Method for detecting a slope of a road

Abstract

A method for detecting a slope of a road on which a vehicle is traveling in at least one spatial direction. The vehicle has a body and a chassis with a plurality of wheels. An inclination of the vehicle body in the spatial direction is determined. For at least one wheel, a vertical distance to the vehicle body is detected. The distance so determined is used to calculate an inclination of the chassis in the spatial direction. The slope of the road in the spatial direction is determined from a difference between the inclination of the vehicle body in the spatial direction and the inclination of the chassis in the spatial direction.

Claims

1. A method for detecting a slope of a road on which a vehicle is traveling in at least one spatial direction, comprising: a vehicle body and a chassis with a plurality of wheels, which are in contact with the road, wherein an inclination of the vehicle body in the at least one spatial direction is determined, wherein for at least one wheel, a vertical distance to the vehicle body is detected, wherein the at least one distance so determined is used to calculate an inclination of the chassis in the at least one spatial direction, and wherein the slope of the road in the at least one spatial direction is determined from a difference between the inclination of the vehicle body in the at least one spatial direction and the inclination of the chassis in the at least one spatial direction, wherein the inclination of the chassis in the at least one spatial direction is determined by transformation of the vertical distance of the at least one wheel to the vehicle body with a transformation matrix: $T=\left[\begin{array}{cccc}{t}_v& -t_v& t_h& -t_h\\ l_v& l_v& -l_h& -l_h\end{array}\right]$ whose elements are arranged in at least one column and at least one row, wherein values for the elements of the transformation matrix are dependent on lengths t.sub.v, t.sub.h, l.sub.v, l.sub.h of the sides of at least one rectangle, wherein the center of gravity of the vehicle body is arranged at a first of two opposite corners of the at least one rectangle and the at least one wheel is arranged at a second one of the two opposite corners, wherein a body-fixed coordinate system is used to ascertain the inclination of the vehicle body, a chassis-fixed coordinate system is used to ascertain the inclination of the vehicle chassis, and an inertial coordinate system is used as a reference coordinate system, wherein the inclination of the vehicle body relative to the reference coordinate system is described by a quaternion, and wherein a filter algorithm configured to merge computational methods is used to provide a signal usable both at low frequency and high frequency, the method comprising providing sensor determined values for acceleration and rate of rotation, performing a correction of the centrifugal force, wherein accelerations measured by the sensor layout are corrected by a component of the centrifugal force to determine a first corrected acceleration, performing a correction of the gravitational force, wherein the first corrected acceleration is corrected, taking into account roll angle and pitch angle, by the gravitational acceleration, resulting in acceleration in the horizontal plane, determining planar velocity taking into account the acceleration in the horizontal plane, a measured velocity of the vehicle, and a steering angle, wherein a first planar velocity is calculated by integration of the acceleration in the horizontal plane and is used in a closed feedback control circuit for the correction of the centrifugal force, performing a correction of the planar velocity change using values of the measured velocity, steering angle, pitch angle, roll angle, and the acceleration corrected by the centrifugal acceleration, wherein the corrected acceleration is corrected by the component of the change in the planar velocity, calculating the inclination of the vehicle body taking into account the rate of rotation and the gravitational acceleration of the vehicle, yielding a pitch angle and roll angle in relation to the inertial coordinate system, and determining the slope of the road using the inclination of the vehicle body.

2. The method according to claim 1, wherein the inclination of the vehicle body and the slope of the road are ascertained in dependence on at least one of a roll angle and a pitch angle .

3. The method according to claim 1, wherein the inclination of the chassis is ascertained by transformation of the distance oriented in the vertical direction between the at least one wheel and the vehicle body with the transformation matrix.

4. The method according to claim 1, wherein to ascertain the inclination of the vehicle body, a first body-fixed coordinate system is used, and to ascertain the inclination of the chassis, a second chassis-fixed coordinate system is used, and wherein a third inertial coordinate system is used as a reference coordinate system, which is related to the force of gravity.

5. The method according to claim 1, wherein a strapdown algorithm is used, with which it is provided that, for determining a corrected acceleration of the vehicle, a sensor-measured acceleration is corrected by a centrifugal acceleration and the gravitational acceleration and from this a speed of the vehicle is determined in a plane, and the inclination of the vehicle body is calculated.

