FR3044994A1 - METHOD FOR DETERMINING A COEFFICIENT VECTOR FOR DETERMINING A BRAKING ANGLE FOR APPLICATION TO WHEELS OF A MOTOR VEHICLE - Google Patents

Abstract

The invention relates to a method for determining a coefficient vector of a proportional corrector (COR) of a driver assistance device fitted to a motor vehicle, said coefficient vector being designed to be multiplied by a vector of state to determine a target steering angle (δ) to be applied for the vehicle to follow a target trajectory. This method comprises: - the determination of several preliminary coefficient vectors each comprising a first coefficient intended to be multiplied by a term of the state vector whose value is not accessible to the driver assistance device, and at least another coefficient provided to be multiplied by a term (r, ΨL, yL) of the state vector whose value is accessible to the driver assistance device, and - the selection of the preliminary coefficient vector for which said first coefficient has the smallest absolute value.

Description

Technical field to which the invention relates

The present invention generally relates to the field of devices and methods for assisting the driving of a motor vehicle.

It relates more particularly to a method for determining a final vector of coefficients of a proportional corrector of a driving aid device equipping a motor vehicle, this final vector of coefficients being designed to be multiplied by a vector of state to determine a target steering angle in which it would be necessary to place a steering member of the motor vehicle for the vehicle to follow a target trajectory.

Technological background

Many motor vehicles today are equipped with a power-assisted steering system that uses an electric motor to exert additional torque on the steering column of the vehicle to assist the driver of that vehicle. to maneuver the steering wheel of the vehicle.

It is also known to equip a motor vehicle with a driver assistance device comprising a front camera, or another sensor such as a radar, for determining a position of this vehicle on a taxiway that he borrows.

When a deviation of the motor vehicle from a target path is detected, or when it is detected that this vehicle is about to exit this lane, the driver assistance device triggers a correction of the trajectory of this vehicle to bring it back to this target trajectory. This target trajectory corresponds for example to the middle of the lane used by the motor vehicle.

For this, a desired steering angle, in which it would be necessary to place the front wheels of the motor vehicle for the latter to follow this target path, is calculated by an electronic control unit of the driver assistance device.

This desired steering angle is calculated based in particular on a lateral deviation of the motor vehicle relative to this target trajectory.

An actuator acting on the steering column of the vehicle is then controlled, depending on the desired steering angle, to correct the trajectory of the motor vehicle.

The patent document filed under the number FR1558107 (but not yet published at the filing date of this patent application) describes a device for correcting the trajectory of a motor vehicle, comprising an electronic control unit adapted to calculate an angle. desired deflection based on: - a lateral deviation between the motor vehicle and a target trajectory, - a heading angle of the motor vehicle with respect to this target trajectory, - a yaw rate of this motor vehicle, and a drift angle of the speed vector of the motor vehicle. The lateral deviation and the heading angle of the motor vehicle with respect to this target trajectory are determined for example by means of an on-board camera at the front of this vehicle and an image processing algorithm associated with this camera.

The yaw rate of the motor vehicle is determined by means of a gyrometer equipping this vehicle. The angle of drift of the speed vector of the motor vehicle is difficult to obtain.

It is explained that it can be estimated by a state observer, following the principles set forth in WO 2005/061305. The disadvantage of this solution is that such a state observer represents an additional computing load for the trajectory correction device.

This angle of drift of the velocity vector could also, alternatively, be determined by means of a Correvit-type sensor from Datron Technology. The disadvantage of this solution is that such a sensor is very expensive and bulky.

Object of the invention

In order to overcome the aforementioned drawbacks of the state of the art, the present invention proposes a method as defined in the introduction, further comprising steps of: a) determining several preliminary coefficient vectors of said proportional corrector, which each comprise a first coefficient expected to be multiplied by a term of the state vector whose value is not accessible to the driver assistance device and at least one other coefficient expected to be multiplied by a term of the state vector whose value is accessible to the driver assistance device, b) selecting the preliminary coefficient vector for which said first coefficient has the smallest absolute value, and c) determining the final coefficient vector of said proportional corrector, wherein each another coefficient is equal to the other corresponding coefficient of the preliminary coefficient vector selected, and wherein said first coefficient is equal to 0. The invention then proposes to find a vector whose coefficients make it possible to better control the dynamics of the motor vehicle and which is such that the first coefficient (that which must be multiplied by the quantity whose value is unknown or at least not accessible to the driver assistance device) is minimum or even zero.

Thus, the proportional corrector, the coefficients of which are determined by the method according to the invention, advantageously takes into account the influence of such a variable on the dynamics of the motor vehicle, without requiring for this purpose the aid device. to conduct, evaluate or measure this variable.

The driver assistance device using this corrector then has improved performance compared to a driver assistance device whose corrector would not take into account the influence of such variables.

The driver assistance device using this corrector is also less expensive than a driver assistance device that would be equipped with a specific sensor to measure this variable difficult to access.

