:A technical benefit may include enabling both longitudinal and lateral components of the tyre force to be considered, providing a more accurate representation of the forces at play. Furthermore, when lateral dynamics are not involved (e.g. while braking in straight lines), Fy= 0 and Ft= Fx, so the controller can function as a basic longitudinal wheel slip controller.

[0013] Optionally in some examples, including in at least one preferred example, the processing circuitry is configured to determine the normal load Fzusing a vehicle model. A technical benefit may include the accurate and efficient provision of a value for the normal load Fz for one or more wheels of the vehicle.

[0014] Optionally in some examples, including in at least one preferred example, the processing circuitry is configured to determine the side slip angle a based on the lateral velocity vy, the longitudinal velocity vx, the yaw-rate co, and / or the wheel steer angle d of the vehicle. A technical benefit may include the accurate and real time provision of a value for the side slip angle a for one or more wheels of the vehicle.

[0015] Optionally in some examples, including in at least one preferred example, the processing circuitry is further configured to transmit the determined longitudinal slip value to a motion controller for the vehicle. A technical benefit may include that the reference longitudinal slip value can be fed to any suitable controller, allowing various controllers to take both longitudinal and lateral dynamics into account without large computational. For example, a standard wheel slip controller may address longitudinal dynamics alone, while the consideration for lateral dynamics is included through the reference longitudinal slip value.

[0016] Optionally in some examples, including in at least one preferred example, the motion controller comprises processing circuitry configured to determine a force control inputfor the vehicle based on the determined longitudinal slip value. A technical benefit may include enabling the determination of force control inputs for a vehicle that ensure the vehicle has sufficient lateral capacity. This can improve torque vectoring and contribute to prevention of jack-knifing and rollover.

[0017] According to a second aspect of the disclosure, there is provided a vehicle comprising the computer system. The second aspect of the disclosure may seek to provide a vehicle with improved motion control.

[0018] According to a third aspect of the disclosure, there is provided a computer- implemented method comprising receiving a normal load Fzassociated with a wheel of a vehicle, receiving a side slip angle a associated with the wheel, determining a longitudinal force Fxassociated with the wheel for a range of values of longitudinal slip based on the normal load Fz and the side slip angle a, determining a lateral force Fyassociated with the wheel for a range of values of longitudinal slip based on the normal load Fzand the side slip angle a, determining a total force Ft associated with the wheel for a range of values of longitudinal slip based on the determined longitudinal force Fxand the determined lateral force, Fy, and determining a longitudinal slip value for the wheel corresponding to the peak value of the total force Ft.

[0019] The third aspect of the disclosure may seek to provide a reference longitudinal slip value for use in vehicle control that takes into account both longitudinal and lateral dynamics. By determining the longitudinal slip value based on a maximum total force, rather than simply a longitudinal force, longitudinal braking and acceleration can be improved by providing sufficient lateral capacity for a vehicle to perform manoeuvres with lateral dynamics. This can reduce the deviation from an intended path and, in braking, reduce the stopping distance of the vehicle. The disclosed approached are simple, robust, flexible, and practical to implement in real-life scenarios.

[0020] According to a fourth aspect of the disclosure, there is provided a computer program product comprising program code for performing, when executed by processing circuitry, the computer-implemented method. The fourth aspect of the disclosure may seek to provide program code for improving motion control of vehicles. A technical benefit may include that new vehicles and / or legacy vehicles may be conveniently configured, by software installation / update, to be controlled in an improved manner.

[0021] According to a fifth aspect of the disclosure, there is provided a non-transitory computer-readable storage medium comprising instructions, which when executed by processing circuitry, cause the processing circuitry to perform the computer-implementedmethod. The fifth aspect of the disclosure may seek to provide program code for improving motion control of vehicles. A technical benefit may include that new vehicles and / or legacy vehicles may be conveniently configured, by software installation / update, to be controlled in an improved manner.

[0022] The disclosed aspects, examples (including any preferred examples), and / or accompanying claims may be suitably combined with each other as would be apparent to anyone of ordinary skill in the art. Additional features and advantages are disclosed in the following description, claims, and drawings, and in part will be readily apparent therefrom to those skilled in the art or recognized by practicing the disclosure as described herein.

[0023] There are also disclosed herein computer systems, control units, code modules, computer-implemented methods, computer readable media, and computer program products associated with the above discussed technical benefits.BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Examples are described in more detail below with reference to the appended drawings.

[0025] FIG. 1 schematically shows a side view of a vehicle according to an example.

[0026] FIG. 2A is an example plot of the relation between tyre force and slip ratio for a constant normal load.

[0027] FIG. 2B is an example plot of the relation between tyre force and slip ratio for a constant normal load for different values of side slip angle.

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

[0029] FIG. 4A is an example plot of the various forces against the longitudinal slip ratio for a side slip angle a of 4°.

[0030] FIG. 4B is an example plot of the various forces against the longitudinal slip ratio for a side slip angle a of 8°.

[0031] FIG. 5 is a schematic diagram of a computer system for implementing examples disclosed herein, according to an example.

[0032] Like reference numerals refer to like elements throughout the description.DETAILED DESCRIPTION

[0033] 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.

[0034] Stability systems in many modern vehicles tend to perform well in straight line braking manoeuvres, but their performance deteriorate during in-tum manoeuvres. This is often due to the fact that they do not take account of lateral dynamics, which play an important role in stability and manoeuvrability both in vehicle braking and acceleration, especially during turning.

