WO2013182257A1

WO2013182257A1 - Sensory feedback when driving near a vehicle's handling limits

Info

Publication number: WO2013182257A1
Application number: PCT/EP2012/068354
Authority: WO
Inventors: Diomidis KATZOURAKIS; Edward HOLWEG
Original assignee: Skf B.V.
Priority date: 2012-06-05
Filing date: 2012-09-18
Publication date: 2013-12-12
Also published as: EP2855239A1

Abstract

The present invention relates to a method of providing sensory feedback to a vehicle driver when driving close to the grip limits of a tire of a front vehicle wheel, the method comprising steps of: determining (42) a current lateral slip state ( Ŝ_y) of the tire; estimating a tire-road coefficient of friction (μ), based on measurement (41 ) of a normal force (F_z) acting on the vehicle wheel and of at least one of a lateral force (F_y) and a longitudinal force (F_x) acting on the wheel; estimating (43) a peak lateral slip state (Ŝ _ymax) at which maximum tire lateral force can be generated, based on the determined current lateral slip state and the estimated friction coefficient; providing sensory feedback to the driver (45), whereby the feedback has a magnitude that varies as a function of the difference between the peak lateral slip state and the current lateral slip state.

Description

Sensory Feedback when Driving near a Vehicle's Handling Linnits FIELD OF THE INVENTION

The present invention relates to a method and a system of providing sensory feedback to a vehicle driver during cornering and when driving close to the grip limits of the front tires.

Background to the invention

Such a system is known from US 7234564. An electric-assisted steering system for a road vehicle is disclosed, which has means for generating an assist-torque signal for the steering system in response to the driver's applied torque and sensed vehicle speed. A yaw-rate haptic torque is generated, which is based on vehicle rate error and is arranged to be added to the torque assist signal such that, when the yaw rate error builds up corresponding to increasing steering instability, the haptic toque added to the torque-assist signal reduces the effective road reaction feedback sensed by the driver in advance of any actual vehicle stability loss, enabling the driver to make appropriate adjustments in good time before terminal instability is reached. The haptic torque can also be based on vehicle lateral acceleration, which is arranged to be subtracted from the torque-assist signal such that when the vehicle lateral acceleration builds up, corresponding to tighter cornering, the driver senses an increase in the effective road reaction feedback, as the cornering forces generated by the vehicle's tires increases.

There is still room for improvement. SUMMARY OF THE INVENTION

By monitoring yaw rate and lateral acceleration, it is possible to give a vehicle driver prior warning that the front tire or tires are approaching their grip limits. It is an aim of the present invention to not only give the driver prior warning, but to give the driver continuous sensory feedback, which varies in magnitude depending on how close the tire or tires are to the grip limit. As a result, the driver gains an improved understanding of the tires' lateral force potentials during cornering. A further aim of the invention is to define such a method and system, which is based on a control parameter that enables the continuous feedback to be provided over a large range of values of the parameter, so that the driver has a significant control region in which to exercise his own judgement.

The aforementioned aims are achieved by means of a method as specified in claim 1 , and by means of a system which is adapted to implement the method of the invention.

Specifically, the invention resides in a method of providing sensory feedback to a vehicle driver when driving close to the grip limits of a front tire of a vehicle wheel, wherein the method comprising steps of:

- determining a current lateral slip state of the tire;

estimating a tire-road coefficient of friction, based on:

^■ the determined lateral slip state; and

^■ measurement of a normal force F_z acting on the vehicle wheel, and at least one of a lateral force F_y and a longitudinal force F_x acting on the wheel;

estimating a peak lateral slip state at which maximum tire lateral force can be generated, based on the estimated friction coefficient;

providing sensory feedback to the driver, whereby the feedback has a magnitude that varies as a function of the difference between the estimated peak lateral slip state and the current lateral slip state.

The present inventors have found that the lateral slip state, which is indicative of the lateral force on the tire, is a parameter which is highly sensitive to change in the region between the onset of loss of grip and actual loss of grip. The sensory feedback can therefore be provided continuously in a broad control region. Suitably, the magnitude of the feedback increases exponentially as the tire approaches the peak forces it can generate, to optimally discourage the driver from exceeding the tire's grip limits.

The sensory feedback may be provided in various different forms. In one example, the feedback is an audible beeping signal, whereby the interval between beeps becomes increasingly shorter as the grip limits are approached. The sensory feedback may also be tactile. For example, the steering wheel may be arranged to vibrate with increasing intensity. Visual feedback can also be provided in the form of e.g. a dynamic barchart that is displayed on a screen. In a preferred embodiment, the sensory feedback is provided in the form of a haptic feedback torque that is added to a steering system's reaction torque, whereby the added torque is a function of the difference between the peak and current lateral slip states. Thus, the haptic torque augments the reaction torque such that the driver experiences increasingly lighter steering as the grip limits are approached.