Preferably, each final and preliminary coefficient vector determined during the method according to the invention comprises - said first coefficient, adapted to be multiplied by a term of the state vector which corresponds to a drift angle of a vehicle speed vector. automobile, - a second coefficient, adapted to be multiplied by a term of the state vector which corresponds to a yaw rate of this motor vehicle, - a third coefficient, adapted to be multiplied by a term of the corresponding state vector at a relative heading angle of the motor vehicle with respect to said target trajectory, and - a fourth coefficient adapted to be multiplied by a term of the state vector which corresponds to a lateral deviation between the motor vehicle and said target trajectory.

During the process according to the invention, it is also possible, prior to step b), to eliminate each preliminary coefficient vector which would, after canceling the value of said first coefficient, lead to an unstable evolution of the trajectory tracking. over time. The invention also provides, in a preferred embodiment, at step a), taking into account a stability equation that is representative of the stable or unstable character of the movement of the motor vehicle relative to said target trajectory when the device of driving assistance is active and which involves said coefficients, that the determination of at least one of the preliminary coefficient vectors comprises the following steps: a1) assigning a predetermined value to an unknown intervening in a non-existent term -linear of said stability equation, and a2) determining said preliminary coefficient vector, so that said stability equation is satisfied, taking into account the value assigned to said unknown in step a1).

Fixing the value of the so-called unknown in the non-linear term of this stability equation makes the determination of this preliminary vector of coefficients more efficient and faster, from a numerical point of view, because this makes this equation of stability linear.

Combine this arrangement with the fact of: - determining several preliminary coefficient vectors, each associated with a different value of said unknown, in step a), - then selecting one of these preliminary coefficient vectors, at step b), makes it possible to obtain the final coefficients of this proportional corrector by means of numerical calculations which are advantageously efficient and fast. Other non-limiting and advantageous features of the process according to the invention are the following: this method further comprises a step a3) of determining at least one new preliminary coefficient vector as a function of the preliminary coefficient vector determined at step a2); the steps a1) and a2) being repeated several times, in step a3), sub-steps of a31) elimination are provided, in the set of preliminary coefficient vectors determined in steps a2), from minus one preliminary coefficient vector for which the absolute value of said first coefficient has, among this set of coefficient vectors, the largest value, a32) determining at least one new value of said unknown, from the values of said unknown associated with at least a part of the preliminary coefficient vectors conserved in the sub-step a31), and a33) determining at least one new preliminary coefficient vector, associated with the new value of said unknown determined in the substep a32), this new preliminary vector of coefficients satisfying said equation of stability, taking into account the value of said unknown; in the sub-step a32), the new value of said unknown is obtained by hybridization of at least two values of said unknown each associated with one of the preliminary coefficient vectors conserved in the substep a31); during the sub-step a32), the new value of said unknown is obtained by mutation of at least one value of said unknown associated with one of the preliminary coefficient vectors conserved in the substep a31); and in step a3), the execution of substeps a31), a32) and a33) is reiterated by considering among the preliminary coefficient vectors conserved in substep a31), each new preliminary coefficient vector calculated when performing each preceding substep a33); thus, when the substeps a31), a32) and a33) are executed again, the set of preliminary coefficient vectors considered in step a31) may comprise the preliminary coefficient vectors retained during the previous execution of sub-step a31), as well as each new preliminary coefficient vector calculated during the previous execution of substep a33).

Detailed description of an example of realization

The following description with reference to the accompanying drawings, given by way of non-limiting examples, will make it clear what the invention consists of and how it can be achieved.

In the accompanying drawings: FIG. 1 shows schematically a model of a motor vehicle in the form of a so-called "bicycle model", and FIG. 2 schematically represents, in the form of a block diagram, operations implemented by a device for assisting the driving of a motor vehicle to correct the trajectory of the motor vehicle, one of these operations being performed by means of a proportional corrector whose coefficients are determined by means of a method according to the invention, - Figure 3 shows schematically, in the form of a logic diagram, the main steps of the method according to the invention for determining the coefficients of the proportional corrector of Figure 2, - Figure 4 shows schematically. in more detail, one of the steps in Figure 3.

The method according to the invention, which will be described in detail in the following of this discussion with reference to FIGS. 3 and 4, makes it possible to determine the coefficient values of a proportional corrector COR (FIG. 2), which corrector can then be set implemented in a device for assisting the driving of a motor vehicle for the vehicle to follow a target trajectory 10 located on a taxiway 20 taken by this vehicle.

The determination of these coefficients is based on a mechanical model of the motor vehicle called "bicycle model", described below with reference to Figure 1.

Figure 1 shows a portion of the taxiway 20 taken by the motor vehicle. The target trajectory 10, towards which the motor vehicle is brought when the flight aid device is active, is drawn in dashed lines in FIG.

This target trajectory 10 is for example a trajectory substantially along the middle of the taxiway that borrows the motor vehicle. This target trajectory may, however, deviate substantially from the middle of this lane, particularly at the bends presented by this lane.

