METHOD FOR DETERMINING AN ORIENTATION OF A VEHICLE

Abstract

The invention relates to a method for determining an orientation () of a vehicle relative to a spatially fixed coordinate system (x.sub.0-0-y.sub.0), the method comprising the following steps: determining a traveled distance (S,dS,S) of at least one reference point (P) of the vehicle and/or at least one wheel of the vehicle, and calculating the orientation () of the vehicle taking the traveled distance (S,dS,S) into consideration. The invention further relates to a method based on this principle for determining a position (X.sub.P,Y.sub.P) of a vehicle, to a method for determining an odometry of a vehicle, and to a corresponding control device of a vehicle.

Claims

1. A method for determining an orientation () of a vehicle in relation to a spatially fixed coordinate system (x.sub.0-0-y.sub.0), comprising: determining a distance covered (S,dS,S) by at least one reference point (P) of the vehicle and/or by at least one wheel of the vehicle; and calculating the orientation () of the vehicle on the basis of the covered distance (S,dS,S).

2. The method as claimed in claim 1, wherein, in the case of a vehicle with front-wheel steering in particular, a midpoint (C.sub.r) between the wheels of the rear axle of the vehicle is used as the reference point (P).

3. The method as claimed in claim 1, further comprising: determining an angle () between a tangent to the covered distance (S,dS,S) and a longitudinal axis (x) of the vehicle or between a velocity vector (V.sub.P) of the vehicle and a vehicle longitudinal axis (x); and calculating the orientation () of the vehicle also on the basis of the angle ().

4. The method as claimed in claim 1, further comprising: determining a course curvature () and/or a course radius () of the covered distance (S,dS,S); and calculating the orientation () of the vehicle on the basis of the course curvature () and/or of the course radius ().

5. The method as claimed in claim 1, wherein the orientation () of the vehicle is determined using or on the basis of at least one of the following expressions: $d.Math..Math.=\frac{\mathrm{dS}}{},d.Math..Math.=.Math.\mathrm{dS},d.Math..Math..Math..Math..Math.S,.Math.\left(S\right)=\underset{0}{\stackrel{S}{}}.Math.\left(s\right).Math.\mathrm{ds}-\left(0\right).$

6. The method as claimed in claim 1, wherein the orientation () of the vehicle is calculated using or on the basis of at least one of the following expressions: $d.Math..Math.=\frac{{\mathrm{dS}}_4-{\mathrm{dS}}_3}{b_r},.Math.d.Math..Math.\frac{{\mathrm{dS}}_2-{\mathrm{dS}}_1}{b_f}.Math.\cos .Math..Math.{}_A,$ where b.sub.f is a track width of the front axle, b.sub.r is a track width of the rear axle, dS.sub.1 . . . 4 is a respective distance covered by a respective wheel of the vehicle and .sub.A is a mean steering lock angle of the front wheels.

7. The method as claimed in claim 1, wherein, for determining the covered distance (S,dS,S), wheel ticks from at least one wheel rotational speed sensor assigned to at least one wheel of the vehicle are used.

8. The method as claimed in claim 1, wherein the distance covered (S,dS,S) by the midpoint (C.sub.r) of the rear axle of the vehicle is determined using or on the basis of at least the following expression: ${\mathrm{dS}}_{\mathrm{Cr}}=\frac{{\mathrm{dS}}_3+{\mathrm{dS}}_4}{2},$ where dS.sub.3,4 is a respective distance covered by a respective wheel of the rear axle of the vehicle.

9. The method as claimed in claim 3, wherein the angle () between a tangent to the covered distance (S,dS,S) and a longitudinal axis (x) of the vehicle or between a velocity vector (V.sub.P) of the vehicle and a vehicle longitudinal axis (x) is determined on the basis of a steering wheel angle (.sub.SW) and/or of a mean steering lock angle of the front wheels (.sub.A) and/or of a behavior of a steering system and of a travel direction signal.