The lateral slip state may be expressed in terms of different slip variables. In a first example, lateral slip angle is used, which is the angle between the wheel's longitudinal axis and the wheel's velocity vector. The peak lateral slip state is then the lateral slip angle at which maximum lateral tire force can be generated.

In a second example, lateral slip is used to express the lateral slip state. Lateral slip is a non-dimensional value defined by the relative velocity of the tire with respect to the road. The peak lateral slip state is then the lateral slip at which maximum lateral tire force can be generated.

According to the invention, the lateral slip state may be determined in two ways. In a first embodiment of the inventive method, the lateral slip state is determined on the basis of wheel force measurements, and the method comprises a step of measuring the following wheel forces on the vehicle wheel: the normal force F_z; the longitudinal force F_x; the lateral force F_y and a self aligning moment M_z.

Preferably, the wheel force parameters are measured directly on the wheel using a wheel bearing unit that is instrumented with strain sensors. In the case of the normal force F_z, this wheel force parameter can be obtained from other measurements on the vehicle, such as the static load distribution and the longitudinal/lateral load transfer under longitudinal/lateral acceleration. The current lateral slip state is calculated from the measured wheel force parameters and from available tire data. The tire data comprises pneumatic trail information relating to the length of the tire's pneumatic trail, which may be obtained from look-up tables or from a relationship between trail length and the lateral slip state. The tire data further comprises tire coefficients B, C, D for different coefficients of friction, such as described in "Tire modelling for use in vehicle dynamics studies" - SAE Paper No. 870421 , 1987 - by Bakker, Nyborg and Pacejka, the contents of which are incorporated herein by reference. This paper will be referred to hereafter as the Bakker et al tire model. Suitably, a numerical solver is used to calculate the necessary slip states, including at least the current lateral slip state. Based on the calculated slip states, the numerical solver then estimates friction coefficients which would have induced the measured wheel forces. The friction coefficient estimates, the calculated slip states and tire data are then used to estimate the value of the lateral slip state (lateral slip angle or lateral slip) at which peak lateral tire forces occur. Finally, the difference between the peak and current lateral slip states is used as a control parameter for generating sensory feedback to the driver.

In a second embodiment of the inventive method, the actual slip states of the tires, comprising at least the lateral slip state, are calculated from measured vehicle parameters. The method thus comprises a step of measuring the following vehicle parameters: longitudinal speed of the vehicle x , lateral speed of the vehicle y , steering angle δ, yaw rate ψ and wheel rotational speed ω. Suitably, the step of measuring further comprises measuring the normal force F_z on the wheel, and one of the lateral force F_y and longitudinal force F_x. The calculated slip states, in combination with the tire coefficients B, C, D as described above, are then used to generate estimates for the friction coefficients that would have induced the measured wheel forces. The lateral slip state at which peak tire forces occur is then estimated and a sensory feedback is provided in an identical manner as described for the first embodiment.

The invention further relates to a system that is arranged to implement the method of the invention and to a vehicle equipped with the inventive system. In a preferred embodiment, the vehicle has a power-assisted steering system which is arranged to provide haptic torque feedback to the driver. DESCRIPTION OF THE FIGURES

The invention will now be described in greater detail, with reference to the accompanying drawings, in which:

Fig. 1 : shows part of a vehicle steering system that may be arranged to provide sensory feedback to the driver according to the invention;

Fig. 2a illustrates a model of a car, for reference purposes;

Fig. 2b, 2c respectively illustrate a side view and a top view of a front wheel from the model depicted in Fig. 2a;

Fig. 3a, 3b: show plots of lateral tire force (fig. 3a) and self-aligning moment (fig. 3b) against lateral slip angle for four tire-road coefficients of friction;

Fig. 4: shows a flow diagram of a first embodiment of a method according to the invention;

Fig. 5: shows a flow diagram of a second embodiment of a method according to the invention;

Fig. 6: shows a flow diagram of a haptic support controller suitable for executing a final step of the method of the invention;

Fig. 7a, 7d: show plots of steering torque against lateral slip angle with no haptic support and with haptic support enabled, under a first set of driving conditions (fig. 7a) and under a second set of driving conditions (fig. 7d);

Fig. 7b, 7e respectively show plots of lateral acceleration against lateral slip angle under the first and second sets of driving conditions

Fig. 7c, 7f: show plots of steering torque against lateral acceleration with no haptic support and with haptic support enabled, under the first set of driving conditions (fig. 7c) and under the second set of driving conditions (fig. 7f);

DETAILED DESCRIPTION

In the vehicle industry, there is a constant desire for improved safety and improved handling. Many modern cars are therefore equipped with advanced driving assist systems, such as electronic stability control (ESC) and active front steering (AFS). If the driver experiences a skid or slide because of poor road conditions, the active steering will react to information from onboard yaw-rate sensors, to modify the steering angle of the front wheels to stabilize the vehicle. This occurs much faster than the driver can react. If the active steering angle is insufficient, then the stability control system intervenes to help as well.