6. The method according to claim 2, wherein a value of the roll angle .sub.s is compared to a reference value in order to describe a slope of the road in the transverse direction, wherein it is determined that a steep curve is being traveled by the vehicle when the value is greater than the reference value.

7. A system for detecting the slope of a road on which a vehicle is traveling in at least one spatial direction, comprising: a vehicle body and a chassis with a plurality of wheels, which are in contact with the road, wherein the system has a plurality of sensors and a control unit, wherein at least one first sensor is designed to determine an inclination of the vehicle body in the at least one spatial direction, wherein at least one second sensor is designed to detect, for at least one wheel, a vertical distance to the vehicle body, wherein the control unit is designed to calculate, via the at least one determined distance, an inclination of the chassis in the at least one spatial direction and to ascertain the slope of the road in the at least one spatial direction from a difference between the inclination of the vehicle body in the at least one spatial direction and the inclination of the chassis in the at least one spatial direction, wherein the inclination of the chassis in the at least one spatial direction is ascertained by transformation of the vertical distance between the at least one wheel and the vehicle body with a transformation matrix: $T=\left[\begin{array}{cccc}{t}_v& -t_v& t_h& -t_h\\ l_v& l_v& -l_h& -l_h\end{array}\right]$ whose elements are arranged in at least one column and at least one row, wherein values for the elements of the transformation matrix are dependent on lengths t.sub.v, t.sub.h, l.sub.v, l.sub.h of the sides of at least one rectangle, wherein the center of gravity of the vehicle body is arranged at a first of two opposite corners of the at least one rectangle, and the at least one wheel is arranged at a second of the two opposite corners, wherein a body-fixed coordinate system is used to ascertain the inclination of the vehicle body, a chassis-fixed coordinate system is used to ascertain the inclination of the vehicle chassis, and an inertial coordinate system is used as a reference coordinate system, wherein the inclination of the vehicle body relative to the reference coordinate system is described by a quaternion, and wherein a filter algorithm configured to merge computational methods is used to provide a signal usable both at low frequency and high frequency, wherein sensor determined values are provided for acceleration and rate of rotation, wherein a correction of the centrifugal force is performed and accelerations measured by the sensor layout are corrected by a component of the centrifugal force to determine a first corrected acceleration, wherein a correction of the gravitational force is performed and the first corrected acceleration is corrected, taking into account roll angle and pitch angle, by the gravitational acceleration, resulting in acceleration in the horizontal plane, wherein planar velocity is determined taking into account the acceleration in the horizontal plane, a measured velocity of the vehicle, and a steering angle, and wherein a first planar velocity is calculated by integration of the acceleration in the horizontal plane and is used in a closed feedback control circuit for the correction of the centrifugal force, wherein a correction of a planar velocity change is performed using values of the measured velocity, steering angle, pitch angle, roll angle, and the acceleration corrected by the centrifugal acceleration, wherein the corrected acceleration is corrected by the component of the change in the planar velocity, wherein the inclination of the vehicle body is calculated taking into account the rate of rotation and the gravitational acceleration of the vehicle, yielding a pitch angle and roll angle in relation to the inertial coordinate system, and wherein the slope of the road is determined using the inclination of the vehicle body.

8. The system according to claim 7, wherein the at least one sensor is designed as a displacement sensor.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 shows in schematic representation an example of a vehicle with an embodiment of the system according to the invention.

(2) FIG. 2 shows a diagram for an embodiment of the method according to the invention.

(3) The figures shall be described in interrelated and overlapping manner, the same reference numbers denoting the same components.

(4) FIG. 1 shows schematically a vehicle 2 designed as a motor vehicle and a roadway 4 in the form of a road on which the vehicle 2 is traveling. The vehicle 2 comprises a vehicle body 6 and four wheels 8, 10 provided for the forward movement of the vehicle 2, of which only a left front wheel 8 and a left rear wheel 10 are shown in FIG. 1. Each wheel 8, 10 is connected at least by one spring 12, 14 to the vehicle body 6 and designed as a component of a chassis of the vehicle 2.

DETAILED DESCRIPTION OF THE DRAWINGS

(5) The embodiment of the system 16 according to the invention encompasses, as its components, a control unit 18, at least one first sensor 19 for determining the inclination of the vehicle body 6 as well as a plurality of second sensors, designed here as displacement sensors 20, 22, each spring 12, 14 being coordinated with one such displacement sensor 20, 22. The at least one first sensor 19 and the displacement sensors 20, 22 are at the same time designed as components of a sensor layout of the system 16. Furthermore, the sensor layout and thus the system 16 encompass sensors, not further represented, for determining, generally for measuring, at least one kinetic variable, usually a speed and/or an acceleration of the vehicle 2 and/or the vehicle body 6.