10. The method as claimed in claim 3, wherein the angle () between a tangent to the covered distance (S,dS,S) and a longitudinal axis (x) of the vehicle or between a velocity vector (VP) of the vehicle and a vehicle longitudinal axis (x) is determined using or on the basis of the following expression: $={}_A\frac{{}_{\mathrm{SW}}}{i_L},$ where i.sub.L is a steering ratio.

11. The method as claimed in claim 4, wherein the course curvature () and/or the course radius () of the covered distance (S,dS,S) are/is determined on the basis of a mean steering lock angle (.sub.A) of the front wheels.

12. A method for determining a position (X.sub.P,Y.sub.P) of a vehicle in relation to a spatially fixed coordinate system (x.sub.0-0-y.sub.0), comprising: calculating the position (X.sub.P,Y.sub.P) of the vehicle on the basis of an orientation () of the vehicle calculated by a method as claimed in claim 1.

13. The method as claimed in claim 12, further comprising: determining an angle () between a tangent to the covered distance (S,dS,S) and a longitudinal axis (x) of the vehicle or between a velocity vector (V.sub.P) of the vehicle and a vehicle longitudinal axis (x); and calculating the position (X.sub.P,Y.sub.P) of the vehicle also on the basis of the determined angle ().

14. The method as claimed in claim 12, wherein the position (X.sub.P,Y.sub.P) of the vehicle is calculated using or on the basis of at least one of the following expressions: $\mathrm{dX}=\cos \left(\left(S\right)+\left(S\right)\right).Math.\mathrm{dS},\mathrm{dY}=\sin \left(\left(S\right)+\left(S\right)\right).Math.\mathrm{dS},X\left(S\right)=\underset{0}{\stackrel{S}{}}.Math.\cos \left(\left(s\right)+\left(s\right)\right).Math.\mathrm{ds},.Math..Math.Y\left(S\right)=\stackrel{S}{\underset{0}{}}.Math.\sin \left(\left(s\right)+\left(s\right)\right).Math.\mathrm{ds},$ where X.sub.P,Y.sub.P are the coordinates of a reference point (P) of the vehicle in the spatially fixed coordinate system (x0-0-y0).

15. A method for determining an odometry of a vehicle, comprising: determining an orientation () of the vehicle in relation to a spatially fixed coordinate system (x0-0-y0); and determining a position (X.sub.P,Y.sub.P) of a vehicle in relation to the spatially fixed coordinate system (x0-0-y0) as claimed in claim 12.

16. A control device for a vehicle comprising a memory and a processor, wherein the control device is configured to carry out at least one method as claimed in claim 1, wherein the method is stored in the memory in the form of a computer program and the processor is suitable for carrying out the method when the computer program is loaded into the processor from the memory.

17. The method as claimed in claim 2, further comprising: determining an angle between a tangent to the covered distance and a longitudinal axis of the vehicle or between a velocity vector of the vehicle and a vehicle longitudinal axis; and calculating the orientation of the vehicle also on the basis of the angle.

18. The method as claimed in claim 13, wherein the position (X.sub.P,Y.sub.P) of the vehicle is calculated using or on the basis of at least one of the following expressions: $\mathrm{dX}=\cos \left(\left(S\right)+\left(S\right)\right).Math.\mathrm{dS},\mathrm{dY}=\sin \left(\left(S\right)+\left(S\right)\right).Math.\mathrm{dS},X\left(S\right)=\underset{0}{\stackrel{S}{}}.Math.\cos \left(\left(s\right)+\left(s\right)\right).Math.\mathrm{ds},.Math..Math.Y\left(S\right)=\stackrel{S}{\underset{0}{}}.Math.\sin \left(\left(s\right)+\left(s\right)\right).Math.\mathrm{ds},$ where X.sub.P,Y.sub.P are the coordinates of a reference point (P) of the vehicle in the spatially fixed coordinate system (x0-0-y0).