As part of this model, the dynamics of the motor vehicle, which can for example be a motor vehicle with two, three or four wheels, is similar to that of a two-wheeled vehicle (a front wheel and a rear wheel).

The following variables (represented graphically in FIG. 1) are then used to describe the dynamics of the motor vehicle with respect to the traffic lane that it follows: lf: distance between the CG center of gravity of the motor vehicle and the front axle of this vehicle; lr: distance between the CG center of gravity of the motor vehicle and the rear axle of this vehicle; 5f: effective steering angle of the front wheels of the motor vehicle, formed between the front wheels of the motor vehicle and a longitudinal axis of the motor vehicle; r: yaw rate of the motor vehicle, that is to say speed of rotation of this vehicle around an axis (ZCg not shown) perpendicular to an average plane of the portion of road on which the vehicle is located and passing by the CG center of gravity of the motor vehicle; (vCg) v: velocity vector of the motor vehicle relative to the traffic lane that it uses, at the center of gravity CG of this vehicle; β: angle of drift of this velocity vector (vCg) v that is to say angle formed between this velocity vector and the longitudinal axis of the motor vehicle; v: speed of the motor vehicle along this longitudinal axis; pref: curvature of the traffic lane 20 (expressed for example in meters at power minus one); and Ψι_: relative heading angle, formed between the longitudinal axis of the vehicle and a tangent Tgte to the target trajectory.

This tangent Tgte to the target trajectory is more precisely a line tangent to the target trajectory at a point Ot of this target trajectory which is defined such that the line passing through this point Ot and the center of gravity CG of the motor vehicle is perpendicular to this tangent Tgte.

When the motor vehicle exactly follows the target trajectory, its center of gravity CG coincides with this point Ot of the target trajectory.

The following variables (represented graphically in FIG. 1) are also used to describe the dynamics of the motor vehicle: yLCG: lateral deviation of the motor vehicle relative to the target trajectory at the center of gravity CG of this vehicle, evaluated perpendicular to the tangent Tgte to the target trajectory; and yL: lateral deviation of the motor vehicle with respect to the target trajectory, evaluated at a sighting distance Is given in front of the motor vehicle.

This lateral deviation yL corresponds more precisely to the distance separating the longitudinal axis of the motor vehicle, which passes through its center of gravity CG, and the tangent Tgte to the target trajectory, this distance being evaluated perpendicularly to the tangent Tgte to the target trajectory , and at the sighting distance Is in front of the motor vehicle.

When the motor vehicle follows exactly the target trajectory, the lateral deviation yL and the relative heading angle Ψι_ are damaged.

On the contrary, the fact that the motor vehicle does not follow the target trajectory results in a non-zero value of the lateral deviation yL and / or by a non-zero value of the relative heading angle Ψ | _.

The dynamics of the motor vehicle also depend on the following variables: m: total mass of the motor vehicle; lz: moment of inertia (expressed for example in Newton.meter) of the motor vehicle with respect to an axis (ZCg) perpendicular to the mean plane of the portion of road on which the motor vehicle is located, and passing through its center of gravity CG;

Cf: drift stiffness of the front wheels (expressed for example in Newton per radian); and cr: rigidity of drift of the rear wheels (expressed for example in Newton per radian).

In the framework of this model, the following hypotheses H1 to H5 are made: H1: The angles β and 5f are sufficiently small to be able to make the following approximations: sin (angle) = angle and cos (angle) "1;

H2: in an orthonormal coordinate system (CG, Xv, Yv, ZCg) whose axis (CG, Xv) is the longitudinal axis of the motor vehicle, the velocity vector (vCg) v is expressed as: (vCg) v = (v, v. (sin β), 0) T "(v, ν.β, 0) T H3: The vehicle is traveling at a constant longitudinal speed v; H4: The lateral contact forces Fyf and Fyr of the front and rear tires are each expressed as the product of the drift af, ar of the corresponding tire, multiplied by the stiffness cf, cr of this tire, ie: Fyf = Cf.af and Fyr = Cr.ar. H5: yL "yLCG + 1s. Ψ, ..

To describe the positioning of the motor vehicle with respect to the target trajectory, a state vector x, defined as follows, is introduced:

The third and fourth components of this state vector x correspond in particular to the relative heading angle Ψ | _ and the lateral deviation yL of the motor vehicle with respect to the target trajectory, which is recalled as being representative whether or not this motor vehicle follows this target trajectory.

Given the hypotheses H1 to H5 above, the evolution of this state vector over time is then described by the equation (E1) below: x = Ax + B5f + Bw pref (E1) la matrix A with

the vectors B and Bw

and the derivative d (x) / dt with respect to the time t of the state vector x being denoted x.

As shown in equation E1 above, the effective steering angle δf of the front wheels of the motor vehicle greatly influences the temporal evolution of the lateral deviation yL of this motor vehicle relative to said target trajectory.

The device for assisting the driving of the motor vehicle, when it is active, makes it possible precisely to control this effective steering angle δf to cancel, or at least reduce, this lateral deviation yL.