[0035] To remedy this, systems, methods and other approaches are provided for determining a reference longitudinal slip value for use in vehicle control. In particular, a reference longitudinal slip value is determined from a maximum total force made up of longitudinal and lateral forces for a range of values of longitudinal slip. The determined longitudinal slip value can then be fed to a controller that can determine force control inputs for the vehicle, for example brake torque requests. As these force control inputs are determined based on a longitudinal slip value for the maximum total force, rather than simply a longitudinal force, longitudinal braking and acceleration can be improved by providing sufficient lateral capacity for a vehicle to perform manoeuvres with lateral dynamics. In particular, a large increase in lateral force can be provided for a relative small reduction in longitudinal force. This can reduce the deviation from an intended path and, in braking, reduce the stopping distance of the vehicle. The determined longitudinal slip value can be fed to any suitable controller, allowing various controllers to take both longitudinal and lateral dynamics into account. This approach is simple, robust, flexible, and practical to implement in real-life scenarios.

[0036] FIG. 1 schematically shows a side view of an example vehicle 100 of the type considered in this disclosure. The vehicle 100 may be any suitable form of vehicle. For example, the disclosure can be applied in heavy-duty vehicles, such as trucks, buses, and construction equipment, in personal vehicles such as cars, vans, or motorbikes, or in any other suitable form of vehicle. The vehicle 100 comprises a number of axles, each generally having two or more wheels 110. Whilst three axles are shown, it will be appreciated that any suitable number of axles may be provided. It will also be appreciated that any number of the axles may be driven axles.

[0037] The vehicle 100 may comprise one or more sources of propulsion. For example, the vehicle 100 may comprise one or more electrical machines 120 such as electric motors and / or generators. The vehicle 100 may comprise one or more batteries (not shown) configured to provide power to the electrical machines 120. 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 120 or the ICE) to the wheels 110.

[0038] The electrical machines 120 are configured to drive, e.g. provide torque and / or steering to, one or more axles or individual wheels 110 of the vehicle 100. The electrical machines 120 can supply either a positive (propulsion) or negative (braking) force. The use of electrical machines 120 to supply a negative force is known as regenerative braking, in which case the electrical machines 120 may be operated as generators, in order to recover energy during braking.

[0039] Furthermore, the vehicle 100 may comprise one or more sets of service brakes 130. The service brakes 130 can supply a negative (braking) force. The service brakes 130 may be, for example, frictional brakes such as pneumatic brakes. Pneumatic brakes use a compressor to fill the brake with air, which may be powered by the batteries. In some examples, the brakes may be electro-mechanical brakes.

[0040] The vehicle 100 may be a vehicle combination comprising a number of units, including a tractor unit and at least one trailing unit. In some examples, the vehicle 100 may be a vehicle combination comprising a number of units, including a tractor unit and at least one trailing unit. In such examples, each unit may comprise its own electrical machines 120, batteries, service brakes 130, and the like.

[0041] In the example of FIG. 1, the vehicle 100 includes a controller 140 comprising processing circuitry 150. The controller 140 is configured to control components of the vehicle, for example the electrical machines 120. FIG. 1 shows a common controller 140 for all electrical machines 120 of the vehicle 100, however it will be appreciated that each electrical machine 120 may have its own respective controller 140. In many cases, the controller 140 may be implemented in the structure of the electrical machine 120 itself. The controller 140 may be a microcontroller. In examples where the vehicle 100 is a vehicle combination, the vehicle 100 may include a global controller and a plurality of unit controllers, for example a controller for each unit.

[0042] The controller 140 may receive control signals from a computer system 160 comprising processing circuitry 170. The computer 160 system may be a vehicle control unitconfigured to perform various vehicle (unit) control functions, such as vehicle motion management. The computer system 160 may be local to the vehicle 100, or may be a remote system, implemented at a distance from the vehicle 100. The computer system 160 may be communicatively coupled to the controller 140 in any suitable way, for example via a circuit or any other wired, wireless, or network connection known in the art. Furthermore, the communicative coupling may be implemented as a direct connection between the controller 140 and the computer system 160, or may be implemented as a connection via one or more intermediate entities.

[0043] One function of the controller 140 and the computer system 160 is to provide force control inputs for the vehicle 100, for example brake torque requests. These force control inputs should enable a requested manoeuvre for the vehicle 100, for example, straight-line driving, cornering, braking and the like, whilst ensuring safe and efficient motion of the vehicle 100. Part of this function is traction control, which may involve determining motion parameters for the vehicle based on a reference longitudinal slip value.

[0044] When the vehicle 100 is in motion, the wheels (or indeed tyres) 110 of the vehicle 100 experience slip. Slip can be expressed as the body slip on the vehicle 100 as a whole, or the slip on a given wheel 110, which can be divided into longitudinal and lateral slip. These parameters are known in the art, and not discussed in detail here. However, it is noted that the side slip angle a for a given wheel 110, i.e. the angle between the longitudinal dimension of the wheel 110 (the direction in which the wheel 110 is pointing) and the traveling direction of the wheel 110, can be defined as:where vwxis the longitudinal velocity of the wheel 110, and vwyis the lateral velocity of the wheel 110. It is also noted that the slip ratio for a given wheel 110 is a ratio between the longitudinal velocity of the wheel 110 and the longitudinal velocity of the vehicle 100. For example, the theoretical longitudinal slip is the ratio between the relative velocity in the tyreroad contact patch and the wheel translational velocity, while the practical longitudinal slip is the ratio between the relative velocity in the tyre-road contact patch and the vehicle velocity at the wheel coordinate.

[0045] FIG. 2A shows an example plot 200 of the relation between the tyre force (the force exerted on the travelling surface by the tyre and / or wheel 110) and the slip ratio for aconstant normal load, taken from Rajesh Rajamani, Vehicle Dynamics and Control, 2nd ed., Springer, 2012. It shows that magnitude of the tyre force increases from 0 for increasing / decreasing slip ratio up to a peak 202, before plateauing. This indicates that there is an optimal value for the slip ratio to ensure maximum tyre force in both acceleration and braking.