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Some particularly advantageous configurations of aspects of the invention are specified in the subclaims. Further preferred embodiments also emerge from the following description of exemplary embodiments on the basis of figures.

[0048] In a schematic representation:

[0049] FIG. 1 shows a vehicle position (X.sub.P,Y.sub.P) and vehicle orientation in a spatially fixed system X.sub.0,Y.sub.0;

[0050] FIG. 2 shows vehicle parameters and movement quantities;

[0051] FIG. 3 shows a relationship between odometry and velocity vector;

[0052] FIG. 4 shows geometric relationships for a road vehicle with front-wheel steering for the purpose of explaining one exemplary embodiment of the method according to an aspect of the invention;

[0053] FIG. 5 shows geometric relationships for a road vehicle with all-wheel steering for the purpose of explaining one exemplary embodiment of the method according to an aspect of the invention; and

[0054] FIG. 6 shows geometric relationships for a road vehicle with limited transverse dynamics and slip angles for the purpose of explaining one exemplary embodiment of the method according to an aspect of the invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0055] Based on the principles for calculating the odometry according to the prior art that have already been explained with the aid of FIG. 1, the method according to an aspect of the invention will be presented below with the aid of FIGS. 2 to 6, by means of which method the yaw angle of the vehicle, in particular also in the case of slow driving, may be more accurately calculated.

[0056] For illustration, typical relevant parameters and movement quantities of a road vehicle are first shown in FIG. 2. Important parameters are for example: [0057] the track width b.sub.f of the front axle; [0058] the track width b.sub.r of the rear axle; and [0059] the wheelbase l=l.sub.f+l.sub.r.

[0060] Important movement quantities are for example the four wheel velocities V.sub.1, V.sub.2, V.sub.3 and V.sub.4, the yaw velocity {dot over ()} and the steering wheel angle .sub.SW. These movement quantities may be measured and provided directly by the four wheel sensors, the angular rate sensor and the steering wheel sensor.

[0061] According to FIG. 3, at time t=T, the reference point P of the vehicle has the velocity vector V.sub.P and drives along a course curve or odometry represented as a curved line up to reference point P with a course radius or a course curvature :

[00008]$\begin{array}{cc}{V}_P=\frac{\mathrm{dS}}{\mathrm{dt}}=\left(\stackrel{.}{}+\stackrel{.}{}\right).Math.=\frac{\left(d.Math..Math.+d.Math..Math.\right)}{\mathrm{dt}}.Math.& \left(4\right)\end{array}$

[0062] where S is the length of the course curve or the distance covered by the reference point P at time t. The following relationship between the distance S and the yaw angle of the vehicle in the case of driving with limited transverse dynamics

[00009]$\left(\frac{d.Math..Math.}{\mathrm{dt}}0\right)$

is obtained from equation (4):

[00010]$\begin{array}{cc}d.Math..Math.=\frac{\mathrm{dS}}{}=.Math.\mathrm{dS}.Math..Math..Math.S& \left(5\right)\end{array}$

[0063] In equation (5), the yaw angle is not dependent on the time t, but is a function of the distance S.

[0064] By calculating the integral according to equation (5) and with the distance S as the independent variable, the yaw angle may be determined using the following equation:

[00011]$\begin{array}{cc}\left(S\right)={}_0^S.Math.\left(s\right).Math.\mathrm{ds}-\left(0\right)& \left(6\right)\end{array}$

[0065] To solve equation (6), the course curvature (S) as a function of the independent variable s and the covered distance S should preferably be known at any point in time.

