Tire stiffness estimation and road friction estimation

Abstract

The disclosed invention makes use of slip related values to calculate friction related values and tire stiffness related values and feeds back an estimated tire stiffness relates value or a calculated friction related as a basis for further calculations. In particular, the disclosure relates to methods, apparatuses and computer program products to achieve the mentioned objective.

Claims

1. A method of determining at least one of a friction potential and a tire stiffness of a wheel of a vehicle, the method comprising: calculating, using at least one vehicle sensor that provides slip related values (k1, k2), a first friction related value (p.sub.a) based on a first slip related value (k.sub.1) and a first tire stiffness related value (C.sub.1), estimating, without requiring a tire identification, a second tire stiffness related value (C.sub.2) based on the first slip related value (k.sub.1), the calculated first friction related value (μ.sub.1) and a second friction related value (μ.sub.2), feeding back the estimated second tire stiffness related value (C.sub.2) as a basis of a calculation of a third friction related value (μ.sub.3), computing a friction uncertainty measure, indicative of an uncertainty of the third friction related value, based on: the estimated second tire stiffness related value and a covariance of the slip related values (k.sub.1, k.sub.2), determining whether the friction uncertainty measure is smaller than a reliability threshold, and responsive to a determination that the friction uncertainty measure is smaller than the reliability threshold, communicating the third friction related value to a vehicle control system and using the third friction related value in the vehicle control system.

2. The method according to claim 1, further comprising: estimating, in a feedforward loop/open loop, a stiffness-correction factor (ΔC), the second tire stiffness related value (C.sub.2) is also based on the stiffness-correction factor (ΔC).

3. The method according to claim 2 the estimating of the stiffness-correction factor is based on at least one of: a pressure of the tire, a temperature of the tire, an ambient temperature, an axle height, a suspension pressure, and a suspension height.

4. The method according to claim 3, the estimating is also based on at least one of: an estimated friction potential from an ABS braking, an estimated friction potential from a TCS event, an estimated friction potential received from vehicle connectivity, a normalized traction force on the wheel, a friction related value, a torque applied on the wheel, a longitudinal acceleration, a lateral acceleration, a brake pressure, a yaw rate, a wheel speed, a vehicle speed, a steering wheel angle, a wheel angle, a tire pressure, a tire temperature, an ambient temperature, an axle height, a suspension pressure, a suspension height, and a control flag register.

5. A non-transitory computer program product including program code configured to, when executed in a computing device, carry out a method of determining at least one of a friction potential and a tire stiffness of a wheel of a vehicle, the method comprising: calculating, using at least one vehicle sensor that provides slip related values (k1, k2), a first friction related value (μ.sub.1) based on a first slip related value (k.sub.1) and a first tire stiffness related value (C.sub.1), estimating, without requiring a tire identification, a second tire stiffness related value (C.sub.2) based on the first slip related value (k.sub.1), the calculated first friction related value (μ.sub.1) and a second friction related value (μ.sub.2), feeding back the estimated second tire stiffness related value (C.sub.2) as a basis of a calculation of a third friction related value (μ.sub.3), computing a friction uncertainty measure, indicative of an uncertainty of the third friction related value, based on: the estimated second tire stiffness related value and a covariance of the slip related values (k.sub.1, k.sub.2), determining whether the friction uncertainty measure is smaller than a reliability threshold, and responsive to a determination that the friction uncertainty measure is smaller than the reliability threshold, communicating the third friction related value to a vehicle control system and using the third friction related value in the vehicle control system.

6. An apparatus to determine at least one of a friction potential and a tire stiffness of a wheel of a vehicle, the apparatus comprising a processing unit, the processing unit configured to perform operations, comprising: calculating, using at least one vehicle sensor that provides slip related values (k1, k2), a first friction related value (μ.sub.1) based on a first slip related value (k.sub.1) and a first tire stiffness related value (C.sub.1), estimating, without requiring a tire identification, a second tire stiffness related value (C.sub.2) based on the first slip related value (k.sub.1), the calculated first friction related value (μ.sub.1) and a second friction related value (μ.sub.2), feeding back the estimated second tire stiffness related value (C.sub.2) as a basis of a calculation of a third friction related value (μ.sub.3), computing a friction uncertainty measure, indicative of an uncertainty of the third friction related value, based on: the estimated second tire stiffness related value and a covariance of the slip related values (k.sub.1, k.sub.2), determining whether the friction uncertainty measure is smaller than a reliability threshold, and responsive to a determination that the friction uncertainty measure is smaller than the reliability threshold, communicating the third friction related value to a vehicle control system and using the third friction related value in the vehicle control system.

