GB2257551A

GB2257551A - Determination of a parameter of motion of a vehicle

Info

Publication number: GB2257551A
Application number: GB9214655A
Authority: GB
Inventors: Chi-Thuan Cao; Thorsten Bertram
Original assignee: Robert Bosch GmbH
Current assignee: Robert Bosch GmbH
Priority date: 1991-07-12
Filing date: 1992-07-10
Publication date: 1993-01-13
Anticipated expiration: 2012-07-10
Also published as: JPH05208608A; DE4123053C2; GB2257551B; DE4123053A1; GB9214655D0

Description

2 2 _) 115) 1

-1DESCRIPTION DETERMINATION OF A PARAMETER OF MOTION OF A VEHICLE

The present invention relates to a method for determining at least one motion parameter of a vehicle and in particular, but not exclusively, parameters such as the yaw velocity, transverse velocity, slip angle, etc.

The yaw velocity,&; and/or the lateral velocity VY in the vehicle as well as the slip angle a and the lateral force F y can only be measured with difficulty or by means of expensive sensors. It is known from an earlier patent application P 40 30 635.4 to determine the slip angle by means of an expensive yaw sensor.

These parameters, however, play an important role when controlling the chassis.

As illustrated in Fig.1, the tyre dynamics in previous considerations are approximated by means of a linear equation with the constant parameter C.:

fy = Ca 0 a (1) This formula is valid only for very small slip angles.

As the slip angle increases, the actual lateral force and the approximate lateral force are no longer identical.

It is therefore an object of the invention first to provide a formula for the lateral force F y which 11 -2covers the entire range of slip. By means of this formula, a technically achievable method is then found which determines initially the yaw velocity and the lateral velocity VY and finally the slip angle a and the lateral forces F y on-line from the parameters 6v, 6h, forward lateral acceleration ayv, rearward lateral acceleration ayh by means of a combination of adaptive equivalent Kalman filters.

In accordance with the present invention a method for determining at least one parameter of motion is provided (for example lateral velocity vy.. yaw velocity,ez7, floating angle A, slip angle av, ah and lateral forces Fyv, Fyh) of a vehicle, wherein the parameter for lateral acceleration a YV is determined forward of the centre of gravity and the parameter for lateral acceleration ayh rearward of the centre of gravity, and these lateral accelerations are applied in the form of an addition (ayv + ayh) to parallel two first adaptive equivalent Kalman filters (first filter pair) and in the form of a difference (ayh- ayh) to parallel two further adaptive equivalent identically constructed Kalman filters (second filter pair), one filter of each filter pair (AkF) is designed in such a way, that it is approximately equal to the lateral forces F y of the tyres in accordance with the stipulation of the regression 1 F y = ca 0 a r with the slip angle a and Ca constant, and wherein the other expanded filter (E-AkF) of each filter pair is designed in such a way that it is approximately equal to the lateral forces F y of the tyres in accordance with the stipulation of the equation FY = ky (a) 0 a + hy (a) and ky (a) and hy (a) are variables dependent on slip angle a, that from the estimate values, provided by the filters in each filter pair, of the' starting quantities, the subtraction is formed and the two functions g(hyv; hyh) and h(hyv; hyh) are obtained, and these are determined from the system of equations, which is therefore available, with two unknowns hyv and hyh and plus the fact that at least one quantity of the following quantities kyvr kyh and vy is taken as an estimated value from the last mentioned filter (E-AkF) and, if necessary, other quantities of motion (such as e.g. the floating angle P, the slip angle av, ah and the lateral forces Fyv/ Fyh) are reconstructed from these values.

With the invention, the lateral accelerations of the vehicle in front of and behind the centre of gravity and the steering angle of the two axles are measured using inexpensive sensors whereby the rear axle steering angle can also be 0 (without rear axle steering). When using the method in accordance with -4the invention, the lateral velocity and the yaw velocity are deducted first, from which it is then possible to deduce in a simple manner the slip angle a, the tyre forces F y and the floating angle P.

The invention will be described further hereinafter, by way of example only, with reference to the accompanying drawings, in which:- Fig.1 is a graph illustrating the tyre dynamics of the prior art;

Fig.2 is a graph illustrating the tyre dynamics of one embodiment of the present invention; and Fig.3 is a partial schematic view of an arrangement for estimating in accordance with the method of the present invention.