[0066] Alternatively or in addition, in particular for vehicles with front-wheel steering, the yaw angle may also be calculated by means of the relative movement of both wheels of the same axle:

[00012]$\begin{array}{cc}d.Math..Math.=\frac{{\mathrm{dS}}_4-{\mathrm{dS}}_3}{b_r}.Math..Math.\mathrm{or}& \left(7\right)\\ d.Math..Math.\frac{{\mathrm{dS}}_2-{\mathrm{dS}}_1}{b_f}.Math.\cos .Math..Math.{}_A& \left(8\right)\end{array}$

[0067] The accuracy of the calculated yaw angle according to equations (5), (6), (7) and (8) is mainly dependent on the resolution and the accuracy of the individual measured distances S.sub.1 to S.sub.4 of the four wheels, which are derived in particular from the respective wheel ticks from the wheel rotational speed sensors, as will be described in more detail further below. However, the vehicle parameters and the steering wheel angle also influence the accuracy of the calculated yaw angle .

[0068] If the vehicle is modeled as a rigid body, all points on the vehicle have the same common yaw angle . To solve it, an arbitrary point P on the vehicle may in principle be used, for which point the covered distance S as a function of time can be calculated and for which point the course curvature (s) and angle (s) between the curve tangent and the vehicle longitudinal axis can be determined. Preferred exemplary embodiments for the calculation will be described further below in the description.

[0069] The coordinates (X.sub.P, Y.sub.P) of the reference point P are preferably likewise calculated as functions of the independent variable s using the following equations in differential form:

dX=cos((S)+(S)).Math.dS(9)

dY=sin((S)+(s)).Math.dS(10)

[0070] or in integral form

[00013]$\begin{array}{cc}X\left(S\right)={}_0^S.Math.\cos \left(\left(s\right)+\left(s\right)\right).Math.\mathrm{ds}& \left(11\right)\\ Y\left(S\right)={}_0^S.Math.\sin \left(\left(s\right)+\left(s\right)\right).Math.\mathrm{ds}& \left(12\right)\end{array}$

[0071] For different reference points, different odometries and different distances S and different coordinates (X.sub.P, Y.sub.P) are obtained.

[0072] If, in equations (5), (9), and (10), a minus symbol is placed in front of the differential dS, the method according to an aspect of the invention may advantageously be used for the calculation in the case of the vehicle being driven in reverse.

[0073] Determining Angle

[0074] To calculate equations (5), (6) and (9) to (12), the angle between the velocity vector V.sub.P of the reference point P and the vehicle longitudinal axis or the change therein is used. This may be determined as follows according to one preferred embodiment.

[0075] Only the front wheels are used for steering in a typical passenger motor vehicle, referred to as a vehicle with front-wheel steering. In the case of slow driving or limited transverse driving dynamics, the slip angles of the individual wheels may be disregarded. In this case, the geometric relationship shown in FIG. 4 is obtained. The mean steering lock angle .sub.A of the front wheels, also known as the Ackermann angle, is a function of the steering wheel angle .sub.SW, which may be measured relatively precisely by means of the steering wheel angle sensor and is present in most vehicles.

[0076] The separate steering lock angles .sub.1 of wheel 1 and .sub.2 of wheel 2 are likewise functions of the steering wheel angle .sub.SW and are known. For wheel 3, wheel 4 and the midpoint C.sub.r of the rear axle, the velocity vector is always parallel to the vehicle longitudinal axis and hence the angle is equal to 0. The velocity vector for wheel 1 and wheel 2 runs along the respective wheel planes, whereby the angle is also known and is equal to the steering lock angle .sub.1 for wheel 1 and to the steering lock angle .sub.2 for wheel 2.

[0077] The relationship between the steering wheel angle .sub.SW (not shown in FIG. 2) and the mean steering lock angle of the front wheels .sub.A may be described approximately within a comparatively wide range by what is referred to as a steering ratio i.sub.L using equation (13). For the midpoint C.sub.f of the front axle, the velocity vector forms an angle .sub.A with the vehicle longitudinal axis, whereby the angle is always equal to the Ackermann angle .sub.A:

[00014]$\begin{array}{cc}={}_A=f\left({}_{\mathrm{SW}}\right)\frac{{}_{\mathrm{SW}}}{i_L}& \left(13\right)\end{array}$