Description

SHORT DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a graph representing typical (normalized) traction forces as a function of slip for a variety of road surfaces with different friction potential.

(2) FIG. 2 is a flow chart of a method according to embodiments.

(3) FIG. 3 is a flow chart of a method according to embodiments.

(4) FIG. 4 is a flow chart of a method according to embodiments.

(5) FIG. 5 is a flow chart of a method according to embodiments.

(6) FIG. 6 is a flow chart of a method according to embodiments.

(7) FIG. 7 is a box chart of an apparatus according to embodiments.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

(8) As mentioned above, any curve displaying normalized traction forces versus slip is referred to as “slip curve”. A friction potential is generally defined as the maximum of a slip curve and depends on a variety of variables, such as road surface and tire characteristics and operating condition (pressure, temperature, vertical load, wear, etc.).

(9) FIG. 1 illustrates the dependence of friction potential on road surface. The relationship between normalized traction force and longitudinal slip is exemplified for three road surfaces, namely on ice, gravel and asphalt. As displayed, the friction potential on asphalt is generally higher than on gravel, whereas the friction potential on gravel is higher than on ice. In FIG. 1 as well as in the rest of the present disclosure, all quantities and values (in particular slip) are understood to refer to the longitudinal direction, unless otherwise noted. A slip curve may be divided in multiple regions, including an approximately linear portion around the origin, e.g. from −10% to +10% of slip in FIG. 1.

(10) In the following, the term “slip slope” is understood to refer to the slope of the linear portion of the slip curve. A slip slope is a preferred example of a slip related value and may be used accordingly in the methods described herein.

(11) The first and second friction related values may specifically, but not exclusively be embodied as values of friction used, i.e. the ordinate of a point on the slip curve, as mentioned above.

(12) Based on a slip slope and a friction used, a multitude of methods are known to the skilled person for estimating at least a lower boundary of the current friction potential. The methods described in the following provide ways to more accurately and more reliably determine the friction potential.

(13) FIG. 2 depicts a flow chart of an embodiment of a method of determining a friction potential of a wheel of a vehicle according to the present invention.

(14) The method 20 uses a first slip related value, namely a first slip slope k.sub.1, and a first tire stiffness related value C.sub.1, as inputs. The first slip slope k.sub.1, is obtained from at least one vehicle sensor for providing slip related values.

(15) In a first step 22, the method 20 calculates a first friction related value μ.sub.1 based on the first slip slope k.sub.1 and the first tire stiffness related value C.sub.1.
μ.sub.1=ƒ(C.sub.1,k.sub.1)

(16) where the function ƒ may be a tailored tire model known to the skilled person, such as for example a Brush tire model.

(17) Further, a second tire stiffness C.sub.2 is estimated (step 24) based on the first slip slope k.sub.1 and a second friction related value μ.sub.2.
C.sub.2=g(μ.sub.1,μ.sub.2)

(18) The second tire stiffness C.sub.2, is fed back, i.e. it is used as an input to a calculation at a later point in time. The fed-back tire stiffness may be intended as a basis for the calculation of a third friction related value μ.sub.3.

(19) As illustrated, the steps 22, 24 and 26 are carried out in closed loop. At each iteration, first and second values are substituted by second and third value, etc. The iteration permits to obtain a time series of slip slope values from the at least one vehicle sensor and to refine the determination of the stiffness estimate by an adaptive model. At each iteration, the most recent slip slope value and the fed-back tire stiffness estimate are used to calculate a more accurate friction value. Thus, using the adaptive model disclosed herein, the effect of the current actual tire stiffness and changes thereof can be accounted for before and during determination of the friction potential.

(20) In some embodiments, in addition or as an alternative to the estimated tire stiffness, a second friction related value is fed back.

(21) FIG. 3 is a flow chart of a further embodiment of a method. The method 30 commences with obtaining (step 32) a first slip slope, which is a slip related value. Based on this slip slope, a friction value is calculated (step 34). A tire stiffness is estimated (step 36), wherein the estimation uses the obtained slip slope and a second friction related value as basis.

