METHOD FOR DETERMINING VEHICLE DRIVING STATUS VARIABLES WHICH ARE NOT DIRECTLY MEASURABLE

Abstract

A method for determining non-directly measurable driving status variables of a vehicle reads in by a sensor device and transmits to a computing device the following: wheel speed of each vehicle wheel, steering angle of the vehicle, yaw angle rate, longitudinal road inclination of the vehicle, transverse road inclination of the vehicle.

Driving status variables are calculated by the computing device with a computational model, so that further driving variables that are difficult to measure or not directly measurable can be determined on the basis of the calculated driving status variables. The calculated and determined variables are transmitted to an actuator device to control and/or regulate the vehicle. The computational model contains a vehicle model, a tire model, and a wheel suspension model and are solved together in the computing device according to the following differential equation system:

[00001]$\left(M_F+\underset{i=1}{\overset{n?3}{.Math.}}{M}_{\mathrm{Ri}}\right)\stackrel{.fwdarw.}{\stackrel{.}{q}}+\left({\stackrel{.fwdarw.}{k}}_F+\underset{i=1}{\overset{n?3}{.Math.}}{\stackrel{.fwdarw.}{k}}_{\mathrm{Ri}}\right)+\left({\stackrel{.fwdarw.}{b}}_g\underset{i=1}{\overset{n?3}{.Math.}}{\stackrel{.fwdarw.}{b}}_i\right)=\stackrel{.fwdarw.}{0}$

Claims

1. A method (1) for determining driving status variables that are not directly measurable of a vehicle using a control device, wherein the control device has at least one computing device, at least one sensor device, and at least one actuator device, the method comprising: in a first step, reading in, by the sensor device, and transmitting to the computing device the following information: a wheel speed of each vehicle wheel, a steering angle of the vehicle, a yaw angle rate, a longitudinal road inclination of the vehicle and a transverse road inclination of the vehicle; in a subsequent step, calculating driving status variables by the computing device using a computational model, such that further driving variables that are difficult to measure or not directly measurable are determined on the basis of the calculated driving status variables, and in a subsequent step transmitting, by the computing device, the calculated driving status variables and determined driving variables to the actuator device, such that the vehicle is advantageously controlled and/or regulated using the calculated driving variables and determined driving variables wherein the computational model contains a vehicle model (8), a tire model, and a wheel suspension model, which are solved together in the computing device according to the following differential equation system: $\left(M_F+\underset{i=1}{\overset{n?3}{.Math.}}{M}_{Ri}\right)\stackrel{.fwdarw.}{\stackrel{.}{q}}+\left({\stackrel{.fwdarw.}{k}}_F+\underset{i=1}{\overset{n?3}{.Math.}}{\stackrel{.fwdarw.}{k}}_{Ri}\right)+\left({\stackrel{.fwdarw.}{b}}_g+\underset{i=1}{\overset{n?3}{.Math.}}{\stackrel{.fwdarw.}{b}}_i\right)=\stackrel{.fwdarw.}{0}$

2. The method as claimed in claim 1, wherein a coefficient of friction estimator for the tire model is used in the computing device of the computational model, with which an estimated coefficient of friction in the tire model is updated.

3. A device for determining non-directly measurable driving status variables of a vehicle with a control device, wherein the control device has at least one computing device, at least one sensor device, and at least one actuator device, wherein the computing device carries out the method according to claim 1.

4. The method as claimed in claim 1, wherein a state vector $\stackrel{.fwdarw.}{q}={\left(\stackrel{?}{x},\stackrel{?}{y},\stackrel{?}{z},\stackrel{?}{?},\stackrel{?}{?},\stackrel{?}{?},{?}_{VL},{?}_{VR},{?}_{HL},{?}_{HL}\right)}^T$ includes in generalized coordinates: speeds {dot over (x)}, , in the direction of the respective axis in an inertial vehicle coordinate system; rotational speeds {dot over (?)}, {dot over (?)}, {dot over (?)} around the z, y, and x axes of the vehicle in a vehicle-fixed coordinate system; and wheel rotational speeds ?.sub.VL, ?.sub.VR, ?.sub.HL, ?.sub.HR front left, front right, rear left and rear right around the y-axis of the vehicle.

5. The method according to claim 1, wherein the computational model includes a multi-body model with five bodies, modeling of wheel suspensions, and full-fledged tire modeling.