[0046] This is the type of relation used in existing wheel slip stability systems, which may define an optimal slip region around the slip ratio that corresponds to the maximum tyre force in both longitudinal acceleration and braking. However, the plot of FIG. 2A only considers longitudinal dynamics, and does not take account of lateral dynamics. As such, existing wheel slip stability systems tend to perform well in straight line braking manoeuvres, but their performance deteriorates during in-tum manoeuvres.

[0047] This is evidenced by FIG. 2B, which is an example plot 204 of the relation between the tyre force and the slip ratio for a constant normal load for different values of the side slip angle a in acceleration. As shown, the peak value of the tyre force decreases as the side slip angle a increases. Furthermore, the slip ratio corresponding to the peak value of the tyre force increases. This is because, in situations where slip is present (e.g. in turns or in straight line motion with side slip), the presence of lateral forces is prominent. If higher lateral slip curves were drawn, the peak will disappear at some point, meaning an extremum seeking algorithm applied to find the peak will fail and lead to wheel lock and an unstable area of tyre force-slip characteristics. As such, wheel slip stability systems that define an optimal slip region based only on longitudinal dynamics do not estimate the peak force accurately and therefore do not provide an optimal solution in real-life cases where lateral forces are present. The lateral forces have a significant effect on longitudinal dynamics, and therefore it is advantageous to consider lateral dynamics, especially during in-turn manoeuvres.

[0048] The peak tyre force is also a function of normal load on the wheel 110. In particular, the magnitude of the peak tyre force increases with increasing normal load. Furthermore, the peak longitudinal force is a function of the surface friction coefficient. Therefore, these parameters should also be taken into account.

[0049] FIG. 3 is a flowchart of a computer-implemented method 300 according to an example. The method 300 may be implemented by processing circuitry of a computer system (e.g., the processing circuitry 150 of the controller 140, or the processing circuitry 170 of the computer system 160 described in relation to FIG. 1). For example, the method 300 may be implemented by a “dynamic reference slip estimator”.

[0050] The method 300 enables the determination of a reference longitudinal slip value for use in vehicle control based on both longitudinal and lateral forces on the wheels of the vehicle. This is achieved by determining a total force made up of longitudinal and lateral forces for a range of values of longitudinal slip, and determining a longitudinal slip value for the maximum total force. The determined longitudinal slip value can then be fed to a controller that can determine force control inputs for the vehicle. Whilst the method 300 is described in relation to a single wheel 110, it will be appreciated that the method 300 could be performed for two or more, including all, wheels 110 of a vehicle 100.

[0051] At 302, a normal load Fzassociated with a wheel 110 of the vehicle 100 is received. In some examples, the normal load Fzmay be provided by a sensor associated with the wheel 110. Whilst estimating the normal load Fzat the wheel-end is currently challenging in practice, it may be envisaged that future sensor technology may address this. In other examples, the normal load Fzmay be determined based on the longitudinal acceleration axof the vehicle 100 and the lateral acceleration ayof the vehicle 100. This may be performed by a normal force estimator, for example implemented in the computer system 160.

[0052] At 304, a side slip angle a associated the wheel 110 is received. In some examples, the side slip angle a may be provided by a sensor associated with the wheel 110, for example by fusing inertial measurement data and different filtering methods. Whilst estimating the side slip angle a at the wheel-end is currently challenging in practice, it may be envisaged that future sensor technology may address this. In other examples, the side slip angle a may be determined based on the longitudinal velocity vxof the vehicle 100, the lateral velocity vyof the vehicle 100, the yaw rate co of the vehicle 100, and / or the wheel steer angle 8 of the vehicle 100. This may be performed by a side slip angle estimator, for example implemented in the computer system 160. In particular, the longitudinal acceleration axof the vehicle 100, the lateral acceleration ayof the vehicle 100, and the yaw acceleration m of the vehicle 100 may be determined and used to determine the longitudinal velocity vxof the vehicle 100 and the lateral velocity vyof the vehicle 100. Taking the wheel steer angle 8 of the vehicle 100 from a control input for the vehicle 100, the side slip angle a associated with individual wheels 110 for a three-axle configuration may be calculated as follows:where aaL is the side slip angle for the left wheel of axle a, aaR is the side slip angle for the right wheel of axle a, / is the distance from the centre of gravity of the vehicle 110 to the front axle, Irb is the distance from the centre of gravity of the vehicle 110 to rear axle / / and twais the track width of axle a. Further axle configurations can be generated based on the three-axle configuration in equations (2) to (7). For steered axles, the relevant equations will correspond to equations (2) and (3). For non-steered axles, the relevant equations will correspond to equations (4) to (7).

[0053] In some examples, the side slip angle a may be determined based on the longitudinal velocity Vxw and the lateral velocity vywof the wheel 110, as discussed in relation to equation (1). The lateral velocity vywof the wheel 110 may be determined based on one or more of the lateral acceleration ay, wheel steer angle b, and / or yaw rate co of the vehicle 100, and / or a corner radius travelled by the vehicle 100. For example, as a larger side slip angle a may be generated by further turning the steering wheel, the side slip angle a may be determined directly from the wheel steer angle d. In some examples, the side slip angle a may be determined using the kinematic equations of a rigid body in relation to velocity vector of a reference point and rotating it by the Euler rotational matrix.

[0054] The determination of the normal load Fzand / or the side slip angle a may be achieved using a vehicle model, for example the full vehicle model disclosed in MSc Mobility Engineering, Chalmers Vehicle Dynamics Compendium, Chalmers University of Technology. In some examples, the vehicle model may be simplified in order to reduce model complexity and provide more efficient use of computational resources. For example, suspension parameters such as spring stiffness and damper stiffness may be neglected, the vehicle 100 may be assumed to be rigid (allowing the normal load, Fz, to be determined based on the longitudinalacceleration axand the lateral acceleration ayof the vehicle 100 only), and certain axels may be lumped together (for example, in a 6x4 model, the two rear axles may be lumped, and the combined rear axle load split equally between both rear axles). Other vehicle models and suitable simplifications will be readily envisaged by the person skilled in the art.