(6) The embodiment of the method of the invention described below with the aid of the diagram in FIG. 2 is to be carried out with the embodiment of the system 16 according to the invention shown schematically in FIG. 1, wherein steps of the embodiment of the method are to be controlled and thus controlled and/or regulated by the control unit 18.

(7) Furthermore, three coordinate systems 24, 26, 28 as well as various parameters thereof, here geometrical parameters, are shown in FIG. 1.

(8) The first, body-fixed coordinate system 24 is coordinated with the vehicle body 6 of the vehicle 2, its origin being situated at the center of gravity 25 of the vehicle body 6. The first coordinate system 24 comprises a first axis in the spatial direction x.sub.a, which is oriented longitudinally to its vehicle body 6 and parallel to a traveling direction of the vehicle 2. A second axis is oriented in the spatial direction y.sub.a, transversely to the vehicle body 6 and parallel to the axles of the vehicle 2, which extend between two wheels 8, 10 of the vehicle 2. A third axis is oriented in the spatial direction z.sub.a parallel to a vertical axis of the vehicle body 6. All three mentioned axes and thus spatial directions x.sub.a, y.sub.a, z.sub.a are oriented perpendicular to each other. It is provided in the embodiment that the first two axes mentioned and thus the spatial directions x.sub.a and y.sub.a subtend a horizontal plane of the vehicle 2, in which the center of gravity 25 lies.

(9) Furthermore, FIG. 1 shows two examples of vertically oriented distances dz.sub.a,VL, dz.sub.a,HL designed as spring travel paths. A first distance dz.sub.a,VL pertains to a distance between the left front wheel 8 and the vehicle body 6. A second distance dz.sub.a,HL pertains to a distance between the left rear wheel 10 and the vehicle body 6. These spring travel paths or distances dz.sub.a,VL, dz.sub.a,HL are oriented along the springs 12, 14 and are to be detected by the displacement sensors 20, 22 coordinated with the springs 12, 14.

(10) Distances of the wheels 8, 10 from the center of gravity 25 of the vehicle body 6 in a plane parallel to the horizontal plane are to be defined here by the lengths or side lengths or stretches t.sub.v, t.sub.h, l.sub.h, l.sub.v. For the left front wheel 8, one must take into account a front transverse stretch t.sub.v, describing the distance of the wheel 8 from the center of gravity 25 in the transverse spatial direction, and a front longitudinal stretch l.sub.v, describing the distance of the wheel 8 from the center of gravity 25 in the longitudinal spatial direction. For the left rear wheel 10, one must take into account a rear transverse stretch t.sub.h, describing the distance of the wheel 10 from the center of gravity 25 in the transverse spatial direction, and a rear longitudinal stretch l.sub.h, describing the distance of the wheel 10 from the center of gravity 25 in the longitudinal spatial direction.

(11) Another spring travel or another vertically oriented distance dz.sub.a,VR pertains to a distance between a right front wheel, not shown here, and the vehicle body 6. An additional spring travel or an additional distance dz.sub.a,HR in the vertical direction pertains to a distance between a right rear wheel, not shown here, and the vehicle body 6. The described distances dz.sub.a,VL, dz.sub.a,HL, dz.sub.a,VR, dz.sub.a,HR or spacings between the wheels 8, 10 and the vehicle body 6 are referred in the embodiment to the horizontal plane in which the center of gravity 25 lies.

(12) Furthermore, for the right front wheel, one must take into account the front transverse stretch t.sub.v, describing the distance of the right front wheel from the center of gravity 25 in the transverse spatial direction, and the front longitudinal stretch l.sub.v, describing the distance of the right front wheel from the center of gravity 25 in the longitudinal spatial direction. For the right rear wheel, one must take into account the rear transverse stretch t.sub.h, describing the distance of this wheel from the center of gravity 25 in the transverse spatial direction, and the rear longitudinal stretch l.sub.h, describing the distance of the right rear wheel from the center of gravity 25 in the longitudinal spatial direction, the rear transverse stretch to be taken into account for the right rear wheel not being indicated in FIG. 1.

