FR2834562A1 - Estimation of the lateral acceleration of a motor vehicle, e.g. for preventing gear changes during a corner or for limiting braking power during cornering using a vehicle dynamic behavior model integrated with a Kalman filter - Google Patents

Abstract

Device comprises means (DV) for measuring the angle of rotation (delta) of a motor vehicle steering wheel, first (c1) and second (c2) means for measuring the longitudinal velocity (U) of the vehicle and its yaw velocity, and means (c4, c5) used in conjunction with the prior means to calculate the vehicle lateral acceleration (ay). Said acceleration calculation means include a Kalman filter (c4) integrating a vehicle dynamic behavior model. The invention also relates to a corresponding method.

Description

<Desc / Clms Page number 1>

 The present invention relates to a method for estimating the lateral acceleration of a motor vehicle and to a device for implementing this method.

 Knowledge of instantaneous lateral acceleration experienced by a motor vehicle is necessary in many applications. Thus, for example, the French patent No. 2,772,703 filed in the name of the applicant describes a method of controlling the braking pressure during a cornering braking, which limits the pressure of the brake fluid. which acts on the front wheel of the vehicle placed inside the turn, this control method involving a measurement of the lateral acceleration of the vehicle.

 Thus again, in a vehicle equipped with an automatic gearbox, it is necessary to prevent a gear change during a turn. The presence of the vehicle in a turn can be detected by the fact that the lateral acceleration experienced by the vehicle is then non-zero, and then prohibit any change of ratio.

 The presence of an accelerometer sensitive to the lateral acceleration of the vehicle obviously strike the price of this vehicle. This results in a need for means for estimating this lateral acceleration that would make it possible to dispense with this accelerometer.

 The need for such estimation means appears even when it is not envisaged to dispense with a "hardware" accelerometer in the vehicle, to allow the detection of a drift of the signal emitted by the accelerometer. or even a failure of it, for example.

 The present invention therefore aims to provide a method and a device for estimating the lateral acceleration experienced by a motor vehicle, both to enable the economy of a "hardware" accelerometer to control the good operation.

<Desc / Clms Page number 2>

 Another object of the present invention is to provide such a method which economically exploits measurements available for other purposes in a motor vehicle, such as measuring the angle of rotation of the steering wheel of the vehicle (used in the servo-steering devices) or measurements of the rotational speeds of the vehicle wheels (used in the anti-lock devices of the wheels).

 The present invention also aims to provide a device for implementing this method.

 These aims of the invention are attained, as well as others which will appear on reading the following description with a method for estimating the lateral acceleration of a motor vehicle, which is remarkable in that model of dynamic behavior of the vehicle, integrated with a Kalman filter whose inputs are the angle of rotation of the steering wheel, the longitudinal speed and the yaw rate of said vehicle and in that said estimate of the acceleration is calculated by means of said filter, a measurement of said steering wheel rotation angle and estimates of said longitudinal and yaw velocities.

 As will be seen below in detail, this method makes it possible to estimate accurately the lateral acceleration of the vehicle, using software means and measurements already available in the vehicle for other purposes, which makes it a particularly economical estimation method.

 According to other characteristics of the present invention: the longitudinal velocity of the vehicle is estimated by calculating the arithmetic mean of the tangential velocities of two non-driven wheels of the same axle of the vehicle, the yaw rate is estimated by means of of the relation r = (u22-U21) / b where U21 and U22 are the tangential velocities

<Desc / Clms Page number 3>

 of the wheels of said axle and b the distance separating these two wheels, - the tangential velocities of the wheels are calculated from measurements of the rotational speeds of the wheels and corrected by at least one of the corrections of the group formed by: a noise filtering , a static drift correction, a gain drift correction, - the estimate of the yaw rate is overestimated, - the Kalman filter delivers estimates of the drift angles of tires fitted to the tires. vehicle wheels, these estimates being used to deliver said estimate of the lateral acceleration of the vehicle.

 The device according to the invention comprises a) means for measuring the angle of rotation of the steering wheel of the vehicle, b) first and second means for estimating the longitudinal speed and the yaw rate of the vehicle respectively, and c) means fed by said measuring and estimating means for calculating an estimate of said lateral acceleration of the vehicle, said calculating means comprising a Kalman filter incorporating a model of dynamic behavior of the vehicle.