[0078] Determining the Change in Distance dS or S

[0079] To calculate equations (5) to (12), the differential dS or the change in distance S(t) within a short time period t is also used, which may be calculated as follows:

dSS=S(t)S(tt)(14)

[0080] Here, the distances covered S.sub.i(t) by the individual wheels may be measured for most road vehicles using the, for example, four wheel rotational speed sensors, which deliver the current number of wheel ticks Z.sub.i(t) as measurement results at all times. When free-rolling (driving without longitudinal slip), there is the following relationship between the covered distance S.sub.i(t) and the total wheel ticks Z.sub.i(t):

S(t)=B.sub.i.Math.Z.sub.i(t)(15)

[0081] where 1=1, 2, 3, 4 is the index for the four different wheels and B is the difference in distance between two ticks and is typically constant for each wheel.

[0082] For wheels subject to longitudinal slip , the longitudinal slip may be estimated using a linear tire model and taken into account in equation (15) using a function K.sub.i(,t) according to equation (16):

S.sub.i(t)=B.sub.i.Math.K.sub.i(,t).Math.Z.sub.i(t)(16)

[0083] K.sub.i(,t) is equal to 1 for free-rolling wheels, smaller than 1 for driven wheels and greater than 1 for braked wheels. Because the longitudinal slip does not remain constant, the covered distances S.sub.i(t) must be divided into small steps, calculated for each step according to equation (17) and then summed:

S.sub.i(t)=B.sub.i.Math.K.sub.i(,t).Math.Z.sub.i(t)(17)

[0084] Using equation (15) or (17), the covered distances S.sub.i(t) for all of the wheels may be very accurately calculated. For the midpoint C.sub.r of the rear axle, the covered distance S.sub.r(t) may be derived from the two rear wheels:

[00015]$\begin{array}{cc}{S}_r\left(t\right)=\frac{S_3\left(t\right)+S_4\left(t\right)}{2}& \left(18\right)\end{array}$

[0085] For the midpoint C.sub.f of the front axle, the covered distance S.sub.f(t) is determined from the two front wheels:

[00016]$\begin{array}{cc}{S}_f\left(t\right)=\frac{S_1\left(t\right)+S_2\left(t\right)}{2}& \left(19\right)\end{array}$

[0086] Determining the Course Curvature (s)

[0087] As can be understood from FIG. 4, when the vehicle is driven in a curve, there is a center of rotation M and hence at least one imaginary right triangle MC.sub.rC.sub.f, where the angle of the triangle at the center of rotation M, for the case of a vehicle with front-wheel steering as shown in FIG. 4, is equal to the Ackermann angle .sub.A. If the midpoint C.sub.r of the rear axle is used as the reference point P, this then therefore gives, in a straightforward manner, the following course curvature:

[00017]$\begin{array}{cc}{}_r=\frac{1}{R_r}=\frac{\tan .Math..Math.{}_A}{l}& \left(20\right)\end{array}$

[0088] The midpoint C.sub.f of the front axle has the following course curvature:

[00018]$\begin{array}{cc}{}_f=\frac{1}{R_f}=\frac{\sin .Math..Math.{}_A}{l}& \left(21\right)\end{array}$

[0089] The course curvatures for wheel 1 to wheel 4 are derived using the corresponding approach as follows:

[00019]$\begin{array}{cc}{}_1=\frac{1}{R_1}=\frac{\tan .Math..Math.{}_A}{l.Math.\sqrt{{\left(1-\frac{b_f.Math..Math.\tan .Math..Math.{}_A}{2.Math.l}\right)}^2+{\left(\tan .Math..Math.{}_A\right)}^2}}& \left(22\right)\\ {}_2=\frac{1}{R_2}=\frac{\tan .Math..Math.{}_A}{l.Math.\sqrt{{\left(1+\frac{b_f.Math..Math.\tan .Math..Math.{}_A}{2.Math.l}\right)}^2+{\left(\tan .Math..Math.{}_A\right)}^2}}& \left(23\right)\\ {}_3=\frac{2.Math..Math.\tan .Math..Math.{}_A}{2.Math.l-b_r.Math..Math.\tan .Math..Math.{}_A}& \left(24\right)\\ \mathrm{and}& \\ {}_4=\frac{2.Math..Math.\tan .Math..Math.{}_A}{2.Math.l+b_r.Math..Math.\tan .Math..Math.{}_A}& \left(25\right)\end{array}$