In order to prevent a skid from occurring in the first place, it is helpful to alert the driver during cornering that he/she is approaching the tires' grip limits. The present invention relates to a method and a system for doing this, by providing sensory feedback, which increases in magnitude as the tires get closer to their grip limits. In a preferred example, the sensory feedback is provided by means of haptic steering support, whereby the driver and the support system share steering control. In effect, information is relayed to the driver through the steering wheel.

Fig. 1 illustrates part of a typical steering system on a vehicle, which can be arranged to implement the method of the invention. The front wheels of the vehicle (only the front right wheel 100 is depicted) are steered by means of a rack 1 10 and pinion 120 arrangement. The pinion 120 is coupled to a steering column 130 having a torsion bar 140 and the system further comprises an assist motor 150, which provides an assist torque T_asSist making it easier for the driver to turn the steering column and a steering wheel 160 coupled thereto. When the vehicle is nearing the front tires' grip limits, the assist motor 150 is arranged to receive a control signal from a haptic support controller, which changes the steering torque experienced by the driver. The haptic support controller in this example injects a force to the steering system's reaction force, which according to the invention is a function of the difference between the current lateral force on the front tires and the peak lateral force that the tires can generate.

In order to explain the method of the invention, a number of terms, parameters and variables will first be defined, with reference to Figure 1 , Figures 2a - 2c and equations (1 ) to (6)

Fig. 2a illustrates a model of a single track vehicle, where the left and right wheels are assumed to be combined in a single front tire 200 and a single rear tire 220 at a centre track (front and rear axle correspondingly). The longitudinal direction is denoted by x; the lateral direction is denoted by y. Figs. 2b and 2c respectively show a side view and a top view of the front tire 200. In Fig. 2c, a tension profile 230 of the front tire is depicted. Term/symbol Definition

Bodyslip angle, β The angle β between the vehicle's velocity vector V and the (rad) vehicle's longitudinal axis x (refer Fig. 2a).

Driver's torque/ Reaction force felt/exerted by the driver at the steering wheel. steering torque,

(Nm)

Front/rear axle The front axle and rear axle position where the left and right wheels are assumed to be combined together.

Longitudinal Non-dimensional value referring to the relative longitudinal velocity slip, s_x V_x of the tire with respect to its circumferential speed oo-r_w (where ω denotes rotational speed of the wheel and r_w denotes the wheel's radius), defined by the following equation:

V_r - ω^■ r

Equation (1 )

o - K.,

Lateral slip, s_: a non-dimensional value referring to the relative velocity of the tire with respect to the road, defined by:

V

^: (ΐ + Ό ^x ·— Equation (2)

y

where V_y is the lateral velocity of the tire.

Wheel slip, s The combined longitudinal and lateral slip, defined by:

s = + ^sl Equation (3)

Friction A dimensionless scalar value which describes the ratio of the coefficient, μ force of friction between tire and the road.

Longitudinal/ The friction force that the tire can generate in the longitudinal μ_χ/ lateral friction lateral _y (x, y) axis, given by:

coefficient μχ_{/ y} D^■ sin(C · atan(B · s)), j : x,y Equation (4)

where B, C and D are tire coefficients as defined in the Bakker et al tire model.

Lateral slip for The lateral slip where the tire can achieve its maximum lateral peak force, s_ymax force, whereby the force may be calculated according to:

F. = μ_} - F , j -. x, y Equation (5)

where F_z is the perpendicular force exerted on the vehicle's wheels.

Lateral slip the angle between the wheel's longitudinal axis and the wheel's angle, a (rad) velocity vector. In Fig. 2a, a_f denotes the lateral slip angle of the

front axle; the angle between the axis x_f and the front axle velocity vector V_f . Correspondingly, a_r denotes the lateral slip angle of the rear axle, whereby V_r is the rear axle velocity vector.

