Method for controlling an automotive machine autonomously

Abstract

The invention relates to a method for controlling actuators of an automotive machine (10) autonomously, said actuators being configured to influence the path and speed of said automotive machine, the method comprising steps of: - acquiring a reference path that said automotive machine must follow, - determining a nominal value of at least one parameter allowing the automotive machine to follow the reference path, - determining a current value of each of said parameters when said automotive machine is following the reference path, - determining a difference in values between the current value and the nominal value of each of said parameters, then - computing, with a computer, a control setpoint for each actuator, depending on each difference in values, by means of a corrector. According to the invention, the corrector allows an exclusively lateral automotive-machine control setpoint and an exclusively longitudinal automotive-machine control setpoint to be computed conjointly.

Description

METHOD FOR AUTONOMOUSLY CONTROLLING AN AUTOMOBILE DEVICE TECHNICAL FIELD OF THE INVENTION

[0001] The present invention relates generally to the automation of the tracking of trajectories of automotive devices.

[0002] It finds a particularly advantageous application in the context of driving aids for motor vehicles, but it can also be applied to the field of aeronautics or robotics.

[0003] It relates more particularly to a method for autonomously controlling actuators of an automotive device which are adapted to influence the trajectory and speed of said automotive device, comprising steps of: - acquisition of a reference trajectory that said automotive device must follow, - determination of a nominal value of at least one parameter allowing the automotive device to follow the reference trajectory, - determination of a current value of each parameter when said automotive device follows the reference trajectory, - determination of a difference in values ​​between the current value and the nominal value of each parameter, then - calculation by a computer of a control instruction for each actuator, based on each value difference, using for this a mathematical object hereinafter called “corrector”.

[0004] It also concerns a device equipped with a calculator suitable for implementing this process.

[0005] It also relates to a method for synthesizing such a corrector.

[0006] This invention applies more particularly, but not exclusively, to the following of an obstacle avoidance trajectory by a motor vehicle. STATE OF THE ART

[0007] In an effort to make motor vehicles safer, they are currently being equipped with driver assistance systems or autonomous driving systems.

[0008] Among these systems, we know in particular the automatic emergency braking systems (better known by the abbreviation AEB, from the English "Automatic Emergency Braking"), designed to avoid any collision with obstacles located in the lane taken by the vehicle, by simply acting on the conventional braking system of the motor vehicle.

[0009] There are, however, situations in which these emergency braking systems do not prevent a collision or are not usable (for example, if a machine closely follows the motor vehicle).

[0010] For these situations, automatic avoidance systems (better known by the abbreviation AES, from the English "Advanced Evasive Steering" or "Automatic Emergency Steering") have been developed which allow the obstacle to be avoided by diverting the vehicle from its trajectory, either by acting on the vehicle's steering or by acting on the vehicle's differential braking system. It should be noted that the obstacle may be in the same lane as the vehicle or in an adjacent lane, in which case it is detected that this obstacle may be in the vehicle's trajectory within a short time.

[0011] However, it sometimes happens that the AES system imposes a trajectory on the vehicle that limits its controllability and does not necessarily allow the driver to regain control of the vehicle in complete safety.

[0012] The problem is that so-called "high dynamic" avoidance maneuvers, i.e. those in which the acceleration experienced by the vehicle exceeds a threshold of, for example, 0.3g, are likely to generate instabilities and trajectory tracking defects, so much so that they prove difficult to control. PRESENTATION OF THE INVENTION

[0013] In order to overcome the aforementioned drawback of the state of the art, the present invention proposes a solution making it possible to couple the lateral and longitudinal controls of the vehicle to ensure precise and stable steering of the vehicle during high dynamic maneuvers, and in particular during obstacle avoidance maneuvers.

[0014] More particularly, the invention proposes a control method as defined in the introduction, in which the corrector is used to jointly calculate an exclusively lateral control setpoint for the automotive device and an exclusively longitudinal control setpoint for the automotive device.

[0015] In the case where the device considered is a motor vehicle, the exclusively lateral steering instruction will be a steering instruction for the vehicle's steered wheels, and the exclusively longitudinal steering instruction will be a traditional braking instruction for the vehicle's wheels (we are therefore not talking about differential braking allowing the vehicle to brake and turn simultaneously).

[0016] Thus, the invention makes it possible to control the dynamics of the device (here the vehicle) not only laterally in relation to the trajectory it must take, but also longitudinally, via a single corrector.

[0017] In other words, when this process is implemented on a motor vehicle in order to avoid an obstacle, it is possible to control the steering and braking (or acceleration) of the vehicle via two actuators controlled jointly.

[0018] This solution ensures better tracking of avoidance trajectory the obstacle and better stability for the vehicle.

[0019] The corrector is in fact capable of guaranteeing the stability and performance of a modeling of the vehicle dynamics by a closed-loop system, for a very large set of reference trajectories at different speeds. Thanks to the invention, it is therefore not necessary to calculate and develop a corrector for each trajectory, the corrector, once correctly calibrated, being valid for a fairly wide range of use.

[0020] In this regard, this corrector is pre-calculated offline (during the design of the vehicle) and is then embedded in the vehicle, so that only simple calculations need to be carried out on the vehicle to find the desired driving instructions.

[0021] The invention is thus easy to implement.

[0022] Preferably, said automotive device being a vehicle which comprises at least one wheel adapted to be steered in a variable direction, at least one power steering actuator, at least one braking actuator and at least one propulsion actuator of the vehicle, the lateral steering instruction is transmitted to said at least one power steering actuator to steer said at least one wheel, and the longitudinal steering instruction is transmitted to said at least one braking actuator and / or to said at least one propulsion actuator to brake or accelerate the vehicle.

[0023] The invention also relates to a method for developing a corrector for use in a piloting method as mentioned above, in which it is provided to: - model the automotive device in a non-linear form, - linearize said model in a linear form with variable parameters, - synthesize a corrector which ensures reference trajectory tracking, and in which the corrector is synthesized by considering a finite number of points defined by distinct values ​​of variable parameters.