(13) A second, chassis-fixed coordinate system 26 is coordinated with the road 4 and comprises a first axis in the spatial direction x.sub.s parallel to a specified traveling direction or longitudinal direction of the road 4, a second axis in the spatial direction y.sub.s, oriented parallel to a transverse direction of the road 4, and a third axis in the spatial direction z.sub.s, all these axes being oriented perpendicular to each other. A slope and thus a position of the road 4 is described here by means of a transverse angle or roll angle .sub.s, describing a slope of the road 4 in the transverse direction, and by means of a longitudinal angle or pitch angle .sub.s, describing a slope of the road 4 in the longitudinal direction and thus a grade or gradient.

(14) A third coordinate system 28 is designed as a reference coordinate system and comprises a first axis in the spatial direction x.sub.ref, a second axis in the spatial direction y.sub.ref and a third axis in the spatial direction z.sub.ref, all of them oriented perpendicular to each other.

(15) Furthermore, there are shown for the first coordinate system 24 a roll angle .sub.a, which describes a rotation of the vehicle body 6 about the first axis, oriented in the spatial direction x.sub.a, a pitch angle .sub.a, which describes a rotation of the vehicle body 6 about the second axis, oriented in the spatial direction y.sub.a, and a yaw angle .sub.a, which describes a rotation of the vehicle body 6 about a third axis, oriented in the spatial direction z.sub.a.

(16) The first, body-fixed coordinate system 24 [x.sub.a, y.sub.a, z.sub.a] at the center of gravity 25 of the vehicle body 6 of the vehicle 2 follows translatory and rotational movements of the vehicle body 6. The third, inertial coordinate system 28 [x.sub.ref, y.sub.ref, z.sub.ref] is used as a reference coordinate system, taking into account that the gravitational acceleration g acts solely in the spatial direction z.sub.ref parallel to a gravitation vector.

(17) In the embodiment of the method, in order to estimate an inclination or position of the vehicle body 6, the pitch and .sub.a and the roll angle .sub.a are referred to the third coordinate system 28, configured as the reference coordinate system.

(18) The angles [.sub.a, .sub.a, .sub.a] are also designated as the inertial pitch angle .sub.a, inertial roll angle .sub.a and inertial yaw angle .sub.a. By the inclination of the vehicle body 6 is meant its orientation in the pitch direction and roll direction, from which the pitch angle .sub.a and the roll angle .sub.a are determined.

(19) In order to estimate the inclination or position of the vehicle body 6, the acceleration {right arrow over (a)}=[{umlaut over (x)}.sub.a, .sub.a, {umlaut over (z)}.sub.a].sup.T of the vehicle body 6 and of the vehicle 2 along the spatial directions x.sub.a, y.sub.a, z.sub.a and the rates of rotation {right arrow over ()}=[{dot over ()}.sub.a, {dot over ()}.sub.a, {dot over ()}.sub.a].sup.T are measured and thus ascertained with the sensor layout for determining the inertia with six degrees of freedom (IMUInertial Measurement Unit), while the sensor layout can also be used independently of the performance of the method in the vehicle 2.

(20) To estimate the inclination of the vehicle body 6, one first considers the physical boundary conditions to which the variables {right arrow over (a)} and {right arrow over ()} are subjected, which are to be ascertained by the sensor layout, for example by measurement. From measurement signals of acceleration sensors of the sensor layout, three different physical variables are deduced: the centrifugal acceleration {right arrow over (a.sub.zf)}, dependent on the rates of rotation {right arrow over ()} and the planar velocity {right arrow over (v.sub.plane)}=[v.sub.Plane,x, v.sub.Plane,y, v.sub.Plane,z].sup.T of the vehicle 2:
{right arrow over (a.sub.zf)}={right arrow over ()}{right arrow over (v.sub.Plane)}(3) the change in the adjusted, planar velocity {right arrow over (v.sub.Plane)} and thus acceleration {right arrow over (a.sub.vp)} of the vehicle 2 and/or the vehicle body 6 in the spatial direction of one axis of a respective acceleration sensor in the horizontal plane of the vehicle:
{right arrow over (a.sub.vp)}=R{right arrow over ({dot over (v)}.sub.Plane)}(4)
the gravitational acceleration {right arrow over (a.sub.gv)}=R[0,0,g].sup.T(5)

(21) In the formulas {right arrow over (v.sub.Plane)} is the velocity of the vehicle 2 in the horizontal plane and R is the Euler rotation matrix (6), which is calculated taking into account the Euler angle in a rotation sequence of the roll angle , the pitch angle and the yaw angle . Here, v.sub.plane,x is the usual velocity of the vehicle v.sub.vehicle in the longitudinal or traveling direction of the vehicle 2, which is measured in terms of the rotary speed of the wheels 8, 10 and indicated on the tachometer.