[0055] At 306, a longitudinal force Fxassociated with the wheel 110 is determined for a range of values of longitudinal slip. The longitudinal force Fxmay be determined for a full range of longitudinal slip values (i.e. a longitudinal slip range of 0%-100%), or may be determined for a subrange of that range. The longitudinal force Fxis determined based on the normal load Fzand the side slip angle a associated with the wheel 110, as determined in 302 and 304, as discussed below.

[0056] The longitudinal force Fxassociated with the wheel 110 may be considered in two ways: as a pure longitudinal force Fxpure or as a combined longitudinal force FXCombined. The pure longitudinal force Fxpure is the longitudinal force caused only by longitudinal dynamics, whereas the combined longitudinal force Fxcombined is the longitudinal force caused by both longitudinal and lateral dynamics.

[0057] The longitudinal force Fxcan be determined in any suitable manner. For example, the longitudinal force Fxis determined using a tyre model. For example, the forces may be determined using the tyre brush model, the Dugoff tyre model, or other suitable analytical or empirical tyre model known in the art. In some examples, force observers can be designed to estimate the longitudinal and / or lateral forces, for example using a simple processed model that considers only the one component of tyre force slip characteristics.

[0058] In one example, the longitudinal force Fx, in particular the longitudinal forces Fxpure and Fxcombined., is determined using the “magic formula” outlined in “Tyre and Vehicle Dynamics” , 2nd ed., Elsevier, 2006 by Hans B. Pacejka. The Magic Formula typically produces a curve that passes through the origin, reaches a maximum and subsequently tends to a horizontal asymptote, and is capable of producing characteristics that closely match measured curves for the tyre forces at issue. The general form of this formula is: y = Dsin [Carctan {Bx — E(Bx — arctan Bx )} ] (8) where y is the output variable (for example Fx, Fxpure, Fxcombined), x is the input variable (for example tan a or the longitudinal slip K), B is a stiffness factor, C is a shape factor, and D isa peak value. Equation (8) may also include shifting factors for x and y to allow the curve to have an offset with respect to the origin.

[0059] Based on equation (8), the pure longitudinal force Fxpure can be determined using:Fx pure = Dsin [Carctan {BK — E (BK — arctan BK )} ] (9)The pure force is quite accurate, but does not capture the effect of lateral dynamics on the longitudinal force, which is a more accurate estimation of the performance of an actual on-road tyre. As discussed in relation to FIG. 2B, when a tyre generates both lateral and longitudinal forces, the peak force for each component is lower than that determined when only one component is at play. Therefore, a combined force that takes lateral dynamics into account may be determined.

[0060] In general, a combined force can be determined by applying a weight G to the pure force. The weight G that is applied is a function having a hill shape, and is generally given by:G = Deos [Carctan (Bx) ] (10) where x is the input variable (for example tan a or the longitudinal slip K), B influences the sharpness of the hill, C determines the height of the hill’s base, and £) is a peak value. Coefficient B constitutes the main factor responsible for the shape of the weighting function.

[0061] The combined longitudinal force Fxcombined can be determined by applying a weight Ga to the pure longitudinal force FxpUre, where the weight Ga is dependent on the side slip angle a. As such, the combined longitudinal force Fxcombined C3.H be determined using:Ga=cos [C arctan Ba) ] (H) Fx combined Fa' Fxpure (12)Equation (12) may also include a vertical shifting factor to allow the curve to have an offset with respect to the origin.

[0062] At 308, a lateral force Fyassociated with the wheel 110 is determined for a range of values of longitudinal slip. The lateral force Fymay be determined for a full range oflongitudinal slip values (i.e. a longitudinal slip range of 0%-100%), or may be determined for a subrange of that range. The lateral force Fyis determined based on the normal load Fzand the side slip angle a associated with the wheel 110, as determined in 302 and 304, as discussed below.

[0063] Similar to the longitudinal force Fx, the lateral force Fyassociated with the wheel 110 may be considered in two ways: as a pure lateral force FypUre or as a combined lateral force Fycombined. The pure lateral force Fypure is the lateral force caused only by lateral dynamics, whereas the combined lateral force Fycombined is the longitudinal force caused by both longitudinal and lateral dynamics.

[0064] Based on equation (8), the pure lateral force Fy pUre can be determined using:Fy pure= Dsin [Carctan {Ba — E(Ba — arctan Ba )} ] (13)Again, the pure force is quite accurate, but does not capture the effect of longitudinal dynamics on the lateral force. Therefore, a combined force that takes longitudinal dynamics into account may be determined. It is noted that the pure lateral force Fypure is not dependent on the longitudinal slip K.

[0065] The combined lateral force Fycombined C3.H be determined by applying a weight GKto the pure lateral force Fy pUre, where the weight GKis dependent on the longitudinal slip K. AS such, the combined lateral force Fycombined C3.H be determined using:Equation (15) may also include a horizontal shifting factor to allow the curve to have an offset with respect to the origin.

[0066] The magic formula may also take surface friction into account when determining the longitudinal force, Fx, and / or the lateral force, Fy. This is achieved by one or more scaling factors that are dependent on the surface friction. The surface friction can be determined in any suitable manner. For example, the surface friction may be obtained based on the longitudinal and lateral acceleration values after the application of brake torque. This works well to identify the road surface type and update the model. In another example, a friction estimator may be used that enables real-time estimation of the road-tyre friction. This allows the longitudinal capabilities of the tyre to be optimised.