[0024] Other advantageous and non-limiting characteristics of this method according to the invention, taken individually or in all technically possible combinations, are the following: - steps are planned consisting of: 51 - acquire a validation grid made up of several points, 52 - create a first grid of points less dense than the validation grid, 53 - synthesize a first corrector with the first grid, 54 - determine whether the first corrector is valid over the entire validation grid, then: n if the first corrector is valid over the entire validation grid, the corrector is considered equal to the first corrector, "otherwise, another grid denser than the first grid is generated and then steps S3 and S4 are repeated with this other grid. - the first grid includes, for a majority of the variable parameters, only the maximum and minimum limits of variation of these variable parameters, said limits being determined for two extreme reference trajectories. - the modeling of the automotive device in non-linear form comes from force balance equations applying to the automotive device. - the forces acting on the motor vehicle comprising normal reaction forces as well as longitudinal and lateral friction forces that the ground exerts on wheels of the motor vehicle, to linearize said model in a linear form with variable parameters, a thresholding function is used applied to the normal reaction forces and to the longitudinal and lateral friction forces. - the model considering actuator control inputs, to linearize said model in a linear form with variable parameters, a saturation function applied to the control inputs is used. - the variable parameters are the longitudinal acceleration of the automobile, its longitudinal speed, its lateral speed, its yaw rate, its heading angle and a steering angle. - the corrector has an “anti-windup”. - the regulator is synthesized from convex optimization criteria under constraints of linear matrix inequalities, at least one of the constraints comprising: o the minimization of the performance in the sense H~ of the relationship between a disturbance applied to the automotive device and a position and / or yaw error of the automotive device, o the minimization of the performance in the generalized sense H2 of the relationship between a disturbance applied to the automotive device and a control signal of the automotive device, o the taking into account of amplitude saturations of the actuators.

[0025] The invention also relates to an automotive device comprising at least one actuator which is adapted to influence the trajectory of said device, at least one actuator which is adapted to influence the speed of said device and a computer for controlling said actuators, programmed to implement a method as mentioned above.

[0026] Of course, the various features, variants and embodiments of the invention may be combined with each other in various combinations to the extent that they are not incompatible or mutually exclusive. DETAILED DESCRIPTION OF THE INVENTION

[0027] The description which follows with reference to the appended drawings, given as non-limiting examples, will make it clear what the invention consists of and how it can be implemented.

[0028] On the attached drawings:

[0029] - figure 1 is a schematic top view of a motor vehicle traveling on a road;

[0030] - Figure 2 is a representation of the bicycle model used to model the motor vehicle of Figure 1;

[0031] - Figure 3 is a graph illustrating the range of variation of the longitudinal and lateral forces exerted on the tires of the vehicle of Figure 1;

[0032] - Figure 4 is a block diagram of a closed loop modeling the dynamics of the motor vehicle of Figure 1;

[0033] - figure 5 is a graph illustrating the variations of a saturation function used in the context of the method according to the invention;

[0034] - figure 6 is a graph illustrating the variations of a threshold function used in the context of the method according to the invention;

[0035] - Figure 7 is a block diagram of another closed loop modeling the dynamics of the motor vehicle of Figure 1;

[0036] - Figure 8 is a graph illustrating a region in which the dynamics of the closed loop of Figure 7 is bounded.

[0037] In Figure 1, a motor vehicle 10 is shown, conventionally comprising a chassis which delimits in particular a passenger compartment and an engine compartment, two front steered wheels 11, and two rear non-steered wheels 12. As a variant, these two rear wheels could also be steered with an adaptation of the control law.

[0038] This motor vehicle 10 comprises a conventional steering system making it possible to act on the orientation of the steered wheels so as to be able to turn the vehicle. This conventional steering system notably comprises a steering wheel connected to connecting rods in order to pivot the steered wheels. In the example considered, it also comprises at least one actuator making it possible to act on the orientation of the steered wheels as a function of the orientation of the steering wheel and / or as a function of a request received from a computer 13. This power steering actuator can, for this purpose, act on the steering column of the vehicle (which is fixed to the steering wheel) or on a rack (which connects the steering column to the steered wheels). Of course, the actuator could be positioned differently.

[0039] The motor vehicle also includes a conventional braking system for braking all four wheels in order to slow the motor vehicle. In the example considered, this conventional braking system includes at least one braking actuator. Here, it includes several to be able to adjust the braking force exerted on each wheel as needed.

[0040] The motor vehicle finally comprises a powertrain, including in particular a propulsion actuator making it possible to control this unit in order to accelerate the motor vehicle 10.

[0041] The computer 13 is then designed to control the power steering actuator, the brake actuators and the powertrain actuator. For this purpose, it comprises at least one processor, at least one memory and various input and output interfaces.

[0042] Thanks to its input interfaces, the computer 13 is adapted to receive input signals from different sensors.

[0043] Among these sensors, for example, it is planned: - a device such as a front camera, making it possible to locate the position of the vehicle in relation to its lane, - a device such as a RADAR or LIDAR remote sensor, making it possible to detect an obstacle located in the path of the motor vehicle 10, - at least one lateral device such as a RADAR or LIDAR remote sensor, allowing observation of the environment on the sides of the vehicle, - a device such as a gyrometer, making it possible to determine the yaw rotation speed (around a vertical axis) of the motor vehicle 10, and - various sensors to estimate, for example, the longitudinal and lateral speed of the vehicle, the rotation speeds of the front and rear wheels of the vehicle, the steering angle of the front wheels, the bank angle and the slope of the road, etc.

[0044] Thanks to its output interfaces, the computer 13 is adapted to transmit an instruction to the power steering actuator, to the powertrain actuator and to the braking actuators.

[0045] It thus allows the vehicle to be forced to follow a reference trajectory T0 which will have been defined beforehand. This reference trajectory T0 is, for example, an obstacle avoidance trajectory.

[0046] Thanks to its memory, the computer 13 stores data used in the process described below.

[0047] In particular, it stores a computer application, consisting of computer programs comprising instructions whose execution by the processor allows the computer to implement the method described below.