This driving assistance device includes, in particular: an image sensor, here a video camera, whose field of vision covers a portion of the traffic lane 20 facing the motor vehicle; a gyrometer adapted to acquire the yaw rate r; and a sensor for determining an effective steering angle δf of a steering member of this motor vehicle.

The driver assistance device also includes an electronic control unit.

This electronic control unit is adapted in particular to determine the lateral deviation yL and the relative heading angle Ψ [_ of the motor vehicle with respect to the target trajectory, by analyzing one or more images acquired by the image sensor. .

This image analysis may comprise, for example, a detection of at least one of the two ground marking lines which delimit the driving lane 20 used by this motor vehicle, followed by a determination of the geometric characteristics of this marking line. , such as its overall shape and its position in the image. The position of the motor vehicle with respect to this marking line, then its position relative to the target trajectory can then be determined on the basis of these geometric characteristics.

Alternatively, the driver assistance device could include a radar or a lidar (according to the acronym of "Light Detection And Ranging"), instead of the image sensor mentioned above. This radar or lidar would also detect objects along this lane, such as a guardrail, a parapet, or a marking line on the ground. The actual steering angle δf of the steering member of the motor vehicle corresponds here to the angle δf formed between the front wheels of the motor vehicle and the longitudinal axis of this motor vehicle.

The sensor for determining this effective steering angle δf is for example mounted on the steering column of this motor vehicle, and adapted to acquire an angular position of the steering column. The effective steering angle δf is then deduced from the angular position of this steering column. As a variant, the actual steering angle δf could, for example, be deduced from a position of the steering rack of this vehicle acquired by means of a sensor mounted on this rack. The electronic control unit of this driver assistance device is also adapted to determine a target steering angle δ in which it would be necessary to place the steering member of the motor vehicle, here the front steering wheels, so that this vehicle follows said target trajectory.

As shown in FIG. 2, this target steering angle δ is determined by means of a proportional corrector COR, as a function of: the lateral deviation yL of the motor vehicle with respect to the target trajectory, the heading angle relative Ψι_ of this vehicle with respect to the target trajectory, and - the yaw rate r of this vehicle.

More precisely, the target steering angle δ is determined by this electronic control unit according to the following equation E2: δ = kfrinal. r + kIjjnLal. Ψι + kjal. yL (E2) The target steering angle δ thus determined is therefore equal to the product (scalar) of a vector of Kfinal coefficients of this proportional corrector COR, multiplied by the state vector x defined previously: δ = Kfinal x where Kfinal = ((kgnal = 0) kfnal k5f kale) (E3)

The vector of Kfinal coefficients is here a line vector (that is to say of dimension 1 x4), while the state vector x is a column vector (that is to say of dimension 4x1).

The values of the components of this Kfinal coefficient vector are determined by means of the method according to the invention described hereinafter. This determination is made during a preliminary development phase, depending on the characteristics of this motor vehicle.

This preliminary phase is for example carried out "offline", that is to say by means of a computer outside the motor vehicle. It can for example be carried out during the design of a motor vehicle model, before this vehicle model is industrialized.

The values of the components of the coefficient vector Kfinal of this proportional corrector COR are intended to be recorded in a memory of the electronic control unit of the vehicle, during the assembly of this vehicle. These values are then used in the operation of this driver assistance device to calculate the target steering angle δ as indicated above (i.e., according to equation E3).

In one embodiment of the invention, it can be provided that the electronic control unit of the driver assistance device is also adapted to control an actuator acting on the orientation of the front steering wheels of the vehicle, so that these wheels reach the target steering angle δ, that is to say, so that the effective steering angle δf reaches the target steering angle δ.

Alternatively, it could have been provided that the electronic control unit is only adapted to display a message in the field of vision of the driver, to indicate to what extent it would be necessary to correct the orientation of the steering wheel to return to the target trajectory.

Here, the actuator used is an electric motor for exerting a correction torque Tc on the steering column of the motor vehicle, in addition to a torque exerted by a driver of the motor vehicle on the steering column of the vehicle. Alternatively, this actuator could act for example on the steering rack of the vehicle, instead of acting on its steering column.

As shown in FIG. 2, this corrective torque Tc is determined by means of a second corrector COR2, called a low-level corrector, as a function, in particular, of the target steering angle δ (determined by the proportional corrector COR), and of the effective steering angle фf.

This corrective torque Tc is for example determined by applying a correction of the PID type (according to the acronym of Proportional, Integral and Derivative) to a difference between this target steering angle δ and the effective steering angle δf of the front wheels of the steering wheel. vehicle.

The method according to the invention, by means of which the Kfinal coefficient vector is determined, can now be described with reference to FIGS. 3 and 4.