Slip angle for the lateral slip angle where the front tire can achieve its maximum peak force, friction force, given by:

a_Fmax (rad) a_F max = tan ¹ (0.02^■ μ - g) Equation (6)

Longitudinal tire The tire force developed at the tire's longitudinal axis. F_rx in Fig. 2a force (N) refers to the combined rear left and rear right longitudinal forces. It therefore denotes the rear axle longitudinal force. Correspondingly, F_f* denotes the front axle longitudinal force.

Lateral tire force The tire force developed at the tire's lateral axis. F_ry in Fig. 2a refers to (N) the combined rear left and rear right lateral forces. It therefore denotes the rear axle lateral force. Correspondingly, F_fy denotes the front axle lateral force.

Normal force, F_z The perpendicular force exerted on the vehicle's wheels preventing (N) them from penetrating the road (refer Fig. 2b).

Pneumatic trail, The distance that the resultant force occurs behind the geometric Lpt (m) centre of a tire's contact patch (refer Fig. 2c). δ (rad) Front axle steering angle (refer Fig. 2a) (average of front right wheel steering angle δ_Γ (refer Fig. 1 ) and front left wheel steering angle δ|. use (Nm/rad/s) Steering column damping

J_sw (kg-m²) Steering wheel moment of Inertia

Jsc (kg-m²) Steering column moment of Inertia k_s (Nm/rad) Torsion bar stiffness Tassist (Nm) Assist torque (refer Fig. 1 ) V_ijx,V_ijy (n\ls) Car's x, y velocity, above the front/rear (i: f, r) left/right (j: I, r)

tires' steering axes

Tcontact (Nm) Driver's hands contact torque on the steering wheel Tdriver (Nm) Driver's torque after the torsion bar

F x, F_ijy, F_ijz (N) Front/rear (i: f, r) left/right (j: I, r) tire's force in the x, y, z axis My_z (Nm) Front/rear (i: f, r) left/right (j: I, r) tire's self -aligning moment

due to the pneumatic trail vt_iJX,vt_iJy (m/s) Front/rear (i: f, r) left/right (j: I, r) tires x, y velocity

Frack (N) Rack force (refer Fig. 1 ). θ ; Θ Rack's pinnion angle; speed

(rad; rad/s) Ttotai (Nm) Resulting torque on the steering column ft · ft Steering column angle; speed

(rad; rad/s) 0_sw (rad) Steering wheel angle (refer Fig. 1 ).

Sfl_y; Sfry (%) Front right; front left wheel lateral slip,which is also dependent on the wheel longitudinal slip.

The rationale behind the haptic support according to the invention derives from an inherent vehicle property to reduce the "stiffness" at the steering wheel before the front tires' peak force is reached. The haptic support torque amplifies/exaggerates this lifelike reducing "stiffness" and makes it profound to the driver, so that he/she avoids excessive lateral slip which will result in lateral force loss. In the context of this example, the term "stiffness" is to be understood as the road reaction torque as a function of the steering wheel angle.

The reducing effect of the self-aligning moment at the steering wheel has been credited as valuable feedback to the driver. This effect only becomes noticeable when the front wheels' forces stop developing more lateral forces with increasing lateral slip angle (referred to as terminal understeer); i.e. when the wheels' forces are already saturated, which is always an undesired effect. The tire peak cornering force is dependent on the tire-road friction coefficient μ, and the normal force F_z. The friction coefficient though, has minor influence on the lateral forces at small slip angles. It is therefore not influenced by, or only barely influenced by the condition wet or dry. This can be seen in the graph of Fig. 3a, which shows a first curve 31 , a second curve 32, a third curve 33 and a fourth curve representing the front axle lateral force F_fy at different slip angles 3F for corresponding first, second, third and fourth tire-road friction coefficient μ values (1 .0, 0.7, 0.5, 0.2). The dashed line 30 represents the front axle's cornering stiffness (slope of the front axle lateral force at zero slip angle) of both front tires combined. The cornering stiffness might be unaffected by μ, but the friction coefficient does determine the peak of the curve (maximum achievable lateral force). For example, looking at the first curve 31 , where μ = 1 .0, the peak force occurs at a slip angle of 10.8 degrees. When μ = 0.7 (second curve 32), the peak force occurs at a slip angle of 7.4 degrees.

The tires offer a mechanism to inform the driver in advance that the cornering limits are being approached, before the cornering forces start to drop. This mechanism is a reduction of the pneumatic trail (see Fig. 2c). The pneumatic trail starts to reduce even before the tire lateral peak force is being approached. The lateral force F_fy multiplied by the pneumatic trail L_pt (decreasing with increasing slip angle) constitutes the resultant self-aligning moment M_z at the front axle (left and right wheels combined). Therefore, the self-aligning moment also decreases before the peak force is being approached, as may be derived from Fig. 3b.