[0048] Before describing this process, we can introduce the different variables that will be used, some of which are illustrated in Figures 1 and 2.

[0049] The total mass of the motor vehicle will be noted “m” and will be expressed in kg.

[0050] The vehicle's center of gravity will be noted as "CG".

[0051] Here we will mainly consider an orthogonal reference frame (CG, X, Y, Z) attached to the vehicle. Its origin is the same as the center of gravity CG. The X axis corresponds to the longitudinal axis of the vehicle. The Y axis corresponds to the lateral axis facing the left of the vehicle. In practice, this Z axis is the axis normal to the road.

[0052] The vertical moment of inertia of the motor vehicle around the Z axis will be noted “Izz” and will be expressed in Nm

[0053] The distance between the center of gravity CG and the front axle of the vehicle will be noted "If" and will be expressed in meters. Generally, in the following, the index f will be associated with the front wheels.

[0054] The distance between the center of gravity CG and the rear axle will be noted "l r » and will be expressed in meters. In the following, the index r will be associated with the rear wheels.

[0055] The lateral moment of inertia of a wheel of the motor vehicle will be noted “Iwy” and will be expressed in Nm

[0056] The effective radius of a wheel will be noted "r e » and will be expressed in meters.

[0057] The coefficient of friction between the ground and a tire will be noted p.

[0058] The air density coefficient will be noted p.

[0059] The aerodynamic drag coefficient of the vehicle will be noted Cd.

[0060] The frontal surface of the vehicle will be noted Af.

[0061] The lateral stiffness of the front wheel tires will be noted c af .

[0062] The lateral stiffness of the rear wheel tires will be noted c ar .

[0063] The longitudinal stiffness of the front wheel tires will be noted CKf.

[0064] The longitudinal stiffness of the rear wheel tires will be noted CKr.

[0065] The coefficient of rolling resistance forces of the front wheels will be noted frf.

[0066] The coefficient of the rolling resistance forces of the rear wheels will be noted f rr .

[0067] The height of the vehicle's center of inertia CG above the ground will be denoted h.

[0068] The ratio of torque distribution between the front and rear wheels will be denoted k T .

[0069] The longitudinal slip rate of a tire will be noted K.

[0070] The lateral slip angle of a tire will be noted a.

[0071] The acceleration of Earth's gravity will be noted g.

[0072] The steering angle that the front steered wheels make with the longitudinal axis X of the motor vehicle 10 will be noted “δf” and will be expressed in rad.

[0073] The steering angle that the rear wheels make with the longitudinal axis X of the motor vehicle 10 will be noted “δ r » and will be expressed in rad. Note here that in the following, this angle will be zero. Alternatively, it could be non-zero and expressed as a function of the steering angle δf.

[0074] The torque at the front drive wheels will be noted T Wf .

[0075] The torque at the rear wheels will be noted T wr . It should be noted here that in the Subsequently, this torque will be expressed as a function of the torque at the front drive wheels. For example, we could write: T wr = 0.3. T wf

[0076] The road's slope angle (i.e. its angle of inclination to the right or left) will be noted θ X and will be expressed in degrees, in the trigonometric sense.

[0077] The slope angle of the road will be noted as 0 y and will be expressed in degrees. It will be positive if the road goes uphill and negative otherwise.

[0078] The vehicle's yaw rate (around the Z axis) will be noted as "r" and will be expressed in rad / s.

[0079] The longitudinal speed of the vehicle, along the X axis, will be noted v and will be expressed in m / s.

[0080] The lateral speed of the vehicle, along the Y axis, will be noted u and will be expressed in m / s.

[0081] The rotation speed of the front wheels of the vehicle, around the axis of rotation of these wheels, will be noted ωwf and will be expressed in rad / s.

[0082] The rotation speed of the rear wheels of the vehicle, around the axis of rotation of these wheels, will be noted ω wr and will be expressed in rad / s.

[0083] The relative heading angle between the X axis and the tangent to the reference trajectory T0 will be noted “ ” and will be expressed in rad.

[0084] Therefore, the yaw angle error between the vehicle heading and the tangent to the reference trajectory T0 will be noted ΔΨ.

[0085] The longitudinal position error between the vehicle and the reference trajectory T0 will be noted XL.

[0086] The lateral position error between the vehicle and the reference trajectory T0 will be noted yL.

[0087] These two errors can be expressed at the level of the vehicle's center of gravity CG.

[0088] The method according to the invention is designed to allow the vehicle to follow the reference trajectory T0 as precisely as possible, in autonomous mode (without driver intervention).

[0089] This method is for example implemented when an AES automatic obstacle avoidance function has been triggered and then a reference trajectory T0 has been calculated. It will be noted that the manner of triggering the AES function and calculating the reference trajectory T0 is not strictly speaking the subject of the present invention, and will therefore not be described here.

[0090] Given this trajectory T0, it is possible to calculate the nominal values ​​of parameters allowing the motor vehicle 10 to follow this trajectory exactly. In the following, the objective will be to ensure that the vehicle follows exactly this trajectory, that is to say that the deviations between the current values ​​of these parameters and the nominal values ​​along the reference trajectory TO are minimal.

[0091] The parameters used to describe the trajectory that the vehicle must follow are here: - the longitudinal position of the vehicle (the nominal value of which is noted xo and the current value x), - the lateral position of the vehicle (the nominal value of which is noted y0 and the current value y), - the vehicle's heading angle (the nominal value of which is noted Ψ0 and the current value - the longitudinal speed v of the vehicle (the nominal value of which is noted v0 and the current value v), - the lateral speed u of the vehicle (whose nominal value is noted u0 and the current value u), - the yaw rate r of the vehicle (the nominal value of which is noted r0 and the current value r).

[0092] These parameters are determined in an absolute reference frame initialized at the start of the maneuver (which corresponds in practice to the reference frame attached to the vehicle at the moment the maneuver begins).

[0093] The calculation of nominal values ​​is considered known here.