[0067] At 310, a total force Ft associated with the wheel 110 is determined for a range of values of longitudinal slip. The total force Ft may be determined for a full range of longitudinal slip values (i.e. a longitudinal slip range of 0%-100%), or may be determined for a subrange of that range. The total force Ft is determined based on the longitudinal force Fxand the lateral force Fyassociated with the wheel 110, as determined in 306 and 308. In one example, a combined total force Ft combined may be determined based on the combined forces Fxcombined and Fy combined.

[0068] The total force Ft may be determined based on the concept of a friction circle. This is outlined, for example, in “Estimation of road frictional force and wheel slip for effective Anti-lock Braking System (ABS) control” by Sulakshan Rajendran, Sarah K Spurgeon, Georgios Tsampardoukas, and Ric Hampson, International Journal of Robust and Nonlinear Control, 2018. In particular, the total force Ft may be determined as follows:The calculation of the total force Ft in this way enables both longitudinal and lateral components of the tyre force to be considered, providing a more accurate representation of the forces at play. When considering the combined forces Fxcombined an y combined., the influence of the respective components on each other is also taken into account. In some examples, the calculation of the total force Ft can be determined based on the equation for an ellipse, rather than a circle. The parameters of the ellipse can be determined based on various vehicle properties.

[0069] At 312, a longitudinal slip value for the wheel 110 corresponding to the peak value of the total force Ft is determined. This can be achieved using any suitable method, for example mathematical or graphical methods known in the art. For example, an extremum seeking algorithm can be used. In one example, a for iterative loop checks the current timestep calculated output force value. If the current timestep value is lower than the previous timestep, then the previous timestep force output is considered the maximum value, and the loop is exited. An example of extremum seeking control for pure longitudinal braking is presented in "Real-Time Optimization by Extremum-Seeking Control", by Kartik B. Ariyur and Miroslav Krstic, 2003.

[0070] FIG. 4A is an example plot of various forces against the longitudinal slip ratio for a side slip angle a of 4°. In particular, the pure longitudinal force Fxpure, the combined longitudinal force Fxcombined., the combined lateral force Fycombined., and the combined total force Ft combined are shown. It is noted that the pure lateral force Fypure is not dependent on the longitudinal slip K. It can be seen from comparing the pure longitudinal force Fxpure and the combined longitudinal force Fxcombined that the combined longitudinal force Fxcombined is somewhat lower than and shifted from the pure longitudinal force Fxpure across the range of longitudinal slip ratio. As such, the longitudinal slip ratio for the peak force is different (11.6% for the pure longitudinal force FxpUre compared with 13.8% for the combined longitudinal force Fxcombined, with a corresponding decrease in peak longitudinal force of around 500N). This can have a significant impact on vehicle control. This effect is consequently present in the total force Ft, where the longitudinal slip ratio for the peak force, and the peak force itself, is different between the pure total force Ft pure and the combined total force Ft combined.

[0071] FIG. 4B is an example plot of the various forces against the longitudinal slip ratio for a side slip angle a of 8°. Here it can be seen that the increase in side slip angle a has a prominent effect on longitudinal dynamics. For example, the longitudinal slip ratio for the peak combined longitudinal force Fxcombined has increased from 13.8% for a side slip angle a of 4° to 18.6% for a side slip angle a of 8°, with a corresponding decrease in peak longitudinal force of around 1000N. This effect is consequently present in the combined total force Ft combined, where the longitudinal slip ratio for the peak force is as increased from 12.5% for a side slip angle a of 4° to 12.8% for a side slip angle a of 8°, with a corresponding decrease in peak total force of around 500N.

[0072] It can be noted from both FIG. 4A and FIG. 4B that a large increase in lateral force can be provided for a relative small reduction in longitudinal force. For example, in FIG. 4B the longitudinal force decreases by around 150N between the combined longitudinal force Fxcombined and the combined total force Ft combined., while the corresponding combined lateral force Fycombined increases by around 900N.

[0073] At 314, the longitudinal slip value determined in 312 may be transmitted to a motion controller for the vehicle 100 as a reference value. For example, if the longitudinal slip value is determined by the computer system 160, it may be transmitted to the controller 140 for further control of the vehicle. If the longitudinal slip value is determined by the controller 140, it may be transmitted to another module of the controller 140 for further control of the vehicle. Alternatively, the control may be provided by the computer system 160.

[0074] The reference longitudinal slip value can be fed to any suitable controller, allowing various controllers to take both longitudinal and lateral dynamics into account. The provision of the reference longitudinal slip value allows a controller to control both lateral and longitudinal performance without large computational cost by employing simple control of longitudinal dynamics. For example, a standard wheel slip controller may address longitudinal dynamics alone, while the consideration for lateral dynamics is included through the reference longitudinal slip value. Therefore, standard wheel slip controllers that are already implemented in existing vehicles can be upgraded via use of the determined reference longitudinal slip value. For example, the disclosed approaches can be adopted in a semi or a fully autonomous vehicle. In the case of an autonomous vehicle, the disclosed approaches can be integrated with modelbased controllers such as model predictive control for further traction improvements. Furthermore, when lateral dynamics are not involved (e.g. while braking in straight lines), the controller may function as a basic longitudinal wheel slip controller, and thus the performance of the vehicle is not affected in this regard.

[0075] The determination of the reference longitudinal slip value can be performed by a subsystem (e.g. a dynamic reference slip estimator) separate to the standard wheel slip controller, and therefore works well with different types of wheel slip controller. A standard wheel slip controller tends to be implemented as a lower-level control which works at wheel level. It may therefore be beneficial to implement a flag or alert that is triggered by vehicle instability. Once the flag is triggered, higher-level systems such as the DSC and RSC would overwrite the wheel level estimator’s slip values and provide them to a sliding mode controller. A sliding mode controller is a non-linear controller that suits slip control application in general, however other methods known in the art may also be applied, such as PID Control, gain scheduling, and the like. It may also be beneficial to estimate the lateral force on the vehicle 100. In some examples, the dynamic reference slip estimator can be used independently, as lateral correction / consideration is always present when lateral dynamics are involved. Therefore, different levels of control are not necessary and a single system can implement the functions described herein.