(22) Once a new (second) slip slope value is obtained (step 38), the method 30 proceeds with updating (step 39) the calculated friction and/or tire stiffness estimate based at least on the new slip slope. In other words, the previously estimated tire stiffness is used as an input to this calculation in a feedback manner.

(23) FIG. 4 is a flow chart of a method according to an embodiment. The depicted embodiment is in general similar to the embodiment of FIG. 2. In addition, the embodiment of FIG. 4 comprises computing a friction uncertainty measure, indicative of the uncertainty of the friction related value.

(24) Based on the estimated tire stiffness C and on a covariance σ.sub.k.sup.2 of the slip related value, a friction uncertainty measure σ.sub.μ is computed (step 48)
σ.sub.μ=h(C,σ.sub.k.sup.2,σ.sub.corr.sup.2,T).

(25) If the slip related value is a slip slope, then the covariance of the slip related value may be provided by a Kalman filter used to estimate the slip slope. The uncertainty measure and its temporal evolution permits to evaluate when the adaptive tire model has reached a certain desired level of reliability. Furthermore, the estimated friction potential σ.sub.μ cannot be relied upon before the tire model has been adequately adapted, meaning the feedback is iterated a sufficient number of times. Therefore σ.sub.corr.sup.2 has a high value before any model adaptation in the feedback loop has taken place. When the model has been adapted, σ.sub.corr.sup.2 has either a low value or a zero value depending on the quality and number of feedback iterations. Only once a certain level or reliability had been reached, the determined friction may be handed over to other system(s), e.g. an ABS system, for further processing. Further, the uncertainty may also be a function of a temperature T, such as at least one of the ambient temperature, the tire cavity temperature and the inner liner temperature. For instance the tire stiffness may be highly temperature-dependent around the freezing point of water. This temperature dependency may vary for different types of tires (summer, winter, all-season, ultra-high performance, etc.).

(26) FIG. 5 is a flow chart of a method according to an embodiment. The depicted embodiment is in general similar to the embodiment of FIG. 2. However, in comparison with the embodiment of FIG. 2, the order of estimating a tire stiffness and calculating a friction related value is reversed. First, the tire stiffness is estimated (step 52) based on an obtained slip related value and a friction related value. Second, a second friction related value is calculated (step 54) based on the estimated tire stiffness and the obtained slip related value. The feeding back (step 56) of the second friction related value is analogous to the case of FIG. 2. The fed-back second tire stiffness related value may be intended as a basis of an estimation of a third tire stiffness.

(27) FIG. 6 depicts a flow chart of an embodiment of a method according to the invention. The depicted embodiment is in general similar to the embodiment of FIG. 2.

(28) In addition, the embodiment of FIG. 6 comprises taking into account a stiffness-correction factor ΔC in the estimation of the first tire stiffness C.sub.1 (step 64).

(29) The stiffness-correction factor ΔC is estimated in feedforward. In particular, the stiffness-correction factor may serve the purpose of taking into account ambient or tire conditions, such as a pressure of the tire, a temperature of the tire, an ambient temperature, an axle height, a suspension pressure, or a suspension height.

(30) For illustration purposes, it is recalled that tire stiffness is—inter alia—a function of e.g. the ambient temperature. The tire stiffness increases as the ambient temperature decreases and approaches the freezing point of water. In view of this fact, a stiffness-correction factor may be added during tire stiffness estimation, dependent on a temperature difference, e.g. relative to a reference temperature. Similarly, as additional examples, the tire stiffness is also a function of pressure and vertical load that will also change the longitudinal stiffness.

(31) The estimated stiffness-correction factor may be a multiplicative or an additive factor.

(32) FIG. 7 depicts a box chart of an apparatus according to some embodiments. The apparatus 70 comprises a processing unit 72. The processing unit 72 is configured to calculate a first friction related value based on a first slip related value and a first tire stiffness related value, to estimate a second tire stiffness related value based on the first slip related value, the calculated first friction related value and a second friction related value, and to feed back the estimated second tire stiffness related value as a basis of a calculation of a third friction related value.

(33) The slip related values are provided by a vehicle sensor 74. In some embodiments, the apparatus 70 may comprise the vehicle sensor 74.

(34) In some embodiments, the apparatus may further comprise a connectivity interface (not shown), which is adapted for communication with entities external to the vehicle, such as vehicle-to-vehicle or vehicle-to-infrastructure communication.