[0094] At this stage, it can be noted that if the reference trajectories are provided by a trajectory planner (DPL, from the English “Decision and Planning”), the latter can also calculate the nominal instructions δf0 and T wf0 .

[0095] If a trajectory planner is not available, from the said reference trajectories T0, we are able to calculate the nominal commands from the following expressions:

[0096] [Math. 0]

[0097]

[0098] In this equation, the term p' refers to the radius of curvature of the reference trajectory T0.

[0099] Before describing the method that will be executed by the computer 13 to implement the invention itself, we can in a first part of this presentation describe the calculations that made it possible to arrive at the invention, so as to clearly understand where these calculations come from and on what springs they are based. We will explain in particular how is synthesized the K corrector which will allow the calculation of vehicle control instructions based on measured data.

[0100] The idea of ​​the first part of the presentation is in fact to describe the way in which it is possible to synthesize a controller K which, once implemented in the computer 13, will allow the vehicle to be piloted so that it follows the reference trajectory T0 in a stable and efficient manner.

[0101] First, we can model the vehicle as well as the forces acting on it that we want to take into account to control the vehicle.

[0102] Here we will consider that the dynamic behavior of the vehicle can be modeled using a nonlinear bicycle model.

[0103] In such a model, the two wheels of the front axle are considered to be merged, and the same is true for the two rear wheels. The vehicle chassis is modeled by a body that connects the two wheel models.

[0104] In the following, when we speak of "front wheel" in the singular, we will designate this modeling of the two front wheels by a single wheel. In the same way, when we speak of "rear wheel" in the singular, we will designate this modeling of the two rear wheels by a single wheel.

[0105] We will then consider, for each wheel, an orthogonal reference (O w, x w , y w , z w ) attached to this wheel. Its origin is the same as the geometric center of this wheel. The y axis w corresponds to the axis of rotation of the wheel. The x axis w corresponds to the wheel axis orthogonal to the aforementioned axis and to the Z axis. Finally, the z axis w is considered parallel to the Z axis.

[0106] At this point, we can note that when in an equation or a reference, a term relates in a similar and obvious way to the front wheel or the rear wheel, we can write it without the subscript "f" or "r". For example, we will speak for simplification of the orthogonal reference frame (O w , x w , y w , z w ) associated with each wheel, whereas we could write these markers more laboriously in the form (O wr , x wr , y wr , z wr ) and (Owf, Xwf, y W f, Zwf).

[0107] The dynamic parameters of the vehicle taken into account, that is to say the parameters characterizing its movements, are as follows: - the longitudinal translational movement of the vehicle body along the X axis, - the lateral translational movement of the vehicle body along the Y axis, - the yaw movement of the vehicle body around the Z axis, - the rolling movement of the front wheel around its rotation axis Y Wf , And - the rolling movement of the rear wheel around its rotation axis Y wr .

[0108] The dynamic parameters of the vehicle neglected in the following are the following: - the vertical translational movement of the vehicle body along the Z axis, and - the rolling and pitching movements of the vehicle body around the X and Y axes.

[0109] In view of the movements considered, the state variables of the vehicle system are: - the longitudinal speed v of the vehicle, - the lateral speed u of the vehicle, - the yaw rate r of the vehicle, and - the rotation speeds ωwf and ω wr front and rear wheels.

[0110] The state of the vehicle system can then be noted:

[0111] The inputs of this vehicle system are: - the steering angle δf of the front wheel, - the T couple wf at the front wheel, - the 0x slope angle of the road, - the slope angle 0y of the road.

[0112] The vehicle system input will then be noted:

[0113] In the following, we will speak of control inputs to designate the torque (δf, Twf) and of disturbance inputs to designate the torque (0x, 0y).

[0114] The forces acting on the vehicle system are partly represented in Figure 2 and are all listed below: - the weight of the vehicle, with its three components (P x , P y , P z ) in the frame (CG, X, Y, Z), - the normal reaction forces oriented along the Z axis (modeling the support of the wheels against the ground) and noted Nf for the front wheel and N r for the rear wheel, - the longitudinal friction forces of the tires on the ground, noted F X f for the front wheel and F xr for the rear wheel, expressed in the reference (O w , x w , y w , z w ) attached to the corresponding wheel, - the lateral friction forces of the tires on the ground, noted F y f for the front wheel and F yr for the rear wheel, expressed in the reference (O w , x w , y w , z w) attached to the corresponding wheel, - the rolling resistance forces of the tires, noted R X f for the front wheel and R xr for the rear wheel, expressed in the reference (O w , x w , y w , z w ) attached to the corresponding wheel and which form the friction forces of the wheels on their axes (they are applied to the center of the wheel), and - aerodynamic drag forces.

[0115] The axis of rotation of a wheel is not necessarily parallel to the Y axis. The longitudinal and lateral friction forces of the tires then each have a longitudinal component and a lateral component in the (CG, X, Y, Z) frame of reference, so that we can write:

[0116] [Math. 1]

[0117]

[0118] These equations can be simplified by considering the steering angle at the rear wheels to be zero, particularly here where only the front wheels of the vehicle are steered.

[0119] The vehicle system is considered in equilibrium so that the resultant and the resulting moment of the external forces are zero.

[0120] We can therefore write the following three equations:

[0121] [Math. 2]

[0122]

[0123] The first equation is the resultant of the forces along the X axis, the second is the resultant of the forces along the Y axis and the third is the resultant of the moment about the Z axis.

[0124] We can also write the equations of motion for rolling wheels:

[0125] [Math. 3]

[0126]

[0127] Note that the disturbance inputs (slope angles 0 X and slope 0 yof the road) will be used to calculate the P components x , P y , P z weight.

[0128] The longitudinal and lateral friction forces produced by the tires of a wheel are proportional to the longitudinal slip rate K and the lateral slip angle a of the tires, respectively. We can then write:

[0129] [Math. 4]

[0130]

[0131] In these equations, the hat " Λ » indicates that this is the input to the saturation function.