(22) $\begin{array}{cc}R=\left(\begin{array}{ccc}\cos \cos & \cos \sin & -\sin \\ \sin \sin \cos -\cos \sin & \sin \sin \sin +\cos \cos & \sin \cos \\ \cos \sin \cos +\sin \sin & \cos \sin \cos -\sin \cos & \cos \cos \end{array}\right)& \left(6\right)\end{array}$

(23) The respectively determined angles , i.e., .sub.a (for the vehicle body), .sub.f (for the chassis) and .sub.s (for the road), and .sub.s i.e., .sub.a (for the vehicle body), .sub.f (for the chassis) and .sub.s (for the road), can usually be ascertained by two different computational methods or calculation approaches: by temporal integration of the rates of rotation {right arrow over ()}, measured by the sensor layout, or by eliminating the centrifugal acceleration {right arrow over (a.sub.zf)} and the change in the planar velocity {right arrow over (v.sub.Plane)} and thus the acceleration {right arrow over (a.sub.vp)} of the vehicle 2 from the accelerations {right arrow over (a.sub.gv)}={right arrow over (a)}{right arrow over (a.sub.zf)}{right arrow over (a.sub.vp)} measured by the sensor layout and calculating the angles through trigonometric functions

(24) ${}_a=a\tan \frac{a_{\mathrm{gv}},x}{a_{\mathrm{gv}},z},{}_a=a\tan \frac{a_{\mathrm{gv}},y}{a_{\mathrm{gv}},z}.$

(25) As already indicated by means of equation (5), {right arrow over (a.sub.gv)} is a vector with the three elements [a.sub.gv,x, a.sub.gv,y, a.sub.gv,z].sup.T=[g*sin , g*sin *cos , g*cos *cos ].sup.T, whereas the acceleration of earth g=9.81 m/s.sup.2 is used here as a scalar, which acts depending on the inclination of the vehicle body 6, as described by the Euler rotation matrix R (6), on different elements of the vector {right arrow over (a.sub.gv)}. If the vehicle body 6 is not inclined, then {right arrow over (a.sub.gv)}=[0,0, g].sup.T. For a roll angle .sub.a=90 and a pitch angle .sub.a=0, {right arrow over (a.sub.gv)}=[0, g, 0].sup.T. If {right arrow over (a.sub.gv)} is known, the pitch angle .sub.a and the mil angle .sub.a can be computed through the above-described a tan functions.

(26) However, it must be taken into account in the computations that, because of time-variable offset errors of rotational rate sensors, an integration of the rotational rates in stationary manner may be inaccurate. This means that calculated angles show low frequency drift and only high-frequency components of measurement signals are usable. For the angles ascertained by acceleration sensors, on the other hand, high-frequency perturbations are to be expected, since hard to detect changes in the velocity cannot be eliminated from the measurement signals such as occur when traveling over potholes.

(27) In the embodiment described here, an inclination filter or position filter based on quaternions is used as a filter algorithm. It is likewise possible to employ a Kalman filter for the merging of both computational methods. In this way, both of the above indicated computational methods are combined, so that a signal is provided which is usable both at low frequency and high frequency.

(28) A quaternion is a four-dimensional vector {right arrow over (q)}=[q.sub.1, q.sub.2, q.sub.3, q.sub.4].sup.T, which can be used to describe the orientation of a rigid vehicle body, here, the vehicle body 6. If a rigid vehicle body is rotated in regard to a reference system by the angle and the axis {right arrow over (r)}=[r.sub.x, r.sub.y, r.sub.z].sup.T, where {right arrow over (r)} is a unitary vector, this orientation in regard to the reference system is described by the quaternion

(29) $\stackrel{.fwdarw.}{q}={\left[\cos \frac{x}{2},-r_x\sin \frac{x}{2},-r_y\sin \frac{x}{2},-r_x\sin \frac{x}{2}\right]}^T.$