The formula as illustrated in Fig.2, implies that the tyre dynamics can be described by a linear formula F y (a) = K y (a) a a + h y (a) (2) with the variable parameters k y (a) and hy(a).

A comparison with the formula (1) shows that - the range of slip can be described in full and - the behaviour of the tyres is described realistically by means of the different parameters ky(a) and hy(a) in dependence upon the slip angle a.

The problem is to determine these parameters using simple means. This is achieved by the arrangement illustrated in Fig.3. If the values for the slip angle a and the variable parameters ky(a) and h y (a) are available, then the lateral force F y can be calculated simply from (2). It is technically possible to achieve this with an estimator as illustrated in Fig.3. The parameters ky, h y and a are estimated as follows:- The starting parameters of the estimator are the lateral acceleration ayv measured in front of the centre of gravity, the lateral acceleration ayh measured behind the centre of gravity, the steering angle in front of 6V and the steering angle behind 6h,' which are required later.

The lateral accelerations are aggregated once as an addition (Fig.3, upper loop) and again as a subtraction (Fig.3, lower loop) (Blocks 1 and 2) and processed in this way. The entire structure of the estimator is divided in this way into two sub-systems and the sub-systems contain identical structures and only differ in the starting parameters. Subsequently, therefore, only one sub-system is to be examined.

The sub-system comprises two adaptive equivalent Kalman filters 3 and 4, and the filter 3 is approximately equal to the lateral force in accordance with equation (1) and the second expanded filter 4 (E-) describes the lateral force by means of equation -6(2). Each filter supplies an "Estimated value of the starting parameter". By subtracting the two estimated values (Subtraction 5), a function g (hyvr hyh) is obtained in the upper sub-system and a function h(hyvi, hyh) in the lower sub-system of hyv and hyh In this way, there is a resolvable system of equations with two equations and two unknowns (Block 6). Plus the fact that the estimation with the filter 4 provides the parameter kyv(a) and kyh(O0 from the regressions kyv(a) = Ln 0 Pull and kyh = M P u12 2 2 It is therefore possible with the invention to determine explicitly the parameters kyvf kyh, h YV and hyh. From the parameter vector of the filter 4, it is possible to reconstruct the variables of state, the lateral velocity VY and the yaw rate. From these two quantities of motion, in accordance with the following regression cfv(k) = 6V - (vv(k) + w(k) VX h(k) ---Sh - ( vV(k)_- 'h w(k)) v X (3a) (3b) it is possible to calculate the slip angle a, so that now all quantities are available to calculate the lateral forces in accordance with equation (2).

The base equation for AkF is used in filter 3:

k 1 y(k) [y(k-1) y(k-3) 1 ul(k-1) ul(k-2) ul(k-3) 1 u2(k-1) U2(k-2) U2(k-3)l Pyl PY2 Pull PU12 PUI3 Pu21 PU22 Pu23 L_ -.i and y(k) - ay(k) ayv(k): ayh(k) ul(k) - Sv(k) U2(k) - Sh(k) The parameter vector p- - IPY1 PY2 1Pull Pu12 PU13 1 Pu21 PU22 PU23]T can be recursively calculated from the data vector m(k-1) ia(k-I) - [y(k-2) y(k-3) ul(k-1) ul(k-2) ul(k-3) uZ(k-1) u2(k-2) u2(k- 3)]T -and an error e(k) - y(k) - y4(k) - y(k) mT(k-1). 12(k-1) by means of an estimate algorithm A p -(k (k) = p -1) + r(k). e(k), and r(k) with "stochastic approximation" is selected, for example, as follows:

r(k) -- 1 + mT(k-1) in(k-1) m (k- 1) 4 The vector of state:

X = [W v Y iT can then be obtained as follows:

2(k) = M(k-1) A p(k), and the matrices M(k-1) can be read from the data vector M T(k-1) and the parameter vector p(k) from the estimate vector R(k):

M(k-1) y(k-1) y(k-2) ul(k-1) ul(k-2) JU2(k-1) U2(k-2) 0 y(k-1) 1 0 ul(k-1) 0 u2(k-1) p(k) = [p Y 1(k) Py2(k)l pu12(k) Pu13(k) Pu22(k) Pu23(k)l z The base equation for E-AkF is used in filter 4:

y(k) = [y(k-2), y(k-3)l ul(k-1), ul(k-2), ul(k-3)t U2(k-1), U2(k-2), U2(k3)j U3(k-1), U3(k-2), U3(k-3)l pyl PY2 Pull PU12 Pu13 Pu21 PU22 Pu23 Pu31 Pu32 Pu33 L_ i 0 and y(k) = ay(k) = ayv(k) ayh(k)5 ul(k) = Sv(k), u2(k) = 60) und u,l(k) = A'(k) t (P) is a function which can be freely selected.