[0132] The coefficients c K * etc a * vary non-linearly depending on the vehicle dynamics, in particular depending on the longitudinal and lateral slippage of the tires, the normal reaction force N acting on the tire and the coefficient of friction p between the tire and the ground.

[0133] They are expressed here in the form:

[0134] [Math. 5]

[0136] In these equations, the terms K* and a* can be written as follows:

[0137] [Math. 6]

[0138]

[0139] The longitudinal slip rate and lateral slip angle for both wheels are expressed as:

[0140] [Math. 7]

[0141]

[0142] And :

[0143] [Math. 8]

[0144]

[0145] The longitudinal and lateral friction forces produced by the tires of a wheel, as expressed by the Math4 equations, can increase indefinitely. But in reality, we see that they saturate.

[0146] As shown in Figure 3, this saturation can be modeled as an ellipse, which shows that the total maximum force that the tire is capable of withstanding .follows the perimeter of an ellipse. In other words, the longitudinal Fx and lateral Fy components of the forces always remain inside an ellipse and are at their maximum equal to thresholds Fxmax and Fymax.

[0147] Here, to simplify the equations, we consider that the ellipse is a circle, so that the two thresholds mentioned above are equal. These thresholds are proportional to the normal reaction force N, so that we can write:

[0148] [Math. 9]

[0149]

[0150] The normal reaction forces N acting on the tires are modeled here by a variable load transfer model between the front wheel and the rear wheel, which depends on the vehicle dynamics (in particular its longitudinal acceleration, and also its lateral speed). It is understood that the stresses acting vertically on the front wheels are greater than those acting on the rear wheels in the event of braking. This is the reason why we consider this variable load transfer model between the front wheel and the rear wheel.

[0151] For example, we can write these forces in the following form:

[0152] [Math. 10]

[0153]

[0154] In these equations, the function d is calculated as follows:

[0155] [Math. 11]

[0156]

[0157] These equations are obtained here by considering that the vehicle system is in equilibrium so that the resultant of the external forces along the Z axis and the resulting moments of the external forces around the X and Y axes are equal.

[0158] The rolling resistance force R x of a wheel is considered proportional to the normal reaction force N, so that we can write:

[0159] [Math. 12]

[0160]

[0161] Since the aerodynamic drag force is mainly oriented along the longitudinal X axis of the vehicle, its components along the Y and Z axes are neglected here. The remaining component, along the X axis, is then expressed in the form:

[0162] [Math. 13]

[0163]

[0164] At this stage, the entire vehicle model considered is therefore well defined.

[0165] We can now explain how this model, non-linear by nature, can be linearized along the reference trajectory T0.

[0166] To do this, we introduce a function f which depends on the state of the vehicle system, its derivative and its input. Taking into account the equations Math2 and Math3, we can then write:

[0167] [Math. 14]

[0169] It can be noted here that because of the non-linear dependence links between the longitudinal and lateral reaction forces F X f , F xr , Fyf, F yr compared to the normal reaction forces Nf, N r , it is not possible to obtain an explicit form of the derivative of the state x (i.e., the dynamics) of the vehicle system.

[0170] In the Math14 equation, we then isolate these forces in order to write:

[0171] [Math. 15]

[0172]

[0173] Using the above equations and in particular the Math4 equation, it is possible to develop the term M as follows:

[0174] [Math. 16]

[0175]

[0176] In this equation, to take into account the saturation of the tire friction forces (according to the ellipse in Figure 3), a vector of saturation functions a has been introduced, which can be written in the following form:

[0177] [Math. 17]

[0178]

[0179] In this equation, we introduced the input h before saturation, whose vector can be written:

[0180] [Math. 18]

[0181]

[0182] Thus, the term M can be reformulated as follows:

[0183] [Math. 19]

[0184]

[0185] Therefore, the equations Math15 and Math19 allow us to write our modeling of the vehicle system in the form:

[0186] [Math. 20]

[0187]

[0188] Figure 4 then represents in the form of a block diagram the closed loop expressed by this equation. We observe that the normal reaction forces to the wheels and the longitudinal and lateral friction forces of the tires of the wheels, represented by the vector o(h), are looped on this model of the dynamics of the state of the vehicle system, since they appear at the input of this system and they depend only on the vector h at the output of this system. It will therefore be possible to describe this situation in the form of a simple equation (Math23 below).

[0189] The linearization of the model expressed by the Math20 equation along the reference trajectory T0 can then be written as follows:

[0190] [Math. 21]

[0191]

[0192] In these equations, the subscript "0" refers to the aforementioned nominal values. The vertical bar refers to the Jacobian at a given point.

[0193] Note that the second equation (Δh) is formed based on the same method as the first equation.

[0194] We use a continuous function with a discontinuous derivative as the saturation function σ. This is a function whose derivative is continuous, except at two distinct points. It has a constant value on either side of these two points, and a value that varies in an affine manner between these two points, in an increasing manner.

[0195] This function, illustrated in Figure 5, can therefore be defined by:

[0196] [Math. 22]

[0197]

[0198] We also introduce, with reference to Figure 6, a continuous threshold function but with a discontinuous derivative. This is a function whose derivative is continuous, except at two distinct points. It has a constant value between these two points, and a value which varies affinely on either side of these two points, so as to decreasing.

[0199] This threshold function can therefore be defined by:

[0200] [Math. 23]

[0201]

[0202] The model is here linearized from this threshold function since, as will become clear from reading the rest of this presentation, there exists for this function a condition which is useful for the synthesis of the K corrector. To summarize, the use of this threshold function in fact makes it possible to guarantee the stability of the closed loop in a zone, while maximizing the size of this zone.

[0203] It is then possible to express the model given by the second Math21 equation as a function of this expression, by performing the following operations:

[0204] [Math. 24]

[0205]

[0206] In the same way, the dynamics of the state of the vehicle system can be described in the following successive forms:

[0207] [Math. 25]

[0208]

[0209] We can then apply the saturation function to the two expressions Math24 and Math25, which allows us to write:

[0210] [Math. 26]

[0211]

[0212] Here we add to the dynamics of the linearized model given by the Math24 equations the dynamics of the absolute longitudinal position errors XL and lateral yi. and yaw angle ΔΨ of the vehicle system:

[0213] [Math. 27]

[0214]

[0215] Thus, the Math26 equations allow the dynamic characteristics of the vehicle to be taken into account, while the Math27 equations allow the vehicle to be required to follow the trajectory correctly. This combination of equations then ensures good control of the vehicle along the reference trajectory T0.