(30) This is used first of all the temporal integration of the rates of rotation {right arrow over ()} measured by the sensor layout, the vehicle body 6 in the present case being rotated in regard to the inertial reference system with the rate of rotation {right arrow over ()}=[.sub.x, .sub.y, .sub.z].sup.T. Starting from an initial position {right arrow over (q.sub.1)} of the vehicle body 6, the change in position or inclination on account of the rates of rotation is described by the equation (7):

(31) $\begin{array}{cc}\stackrel{.fwdarw.}{{\stackrel{.}{q}}_{}}=\frac{1}{z}\stackrel{.fwdarw.}{q_L}.Math.\left[0,{}_x,{}_y,{}_z\right]& \left(7\right)\end{array}$

(32) The operator .Math. here symbolizes a quaternion multiplication in a time-discrete case, a resulting differential equation can be solved, e.g., by a Euler integration (8):
{right arrow over (q.sub.,k)}={right arrow over (q.sub.L,k1)}+{right arrow over ({dot over (q)}.sub.)}t(8)

(33) where t corresponds to a time increment between two moments of time k and k1.

(34) In order to describe with quaternions an orientation of the vehicle body 6 from the acceleration {right arrow over (a)} measured by the sensor layout and the resulting, adjusted gravitational acceleration
{right arrow over (a.sub.gv)}=[a.sub.gv,x,a.sub.gv,y,a.sub.gv,z].sup.T=[g*sin ,g*sin *cos ,g*cos *cos ].sup.T

(35) the following optimization problem (9) needs to be solved:

(36) There

(37) $\begin{array}{cc}\stackrel{.fwdarw.}{q_a}=\underset{q_L{}^{-1}}{\min }\stackrel{.fwdarw.}{f}\left(\stackrel{.fwdarw.}{q_L},\stackrel{.fwdarw.}{a_{\mathrm{gv}}}\right)\mathrm{mit}\stackrel{.fwdarw.}{f}\left(\stackrel{.fwdarw.}{q_L},\stackrel{.fwdarw.}{a_{\mathrm{gv}}}\right)=\left[\begin{array}{c}2\left(q_{L,2}{q}_{a,4}-q_{L,1}{q}_{L,3}\right)-a_{\mathrm{gv},x}\\ 2\left(q_{L,1}{q}_{L,2}+q_{L,3}{q}_{L,4}\right)-a_{\mathrm{gv},y}\\ 2\left(0.5-q_{L,2}^2-q_{L,3}^2\right)-a_{\mathrm{gv},z}\end{array}\right]\left[\mathrm{mit}=\mathrm{with}\right]& \left(9\right)\end{array}$

(38) A direct calculation of the inclination is not possible, since infinitely many solutions exist about an axis of rotation which is oriented parallel to the gravitation vector. For the time-discrete solution of the optimization problem, a gradient-based approach (10) with en adjustable increment is used:

(39) $\begin{array}{cc}\stackrel{.fwdarw.}{q_{a,k}}=\stackrel{.fwdarw.}{q_{L,k-1}}=\mathrm{.Math.}\frac{\stackrel{.fwdarw.}{f}\left(\stackrel{.fwdarw.}{q_{L,k-1}},\stackrel{.fwdarw.}{a_{\mathrm{gv}}}\right)}{.Math.\stackrel{.fwdarw.}{f}\left(\stackrel{.fwdarw.}{q_{L,k-1}},\stackrel{.fwdarw.}{a_{\mathrm{gv}}}\right).Math.}& \left(10\right)\end{array}$

(40) In order to merge information about the inclination resulting from the measured rates of rotation {right arrow over (q.sub.,k)} and from the accelerations {right arrow over (q.sub.a,k)}, the two quaternions {right arrow over (q.sub.a,k)}, {right arrow over (q.sub.L,k)} are added with weighting by equation (11):
{right arrow over (q.sub.L,k)}={right arrow over (q.sub.a,k)}+(1){right arrow over (q.sub.,k)}(11)

(41) where 01 is an adjustable parameter. The pitch angle and roll angle are then computed with the equations (12a), (12b):