[0090] Consequently, all six of the points on the vehicle considered above may be used as reference points for calculating the yaw angle or for calculating the odometries, as long as all four wheel sensors are operating without fault. It is however advantageous to use the midpoint C.sub.r of the rear axle as the reference point for calculating the odometry, since, on the one hand, the tangent for the odometry is always identical to the vehicle longitudinal axis and, on the other hand, the differential dS or the change in distance S.sub.r(t) may be calculated both using the two sensors of the rear wheels and using the two sensors of the front wheels:

[00020]$\begin{array}{cc}\mathrm{dS}.Math..Math.S=S_r\left(t\right)-S_r\left(t-.Math..Math.t\right)=\frac{\left(S_3\left(t\right)-S_3\left(t-.Math..Math.t\right)\right)+\left(S_4\left(t\right)-S_4\left(t-.Math..Math.t\right)\right)}{2}& \left(26\right)\\ .Math.\mathrm{or}& \\ \mathrm{dS}.Math..Math.S=S_r\left(t\right)-S_r\left(t-.Math..Math.t\right)=\frac{\left(S_1\left(t\right)-S_1\left(t-.Math..Math.t\right)\right)+\left(S_2\left(t\right)-S_2\left(t-.Math..Math.t\right)\right)}{2}.Math.\cos .Math..Math.{}_A& \left(27\right)\end{array}$

[0091] Because the angle for the rear axle is always equal to 0, the coordinates of the midpoint C.sub.r of the rear axle may be calculated according to equations (11) and (12) in a particularly straightforward manner:

[00021]$\begin{array}{cc}{X}_R\left(S\right)=\underset{0}{\stackrel{S}{}}.Math.\cos \left(\left(s\right)\right).Math.\mathrm{ds}.Math..Math.Y_R\left(S\right)=\underset{0}{\stackrel{S}{}}.Math.\sin \left(\left(s\right)\right).Math.\mathrm{ds}& \left(28\right)\end{array}$

[0092] Especially in the case of parking (into or out of a space), situations arise in which the steering wheel is actuated while stationary and consequently the steering lock angle .sub.A and, in the case of vehicles with all-wheel drive, also .sub.R, changes greatly while stationary in a given position S=S.sub.B. This means that the course curvature (s) in equations (5) and (6) changes abruptly when s=S.sub.B and the function (s) of the distance s is not continuous when s=S.sub.B. As such, the direction angle ++ of the velocity vector of reference point P cannot be differentiated with respect to the independent variable s when s=S.sub.B. Thus

[00022]${\frac{d\left(+\right)}{\mathrm{dS}}.Math.}_{S=S_B}=\left(S_B\right)$

does not exist. Therefore, when calculating the yaw angle according to equation (6), in particular when the vehicle is stationary, this point is preferably bypassed with s=S.sub.B and the integral for the yaw angle with S>S.sub.B is calculated in sections [0, SB) and (SB+,S] as follows:

[00023]$\begin{array}{cc}\left(S\right)=\stackrel{S_{B-}}{\underset{0}{}}.Math.\left(s\right).Math.\mathrm{ds}+\underset{S_{B+}}{\stackrel{S}{}}.Math.\left(s\right).Math.\mathrm{ds}& \left(29\right)\end{array}$

[0093] It can be seen that the change in the steering wheel angle when stationary does not cause any sudden change in the yaw angle and the yaw angle remains continuous with respect to the independent variable s when S=S.sub.B.