[0216] At this stage, the model being linearized and extended to the Math26 and Math27 equations, we wish to transform it into a grid-based LPV model (better known under the English name “LPV grid-based”).

[0217] An LPV model allows a system to be represented in linear form with varying parameters.

[0218] The variation space of these parameters is, in our LPV model, bounded by maximum and minimum thresholds.

[0219] The idea of ​​a "grid" model is then to synthesize a corrector K by considering a very limited number of points in this space, then to try to validate it by verifying that this corrector K is valid for a larger number of points in this space, and finally to use this corrector K if the solution is validated, or otherwise to start again by synthesizing the corrector K with a larger number of points.

[0220] To model our system in this way, we consider two distinct vectors, namely a first vector Au for the control inputs and a second vector Aw for the disturbance inputs. We therefore express our linearized model by:

[0221] [Math. 28]

[0223] It will be noted here that the order of the system n (namely the dimension of the square matrix A(t)) is equal to 8, that the number of disturbance inputs m w is equal to 2, that the number of measurement inputs m uis equal to 2, that the number of parameters of the vector h is noted Ph and is here equal to 6.

[0224] The matrices of the model given by the first expression of the Math28 equation depend on the state variables and the inputs of the system, and more particularly on: - the longitudinal acceleration dv / dt of the vehicle, - its longitudinal speed v, - its lateral speed u, - its yaw speed r, - its yaw angle ψ, - its rotation speeds at the wheels Wwf and w wr , And - its steering angle δf.

[0225] These eight variables could be used as variable parameters of the LPV model in grid.

[0226] However, the number of grid points increases exponentially with the number of time-varying parameters, which makes the calculations very cumbersome. It was therefore decided to reduce this number of variable parameters to limit the grid points and simplify the synthesis of the K corrector.

[0227] To do this, the wheel rotation speeds are calculated based on the longitudinal speed v of the vehicle, assuming that no wheel slip is present. We can then write:

[0228] [Math. 29]

[0229]

[0230] For the synthesis of the correctors, we arbitrarily considered two distinct reference trajectories T0, namely: - a trajectory T01 associated with a change of two lanes without braking (the vehicle moves from its lane to the immediately adjacent lane and then to the next lane, without braking, at 70 km / h), and - a T02 trajectory associated with a change of a single lane with braking (the vehicle moves from its traffic lane to the immediately adjacent traffic lane while decelerating from 85km / h to 35km / h).

[0231] These two trajectories symbolize two types of extreme maneuvers for which we want to stabilize the vehicle.

[0232] The objective is then to develop a single K corrector which is capable of controlling the vehicle according to these two “extreme” reference trajectories and, therefore, according to all the reference trajectories between these two trajectories.

[0233] In these two extreme conditions, the approximation of the Math29 equation is reasonable (especially in the case of avoidance with braking) because the slip is low (which can be controlled during tests or simulation). Consequently, it is possible to reduce the number of variable parameters to six. These variable parameters pi together constitute the vector p, which can be written in the form:

[0234] These tests then made it possible to record the maximum and minimum values ​​taken by these variable parameters.

[0235] It is therefore chosen here to limit the variation intervals of the state variables and the inputs of the vehicle system along the two reference trajectories in order to define the maximum and minimum thresholds of the variable parameters pi. These thresholds are presented in the tables below, successively for the two reference trajectories TO1 and T02.

[0236] Thus, the thresholds for the reference trajectory TO1 (without braking) are:

[0237] [Table 1] 0238] The thresholds for the reference trajectory TO2 (with braking) are:

[0239] [Table 2] 0240] We are looking for a K corrector capable of controlling the vehicle along the two reference trajectories.

[0241] Therefore the most extreme values ​​among the limits associated with the two maneuvers are used for the definition of the grid LPV model.

[0242] A notable exception is made for the yaw angle ψ . We consider the upper bound in absolute value and use it to establish a variation interval symmetrical with respect to zero. Indeed, to establish the two tables above, the vehicle was moving to the left, so the minimum yaw angle threshold is 0 degrees. However, we want to be able to carry out maneuvers from the right, with a negative yaw angle.

[0243] In summary, the following limits will be used for all reference trajectories T0 (with or without braking):

[0244] [Table 3] 0245] It should be noted that these values ​​are given as an illustrative example, for a given vehicle model (the one on which the tests were carried out).

[0246] The LPV model is therefore expressed by the following equations:

[0247] [Math. 30]

[0248]

[0249] With the LPV grid approach, LTI (linear time invariant) models propose to freeze the values ​​of the variable parameters p, on a set of points in the variation domain of the vector p in order to define a grid.

[0250] For the synthesis of the K corrector with the LPV grid approach, two different grids are used, namely: - a synthesis grid (to synthesize the K corrector as simply as possible), and - a validation grid denser than the synthesis grid (to check whether the K corrector thus synthesized is indeed valid over the entire domain).

[0251] The way to proceed is then as follows: - we create the least dense synthesis grid possible, - we carry out the synthesis of the K corrector with the synthesis grid, - we determine whether the synthesized K corrector works on the entire validation grid, then: o if the solution is validated on the validation grid, the K corrector is confirmed, o otherwise, a new synthesis grid denser than the previous one is generated then the procedure is restarted.

[0252] It is chosen to start the process using a synthesis grid that is as less dense as possible but which is located along the boundaries of the variation space of the vector g. This first synthesis grid is then formed here only by the vertices of the hypercube containing the variation domain of this vector p.

[0253] However, it was observed that by considering this first synthesis grid at 2 6 points, it was not possible to synthesize a valid corrector.