(42) $\begin{array}{cc}{}_{a,k}=-{\sin }^{-1}\left(2q_{L,k,2}{q}_{L,k,4}+q_{L,k,1}{q}_{L,k,3}\right)& \left(12a\right)\\ {}_{a,k}=\mathrm{atan}\left(\frac{2q_{L,k,2}{q}_{L,k,4}+2q_{L,k,1}{q}_{L,k,3}}{2q_{L,k,1}^2+2q_{L,k,4}^2-1}\right)& \left(12b\right)\end{array}$

(43) In order to eliminate the centrifugal acceleration {right arrow over (a.sub.zf)} and the change {right arrow over (a.sub.vp)} in the planar velocity {right arrow over (v.sub.Plane)} from the accelerations measured by the sensor layout, the pitch and roll angle need to be taken into account, which in turn are computed with the aid of the gravitational acceleration vector {right arrow over (a.sub.gv)}.

(44) To carry out the embodiment of the method, a so-called strapdown approach is used, as represented in the diagram of FIG. 2. Individual steps 40, 42, 44, 46, 48 of the method shall be described more closely below.

(45) At the start of the method, sensor-determined values are provided for the acceleration {right arrow over (a)} and the rate of rotation {right arrow over ()}. With these values, in a first step 40, a correction of the centrifugal force is carried out, wherein the accelerations measured by the sensor layout are corrected by the component of the centrifugal force {right arrow over (a.sub.zf)}={right arrow over ()}{right arrow over (v.sub.Plane)}. A first corrected acceleration {right arrow over (a)}{right arrow over (a.sub.zf)} is determined. This first corrected acceleration {right arrow over (a)}{right arrow over (a.sub.zf)} is corrected in a second step 42, taking into account values for the roll angle .sub.a and the pitch angle .sub.a, by the gravitational acceleration {right arrow over (a.sub.gv)}, performing a correction of the gravitational force, resulting in the acceleration {right arrow over (a.sub.vp)} in the horizontal plane.

(46) In the context of the method, two options are provided for calculating the planar velocity {right arrow over (v.sub.Plane)}.

(47) A determination of the velocities is carried out in a third step 44, taking into account the acceleration {right arrow over (a.sub.vp)} of the vehicle 2, the measured velocity v of the vehicle 2 and its steering angle .sub.steer, wherein the first planar velocity of the vehicle {right arrow over (v.sub.Int)}=[v.sub.Int,x, v.sub.Int,y, v.sub.Int,z].sup.T is calculated by integration (13):
{right arrow over (v.sub.Int)}={right arrow over (a.sub.vp)}dt(13)

(48) of the acceleration {right arrow over (a.sub.vp)} of the vehicle 2 and thus determined. This planar velocity {right arrow over (v.sub.Int)} in turn is used in a closed feedback control circuit for the correction of the centrifugal force in the first step 40.

(49) For the velocity v.sub.plane,x in the spatial direction of a longitudinal axis of the vehicle 2, we may use the velocity v.sub.vehicle in the direction x.sub.a of the vehicle 2 as measured by the rotary speed of the wheels. With the aid of a single-track model, it is furthermore possible to calculate an effective velocity v.sub.y,ESM for the transverse axis of the motor vehicle from the steering angle .sub.steer and the measured velocity v.sub.vehicle. For the vertical velocity v.sub.plane,z no other measurement or calculation method is available. The alternatively determined second planar velocity of the vehicle (14):
{right arrow over (v.sub.alt)}=[v.sub.Vehicle,v.sub.y,ESM,0].sup.T(14)

(50) and the velocity {right arrow over (v.sub.Int)} calculated by integration (13) can be merged by a suitable filter algorithm, such as a Kalman filter (15), by a computational procedure including a weighting factor :
{right arrow over (v.sub.Plane)}={right arrow over (v.sub.Int)}+(1){right arrow over (v.sub.alt)} with 01(15)

(51) In a fourth step 46 for the correction of the planar velocity change, values of the measured velocity v.sub.vehicle, the steering angle .sub.steer, the angles .sub.a, .sub.a and the acceleration {right arrow over (a)}{right arrow over (a.sub.zf)} corrected by the centrifugal acceleration {right arrow over (a.sub.zf)} are taken into account, the corrected acceleration being corrected by the component of the change in the planar velocity {right arrow over (a.sub.vp,alt)}=R {right arrow over ({dot over (v)}.sub.alt)}. In order to avoid a negative feedback, the derivation of a vector of the velocity {right arrow over (v.sub.alt)} is used instead of the velocity {right arrow over (v.sub.Plane)} determined according to the computational procedure (15).