6. The method according to claim 1, wherein the vehicle model is a ten-degree of freedom vehicle model.

7. The method according to claim 1, wherein the method locks one degree of freedom of the vehicle model and four degrees of freedom of the wheels, and adopts these as an input for the computational model.

8. The method according to claim 7, wherein a vehicle bus receives the input and connects the computing device, the sensor device, and the actuator device to each other for signal transmission, wherein the method includes generating wheel torques and yaw torque as output variables.

9. The method according to claim 1, wherein the further driving variables that are difficult to measure or not directly measurable comprise at least one of: a vehicle reference speed over ground; a float angle of the vehicle; a roll rate and roll angle of the vehicle; a pitch rate and pitch angle of the vehicle; wheel loads of the wheels; transmitted wheel forces and wheel torques; a yaw moment of the vehicle; a coefficient of friction of the road on which the vehicle is travelling; or a slip angle on the wheels of the vehicle.

10. The method according to claim 1, wherein the wheel suspension model models the wheel suspensions as a vertical spring and a vertical damper for each wheel of the vehicle.

11. The method according to claim 10, wherein in the wheel suspension model, the following force elements are used per vehicle wheel: a spring with constant stiffness or the spring characteristic curve thereof; a damper with constant damping or the damping curve thereof; and a stabilizer bar with constant torsional rigidity.

12. The method as claimed in claim 2, wherein the coefficient of friction estimator compares the lateral and longitudinal accelerations of the vehicle measured and possibly transmitted via the vehicle bus with the respective accelerations calculated by the computational model and returns them as a weighted difference back to the tire model to update the coefficient of friction within the tire model.

13. The method as claimed in claim 1, wherein the suspension model and the tire model are downstream of the vehicle model, and the outputs of the suspension model and the tire model influence the vehicle model in a feedback manner.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0058] The drawings described herein are for illustrative purposes only of selected embodiments and not all possible implementations, and are not intended to limit the scope of the present disclosure.

[0059] In the following, schematic diagrams show exemplary embodiments of the invention. In the figures:

[0060] FIG. 1 shows a method and a computational model in the form of a block diagram,

[0061] FIG. 2 shows a possible assignment of the parameters of the computational model and

[0062] FIG. 3 shows a possible definition of the axes used by the method and in the computational model according to Schramm, Hiller and Bardini (D. Schramm, M. Hiller and R. Bardini, Modellbildung und Simulation der dynamik von Kraftfahrzeugen. Berlin, Heidelberg: Springer Berlin Heidelberg, 2018).

DETAILED DESCRIPTION

[0063] FIGS. 1 to 3 show a method 1 according to the invention for the determination of non-directly measurable driving status variables 2 with a computing device 3, wherein the driving status variables 2 are transferred from the computing device 3 to an actuator device 5 via a vehicle bus 4. At the inputs, a sensor device 6 detects the following as input variables 7 [0064] the wheel rotation speeds ?.sub.VL, ?.sub.VR, ?.sub.HL and ?.sub.HR for each vehicle wheel 13 of the vehicle 9, [0065] a steering angle ? on the steered wheels 13, [0066] a yaw rate ?; of the vehicle 9 as a rotational speed about the z-axis [0067] a gradient ? of the road on which the vehicle 9 is travelling, [0068] a transverse inclination ? of the road on which the vehicle 9 is travelling, and [0069] a measured lateral a.sub.lat and longitudinal a.sub.long acceleration of the vehicle 9.

[0070] These input variables are transmitted via the vehicle bus 4 to a ten degree of freedom vehicle model 8 for describing the dynamic behavior of the vehicle body of the vehicle 9, wherein five input variables 7 superimpose a total of five entries of a state vector {dot over ({right arrow over (q)})} of the vehicle model 8 and thus block them. Downstream of the vehicle model 8 are a suspension model 10 and a tire model 11, but these models react on the vehicle model 8 with their output variables 12 and thus influence it in a feedback manner.

[0071] The suspension model 10 is a modelling of the wheel suspensions as a vertical spring and vertical damper for each vehicle wheel 13 of the vehicle 9, wherein the wheels 13 are assumed to be standing horizontally on the road, the vehicle body is assumed to carry out roll and pitch movements, and a deflection in the direction of a z-axis is assumed. The following force elements are used for each vehicle wheel x: [0072] a spring with a constant stiffness or the spring characteristic curve thereof, [0073] a damper with a constant damping or the damping characteristic curve thereof, and [0074] a stabilizer bar with a constant torsional rigidity.