[0254] Therefore, in accordance with the process outlined above, a second, denser synthesis grid, at 2, was considered7 points (i.e. 128 points).

[0255] The values ​​considered for each variable parameter pi of this first synthesis grid are as follows:

[0256] [Table 4] 0257] It can be seen that for all parameters, except the longitudinal velocity v, only the extreme values ​​of the variation domain were considered (i.e. their vertices of the hypercube). For the longitudinal velocity v, it was observed that a greater number of values ​​was necessary for the solution found to be verified with the validation grid.

[0258] In other words, all possible combinations of these values ​​were considered to synthesize the K corrector.

[0259] Regarding the validation grid, it was chosen to use twelve values ​​per variable parameter, uniformly distributed over its variation domain. In this case, all possible combinations of parameter values ​​constitute the points of the grid, which therefore contains approximately three million points (12 6 ).

[0260] It is understood that synthesizing the K corrector by considering only this validation grid would have required too much computing power to quickly arrive at a solution. This is the reason why it was chosen to operate with two grids, according to the process explained above.

[0261] We can now explain how the dynamic K corrector is synthesized.

[0262] The synthesis of the dynamic LPV corrector given by the Math30 equation takes into account the saturations of the tire forces, thanks to the threshold function. Here we also want to consider the saturations of the control inputs, thanks to the saturation function σ.

[0263] We can therefore rewrite our LPV system in the following form:

[0264] [Math. 31]

[0265]

[0266] In this equation, the vector z is expressed in the form: . It This is therefore the position and yaw error vector.

[0267] For the saturation of the vehicle actuators, we consider the inequalities following: - 30 deg ≤ δf 30 deg, and - 5000Nm ≤ T Wf ≤1230 Nm.

[0268] These thresholds are here substantially equal to the maximum capacities of the actuators.

[0269] As shown in Figure 7, to impose on the closed loop a behavior respecting these saturations, we add the filters W to the system e (s), W u (s) and W d (s). We can then synthesize using the augmented system G a (s).

[0270] To summarize, we will note that the W filter d (s) is not used since the reference input is not used in the system. The W filters e (s) and W u (s) are then sufficient to adjust the two input-output relationships between the disturbance signals Aw and the controlled outputs zi and Z2 (which measure the performance of the system, respectively in terms of setpoint tracking and trajectory tracking).

[0271] W filters e (s) and W u (s) used are:

[0272] [Math. 32]

[0273]

[0274] The desired K corrector (dynamic LPV) has the following form:

[0275] [Math. 33]

[0276]

[0277] In this equation, we observe that the corrector K is expressed in the form of the state representation Xk.

[0278] The term EKu(p).Φ(Δu) represents an “anti-windup” component for the saturation of control signals. This term is negligible as long as no saturation appears but takes on a non-zero and non-negligible value in the event of saturation, which makes it possible to counter the error drifts due to this saturation phenomenon on the control inputs.

[0279] In other words, the proposed synthesis using an "anti-windup" component is a corrector retouching technique that allows to explicitly take into account the saturation phenomena of the actuators and to reduce their negative impact on the dynamics of a controlled system. The method proposed below is then based on the use of sector conditions in order to encapsulate the saturation function. It exploits the Lyapunov stability through quadratic functions allowing to express the stability and performance conditions by linear matrix inequalities (LMI).

[0280] Thus, to synthesize the K corrector on this basis, the method is carried out using convex optimization criteria under constraints of linear matrix inequalities LMI (the linearity of the terms of the matrices used guarantees that the mathematical problem can be solved without requiring too much computational load).

[0281] The objective is more precisely to optimize the gains of the closed loop defined by the K corrector by playing on the choice of poles.

[0282] The closed-loop stability is calculated by taking into account the sector nonlinearities that are input to the system through the generalized sector condition.

[0283] For the synthesis of the corrector we consider the following constraints: - limiting the performance H~ of the input-output relationships between the disturbance signals Aw and the controlled outputs zi and Z2 of the closed loop, to maximize its robustness and rejection of disturbances, - limitation of the ^-generalized performance of the input-output relationship between the disturbance signals Aw and the outputs z2 of the closed loop, to reduce the possibility of saturation of the control signals, - the placement of the poles of all LTI realizations of the closed loop in the variation domain of the vector g in the LMI region noted represented in figure 8 and whose values ​​are:

[0284] We can then define this region as follows:

[0285]

[0286] The theorem used, derived from the document Scherer, Gahinet and Chilali 1997 and Tarbouriech et al. 2011, is as follows:

[0287] If there exist matrices of suitable dimensions X (of dimension nxn and such that X = X T >0), Y (of dimension nxn and such that Y = Y T >0), S u (of dimensions m u xm u , strictly positive diagonal), J u1 (of dimension m u xn), J U2 (of dimension m u xn), R u (of dimension nxm u ), S h (dimensions phxp h , strictly positive diagonal), J h1 (of dimension phxn), J h2 (of dimension phxn), Â (of dimension nxn), B (of dimension nxp y ), C (of dimension m u xn), D (of dimension m u xp y ), a region such as the aforementioned, and strictly positive scalars y∞ and Y2g such that the optimization problem below is feasible, we therefore obtain a controller K which satisfies our objectives.

[0288] The matrix inequalities used here are nine in number and are defined by the following inequalities (for all i ranging from 1 to Ng, Ng being the number of points on the grid used).

[0289] [Math. 34]

[0291] Note that in these inequalities: - Y j and J uj are the rows of the matrices Y and J u (for all j ranging from 1 to m u ), are the maximum values ​​of the control inputs being therefore the values maximum of - Y k and Jh are the rows of the matrices Y and Jh (for all k ranging from 1 to ph), are the maximum values ​​of the deviations of the friction forces of the tires along the reference trajectory, i.e. the maximum values ​​of ΔF X f, ΔF xr , ΔFyf and ΔF yr .

[0292] It will be observed that these nine inequalities are respectively linked to the following constraints.

[0293] The first of these inequalities imposes a bound on the H" norm (between the transfers of the disturbance inputs to the controlled outputs z1 and z2). This amounts to minimizing the performance in the H∞ sense of the relationship between a disturbance and a position and / or yaw and / or control error.