 Other features and advantages of the present invention will appear on reading the following description and on examining the appended drawing in which: FIG. 1 schematically represents a motor vehicle equipped with the device according to the invention and, Fig. 2 is a block diagram of the portion of the device of Fig. 1 which comprises a Kalman filter.

 Referring to Figure 1 of the accompanying drawing which shows schematically the two front wheels Ru and R12 conducted and the two rear wheels Ii R22 not driven of a motor vehicle powered, for example, by an internal combustion engine

<Desc / Clms Page number 4>

 (not shown) All the wheels of the vehicle are conventionally equipped with tires.

où r2l et r22 sont les rayons dynamiques, supposés constants, des pneumatiques équipant les roues R21, R22 respectivement. The two rear wheels R 1 and R 22 are associated with detectors D 21, D 22, respectively, which are sensitive to their angular rotation speeds iy 21, (J) 22 respectively. The detectors D21 and D22 deliver signals representative of the tangential velocities u21, U22 of the wheels Ri and R22, calculated by the relationships:

where r2l and r22 are the dynamic rays, assumed to be constant, of tires fitted to the wheels R21, R22 respectively.

représentatif de l'angle de rotation du volant 5. The vehicle also includes a steering wheel Vo associated with a detector Dy delivering a signal

representative of the angle of rotation of the steering wheel 5.

The signals representative of this angle 8 and tangential velocities Usi and U22 are digitized and delivered to a computer C which constitutes the heart of the estimation device according to the invention.

délivrées par les blocs C2 et C3 respectivement. En sortie, A ce filtre produit un vecteur d'état estimé x, défini dans As represented in FIG. 1, this computer C comprises several functional blocks: a block C1 comprising means for correcting the tangential velocities of wheels Usai, U22, blocks C2 and C3 constituting first and second means of estimating the longitudinal velocity U and the yaw rate r of the vehicle respectively, the blocks C2 and C3 receiving the tangential velocity measurements u21 and U22 after correction thereof in the block Ci, - a block C4 comprising a Kalman filter receiving in entry angle 8 of rotation of the Vo steering wheel and estimates of longitudinal velocity U and yaw rate r

delivered by blocks C2 and C3 respectively. At output, at this filter produces an estimated state vector x, defined in

<Desc / Clms Page number 5>

la suite de la présente description, à un bloc C5 exécutant une fonction de sortie Coût propre à tirer du vecteur d'état A x l'estimation recherchée ay de l'accélération latérale du véhicule. La fonction Coût sera également définie dans la suite.

As a result of the present description, to a block C5 executing an output function Cost proper to draw from the state vector A x the desired estimate ay of the lateral acceleration of the vehicle. The Cost function will also be defined later.

 As is well known, it is recalled that the yaw rate mentioned above is the angular velocity of the body of the vehicle about an axis passing through its center of gravity G and perpendicular to the mean plane of the vehicle frame.

 We also know that a Kalman filter is used to observe the behavior of a physical system, in this case a motor vehicle, by comparing the behavior of this system with that of a mathematical model of this behavior, operating in parallel with the system. We define in the following the structure of this model, which uses the 8, U and r measurements observed on the system.

Before proceeding with this description, it is specified below how the speeds U 21, Us 2 are measured and how, according to the invention, the values of U and r delivered to the Kalman filter are derived from them.

As seen above, the measurements Uni and U22 undergo first in the block Ci various corrections: - a noise filtering, for example using a second-order Butterworth low-pass filter, a static drift correction. This correction can be made, for example, by measuring U2I, U22, while the vehicle is at rest, for a certain period of time. The average values of U2I, one during this rest period, are then determined to subtract these averages from the future measurement signals, a gain drift correction, this drift being a proportional error affecting the speed measurements, resulting from variations in the "dynamic" radius

<Desc / Clms Page number 6>

 pneumatic tires equipping the corresponding wheels. This error can be corrected by means of a measurement of the angle of rotation of the steering wheel, a correction to avoid, in the block C3, an overestimation of the yaw rate r. This overestimation is due to a variation of the spokes of the tires under the effect of a displacement of the center of gravity G of the vehicle towards the outside of the trajectory of the vehicle, a variation all the more noticeable that the lateral acceleration is high.

où b est la distance, ou"voie", séparant les plans moyens des roues R21 et R (voir figure 1). In block C2 we estimate this yaw rate r using the formula:

where b is the distance, or "track", separating the average planes of the wheels R21 and R (see Figure 1).