[0076] Knowing the real-time lateral force requirement based on the road trajectory allows the dynamic reference slip estimator to optimize the longitudinal capabilities of the tyre, already keeping a safe margin for the required lateral force. This heavily reduces any yaw error and improves vehicle stability during braking. This is particularly applicable to autonomous vehicles having some form of trajectory planning.

[0077] The motion controller for the vehicle 100 (for example the controller 140) may receive the reference longitudinal slip value and implement it in motion control for the vehicle 100. For example, one or more force control inputs for the vehicle 100 may be determined based on a reference longitudinal slip value that takes into account both longitudinal and lateral dynamics of the vehicle 100. It can therefore be ensured that sufficient lateral capacity for the vehicle 100 to perform manoeuvres in a safe and efficient manner.

[0078] In one example, this approach can improve torque vectoring of the vehicle 100. By taking into account lateral dynamics, the controller 140 can provide improved tractive performance. This applies both in acceleration and braking. This can reduce the deviation from an intended path and, in braking, reduce the stopping distance of the vehicle.

[0079] In another example, this approach can contribute to prevention of jack-knifing of a vehicle combination. Jack-knifing occurs when the tractor unit of a vehicle combination starts to skid sideways in slippery road conditions and the driver is not able to correct the skidding in time with the proper amount of steering. The trailer unit pushes the tractor unit causing the tractor unit to turn around a vertical axis until it hits the trailer unit. Jack-knifing is one of the major sources of accidents in multi-unit vehicle combinations. The disclosed approach can be applied to both tractor and trailer units, thus ensuring that both the tractor and trailer units brake together as one unit. Safe operation margins and triggers can be set for the vehicle combination to avoid jack-knifing scenarios by reducing torque when appropriate.

[0080] In another example, this approach can contribute to prevention of rollover. Rollover occurs when the severe steering and / or braking causes a vehicle’s lateral acceleration to surpass a critical point. The disclosed approach can be used to ensure that sufficient lateral capacity is available for the vehicle 100, which can contribute to roll-over prevention. For example, in case of impending roll-over, further longitudinal braking could be provided in order to decrease the lateral force capability of the wheel, and thus the lateral acceleration.

[0081] FIG. 5 is a schematic diagram of a computer system 500 for implementing examples disclosed herein. The computer system 500 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 500 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 500 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.

[0082] The computer system 500 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 500 may include processing circuitry 502 (e.g., processing circuitry including one or more processor devices or control units), a memory 504, and a system bus 506. The computer system 500 may include at least one computing device having the processing circuitry 502. The system bus 506 provides an interface for system components including, but not limited to, the memory 504 and the processing circuitry 502. The processing circuitry 502 may include any number of hardware components for conducting data or signal processing or for executing computer code stored in memory 504. The processing circuitry 502 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 502 may further include computer executable code that controls operation of the programmable device.

[0083] The system bus 506 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 504 may be one or more devices for storing data and / or computer code for completing or facilitating methods described herein. The memory 504 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 504 may be communicably connectedto the processing circuitry 502 (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 504 may include non-volatile memory 508 (e.g., read-only memory (ROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), etc.), and volatile memory 510 (e.g., randomaccess 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 502. A basic input / output system (BIOS) 512 may be stored in the non-volatile memory 508 and can include the basic routines that help to transfer information between elements within the computer system 500.

[0084] The computer system 500 may further include or be coupled to a non-transitory computer-readable storage medium such as the storage device 514, 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 514 and other drives associated with computer-readable media and computer-usable media may provide nonvolatile storage of data, data structures, computer-executable instructions, and the like.

[0085] 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 514 and / or in the volatile memory 510, which may include an operating system 516 and / or one or more program modules 518. All or a portion of the examples disclosed herein may be implemented as a computer program 520 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 514, which includes complex programming instructions (e.g., complex computer-readable program code) to cause the processing circuitry 502 to carry out actions described herein. Thus, the computer-readable program code of the computer program 520 can comprise software instructions for implementing the functionality of the examples described herein when executed by the processing circuitry 502. In some examples, the storage device 514 may be a computer program product (e.g., readable storage medium) storing the computer program 520 thereon, where at least a portion of a computer program 520 may be loadable (e.g., into a processor) for implementing the functionality of the examples described herein when executed by theprocessing circuitry 502. The processing circuitry 502 may serve as a controller or control system for the computer system 500 that is to implement the functionality described herein.

[0086] The computer system 500 may include an input device interface 522 configured to receive input and selections to be communicated to the computer system 500 when executing instructions, such as from a keyboard, mouse, touch-sensitive surface, etc. Such input devices may be connected to the processing circuitry 502 through the input device interface 522 coupled to the system bus 506 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 500 may include an output device interface 524 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 500 may include a communications interface 526 suitable for communicating with a network as appropriate or desired.

[0087] 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.

[0088] According to certain examples, there is also disclosed:

[0089] Example 1 : A computer system (140, 160, 500) comprising processing circuitry (150, 170, 502) configured to receive a normal load, Fz, associated with a wheel (110) of a vehicle (100), receive a side slip angle, a, associated with the wheel (110), determine a longitudinal force, F, associated with the wheel (110) for a range of values of longitudinal slip based on the normal load, Fz, and the side slip angle, a, determine a lateral force, Fy, associated with the wheel (110) for a range of values of longitudinal slip based on the normal load, Fz, and the side slip angle, a, determine a total force, Ft, associated with the wheel (110) for a range of values of longitudinal slip based on the determined longitudinal force, c, and the determined lateral force, Fy, and determine a longitudinal slip value for the wheel (110) corresponding to the peak value of the total force, Ft.