[0075] The tire model 11 is an approximation of the tire behavior including a coefficient of friction dependence, a longitudinal and lateral force characteristic, a degressive influence of the wheel load and a combined tire behavior. The coefficient of friction estimator 14 compares the measured accelerations with the acceleration calculated by the method 1 and feeds a weighted difference back to the tire model 11, which can adjust and update its coefficient of friction 15 within the model.

[0076] Below, the notation is as follows:

[00004]${\stackrel{.fwdarw.}{\stackrel{.}{r}}}_i^{n,T,k}$ [0077] r stands for a vector or a bold matrix or tensor. [0078] the dot above the r stands for the first derivative against time. [0079] the arrow above the dot above r stands for a vector. [0080] n stands for potency. [0081] T stands for a transposed representation of r. [0082] k stands for the respective coordinate system. [0083] i stands for the respective selection of the component of the vehicle.

[0084] In the following, the computational model according to the invention is shown parametrized using FIGS. 2 and 3. The 10?10 mass matrix M.sub.F=(M.sub.zs) with z=s?{1, . . . , 10} includes the following non-zero entries:

[00005]$\begin{array}{c}{m}_{11}=m_F{\cos }^{-2}\left(?\right)\\ m_{12}=-m_F\tan \left(?\right)\tan \left(?\right){\cos }^{-1}\left(?\right)\\ m_{13}=-m_F\tan \left(?\right)\\ m_{15}=m_F{z}_{\mathrm{dyn}}\cos \left(?\right){\cos }^{-1}\left(?\right)\\ m_{16}=m_F{z}_{\mathrm{dyn}}\cos \left(?\right)\sin \left(?\right){\cos }^{-1}\left(?\right)\\ m_{21}=-m_F\tan \left(?\right)\tan \left(?\right){\cos }^{-1}\left(?\right)\\ m_{22}=m_F+m_F{\tan }^2\left(?\right){\cos }^{-2}\left(?\right)\\ m_{23}=m_F\tan \left(?\right){\cos }^{-1}\left(?\right)\\ m_{25}=m_F{z}_{\mathrm{dyn}}\left(\sin \left(?\right){\cos }^{-1}\left(?\right)-\cos \left(?\right)\tan \left(?\right)\tan \left(?\right)\right)\\ m_{26}=m_F{z}_{\mathrm{dyn}}\cos \left(?\right)\left(\cos \left(?\right){\cos }^{-1}\left(?\right)+\sin \left(?\right)\tan \left(?\right)\tan \left(?\right)\right)\\ m_{31}=-m_F\tan \left(?\right)\\ m_{32}=m_F\tan \left(?\right){\cos }^{-1}\left(?\right)\\ m_{33}=m_F\\ m_{35}=m_F{z}_{\mathrm{dyn}}\left(-\cos \left(?\right)\sin \left(?\right)+\sin \left(?\right)\cos \left(?\right)\sin \left(?\right)\right)\\ m_{36}=-m_F{z}_{\mathrm{dyn}}\cos \left(?\right)\left(\sin \left(?\right)\sin \left(?\right)+\cos \left(?\right)\cos \left(?\right)\sin \left(?\right)\right)\\ m_{44}=0.25\left(2{?}_{{\mathrm{SF}}_{\mathrm{xx}}}^F+{?}_{{\mathrm{SF}}_{\mathrm{yy}}}^F+{?}_{{\mathrm{SF}}_{\mathrm{zz}}}^F+2\cos \left(?\right)\left(-2{?}_{{\mathrm{SF}}_{\mathrm{xx}}}^F+{?}_{{\mathrm{SF}}_{\mathrm{yy}}}^F+{?}_{{\mathrm{SF}}_{\mathrm{zz}}}^F\right)+2{\cos }^2\left(?\right)\cos \left(2?\right)\left(-2{?}_{{\mathrm{SF}}_{\mathrm{yy}}}^F+{?}_{{\mathrm{SF}}_{\mathrm{zz}}}^F\right)\right)\\ m_{45}=m_{54}=\left({?}_{{\mathrm{SF}}_{\mathrm{yy}}}^F-{?}_{{\mathrm{SF}}_{\mathrm{zz}}}^F\right)\cos \left(?\right)\sin \left(?\right)\cos \left(?\right)\\ m_{46}=-{?}_{{\mathrm{SF}}_{\mathrm{xx}}}^F\sin \left(?\right)\\ m_{55}=0.5\left({?}_{{\mathrm{SF}}_{\mathrm{yy}}}^F+{?}_{{\mathrm{SF}}_{\mathrm{zz}}}^F+\cos \left(2?\right)\left({?}_{{\mathrm{SF}}_{\mathrm{yy}}}^F-{?}_{{\mathrm{SF}}_{\mathrm{zz}}}^F\right)\right)\\ m_{64}=-{?}_{{\mathrm{SF}}_{\mathrm{xx}}}^F\sin \left(?\right)\\ m_{66}={?}_{{\mathrm{SF}}_{\mathrm{xx}}}^F\end{array}$