In the block C3 the longitudinal velocity U of the vehicle is estimated, along the longitudinal axis thereof, with the aid of the relation:

It will be noted that the estimates of r and U are advantageously made using the tangential velocities of the rear wheels of the vehicle, not driven, rather than the tangential speeds of the front wheels, carried out. Indeed, these last measurements may be affected by errors due to forward wheel slippage, when significant engine torques are applied to them.

 The estimates of r and U made as above are delivered, with the measurement of the "flywheel" angle 8, to block C4 constituted by a Kalman filter (shown in more detail in FIG. 2 of the attached drawing) which constitutes the

<Desc / Clms Page number 7>

 heart means estimation according to the invention, the instantaneous acceleration ay of the vehicle.

de passer dans un bloc Z-1 (l'opérateur retard) qui délivre ^ un vecteur d'état estimé X au bloc C5 où la fonction Coût appliquée à ce vecteur produit une estimation ay de l'accélération latérale recherchée. As shown in FIG. 2, the Kalman filter (block C4) conventionally comprises a plurality of processing sub-blocks of the values of r, 8 and U. Sub-blocks r and K deal with 8 and r, respectively, the outputs of these subblocks being summed and the resulting sum adding itself to the output of a block # -KC before

to pass in a block Z-1 (the delay operator) which delivers ^ an estimated state vector X to the block C5 where the Cost function applied to this vector produces an estimate ay of the lateral acceleration sought.

 (b, r, C and Cost are, in fact, matrices defining a fourth-order model of the dynamic behavior of the vehicle, in turns, established as follows, K being a gain matrix.

où : - mv est la masse du véhicule, - v la dérivée de la vitesse latérale, - FY1'Fy2 les forces latérales développées par les pneumatiques des essieux avant et arrière du véhicule, respectivement (voir figure 1), - Iz le moment d'inertie du véhicule par rapport à l'axe perpendiculaire au plan moyen du châssis du véhicule et passant par le centre de gravité G, li, li les distances des essieux avant et arrière respectivement, au centre de gravité G. Newton's second law and Euler's law are applied to the lateral movements of the vehicle, which gives:

where: - mv is the mass of the vehicle, - v the derivative of the lateral speed, - FY1'Fy2 the lateral forces developed by the tires of the front and rear axles of the vehicle, respectively (see figure 1), - Iz the moment of the inertia of the vehicle relative to the axis perpendicular to the mean plane of the vehicle chassis and passing through the center of gravity G, li, li the distances of the front and rear axles respectively, at the center of gravity G.

<Desc / Clms Page number 8>

 Side forces are particularly important when the vehicle turns at a high speed. In this situation, it can be seen that the direction of movement of the tires is different from that of the wheels carrying them. The difference is called the drift angle.

OÙ Ca1, Ca2 sont les rigidités de dérive des pneumatiques des roues des essieux avant et arrière respectivement. The lateral forces are modeled as linear functions of the angles of drift al'a2 of the tires of the front and rear axles, respectively (see Figure 1) either:

Where Ca1, Ca2 are the drift rigidities of the tires of the front and rear axles respectively.

où - crI, cr2 sont les longueurs de relaxation des pneumatiques avant et arrière, respectivement, et - is le rapport de démultiplication du volant de direction. The equations describing the first-order tire models for front and rear axle tires are respectively:

where - crI, cr2 are the relaxation lengths of the front and rear tires, respectively, and - is the gear ratio of the steering wheel.