[0090] Example 2: The computer system (140, 160, 500) of claim 1, wherein the processing circuitry (150, 170, 502) is configured to determine the longitudinal force, Fc, and / or the lateral force, Fy, using a tyre model.

[0091] Example 3: The computer system (140, 160, 500) of claim 1 or 2, wherein the processing circuitry (150, 170, 502) is configured to determine the longitudinal force, Fx, and / or the lateral force, Fy, using the magic formula tyre model.

[0092] Example 4: The computer system (140, 160, 500) of any preceding claim, wherein the longitudinal force, Fx, comprises a pure longitudinal force, Fx pure and / or wherein the lateral force, Fy, comprises a pure lateral force, FyPure.

[0093] Example 5: The computer system (140, 160, 500) of claim 4, wherein the longitudinal force, Fx, comprises a combined longitudinal force, Fxcombined, the processing circuitry (150, 170, 502) is configured to determine the combined longitudinal force, FXcombi ed, by applying a first weight, Ga, to the pure longitudinal force, Fxpure, and the first weight, Ga, is dependent on the side slip angle, a.

[0094] Example 6: The computer system (140, 160, 500) of claim 4 or 5, wherein the lateral force, Fy, comprises a combined lateral force, Fycombined, the processing circuitry (150, 170, 502) is configured to determine the combined lateral force, Fycombined, by applying a second weight, GK, to the pure lateral force, Fy pure, and the second weight, GK, is dependent on longitudinal slip, K.

[0095] Example 7: The computer system (140, 160, 500) of any preceding claim, wherein the processing circuitry (150, 170, 502) is configured to determine the total force, Ft, according to:

[0096] Example 8: The computer system (140, 160, 500) of any preceding claim, wherein the processing circuitry (150, 170, 502) is configured to determine the normal load, Fz, using a vehicle model.

[0097] Example 9: The computer system (140, 160, 500) of any preceding claim, wherein the processing circuitry (150, 170, 502) is configured to determine the side slip angle, a, based on the lateral velocity, vy, the longitudinal velocity, vx, the yaw-rate, co, and / or the wheel steer angle, 0, of the vehicle.

[0098] Example 10: The computer system (140, 160, 500) of any preceding claim, wherein the processing circuitry (150, 170, 502) is further configured to transmit the determined longitudinal slip value to a motion controller (140) for the vehicle (100).

[0099] Example 11 : The computer system of (140, 160, 500) claim 10, wherein the motion controller (140) comprises processing circuitry (150) configured to determine a force control input for the vehicle based on the determined longitudinal slip value.

[0100] Example 12: A vehicle (100) comprising the computer system (140, 160, 500) of any preceding claim.

[0101] Example 13: A computer-implemented method (300), comprising receiving (302), by processing circuitry (150, 170, 502), a normal load, Fz, associated with a wheel (100) of a vehicle (100), receiving (304), by the processing circuitry (150, 170, 502), a side slip angle, a, associated with the wheel (100), determining (306), by the processing circuitry (150, 170, 502), a longitudinal force, Fx, associated with the wheel (100) for a range of values of longitudinal slip based on the normal load, Fz, and the side slip angle, a, determining (308), by the processing circuitry (150, 170, 502), a lateral force, Fy, associated with the wheel (100) for a range of values of longitudinal slip based on the normal load, Fz, and the side slip angle, a, determining (310), by the processing circuitry (150, 170, 502), a total force, Ft, associated with the wheel (100) for a range of values of longitudinal slip based on the determined longitudinal force, Fx, and the determined lateral force, Fx, and determining (312), by the processing circuitry (150, 170, 502), a longitudinal slip value for the wheel (100) corresponding to the peak value of the total force, Ft.

[0102] Example 14: The computer-implemented method (300) of claim 13, comprising determining, by the processing circuitry (150, 170, 502), the longitudinal force, Fx, and / or the lateral force, Fy, using a tyre model.

[0103] Example 15: The computer-implemented method (300) of claim 13 or 14, comprising determining, by the processing circuitry (150, 170, 502), the longitudinal force, Fx, and / or the lateral force, Fy, using the magic formula tyre model.

[0104] Example 16: The computer-implemented method (300) of any of examples 13 to 15, wherein the longitudinal force, Fx, comprises a pure longitudinal force, Fx pure and / or wherein the lateral force, Fy, comprises a pure lateral force, FyPure.

[0105] Example 17: The computer-implemented method (300) of claim 16, wherein the longitudinal force, Fx, comprises a combined longitudinal force, Fxcombined, the processing circuitry (150, 170, 502) is configured to determine the combined longitudinal force, Fxcombi ed, by applying a first weight, Ga, to the pure longitudinal force, Fxpure, and the first weight, Ga, is dependent on the side slip angle, a.

[0106] Example 18: The computer-implemented method (300) of claim 16 or 17, wherein the lateral force, Fy, comprises a combined lateral force, Fycombined, the processing circuitry (150, 170, 502) is configured to determine the combined lateral force, Fycombined, by applying a second weight, GK, to the pure lateral force, Fy pUre, and the second weight, GK, is dependent on longitudinal slip, K.

[0107] Example 19: The computer-implemented method (300) of any of examples 13 to 18, comprising determining, by the processing circuitry (150, 170, 502), the total force, Ft, according to:

[0108] Example 20: The computer-implemented method (300) of any of examples 13 to 19, comprising determining, by the processing circuitry (150, 170, 502), the normal load, Fz, using a vehicle model.