[0094] According to a further embodiment, the method according to an aspect of the invention may also be used for vehicles with all-wheel steering. For this, the course curvatures or course radii for the reference points are preferably calculated according to the geometric relationship shown in FIG. 5. Here, .sub.R is the mean steering lock angle of the rear wheels and it normally has a defined relationship with the steering wheel angle .sub.SW. Therefore, .sub.A and .sub.R are known. The six radii are dependent only on vehicle parameters b.sub.f, b.sub.r and l, and on the steering lock angles .sub.A and .sub.R.

[0095] Although, in the case of a vehicle exhibiting limited transverse acceleration as illustrated in FIG. 6, the slip angles are not negligible, it is nonetheless still possible to calculate them relatively accurately using a linear tire model:

.sub.F=C.sub.F.Math.F.sub.YF

.sub.R=C.sub.R.Math.F.sub.YR(30)

[0096] Here, the slip angle is proportional to the lateral force, which may be determined from the measured vehicle transverse acceleration. The tire lateral stiffnesses C.sub.F and C.sub.R are vehicle parameters and generally constant. The method according to an aspect of the invention may also be used in such situations. Here, the slip angles .sub.R and .sub.R are expediently taken into account when calculating the course radii.

[0097] If it turns out in the course of the proceedings that a feature or a group of features is not absolutely necessary, then the applicant aspires right now to a wording for at least one independent claim that no longer has the feature or the group of features. This may be, by way of example, a subcombination of a claim present on the filing date or may be a subcombination of a claim present on the filing date that is limited by further features. Claims or combinations of features of this kind requiring rewording can be understood to be covered by the disclosure of this application as well.

[0098] It should further be pointed out that configurations, features and variants of aspects of the invention that are described in the various embodiments or exemplary embodiments and/or shown in the figures can be combined with one another in any way. Single or multiple features can be interchanged with one another in any way. Combinations of features arising therefrom can be understood to be covered by the disclosure of this application as well.

[0099] Back-references in dependent claims are not intended to be understood as dispensing with the attainment of independent substantive protection for the features of the back-referenced subclaims. These features can also be combined with other features in any way.

[0100] Features that are disclosed only in the description or features that are disclosed in the description or in a claim only in conjunction with other features may fundamentally be of independent significance essential to aspects of the invention. They can therefore also be individually included in claims for the purpose of distinction from the prior art.

LIST OF REFERENCE SIGNS

[0101] x.sub.0-0-y.sub.0 spatially fixed coordinate system [0102] x-0-y vehicle coordinate system [0103] P reference point [0104] X.sub.P,Y.sub.P coordinates of the reference point P in the spatially fixed coordinate system [0105] V.sub.P velocity vector of reference point P [0106] v.sub.x0,v.sub.y0 velocity components of velocity vector V.sub.P [0107] V.sub.i velocity of wheel i [0108] vehicle orientation (angle of vehicle longitudinal axis to x.sub.0-axis of spatially fixed coordinate system) [0109] {dot over ()} yaw velocity [0110] angle between velocity vector of reference point P and vehicle longitudinal axis [0111] course radius [0112] course curvature [0113] S length of course curve [0114] b.sub.f track width of front axle [0115] b.sub.r track width of rear axle [0116] l.sub.f,l.sub.r front axle/rear axle distance to reference point [0117] l=l.sub.f+l.sub.r front axle-to-rear axle distance [0118] C.sub.f midpoint of front axle [0119] C.sub.r midpoint of rear axle [0120] M center of rotation of the vehicle [0121] .sub.SW steering wheel angle [0122] .sub.i steering lock angle of wheel i [0123] .sub.A mean steering lock angle of front wheels [0124] .sub.R mean steering lock angle of rear wheels [0125] i.sub.L steering ratio [0126] Z.sub.i total wheel ticks from wheel i [0127] B.sub.i difference in distance between two wheel ticks from wheel i [0128] .sub.F,.sub.R slip angle of front/rear axle wheels [0129] C.sub.F,C.sub.R tire lateral stiffnesses