According to a particularly remarkable characteristic, this method comprises the following steps (represented in FIG. 3): a) determination of several preliminary coefficient vectors

Kprelim'1, Kprelim'2, Kprelim, N of the proportional corrector COR, which each comprise a first coefficient intended to be multiplied by a term of the state vector x whose value is not accessible to the device for assisting the and at least one further coefficient to be multiplied by a term of the state vector x whose value is accessible to the driver assistance device, b) selection of the preliminary coefficient vector for which said first coefficient has the value absolute minimum, and c) determining the final coefficient vector Kfinal of said proportional corrector COR, wherein each other coefficient is equal to said other corresponding coefficient of the selected preliminary coefficient vector, and wherein said first coefficient is equal to 0.

Certain variables that influence the dynamics of this motor vehicle with respect to the traffic lane that it uses are not accessible or difficult to access in practice for the driving assistance device of this vehicle.

By virtue of the characteristic mentioned above, the coefficients of this proportional corrector COR are determined by taking advantage advantageously of the influence of such a variable on the dynamics of the motor vehicle, without requiring, for this purpose, the aid device to conduct, evaluate or measure this variable difficult to access.

Otherwise formulated, since a value of a variable of the state vector x is unknown, the objective of the method according to the invention will be to find a coefficient vector of this proportional corrector COR (which is recalled that it is expected to be multiplied by the state vector x) whose coefficient which is expected to be multiplied by this unknown variable is the lowest. In this way, when we neglect the influence of this variable to determine the target steering angle δ, the error induced by this negligence will have no influence on the final result.

Here, this variable, which is difficult to access in practice for the driving assistance device of this vehicle, is more precisely the angle of drift β of the velocity vector (vCg) v of the motor vehicle. It is recalled that this drift angle is difficult to obtain, whereas it directly influences the evolution over time of the lateral deviation yL, as shown by the equation El.

Each final coefficient vector Kflnal and preliminary Kprelim · 1, Kprelim'2,

KprelimN more particularly comprises, here: - said first coefficient kpnal, kprehm'1, k | felim'2, ..., kprelim, N (which is recalled that it will be considered equal to 0 in the final coefficient vector Kfinal of proportional corrector COR),

a second coefficient kfnai, tf "· * 1, kr" m'2, ..., kpreiim'N - a third coefficient k $ * Lal, kÿLelim'1, kprLelim'2, ..., kprLeiim'N, and

a fourth coefficient kj ™ ', kp [elim'1, kpfm'2, ..., kp [eiim'N this coefficient vector Kfinal, Kprelim · 1, Kprelim · 2, ..., KprelimN being adapted to be multiplied (scalar) by the state vector x to obtain the target steering angle δ.

Firstly, although the value of the drift angle β is not practically accessible to the driver assistance device, this drift angle β will be considered (temporarily, in order to determine the coefficient vectors Preliminary Kprelim · 1, Kprelim · 2, ..., KprelimN).

During step a) of this determination method, each preliminary coefficient vector Kprelim · 1, Kprelim · 2, ..., Kprelim, N is then determined, here, for the motor vehicle to follow said target trajectory under the action of the driver assistance device (for which it is considered - temporarily - that the angle of drift β is taken into account when determining the target steering angle δ).

More specifically, each preliminary coefficient vector Kprelim'1, Kpre "m 2 2 ^ Kprelim N is determined to enable, during a course correction phase, to reduce the lateral deviation yL of the motor vehicle with respect to said target trajectory while ensuring the following stability conditions: 1. in the absence of disturbance, or if the disturbances gradually diminish, the motor vehicle approaches the target trajectory, and 2. in the presence of disturbances, the lateral deviation yL of the motor vehicle with respect to the target trajectory remains bounded.

For this, each preliminary coefficient vector is determined here as being the solution of a constrained optimization problem, in this case a problem of minimizing the lateral deviation of the motor vehicle relative to the target trajectory, under constraint. in particular the stability conditions indicated above.

This optimization problem is solved here by minimizing the quantity

while checking the following E4 stability equation:

(E4). The equation of stability E4 above is representative of the stable or unstable character of the movement of the motor vehicle with respect to said target trajectory when the driver assistance device (for which it is considered - temporarily - that the angle of drift β is taken into account when determining the target steering angle δ) is active.

The unknowns determined during the resolution of this optimization problem are: Q: matrix with real coefficients of dimension 4x4, defined positive and symmetrical, R = Kprelim'1 Q: vector (line) with real coefficients, dimension 1 x4, and γι and y2: positive real numbers.

The preliminary coefficient vector Kprelim '' (i = 1,2, ..., N) resulting from the resolution of this optimization problem is then calculated according to the following relation:

Kprelim '' = R Q "1

As a variant, the mathematical formulation of this optimization problem could be modified, in particular to take into account other optimization criteria in order, for example, to further minimize the lateral speed of the motor vehicle during a correction phase. trajectory. The equation of stability E4 involves a non-linear term γ-iQ, which makes the numerical resolution of this optimization problem particularly difficult.

In order to overcome this difficulty, it is envisaged, during the above step a), to produce at least one of the preliminary coefficient vectors.