The parameter vector P- ' [PyI Py2 1Pull Pu12 Pu13 IPU21 Pu22 Pu23 IPU31 Pu32 Pu33]T can be recursively calculated from the data vector m(k-1) m(k-1) = [y(k-2) y(k-3) jul(k-1) ul(k-2) ul(k-3)t U2(k-1) ul(k-2) U2(k-3)l ul(k-1) U3(k-2) ul(k-3)l and the error T e(k) = y(k) - y(k) = y(k) - m (k-1). 11(k-1) by means of an estimate algorithm:

A A 2(k) = p(k-1) + r(k). e(k), and e.g. 2:(k) with "stochastic approximation" is selected as follows:

t !9 r(k) 1 1 + MT(k-1). m(k-1) m The vector of state X = [W VY1T can then be obtained as follows:

4 x(k) = M(k-l-) A p(k), and the matrices M(k-1) can be read from the data vector M T(k-1) and the parameter vector p(k) from the estimate vector p(k):

(k-1) y(k-2) ul(k-1) ul(k-2) U2(k-2) U2(k-2) U3(k-1) ul(k-2) 0 y(k-1) 0 ul(k-1) 0 U2(k-1) 0 ul(k-1)l (k) 1(k) "P4u13(k) 1Pu22(k) p Pu32(k) 33(k)]T PI Py PY2(k) 1Pu12(k) u23(k) 1 PU -12 Other parameters of motion in addition to the slip angle 4rand the lateral velocity VY can be derived from the following:- A p(k) = vy(k) VX av (k) = 6V - A 2h(k) 2 6h - ( v v A A ( vy(k) + lvw(k) 1 v X (k) A - lhco(k) 1 A kyv f a). av + hyv(a) A ky h (0) % + hy h (0) 4 VX: Vehicle velocity Distance centre of gravity front axle 'h: Distance centre of gravity rear axle MF: Vehicle mass 4 11

Claims

1. A method for determining at least one parameter of motion (for example lateral velocity VY.yaw velocity, floating angle P, slip angle av, ah and lateral forces Fyv, Fyh) of a vehicle, wherein the parameter for lateral acceleration a YV is determined forward of the centre of gravity and the parameter for lateral acceleration ayh rearward of the centre of gravity, and these lateral accelerations are applied in the form of an addition (a YV + ayh) to parallel two first adaptive equivalent Kalman filters (first filter pair) and in the form of a difference (ayh- ayh) to parallel two further adaptive equivalent identically constructed Kalman filters (second filter pair), one filter of each filter pair (AkF) is designed in such a way, that it is approximately equal to the lateral forces F y of the tyres in accordance with the stipulation of the regression F y = Ca 0 a, with the slip angle a and Ca constant, and wherein the other expanded filter (E-AkF) of each filter pair is designed in such a way that it is approximately equal to the lateral forces F y of the tyres in accordance with the stipulation of the equation FY = ky (a) a + h y (a) and ky (a) and h y (a) are variables dependent on slip angle a, that from the estimate values, -14 provided by the filters in each filter pair, of the starting quantities, the subtraction is formed and the two functions g(hyv; hyh) and h(hyv; hyh) are obtained, and these are determined from the system of equations, which is therefore available, with two unknowns hyv and hyh and plus the fact that at least one quantity of the following quantities kyv, kyh and 0, vy is taken as an estimated value from the last mentioned filter (E-AkF) and, if necessary, other quantities of motion (such as e.g. the floating angle P, the slip angle av, ah and the lateral forces Fyvi, Fyh) are reconstructed rom, these values.

2. A method substantially as herein described, with reference to, and as illustrated in, the accompanying drawings.

i R A