Fig. 3b shows a fifth curve 35, a sixth curve 36, a seventh curve 37 and an eighth curve 38 representing plots of self-aligning moment M_z against front axle slip angle a_F for the same four μ values as in Fig. 3a. Looking at the fifth curve 35 (μ = 1 .0), it can be seen that the maximum M_z value occurs at a slip angle of 7.4 degrees, while the peak force occurs at a slip angle of 10.8 degrees (refer first curve 31 ).

Figs. 3a and 3b have been generated assuming a normal force F_z of 7891 N and using the Bakker et al tire model and the pneumatic trail definition of Hsu and Gerdes in "The Predictive Nature of Pneumatic Trail: Tire Slip Angle and Peak Force estimation using Steering Torque" - in the proceedings of AVEC08 - the contents of which are incorporated herein by reference.

The property of the pneumatic trail to decrease as a function of both friction coefficient μ and slip angle, even while the lateral force is in the linear region, makes it a valuable source of detecting the limits prior to reaching them. According to the invention, the reduction in pneumatic trail is detected by determining a lateral force state of the front tires.

In a first embodiment, the wheel forces are measured to determine the force state. Preferably, this is done using a load-sensing wheel bearing unit that is equipped with strain sensors and a processing unit for determining the following wheel forces: longitudinal force F_x, lateral force F_y, normal force F_z and self-aligning torque M_z. Assuming known tire characteristics, these forces can be used to determine the relative position of the tires' current force and their peak force. This can be interpreted through: 1 ) the wheel's current lateral slip and the lateral slip where maximum peak force occurs; or 2): the current slip angle and the slip angle where maximum peak force occurs.

Figure 4 shows a flowchart of a method of providing haptic torque feedback according to the invention, based on the first embodiment and whereby lateral slip is used to determine the relative position of the tires' current and peak lateral forces.

In a first step 41 , the wheel forces: longitudinal force F_x, lateral force F_y, normal force F_z and self-aligning torque M_z are measured using a load sensing bearing. NB: It is also possible to derive the normal force F_z from other measurements on the vehicle.

The aforementioned wheel forces are then fed into a nonlinear equation solver, which in a second step 42, calculates an estimate for the longitudinal slip s_x , the lateral slip s_y , the combined slip s and the tire-road friction coefficient i that would have induced the measured wheel forces. NB: the ^Λ above the parameters indicates an estimated value.

Tire data e.g. the B, C, D coefficients of the Bakker et al tire model for multiple friction coefficient μ values is also fed into the nonlinear equation solver, which solves the system of nonlinear equations (1 ) - (5) to derive estimates for the longitudinal slip s_x , the lateral slip s , the combined slip s and the tire road friction coefficient μ .

Suitably, the nonlinear solver employs optimization techniques to find the set of the unknown parameters (the tires' slip states and friction coefficient in our case) that can be defined as "optimal". This would be achieved by minimizing the difference between the measured measured F_x, F_y and M_z and their corresponding estimates from the set of the nonlinear equations (1 ) to (5) that are dependent on the tire slip states and friction coefficient. This can be achieved using trust-region techniques (e.g. the Powell dogleg method).

In order for the nonlinear solver to converge to a global solution (the correct estimates for s_x and s_y), the length of the pneumatic trail (dependent on the slip angle and μ), is preferably also part of the nonlinear system set. This can be 1 ) a look-up table function of μ and lateral slip, or 2) a pneumatic trail formula (dependent on the slip angle and μ) such the one described by Hsu and Gerdes.

The estimates for longitudinal slip S_x , lateral slip s , combined slip s and the tire road friction coefficient μ are then fed into a haptic-feedback HF state collector, which in a third step 43 calculates an estimate for the lateral slip s_ym!ai where maximum peak force occurs. Tire data is also used in this calculation.

The estimates for current lateral slip and lateral slip for peak force are then fed into a haptic support controller which, in a fouth step 44 calculates a haptic support torque T_HF- The magnitude of the calculated haptic support torque is a function of the difference between s_v and s_vmx .

In a fifth step 45, the controller adds the calculated haptic support torque T_HF to the steering column reaction force, and the output of the torque assist motor is controlled based on the resultant torque, such that the driver feels an amplified reduction in stiffness at the steering wheel.

An example of a suitable haptic support controller will be described in more detail later on.

It is also possible to directly calculate the actual slip states of the wheels using the vehicle's longitudinal and lateral velocities. This can be achieved either from a bodyslip angle estimator or by using a twin antenna GPS system, the yaw rate from a gyroscope and individual wheel rotational speed (so as to calculate the longitudinal slip).