Kprelim'1, Kprelim'2, KprelimN by implementing the following steps: a1) assigning a predetermined value γ \ (i = 1,2, ..., N) to the unknown γι intervening in the non term -linear γ-iQ of the equation of stability E4, and a2) determining the preliminary vector of coefficients Kprelim · '(i = 1,2, ..., N) corresponding, so that said equation of stability E4 is checked, taking into account the value γ \ (i = 1,2, ..., N) attributed to this unknown yi in step a1).

Here, more specifically, each preliminary coefficient vector Kprelimj (i = 1,2, ..., N) determined in step a) is determined by the execution of steps a1) and a2) (these steps a1) and a2) are thus executed several times).

Preferably, the values γ {, y2, ..., yf attributed to this unknown γι, each of which corresponds to one of these preliminary coefficient vectors, are different two by two.

These values y *, y2, ..., yf are determined on the basis of known physical characteristics of the motor vehicle and the driver assistance device. Each of these values γ \, y2, ..., yf is determined by a trial-and-error procedure, so that the optimization problem described above has a solution when this value is attributed to the unknown γ -ι.

Thus setting the value of the unknown γι (in step a1) greatly facilitates the numerical resolution of the optimization problem described above, and thus obtaining a preliminary vector of coefficients (in step a2). )) satisfying the stability conditions mentioned above.

Indeed, once the value of the unknown γι fixed, this problem of optimization corresponds to a problem of quadratic optimization convex under constraints of the type LMI (according to the Anglo-Saxon acronym of "Linear Matrix Inequalities") which can to be solved numerically quickly and efficiently.

Here, step a2) comprises, in addition to the determination of one of these preliminary coefficient vectors Kprelim '' (i = 1,2, ..., N), the determination of an optimization variable Fobj associated with it.

This optimization variable Fobj is then used in particular to select, among these vectors preliminary coefficients, or those whose first coefficient has the smallest absolute value.

Here, step a2) thus comprises a first substep a21) (shown in FIG. 4), during which a preliminary vector of coefficients is determined Kprelim · '(i = 1.2, ..., N) as explained above.

When the determination of this preliminary coefficient vector Kpre "rru (j = i, 2,..., N) has failed, step a2) continues with a substep a22). During this substep a22), the value "+ oo" is assigned to the optimization variable Fobj This value "+ oo" corresponds for example to the largest numerical value attributable to the optimization variable Fobj, from a point of view computer science.

When, on the other hand, the determination of this preliminary coefficient vector Kprelim '' (i = 1,2, ..., N) is successful, in sub-step a21), step a2) is followed by a sub-step. step a23).

Sub-step a23) comprises determining the stable or unstable character of a tracking of the target trajectory that would be obtained by using, for the driver assistance device, a final vector of coefficients Kfinal ,, of which: the values of the second, third and fourth coefficients kprelim '\ kPrehm,', ^ preiim.i ^ preliminary coefficient calculator Kprehm · 1 determined in step a21) are respectively equal to the second, third and fourth kfrmal, test, kfmai. This is the effect of this final coefficient vector Kfinal, test, and of which - the first coefficient kpnal, test is zero: .final, test _ n .final, test _. prelim, i.final, test _ .prelim, i. .final, test _. prelim i

K.p - U, Kr - Kr. κΨί. - KqJL and KyL - KyL

For that, it is tested if the eigenvalues of the matrix (A + B.Kfinal, test) are with real negative parts (which corresponds to a stable tracking of the target trajectory).

When one of the eigenvalues of the matrix (A + B.Kfinal, test) has a positive real part, the step a2) continues with the sub-step a22) described above.

When each eigenvalue of the matrix (A + BK 31.1 51) has a negative real part, step a2) continues with a substep a24).

During this substep a24), the absolute value k ^ rehm'1 of the first coefficient of the preliminary coefficient vector Kprelim · 'determined in substep a21) is assigned to the optimization variable Fobj associated with this vector : = | kprelinU.

During the method of determination described herein, an optimization process, of a type that could be described in a pictorial way of genetics, is furthermore used to obtain, from the preliminary coefficient vectors from steps a1) and a2), new vectors of preliminary coefficients.

This process aims, once we have obtained at least one preliminary coefficient vector that satisfies the above conditions, to rely on this vector to obtain others. This process makes it possible, with high probability, to obtain new preliminary coefficient vectors that satisfy the aforementioned conditions and whose first coefficient has a smaller absolute value than for the preliminary coefficient vectors initially derived from steps a1) and a2). .

This genetic type optimization process, represented in FIG. 3 by step a3), begins after steps a1) and a2) described above have been executed (several times) to obtain a first set of vectors of Preliminary coefficients Kprelim \ Kprelim · 2, ..., KprelimN. Step a3) begins with a sub-step a31), during which a given number q of preliminary coefficient vectors Kprehm · 1, Kprehm · 2,..., KprelimN determined previously is eliminated. The vectors of preliminary coefficients thus eliminated are those whose associated optimization variable Fobj (i = 1,2,. ,, N) is one of the largest among the set of preliminary coefficient vectors Kprelim'1. Kprehm · 2, ..., Kprelim, N previously determined.