[0109] Example 21 : The computer-implemented method (300) of any of examples 13 to 20, comprising determining, by the processing circuitry (150, 170, 502), the side slip angle, a, based on the lateral velocity, vy, the longitudinal velocity, vx, the yaw-rate, co, and / or the wheel steer angle, 3, of the vehicle.

[0110] Example 22: The computer-implemented method (300) of any of examples 13 to 21, further comprising transmitting, by the processing circuitry (150, 170, 502), the determined longitudinal slip value to a motion controller (140) for the vehicle (100).

[0111] Example 23: The computer-implemented method (300) claim 22, wherein the motion controller (140) comprises processing circuitry (150) configured to determine a force control input for the vehicle based on the determined longitudinal slip value.

[0112] Example 24: A computer program product comprising program code for performing, when executed by processing circuitry (150, 170, 502), the computer-implemented method (300) of any of examples 13 to 23.

[0113] Example 25: A non-transitory computer-readable storage medium comprising instructions, which when executed by processing circuitry (150, 170, 502), cause the processing circuitry to perform the computer-implemented method (300) of any of examples 13 to 23.

[0114] The 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.

[0115] 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.

[0116] 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.

[0117] 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.

[0118] 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.

Claims

ClaimsWhat is claimed is:

1. A computer system (140, 160, 500) comprising processing circuitry (150, 170, 502) configured to: receive a normal load, Fz, associated with a wheel (110) of a vehicle (100); receive a side slip angle, a, associated with the wheel (110); determine a longitudinal force, Fx, associated with the wheel (110) for a range of values of longitudinal slip based on the normal load, Fz, and the side slip angle, a; determine a lateral force, Fy, associated with the wheel (110) for a range of values of longitudinal slip based on the normal load, Fz, and the side slip angle, a; determine a total force, Ft, associated with the wheel (110) for a range of values of longitudinal slip based on the determined longitudinal force, Fx, and the determined lateral force, Fy,- and determine a longitudinal slip value for the wheel (110) corresponding to the peak value of the total force, Ft.

2. The computer system (140, 160, 500) of claim 1, wherein the processing circuitry (150, 170, 502) is configured to determine the longitudinal force, Fx, and / or the lateral force, Fy, using a tyre model.

3. The computer system (140, 160, 500) of claim 1 or 2, wherein the processing circuitry (150, 170, 502) is configured to determine the longitudinal force, Fx, and / or the lateral force, Fy, using the magic formula tyre model.

4. The computer system (140, 160, 500) of any preceding claim, wherein the longitudinal force, Fx, comprises a pure longitudinal force, Fxpure and / or wherein the lateral force, Fy, comprises a pure lateral force, FyPure.

5. The computer system (140, 160, 500) of claim 4, wherein: the longitudinal force, Fx, comprises a combined longitudinal force, Fxcombinedthe processing circuitry (150, 170, 502) is configured to determine the combined longitudinal force, Fxcombined, by applying a first weight, Ga, to the pure longitudinal force, Fxpure} and the first weight, Ga, is dependent on the side slip angle, a.

6. The computer system (140, 160, 500) of claim 4 or 5, wherein: the lateral force, Fy, comprises a combined lateral force, Fycombined the processing circuitry (150, 170, 502) is configured to determine the combined lateral force, Fycombined., by applying a second weight, GK, to the pure lateral force, FypUre, and the second weight, GK, is dependent on longitudinal slip, K.

7. The computer system (140, 160, 500) of any preceding claim, wherein the processing circuitry (150, 170, 502) is configured to determine the total force, Ft, according to:

8. The computer system (140, 160, 500) of any preceding claim, wherein the processing circuitry (150, 170, 502) is configured to determine the normal load, Fz, using a vehicle model.

9. The computer system (140, 160, 500) of any preceding claim, wherein the processing circuitry (150, 170, 502) is configured to determine the side slip angle, a, based on the lateral velocity, vy, the longitudinal velocity, vx, the yaw-rate, co, and / or the wheel steer angle, F of the vehicle.

10. The computer system (140, 160, 500) of any preceding claim, wherein the processing circuitry (150, 170, 502) is further configured to transmit the determined longitudinal slip value to a motion controller (140) for the vehicle (100).

11. The computer system of (140, 160, 500) claim 10, wherein the motion controller (140) comprises processing circuitry (150) configured to determine a force control input for the vehicle based on the determined longitudinal slip value.

12. A vehicle (100) comprising the computer system (140, 160, 500) of any preceding claim.

13. A computer-implemented method (300), comprising: receiving (302), by processing circuitry (150, 170, 502), a normal load, Fz, associated with a wheel (100) of a vehicle (100); receiving (304), by the processing circuitry, a side slip angle, a, associated with the wheel (100); determining (306), by the processing circuitry (150, 170, 502), a longitudinal force, Ft, associated with the wheel (100) for a range of values of longitudinal slip based on the normal load, Fz, and the side slip angle, a; determining (308), by the processing circuitry (150, 170, 502), a lateral force, Fy, associated with the wheel (100) for a range of values of longitudinal slip based on the normal load, Fz, and the side slip angle, a; determining (310), by the processing circuitry (150, 170, 502), a total force, F, associated with the wheel (100) for a range of values of longitudinal slip based on the determined longitudinal force, Fc, and the determined lateral force, Fx, and determining (312), by the processing circuitry (150, 170, 502), a longitudinal slip value for the wheel (100) corresponding to the peak value of the total force, Ft.

14. A computer program product comprising program code for performing, when executed by processing circuitry (150, 170, 502), the computer-implemented method (300) of claim 13.

15. A non-transitory computer-readable storage medium comprising instructions, which when executed by processing circuitry (150, 170, 502), cause the processing circuitry to perform the computer-implemented method (300) of claim 13.

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