L'équation d'état standard s'écrit :

To write the equations of state of the system, one defines a vector of state x whose transpose xT is written:

The standard state equation is written:

<Desc / Clms Page number 9>

où : - A et B sont des matrices, - x représente l'état du système (vitesse latérale v, vitesse de lacet r, angles de dérive ai et (), - u est"l'entrée"du système, soit u=8, On tire les expressions des matrices A et B des équations (1) à (6) ci-dessus, qui donnent :

Q 1 a1 2 (x2 m, m, 0 0-2C,,, Ill 2C,, 212 0 A= z iz B= U 1 Il-u 0 ( : il is 11 U 8= U " -- 0 -- ~ ~'2 0 1 - U 0 - 0

Les équations de sortie du modèle peuvent être choisies en fonction de la ou des variables à estimer, l'accélération latérale ay dans le cas présent. On calcule celle-ci à l'aide d'une combinaison linéaire d'états du système modélisé. L'application de la deuxième loi de Newton donne :

F 2 ay=-=-- (Ca, +C) avec F, =F,, +F mv mv

L'équation d'observation des états du système est :

where: - A and B are matrices, - x represents the state of the system (lateral velocity v, yaw rate r, angles of drift ai and (), - u is the "entry" of the system, ie u = 8, the expressions of matrices A and B are derived from equations (1) to (6) above, which give:

Q 1 a1 2 (x2 m, m, 0 0-2C ,,, Ill 2C ,, 212 0 A = z iz B = U 1 Il-u 0 (: it is 11 U 8 = U "- 0 - ~ ~ '2 0 1 - U 0 - 0

The output equations of the model can be chosen according to the variable (s) to be estimated, the lateral acceleration ay in this case. This is calculated using a linear combination of states of the modeled system. The application of Newton's second law gives:

F 2 ay = - = - (Ca, + C) with F, = F ,, + F mv mv

The observation equation of the states of the system is:

avec D = 0 et

with D = 0 and

<Desc / Clms Page number 10>

The model of behavior of the vehicle, as presented above, is a parameterized continuous model in which only the speed U is variable. The other parameters can, for one part, be measured and, on the other hand, evaluated by tests.

 The problem posed by the temporal variation of the longitudinal velocity U of the vehicle is solved, according to the present invention, as follows. N sets of matrices (A, B) each calculated for one of n particular values of this longitudinal velocity U, distributed regularly over the whole range of variation of the velocity U, and is used in the calculations involving these matrices, the set of matrices corresponding to that of the n particular values of the speed U which is the closest to the estimated instantaneous value of U. The calculator C must then comprise means for storing n different values of the matrix A and as many different values of matrix B.

 The elements of the Cost matrix do not depend on the speed U, which makes it possible to store only one value of this matrix.

 Of course, the higher n is, the more accurate the estimation of the lateral acceleration ay is.

 Finally, the n behavioral models thus stored must be discretized so that they can process, as is usual, sampled measurement signals.

The state equations of a discrete system are given by:

The matrices (D and r) depend on the sampling period h and the matrices A and B according to the following relationships:

<Desc / Clms Page number 11>

< f > = eAh h r-} edsB 0

Par l'approximation de la matrice exponentielle on peut discrétiser un modèle continu, ce qui donne :

C= ! +AT et r ='PB, avec : Ah2 Ah'A'h'A'h' T= ! h±-±-+.... ±--+...

<f> = eAh hr-} edsB 0

By the approximation of the exponential matrix we can discretize a continuous model, which gives:

C =! + AT and r = 'PB, with: Ah2 Ah'A'h'A'h' T =! h ± - ± - + .... ± - + ...

On retrouve ainsi les matrices (D et r du filtre de Kalman classique représenté à la figure 2. 2! 3! (i + 1)!

We thus find the matrices (D and r of the classical Kalman filter represented in FIG.

 With regard to the matrix, if the period h is chosen sufficiently short, for example 1 / 300s, we can keep only the first two terms of the equation giving T.

 The matrix K reflects the importance of the predictable noise.

It makes it possible to ensure the robustness of the estimator constituted by the blocks C4 and C5 with respect to errors on the model (mass mv of the vehicle, drift stiffness Cai, C) with respect to noise on the signals exploited, and therefore of variations in the time of the corresponding characteristics of the vehicle, because the estimator operates in a closed loop.

 If K is a high gain matrix, the estimator response is fast, but it is sensitive to noise on the measurements. If K is a low gain matrix, the estimator behaves as an open loop and is sensitive to model errors.

 The matrix K can be obtained by solving the Riccati equation or by pole placement methods. The development of this matrix aims to establish a

<Desc / Clms Page number 12>

 compromise between robustness and performance, as is well known to those skilled in the art.

 It now appears that the invention makes it possible to achieve the stated objective of providing an estimate of the lateral acceleration of a motor vehicle using software means and measurement of quantities available for other purposes in said vehicle.