Basing this selection on the optimization variables Fobj (i = 1,2, ... N) makes it possible to eliminate vectors of preliminary coefficients which would lead, after cancellation of said first coefficient k ^ relim '', to an unstable evolution of the tracking the target trajectory over time. Otherwise formulated, this eliminates vectors of preliminary coefficients that would lead to a final coefficient vector of the proportional corrector COR for which the trajectory tracking would be unstable over time.

Basing this selection on the optimization variables Fobj (i = 1,2, ... N) also preserves the preliminary coefficient vectors presenting a first coefficient kprehm'1 whose absolute value is one of the smallest, from the set of preliminary coefficient vectors Kprehm · 1, Kprelim'2,, Kprelim, N previously determined.

During the following sub-step a32), new values of the unknown γι (involved in the stability equation E4) are determined by hybridization and / or mutation of the values of this unknown γι associated with the preliminary coefficient vectors. retained in the previous sub-step a31). More precisely, a number q 'of new values of the unknown γι are thus obtained. One of these new values can for example be obtained by hybridization of two of the unknown values γ1 conserved in the substep a31). This hybridization can for example be performed by calculating an arithmetic mean, or a geometric mean of these two values of the unknown γ-ι conserved in the substep a31).

Alternatively, one of these new values can be obtained by mutation of one of the values of the unknown γι stored in the substep a31). This mutation can for example be achieved by multiplying the value of the unknown γι stored in the sub-step a31) by a random number, for example, between 0.9 and 1.1.

Alternatively, other types of hybridizations or mutations could of course be used to obtain these q new values of the unknown γ-ι.

During the following sub-step a33), new preliminary coefficient vectors are determined, based on q 'new values of the unknown γ-ι determined in the preceding sub-step a32). Each new vector of preliminary coefficients is determined on the basis of one of these q 'new values of the unknown γ-ι, in the same way as in step a2) described previously. An optimization variable associated with this new preliminary coefficient vector is also determined, during the sub-step a33), in the same way as in step a2).

At the end of step a33), a new set of preliminary coefficient vectors is thus obtained. This new set of preliminary coefficient vectors comprises the new preliminary coefficient vectors determined in substep a33), as well as the preliminary coefficient vectors conserved at the end of substep a31). Here, the numbers q and q 'will preferably be chosen equal. The execution of the set of substeps a31), a32) and a33) is repeated a given number of times.

During the first execution of the set of substeps a31), a32) and a33), the set of preliminary coefficient vectors considered in sub-step a31) (and of which q vectors are eliminated) corresponds to the vectors of preliminary coefficients determined during the previous executions of steps a1) and a2).

In subsequent executions of the set of substeps a31), a32) and a33), the set of preliminary coefficient vectors considered in substep a31) (and of which q vectors are eliminated) corresponds to the set of preliminary coefficient vectors obtained at the end of the previous execution of the set of substeps a31), a32) and a33).

The genetic optimization process of step a3) is followed by step b) mentioned above.

During this step b), the preliminary coefficient vector KPreiim.opt | g varja | ·) ^ of optimization F ° pj associated is the smallest is selected, among the set of vectors of preliminary coefficients obtained at the end of the last execution of the set of substeps a31), a32) and a33).

Finally, during the following step c), the final coefficient vector Kfinal of the proportional corrector COR is determined. Recall that this final coefficient vector Knnal is determined as follows: - the values of the second, third and fourth coefficients kprelim, opt, kpreiim.opt ^ kpreiim, oPt of the preliminary coefficients kprelim, opt selected at step b) are assigned respectively to the second, third and fourth kfrmal, ki | jnLal, kyL3 'coefficients of this final coefficient vector Kfinal, and - the first coefficient kpnal of this final coefficient vector Kfinal is canceled: .final _ n .final _ .prelim.opt .final _ .prelim.opt. .final _ .prelim.opt

Κβ - U, Kr - Kr, Κψι - KqjL ei KyL - KyL

Claims (9)