(52) In a fifth step 48, taking into account the rate of rotation {right arrow over ()} and the gravitational acceleration {right arrow over (a.sub.gv)} of the vehicle 2, the pitch angle .sub.a as well as the roll angle .sub.a and thus the inclination or position of the vehicle body 6 of the vehicle 2 are calculated with the above-described quaternion-based inclination filter. With the above-described procedure, the pitch angle .sub.a and the roll angle .sub.a are determined in terms of the inertial coordinate system 28 and used in a closed feedback control circuit for the correction of the gravitational force in the second step 42 and for the correction of the planer velocity change in the third step.

(53) Starting from the inclination of the vehicle body 6 as determined in the fifth step 48, the slope and thus the position of the road 4 is determined, wherein the distances {right arrow over (dz.sub.a)}=[dz.sub.a,VL, dz.sub.a,VR, dz.sub.a,HL, dz.sub.a,HR].sup. between the wheels 8, 10 and the vehicle body 6 are used as measured variables, thus calculating at first the pitch angle .sub.f and the roll angle .sub.f of the chassis of the vehicle 2, the calculation being carried out in dependence one transformation matrix (18):

(54) $\begin{array}{cc}T=\left[\begin{array}{cccc}{t}_v& -t_v& t_h& -t_h\\ l_v& l_v& -l_h& -l_h\end{array}\right]& \left(16\right)\end{array}$

(55) with which a geometrical position of the center of gravity 25 is described in terms of the positions of the wheels 8, 10. The first column here describes the distance of the left front wheel 8, the second column the distance of the right front wheel, the third column the distance of the left rear wheel 10 and the fourth column the distance of the right rear wheel from the center of gravity 25 within the horizontal plane.

(56) The inclination of the chassis is then determined through the vectorial relation (17):

(57) 0$\begin{array}{cc}\left[\begin{array}{c}{}_f\\ {}_f\end{array}\right]=T\stackrel{.fwdarw.}{{\mathrm{dz}}_a}& \left(17\right)\end{array}$

(58) By subtracting the inclination of the chassis from the inclination of the vehicle body 6, the slope of the road 4 is calculated in relation to the body-fixed first coordinate system 24 through the vectorial relation (18):

(59) $\begin{array}{cc}\left[\begin{array}{c}{}_a\\ {}_a\end{array}\right]=\left[\begin{array}{c}{}_a\\ {}_a\end{array}\right]-\left[\begin{array}{c}{}_f\\ {}_f\end{array}\right]& \left(18\right)\end{array}$

(60) Since a tire deflection of the wheels 8, 10 is very slight as compared to a spring travel and thus the distance to be taken into account, this is disregarded in the above calculation.

(61) Since the angles .sub.a and .sub.a are vector-related estimated variables for the inclination of the vehicle body 6 and .sub.f and .sub.f describe the relative angles between the vehicle body 6 and the surface of the road 4, with .sub.s and .sub.s we likewise have angles available as estimated variables for the slope of the road 4 or road in terms of the gravitational vector.

(62) In a further embodiment, the method can recognize among other things a steep curve being traveled, involving a curve banked toward an inner side of the vehicle 2, which is used for example at race courses in order to increase the velocity on the curve. Certain feedback control algorithms, however, are not adapted for travel on steep curves, so that a recognition of such curves should be provided.

(63) The above described roll angle .sub.s, ascertained by estimation, indicates how much the road 4 is inclined in the transverse direction of the vehicle 2. If the estimated variable is compared to a threshold value, an indicator (19)

(64) $\begin{array}{cc}{I}_{\mathrm{steep}\mathrm{curve}}=\{\begin{array}{cc}1,& \mathrm{if}.Math.{}_n.Math.{}_{\min ,\mathrm{steep}\mathrm{curve}}\\ 0& \mathrm{otherwise}\end{array}& \left(19\right)\end{array}$

(65) is provided, which takes on the value 1 as soon as the roll angle .sub.s has fallen below a reference value .sub.min,steep curve for the slope of the road 4 in the transverse direction. Furthermore, a feedback control strategy should be adapted to this situation for a chassis stabilization system affected by the steep curve. For example, a leveling control of an air suspension system should be disabled for the duration of traveling along the steep curve, so as not to respond to the increased acceleration in the z spatial direction, only occurring on the steep curve.