[0085] The 10?10 mass matrices M.sub.Ri=(m.sub.zs) with z=s?{1, . . . , 10} of the multibody vehicle model include the following non-zero entries:

[00006]$\begin{array}{c}{m}_{24}=m_{42}=m_{R_i}{\cos }^{-1}\left(?\right)(a_i\cos \left(?\right)-b_i\sin \left(?\right)+\tan \left(?\right)\sin \left(?\right)(b_i\cos \left(?\right)+?a_i\sin \left(?\right)))\\ m_{44}=m_{R_i}\left(a_i^2+b_i^2\right)+{?}_{{\mathrm{Si}}_{\mathrm{zz}}}^{\mathrm{Ri}}\left(?\right)\\ m_{21}=-m_{R_i}\tan \left(?\right)\tan \left(?\right){\cos }^{-1}\left(?\right)\\ m_{22}=m_{R_i}\left({\sec }^2\left(?\right){\cos }^{-2}\left(?\right)-{\tan }^2\left(?\right)\right)\\ m_{75}={?}_{{\mathrm{Si}}_{\mathrm{zz}}}^{\mathrm{Ri}}\end{array}$

[0086] The 10?1 gyroscopic force vector {right arrow over (k)}.sub.F=(k.sub.z) with z?{1, . . . , 10} of the vehicle includes the following non-zero entries:

[00007]$\begin{array}{c}{k}_1=-m_F{z}_{\mathrm{dyn}}{\cos }^{-1}\left(?\right)\left(\sin \left(?\right)\stackrel{.}{?}\left(\sin \left(?\right)\stackrel{.}{?}+\stackrel{.}{?}\right)-\cos \left(?\right)\cos \left(?\right)\stackrel{.}{?}\stackrel{.}{?}\right)\\ k_2=m_F{z}_{\mathrm{dyn}}\left(\cos \left(?\right)\left(\sin \left(?\right){\cos }^{-1}\left(?\right)-\cos \left(?\right)\tan \left(?\right)\tan \left(?\right)\right)\stackrel{.}{?}\stackrel{.}{?}+\left(\cos \left(?\right){\cos }^{-1}\left(?\right)+\sin \left(?\right)\tan \left(?\right)\tan \left(?\right)\right)\stackrel{.}{?}\left(\sin \left(?\right)\stackrel{.}{?}+\stackrel{.}{?}\right)\right)\\ k_3=m_F{z}_{\mathrm{dyn}}\left(-\cos \left(?\right)\left(\sin \left(?\right)\cos \left(?\right)+\sin \left(?\right)\cos \left(?\right)\sin \left(?\right)\right)\stackrel{.}{?}\stackrel{.}{?}+\left(\sin \left(?\right)\sin \left(?\right)+\cos \left(?\right)\cos \left(?\right)\sin \left(?\right)\right)\stackrel{.}{?}\left(\sin \left(?\right)\stackrel{.}{?}+\stackrel{.}{?}\right)\right)\\ k_4=0.5\cos \left(?\right)\left(\left({?}_{{\mathrm{SF}}_{\mathrm{yy}}}^F-{?}_{{\mathrm{SF}}_{\mathrm{zz}}}^F\right)\cos \left(?\right)\sin \left(2?\right)\stackrel{.}{?}\stackrel{.}{?}+\stackrel{.}{?}\left(2{?}_{{\mathrm{SF}}_{\mathrm{xx}}}^F\sin \left(?\right)\stackrel{.}{?}+\left(-{?}_{{\mathrm{SF}}_{\mathrm{yy}}}^F-{?}_{{\mathrm{SF}}_{\mathrm{zz}}}^F+\left({?}_{{\mathrm{SF}}_{\mathrm{yy}}}^F-{?}_{{\mathrm{SF}}_{\mathrm{zz}}}^F\right)\cos \left(2?\right)\right)\left(\stackrel{.}{?}+\sin \left(?\right)\stackrel{.}{?}\right)\right)\right)\\ k_5=0.5\cos \left(?\right)\left({?}_{{\mathrm{SF}}_{\mathrm{yy}}}^F+{?}_{{\mathrm{SF}}_{\mathrm{zz}}}^F+\left({?}_{{\mathrm{SF}}_{\mathrm{yy}}}^F-{?}_{{\mathrm{SF}}_{\mathrm{zz}}}^F\right)\cos \left(2?\right)\right)\stackrel{.}{?}\stackrel{.}{?}-\left({?}_{{\mathrm{SF}}_{\mathrm{yy}}}^F-{?}_{{\mathrm{SF}}_{\mathrm{zz}}}^F\right)\sin \left(2?\right)\stackrel{.}{?}\left(\stackrel{.}{?}+\sin \left(?\right)\stackrel{.}{?}\right))\\ k_6=-{?}_{{\mathrm{SF}}_{\mathrm{xx}}}^F\cos \left(?\right)\stackrel{.}{?}\stackrel{.}{?}\end{array}$