A method for determining a target steering angle (δ) of a steering member of a motor vehicle, for following a target trajectory to said motor vehicle, comprising the following steps: - determination, by means of a computer, a final coefficient vector (Kfinal) of a proportional corrector (COR) of a driver assistance device fitted to the motor vehicle, and - determination of said target steering angle (δ), by means of of said driver assistance device, by multiplication of said final coefficient vector (Κηη3 ') with a state vector (x) representative of the positioning of the motor vehicle relative to said target trajectory, characterized in that the step of Determining the final coefficient vector (Kfinal) comprises steps of: a) determining a plurality of preliminary coefficient vectors pre i i, ^ ^ ^ ^ 2 2 2 2 2 2 2 COR COR COR COR COR COR COR COR COR COR COR COR ), each of which comprises a first coefficient (kprehm'1, kprehm'2, kprelim, N) intended to be multiplied by a term (β) of the state vector (x) whose value is not accessible to the device. a driving aid and at least one other coefficient (k ^ 11 '"1,1, kj? 1®1" 11'2, kprelim, Nj ^ relim ^ kprelim, N) intended to be used by a term (r, Ψι_, yL) of the state vector (x) whose value is accessible to the driver assistance device, b) selection of the preliminary coefficient vector (Kprelim opt) for which said first coefficient ( kprehm, opt) presents the smallest absolute value, and c) determination of the final coefficient vector (Kf, nal) of said proportional corrector (COR), in which each other coefficient (k? nal, kiji1®1, ky al) is equal to said other coefficient (kprel'm opti kÿ®lim opt, ^ [®, ΙΓΤ1'ορ, :) corresponding to the preliminary coefficient vector (Kprelimopt) selected, and wherein said first the coefficient (kpnal) is equal to 0. 2. Method according to claim 1, in which each final (Kfinal) and preliminary coefficient vector (| <prel'm'1, Kprehm'2, Kprelim, N) comprises: - said first coefficient (kjnal, kprelim'1, kprelim'2, kprelim'N), adapted to be multiplied by a term of the state vector which corresponds to a drift angle (β) of a velocity vector ((vCg) v) of the motor vehicle, - a second coefficient (kfr'nal, kj? relim'1, k | relim'2, kj? relim, N), adapted to be multiplied by a term of the state vector which corresponds to a yaw rate (r) of this vehicle automobile, - a third coefficient (kp1, kp1 '"1'1, kplim'2, kphm, N), adapted to be multiplied by a term of the state vector which corresponds to a relative heading angle (Ψι_) of the vehicle with respect to said target trajectory, and - a fourth coefficient (kjal, kplim'1, kplim'2, kpim'N) adapted to be multiplied by a term of the state vector which corresponds to a lateral cart (yL) between the motor vehicle and said target trajectory. 3. Method according to one of claims 1 and 2, wherein it is provided, prior to step b), to eliminate each vector of preliminary coefficients ^ preiim.ii ^ preiim ^ Kprelim, N) quj concjujrajtj after cancellation from the value of said first coefficient (kpm'1, kplim'2, kprelim N) to an unstable evolution of trajectory tracking over time. 4. Method according to one of claims 1 to 3, wherein, in step a), given a stability equation (E4) which is representative of the stable or unstable nature of the movement of the motor vehicle with respect to said target trajectory when the driving assistance device is active and which involves said coefficients (kgrelim'1, kp1'2, kpm'N, kprelim '\ kp "1'2, kp" 1' ", kpim ' 1, kpim'2, kplim'N, Çlim'1, kp "1'2, kpim'N), the determination of at least one of the preliminary coefficient vectors (Kprelim'1, Kprehm'2, KprehmN) comprises steps of: a1) assigning a predetermined value (γ {, γ \, yf) to an unknown (γ-ι) involved in a non-linear term (γ-iQ) of said stability equation (E4), and a2) determining said preliminary coefficient vector (Kprehm'1, Kprelim'2, Kpreiim, N, so that the equation of stability (E4) is checked, given the value attributed to said known (γβ in step a1). 5. Method according to claim 4, wherein, after step a2), there is provided a step a3) of determining at least one new preliminary coefficient vector according to the preliminary coefficient vector (Kprehm'1, KPreiim , 2, Kpreiim, N ^ determined in step a2). 6. The method of claim 5, wherein, the steps a1) and a2) being repeated several times, in step a3), sub-steps are provided for: a31) elimination, in the set of vectors of preliminary coefficients (Kprehm'1, | <prelim'2, Kprelim, N) determined in steps a2), of at least one preliminary coefficient vector for which the absolute value of said first coefficient (kprelim'1, kprehm'2, kprelim , N) has, among this set of coefficient vectors, the largest value, a32) determining at least one new value of said unknown (γι), from the values (yi, y2, yf) of said unknown (γι) associated with at least a portion of the preliminary coefficient vectors (| <prel'm'1, Kprel, m'2, Kprelim, N) stored in substep a31), and a33) determination of at least a new preliminary vector of coefficients, associated with the new value of said unknown (γι) determined at the us-step a32), this new preliminary coefficient vector satisfying said stability equation (E4), taking into account the new value of said unknown (n) · 7. Method according to claim 6, wherein during the sub-step a32), the new value of said unknown (γι) is obtained by hybridization of at least two values y2, yf) of said unknown each associated with the one of the vectors of preliminary coefficients (Kprelim'1, Kprelim'2, Kprehm, N) preserved in the sub-step a31). 8. Method according to one of claims 6 and 7, wherein, in the sub-step a32), the new value of said unknown (γ-i) is obtained by mutation of at least one value (γΐ, γΐ , yf) of said unknown associated with one of the preliminary coefficient vectors (Kprehm'1, Kprehm'2, Kprellm, N) conserved in sub-step a31). 9. Method according to one of claims 6 to 8, wherein, in step a3), the execution of substeps a31), a32) and a33) is reiterated by considering among the vectors of preliminary coefficients (Kprelim · 1, Kprehm'2, Kprehm, N) retained in substep a31), each new preliminary coefficient vector calculated during the execution of each preceding substep a33).