The flowchart of Figure 5 shows a second embodiment of a method of providing haptic torque feedback to a driver, based on direct calculation of the slip states.

In a first step 51 a, the following vehicle parameters are measured: longitudinal speed x ; lateral speed y ; yaw rate ψ ; individual wheel's rotational speed ω, as well as its steering angle δ.

These parameters are fed into a slip calculation block, which in a second step 52 calculates the tire's longitudinal slip s_x , lateral slip s_y and combined slip s. To derive the slip states, the individual tire's longitudinal and lateral velocity components V_x and V_y on the tire's reference frame are needed. These may be calculated using the following equations:

V_ilx = x - (t_r Ι 2) · ψ, V_irx = x + d -ψ , i : front, rear Equation (7) vfjy = y ⁺ h ^' Ψ ' ^ν = y - ^lr ^■ Ψ > J ^{: ι ri}S^ht Equation (8)

Vt_fjx = V_fjx ^■ cos(5_j)+V_fjy -sm(5_j), j : left, right Equation (9)

^Vts_y = ^~vs* ' ^ύη(^δ^^{+ ν} _β>^■∞ S_j ), j : left, right Equation (10)

Based on the calculated tire's velocities, as well as individual wheel's rotational speed ω, the tires' longitudinal slip s_x, lateral slip _sy and combined slip s are then calculated using equations (1 ), (2) and (3) respectively.

The step of measuring further comprises a step 51 b of measuring the normal force F_z and at least one of the longitudinal force F_x and the lateral force F_y on the wheel.

Again, this is preferably done using a load-sensing wheel bearing unit as described previously.

The measured wheel forces F_z and (F_x or F_y) and the calculated slip states s_x, s_y and s, along with tire data are then fed into a nonlinear equation solver, which in a third step 53 solves the set of non-linear equations (1 ) to (5) to derive an estimate for the friction coefficient μ that would have induced the measured wheel forces.

In a fourth step 54, the lateral slip s_ym!ai where peak force can be generated is determined, based on the estimated friction coefficient, the calculated slip states and tire data.

In a fifth step 55, the values for the current lateral slip s_y and the lateral slip where peak force is generated s_ym!ai are used by a haptic steering support controller, to calculate a haptic support torque T_HF- The magnitude of the calculated haptic support torque is a function of the difference between s_y and s . In a sixth step 56, the controller adds the calculated haptic support torque T_HF to the steering column reaction force, and the output of the torque assist motor is controlled based on the resultant torque, such that the driver feels an amplified reduction in stiffness at the steering wheel.

A flow diagram of a haptic steering support controller 600, for use in combination with a power-assisted steering system 620, is illustrated in Figure 6. The diagram also shows how the controller 600 interacts with the steering system 620, which is a hydraulic power-assisted steering (HPAS) system in this example. The controller uses the front left Sfiy and right s_fry wheels' lateral slip and lateral slip for peak, which are determined by a slip state estimator 602 using the method of Fig. 4 or of Fig. 5.

We shall describe a signal flow for a 'front left wheel block' 605 of Figure 6. The same flow applies to the front right wheel block 610. The absolute 1 of the lateral slip s_fly is subtracted 2 from the absolute 3 lateral slip Sfi_ymax where peak lateral force occurs. The estimator 602 takes into account the direction of the lateral slip (positive wheel force to the left). The signs of the lateral slip and the lateral slip where peak force occurs are therefore the same. The output of the subtraction 2, Sfi_ye, is then checked 4. If Sfi_ye is greater than zero, then the output of the check 4 is Sfi_ye. Otherwise the output is zero, meaning that Sfi_y has exceeded Sfi_ymax.

The output of the check 4 is then divided 5 (normalization) with the absolute 2 lateral slip Sfi_ymax where peak lateral force occurs. This produces a signal Sfi_ysig. The Sfi_ysig signal has the value zero if the lateral slip Sfi_y is greater than or equal to Sfi_ymax and has the value '1 ' if Sfi_y = 0. The signal Sfi_ysig is then added 6 to its corresponding signal SfrySig from the 'front right wheel' block 610. The output of the addition 6 is then fed into a calculator block 7, where an HF factor is calculated. The HF factor is a number between 0 and 1 . In this example, the HF factor is obtained from ^HF factor = ⁱ - (^sfly_Slg ^{+ s}fi_7Slg ) ^{/ 2}) ² · ^{Dut tne} exponential function may be adjusted (besides the quadratic approach) and the weighting function (difference between 1 and the average of SfiySig and Sf_rysig) may also be tuned so as achieve the desired haptic cue. If Sfi_ysig=0 and SfrySig=0, then the HF factor=0 (maximum HF activation); if s_flysig=1 and s_frysig=1 , then the HF factor=1 (no activation). The HF factor is then multiplied 8 with the driver's torque T_dnver, which is calculated in a calculator block 615. The driver exerts a contact torque T_COntact with his hands on the steering wheel. This torque, through the steering wheel inertia J_sw, would displace the steering wheel at an angle 0_SW- The relative angular displacement of the steering wheel 0_SW and the steering column angle 0_SC multiplied with the stiffness K_s of the torsion bar constitutes the driver's torque T_driVer-