 It is thus possible to replace a "hardware" accelerometer designed to measure this lateral acceleration, by the "software" accelerometer according to the present invention.

 Such a replacement is advantageous from the economic point of view. Indeed the cost of development of the necessary software can be very quickly covered in applications with large production volume such as those in the field of automotive construction. In addition, no specific accommodation for this software is expected since this accommodation can be provided by the engine management computer, for example, which is now commonly found in a motor vehicle or, better still , by the anti-lock wheel calculator, which receives measurements of the wheel speeds of the vehicle.

Claims (13)

A method for estimating the lateral acceleration (ay) of a motor vehicle, characterized in that a model of dynamic behavior of the vehicle integrated in a Kalman filter whose inputs are the angle of rotation ( 8) of the steering wheel, the longitudinal speed (U) and the yaw rate (r) of said vehicle and in that said estimate of the lateral acceleration (ay) by means of said filter, of a measurement of said angle of rotation of the flywheel (5) and estimates of said longitudinal (U) and yaw (r) speeds.  2. Method according to claim 1, characterized in that said longitudinal velocity (U) is estimated by calculating the arithmetic mean tangential velocities (usai, U22) of two wheels (R21, R22) not driven by a same axle of the vehicle.  3. Method according to claim 2, characterized in that said yaw rate (r) is estimated by means of the relation r = (uu) / b where U21 and U22 are the tangential velocities of said wheels and b the distance separating these two wheels.  4. Method according to claim 3, characterized in that the estimate of the yaw rate (r) is subject to overestimation correction.  5. Method according to any one of claims 2 to 4, characterized in that said tangential velocities (U21, U22) are calculated from measurements of rotational speeds (co2i / 22) of said wheels and corrected by one of at least corrections of the group formed by: noise filtering, static drift correction, gain drift correction.  6. Process according to any one of claims 1 to 5, characterized in that said filter of <Desc / Clms Page number 14>  Kalman delivers estimates of the drift angles (a1, a2) of tires fitted to the wheels of said vehicle, said estimates being used to deliver said estimate of the lateral acceleration of the vehicle.  7. Method according to claim 6, characterized in that said model of vehicle behavior is discretized and comprises a set of matrices (A, B, C), in that n sets of matrices (A, B) are available. ) each calculated for one of n particular values of the longitudinal velocity (U) of the vehicle, distributed over the entire range of variation of said velocity (U), and in that the calculations are used for the whole ( A, B) of matrices corresponding to said particular value of the longitudinal velocity (U) which is adapted to the estimated instantaneous value of said longitudinal velocity.  8. Device for carrying out the method according to any one of claims 1 to 7, characterized in that it comprises: a) measuring means (Dv) of the rotation angle (8) of the steering wheel for steering the vehicle, b) first (and second) means (C2) for estimating the longitudinal speed (U) and the yaw rate (r) of said vehicle respectively, and c) means (C4, c fed by said measuring and estimating means for calculating an estimate of said lateral acceleration of the vehicle, said calculating means comprising a Kalman filter (C4) incorporating a model of dynamic behavior of the vehicle.  9. Device according to claim 8, characterized in that it comprises measuring means (D21, D22) tangential speeds (U21, U22) of two non-driven wheels (R21, R22) of the same axle of the vehicle , said first estimating means (Ci) calculating the arithmetic mean <Desc / Clms Page number 15>  of these speeds, identified with said estimated longitudinal velocity (U) of the vehicle.  10. Device according to claim 9, characterized in that said second estimation means (C3) calculate said yaw rate (r) from the relation r = (u22-U21) / b where b is the distance separating said wheels (R21, R) not driven.  11. Device according to claim 10, characterized in that it comprises means (ci) for providing overestimation correction of the yaw rate (r) calculated by said second estimating means.  12. Device according to any one of claims 9 to 11, characterized in that it comprises means (ci) for applying to the measured wheel speeds (uni U22) at least one group correction formed by: a filtering of noise, a static drift correction, a gain drift correction.  13. Device according to any one of claims 8 to 12, characterized in that it comprises

 means (Cost) for calculating said estimated lateral acceleration (ay), from drift angles (0. 1, 02) of tires fitted to the front and rear wheels of the vehicle respectively, the values of said angles being delivered by said tire filter; Kalman (C4).