[0087] The 10?1 gyroscopic force vectors {right arrow over (k)}.sub.Ri=(k.sub.z) with z?{1, . . . , 10} of the multibody include the following non-zero entries:

[00008]$$\begin{gathered} k_1=m_{R_i}{\cos }^{-1}\left(?\right)\left(b_i\sin \left(?\right)-a_i\cos \left(?\right){\stackrel{.}{?}}^2 \\ {k}_2=m_{R_i}\left({\cos }^{-1}\left(?\right)\left(b_i\cos \left(?\right)+a_i\sin \left(?\right)\right)+b_i\sin \left(?\right)-a_i\cos \left(?\right)\right)\tan \left(?\right)\tan \left(?\right){\stackrel{.}{?}}^2\right) \end{gathered}$$

[0088] The applied 10?1 forces and torques vector {right arrow over (b)}.sub.g=(b.sub.z) with z?{1, . . . , 10} of the vehicle includes the following non-zero entries:

[00009]$\begin{array}{c}{b}_1=-{\cos }^{-1}\left(?\right)F_W\cos \left(?\right)\cos \left(?\right)-g\tan \left(?\right)m_F\\ b_2=g{\cos }^{-1}\left(?\right)m_F\tan \left(?\right)+F_W\cos \left(?\right)\left({\cos }^{-1}\left(?\right)\sin \left(?\right)+\cos \left(?\right)\tan \left(?\right)\tan \left(?\right)\right)\\ b_3=m_F.Math.g+F_W\cos \left(?\right)\cos \left(?\right))\sin \left(?\right)+F_W\cos \left(?\right)\cos \left(?\right))\sin \left(?\right)-\cos \left(?\right)\sin \left(?\right)\sin \left(?\right))\\ b_7=-M_{{\mathrm{AB}}_{\mathrm{VL}}}-M_{R_{\mathrm{VL}}}+F_{G_{\mathrm{VL}}}^{R1}.Math.r_{{\mathrm{dyn}}_{\mathrm{VL}}}\\ b_8=-M_{{\mathrm{AB}}_{\mathrm{VR}}}-M_{R_{\mathrm{VR}}}+F_{G_{\mathrm{VR}}}^{R2}.Math.r_{{\mathrm{dyn}}_{\mathrm{VR}}}\\ b_9=-M_{{\mathrm{AB}}_{\mathrm{HL}}}-M_{R_{\mathrm{HL}}}+F_{G_{\mathrm{HL}}}^{R3}.Math.r_{{\mathrm{dyn}}_{\mathrm{HL}}}\\ b_{10}=-M_{{\mathrm{AB}}_{\mathrm{HR}}}-M_{R_{\mathrm{HR}}}+F_{G_{\mathrm{HR}}}^{R4}.Math.r_{{\mathrm{dyn}}_{\mathrm{HR}}}\end{array}$

[0089] The applied 10?1 forces and torques vectors {right arrow over (b)}.sub.i=(b.sub.z) with z?{1, . . . , 10} of the multiple components include the following non-zero entries:

[00010]$\begin{array}{c}{b}_1={\cos }^{-1}\left(?\right)\left(-F_{G_{\mathrm{ix}}}^{Ri}\cos \left({?}_i+?\right)+g\sin \left(?\right)m_{R_i}+F_{G_{\mathrm{iy}}}^{Ri}\sin \left({?}_i+?\right)\right)\\ b_2={\cos }^{-1}\left(?\right)g\tan \left(?\right)m_{R_{\mathrm{VL}}}+\cos \left({?}_{\mathrm{VL}}+?\right)\left(-{\cos }^{-1}\left(?\right)F_{G_{\mathrm{iy}}}^{Ri}+F_{{\mathrm{Ri}}_{\mathrm{ix}}}\tan \left(?\right)\tan \left(?\right)\right)-\sin \left({?}_i+?\right)\left({\cos }^{-1}\left(?\right)F_{G_{\mathrm{iy}}}^{Ri}+F_{G_{\mathrm{iy}}}^{Ri}\tan \left(?\right)\tan \left(?\right)\right)\\ b_3=-F_{{\mathrm{FD}}_i}^F\cos \left(?\right)\cos \left(?\right)\\ b_4=\left(b_i{F}_{G_{\mathrm{ix}}}^{Ri}-a_i{F}_{G_{\mathrm{iy}}}^{Ri}\right)\cos \left({?}_{\mathrm{VL}}\right)-\left(a_i{F}_{R{i}_{\mathrm{ix}}}+b_i{F}_{G_{\mathrm{iy}}}^{Ri}\right)\sin \left({?}_i\right)+g.Math.m_{R_i}\sin \left(?\right)\left(b_i\cos \left(?\right)+a_i\sin \left(?\right)+\cos \left(?\right)\sin \left(?\right)\left(b_i\sin \left(?\right)-a_i\cos \left(?\right)\right)\right))\\ b_5=F_{{\mathrm{FD}}_i}^F\left(a_i\cos \left(?\right)+b_i\sin \left(?\right)\sin \left(?\right)\right)\\ b_6=-b_i{F}_{{\mathrm{FD}}_i}^F\cos \left(?\right)\cos \left(?\right)\end{array}$

REFERENCE SIGN LIST

[0090] 1. method/block diagram [0091] 2. driving status variables [0092] 3. computing device [0093] 4. vehicle bus [0094] 5. actuator device [0095] 6. sensor device [0096] 7. input variables [0097] 8. vehicle model [0098] 9. vehicle [0099] 10. wheel suspension model [0100] 11. tire model [0101] 12. output variables [0102] 13. vehicle wheel [0103] 14. coefficient of friction estimator [0104] 15. coefficient of friction [0105] 16. vehicle distance in longitudinal vehicle direction a [0106] 17. vehicle distance in lateral vehicle direction b [0107] 18. applied forces {right arrow over (b)} [0108] 19. steering angle ? [0109] 20. spring and damper force F.sub.FD [0110] 21. sliding forces at the wheel contact points F.sub.G [0111] 22. aerodynamic drag force in the vehicle coordinate system F.sub.W [0112] 23. gravitational acceleration g [0113] 24. selection of the component i with wheels 1 to 4 or VL, VR, HL, HR; with the vehicle F or the wheel R [0114] 25. extension of the component i.sub.j by a rotational or translational direction of motion (?F.sub.xx as a rotation about the x-axis or F.sub.VL.sub.x.sup.RI as a movement in the x-axis) [0115] 26. gyroscopic forces {right arrow over (k)} [0116] 27. mass of vehicle body m.sub.F [0117] 28. mass of the wheel m.sub.R [0118] 29. mass matrix M [0119] 30. drive and braking torque M.sub.AB [0120] 31. rolling resistance torque M.sub.R [0121] 32. Generalized coordinates {right arrow over (q)} [0122] 33. location vector {right arrow over (r)} [0123] 34. dynamic tire radius r.sub.dyn [0124] 35. static tire radius r.sub.stat [0125] 36. moment of inertia at center of gravity ?.sub.s [0126] 37. vertical movement of the vehicle body (simplified representation) z.sub.dyn [0127] 38. pitch angle, angle around the vehicle's transverse axis ? [0128] 39. yaw angle, angle around the vehicle's vertical axis ? [0129] 40. roll angle, angle around the vehicle's longitudinal axis ? [0130] 41. wheel rotation speed ? [0131] 42. gradient of the road ? [0132] 43. inclination of the road ?