The driver's torque is then filtered 9, using a suitable low-pass filter. The filtered output is then multiplied 10 with a gain G_HF (G_HF<1 )- The output of the multiplication 8 is the haptic support torque T_HF- The HF factor constitutes the primary control variable of the haptic support. The output T_HF of the multiplication 8 of the HF factor can be zero, unless predefined conditions are met. For example, an enable block 1 1 with binary output (0|1 ) may be programmed to enable haptic support only if V > 3 km/h. Needless to say, another value or other criteria can be set as necessary.

Assuming a haptic support torque T_HF is generated from the multiplication step 8, T_HF and the driver's torque T driver are then fed into a 'torque augmentation' block 13, the output of which is the driver haptic support torque T_driver HF- The block 13 can be implemented either mechanically A) or virtually B).

A) The mechanical implementation is suitable for the hydraulic power assisted steering system 620. The mechanical implementation requires an electric motor delivering the T_HF torque on the steering column. The reaction torque T_react of the steering system is the subtracted 14 from the driver haptic support torque TdriverHF, which constitutes the resulting torque on the steering column. The resulting torque T_totai, through the dynamics of the steering column represented by block 15 (J_sw steering column inertia and b_sc steering column damping) dictates the steering column angle 0_SC. Thus, the control input for the HPAS is a function of the difference of the steering column angle 0_SC and the rack's pinion angle θ_ρ (and their corresponding speeds due to the steering column damping), as well as the spool valve's stiffness K_sp0oi-

B) The virtual implementation would be suitable for an electric power assisted steering system (such as shown in Fig. 1 ). For an EPAS system, the control input for the assist motor is the driver haptic support torque T_driverHF; i.e. the output of the torque augmentation block 13. However, the actual mechanical torque delivered from block 13 would be equal to Tdrivei-; the T_HF component would only be virtually implemented and would only virtually boost a T_driver measurement fed into the power assist system.

The methods of the invention described with reference to Figs. 4 and 5 and the haptic support controller of Fig. 6 are based on the determination of the lateral slip s_y and the lateral slip s_{y ma}x where peak forces occur. It is also possible to use the lateral slip angle 3F and the lateral slip angle 3F max where peak forces occur. With reference to the flowchart of Fig. 5, the lateral slip angle BF would be calculated in the second step 52 according to the following equation:

equation (10),

whereby

Vjjy is the car's lateral velocity above the front/ rear tires' steering axes and

V x is the car's longitudinal velocity above the front/ rear tires' steering axes, which may be calculated using equations (7) - (9).

The lateral slip angle BF max where peak forces occur would be calculated in the fourth step 54, using equation (6) and the estimated tire-road friction coefficient.

When the method of Figure 4 is employed, it is also possible to derive the lateral slip angle based on the wheel force measurements. The effect of providing haptic support according to the invention is illustrated in the graphs of Figs. 7a - 7f, whereby the plots in Figs. 7a - 7c were obtained from simulations of open loop dry road conditions (μ=0.9), assuming a longitudinal speed of 48 km/h. The plots in Fig. 7d - 7f were obtained from simulations of slippery (μ=0.28) road conditions, assuming a longitudinal speed of 22 km/h. Furthermore, each plot is based on an increasing steering wheel angle (6_SW=0.3 rad/s), and the vertical line in each figure corresponds to the lateral slip angle aFmax where peak lateral forces occur.

Fig. 7a and 7d show plots of steering torque against front axle lateral slip angle. The upper curve 71 in Figs. 7a and 7d represents the 'normal' steering torque T_dnver which the driver experiences with no haptic support, while the respective lower curves 72 represent the haptic feedback torque which would be experienced with haptic support enabled. In this example, lateral slip angle (current value and value at which peak forces occur) was used as the control parameter for the haptic support controller which generated Figs 7a and 7d.

As can be seen from Figs 7a and 7d, the steering torque with haptic feedback starts dropping well before the driver approaches the theoretical lateral slip angle at max where peak forces occur, resulting in a noticeably "lighter" steering. Furthermore, looking at Fig. 7a, for example, the difference between the upper 71 and lower 72 curves increases as the slip angle increases from 5 to 10 degrees. The corresponding lateral acceleration barely increases in this region, however, which may be seen from from Fig. 7b. (Fig. 7e shows a corresponding relationship for the slippery conditions). The lateral acceleration even drops when a_{F m}ax has been exceeded, which could lead to loss of vehicle control. Consequently, lateral acceleration is not a sensitive indicator of lateral forces at relatively large slip angles.

Fig. 7c shows a plot of steering torque against lateral acceleration. Again, the upper curve 71 represents the "normal" condition with no haptic feedback and the lower curve 72 represents the steering torque with haptic feedback enabled. The difference between the upper and lower curves only becomes substantial when the front tires are almost at their grip limits. (Fig. 7e shows a corresponding marginal difference for the slippery conditions). By contrast, the lateral slip state, represented by lateral slip angle in this case, is a parameter which allows the driver to feel a difference well before there is a risk of loss of grip.

The haptic support concept which reduces the road reaction torque before the driver approaches the maximum lateral peak forces can be applied to all road vehicles that provide steering feedback to the driver through a steering column. The vehicles can be passenger cars, vans & pickups, motorcycles and three wheelers, lift trucks, buses and heavy trucks. Haptic steering support on motorcycles is also possible when an electric actuator is provided on the steering column.

The support information that the driver is approaching the maximum lateral peak forces can also be fed back to the driver using other means, such as visual, auditory and tactile. A visual support system can have multiple feedback variants; from lights changing intensity to advanced HMI graphical displays, illustrating the forces on the wheels with a change of color if the peak forces are about to be reached. The same applies for auditory signals, which can change frequency or volume as maximum forces are being approached. The tactile feedback could be a vibration on the steering wheel or the seats of a road vehicle, or for a motorcycle a tactile feedback on the rider's glove or throttle, or a haptic feedback on throttle modifying the tension felt by the rider. In all of the aforementioned examples, the same control parameter is used, namely: the relative difference between the current and the peak lateral force the tire can generate.

A number of aspects/embodiments of the invention have been described. It is to be understood that each aspect/embodiment may be combined with any other aspect/embodiment. Moreover the invention is not restricted to the described embodiments, but may be varied within the scope of the accompanying patent claims.

Claims

1 A method of providing sensory feedback to a vehicle driver when driving close to the grip limit of a tire of a front vehicle wheel (100, 200), the method comprising steps of:

measuring wheel forces acting on the vehicle wheel, the wheel forces comprising a normal force F_z and at least one of a lateral force F_y and a longitudinal force F_x;

determining a current lateral slip state of the tire;

- estimating a tire-road coefficient of friction μ, based on the determined current lateral slip state and on the measured wheel forces;

estimating a peak lateral slip state at which maximum tire lateral force can be generated, based on the determined current lateral slip state and the estimated friction coefficient;

- providing sensory feedback to the driver, whereby the feedback has a magnitude that varies as a function of the difference between the peak lateral slip state and the current lateral slip state.

2. The method according to claim 1 , wherein the lateral slip state is represented by a lateral slip angle 3F and the peak lateral slip state is represented by the slip angle 3F MAX where the tire can generate its maximum lateral force.

3. The method according to claim 1 , wherein the lateral slip state is represented by lateral slip SY and the peak lateral slip state is represented by the lateral slip SY MAX where the tire can generate its maximum lateral force.

4. The method of any preceding claim, wherein the step of measuring wheel forces comprises measurement of the normal force F_z, the lateral force F_y, the longitudinal force F_x and a self-aligning moment M_z, and wherein the current lateral slip state is determined from the measured wheel forces.

5. The method according to claim 4, wherein the determination of the lateral slip state is further based on a pneumatic trail length L_PT of the tire, which may be calculated based on a correlation between the tire-road coefficient of friction and the lateral slip state.

6. The method according to any of claims 1 to 3, further comprising a step of measuring the following vehicle parameters: longitudinal speed of the vehicle x, lateral speed of the vehicle y, steering angle δ, yaw rate ψ and wheel rotational speed ω, wherein the current lateral slip state is determined from the measured vehicle parameters.

7. The method according to any preceding claim, wherein the step of measuring wheel forces is performed using a wheel bearing unit that is instrumented with strain sensors.

8. The method according to claim any preceding claim, wherein the sensory feedback is visual, auditory or tactile.

9. The method according to any of claims 1 to 7, wherein the step of providing sensory feedback comprises providing a haptic torque T_HF which is added to a reaction torque on a steering column (130) of the vehicle.

10. A system arranged to perform the method steps of any preceding claim.

A vehicle comprising the system according to claim 10.