[0294] The second and third inequalities impose a bound on the norm H2 (between the transfers of the disturbance inputs to the controlled output z2). This amounts to minimizing the performance in the generalized H2 sense of the relationship between a disturbance and a control signal.

[0295] The fourth inequality allows us to place the poles in the LMI region of the plane complex.

[0296] The fifth inequality ensures that there exists a Lyapunov matrix that can be written in a suitable form.

[0297] The sixth and seventh inequalities relate to sector conditions generalized for the saturation of control inputs (that of the actuators).

[0298] The last two inequalities relate to generalized sector conditions for the saturation of friction forces acting on tires.

[0299] Thus, if the above system of inequalities is solved, then the dynamic K corrector can be calculated using the following matrices:

[0300] [Math. 35]

[0301]

[0302] And then, this K corrector ensures: - the stability of the LPV system given by the equation Math31 where the ellipsoid ε(P, 1 ) is an Asymptotic Stability Region (or RSA) of the system with saturated inputs in closed loop, - that the poles of all realizations in the LTI sense of the closed loop in the domain of variation of the parameters are in the region and - that the H∞ and H2-generalized performances of the closed loop are inferior to the scalars Y∞ and Y2g.

[0303] The matrix P of the quadratic Lyapunov function is such that:

[0304] [Math. 36]

[0306] The conditions laid down by the last two inequalities of the Math34 system (for all j ranging from 1 to m u and any k ranging from 1 to ph) consider that the saturation limits of the controls and the friction forces of the tires are symmetrical with respect to zero.

[0307] In practice, in our case, these bounds are not symmetrical. To make them so, we use a conservative approach consisting of considering the smallest saturation threshold of the parameters Δδf, ΔT Wf , ΔFXf , ΔF xr , ΔF yf and ΔF yr along the two reference trajectories considered.

[0308] We also observe that the bilinearity ShB^Y appears in the condition given by the penultimate inequalities of the Math34 system. The resulting optimization problem that uses this constraint is therefore not convex. To avoid having to solve a non-convex optimization problem, there are two solutions.

[0309] The first solution is to choose a value for Sh a priori, which would therefore no longer be a decision variable. This solution is complicated to implement if we want to obtain reliable and non-conservative results.

[0310] The second solution is to use the method proposed in Garcia et al. 2009 and Silva et al. 2008, which requires adding an anti-windup component to the K corrector, also for tire force saturation.

[0311] It should also be noted that estimating tire friction forces is a difficult task. A corrector that does not require measuring the expression (Δh) is therefore desired. Therefore, to obtain a corrector without an "anti-windup" component for tire friction forces, it is possible to use the following procedure: - we use the second of the above-mentioned solutions in order to calculate a corrector K with anti-windup for the expression Φ (Δh), as shown below, then - the solution of the Sh matrix is ​​recovered and used to solve an optimization problem under the constraints of the Math34 inequalities.

[0312] In order to calculate this corrector with anti-windup, we again use the LMI matrix inequalities here, but in a very simplified way.

[0313] This time the theorem used is the following.

[0314] If there exist matrices of suitable dimensions X (of dimension nxn and such that X = X T >0), Y (of dimension nxn and such that Y = Y T >0), S u (of dimensions m u xm u , strictly positive diagonal), J ui (of dimension m u xn), J U2 (of dimension m u xn), R u (of dimension nxm u ), Sh (of dimensions phxph, strictly positive diagonal), Jh1 (of dimension p xn), J 2 (of dimension phxn), Â (of dimension nxn), B (of dimension nxp y ), C (of dimension m u xn), D (of dimension m u xp y ), a region as mentioned above, and strictly positive scalars y∞ and Y2g such that all the inequalities of the Math 34 system are valid (except for the penultimate one whose validity is not sought) and that the following inequality is valid for all i ranging from 1 to N g :

[0315] [Math. 37]

[0316]

[0317] then we find a solution of the dynamic corrector with anti-windup component also for the friction forces of the tires.

[0318] The solution of the S matrix thus found can be used to make convex the problem of synthesizing the regulator without anti-windup.

[0319] For the search for the corrector K, we want to maximize the region of attraction of the closed loop with respect to the saturations of the control inputs and the tire friction forces. To do this, we seek to minimize the trace of P, which can be done by minimizing a strictly positive scalar pp and adding the constraint given by the following LMI inequality:

[0320] [Math. 38]

[0321]

[0322] Finally we solve the following optimization problem:

[0323] [Math. 39]

[0324]

[0325] respecting the inequalities Math34 and Math38.

[0326] So, using the Math33 equation, we can deduce the corrector K.

[0327] To solve this optimization problem, we used the YALMIP toolbox from MATLAB, cf. Lofberg 2004”, with “Mosek solver, cf. Andersen and Andersen 2000”. Of course, other methods could be used.

[0328] The following two observations can be noted concerning the iteration of the solution presented here with other algorithms already commonly present on a motor vehicle (typically the algorithm for keeping the vehicle in the center of its lane).

[0329] First, as long as these other algorithms have higher dynamics than this control and do not actively interfere with the vehicle's yaw, there will be no stability issues related to nested loops, and traction control (which intelligently distributes torque between the four wheels) could possibly contribute to closed-loop stability.

[0330] Second, the idea of ​​the solution presented here is to perform avoidance and, as such, when this algorithm is activated, the other algorithms present which would be likely to have an influence on the trajectory of the vehicle will be deactivated.

[0331] The calculation hypotheses now being well established, we can describe the process which will be executed by the computer 13 of the motor vehicle to implement the invention.

[0332] The computer 13 is programmed here to implement this process recursively, that is to say step by step, and in a loop.

[0333] To do this, during a first step, the computer 13 checks that the autonomous obstacle avoidance (AES) function is activated and that an obstacle reference trajectory has been planned.

[0334] The computer 13 will then seek to define a control instruction for the conventional steering system and for the conventional braking system, allowing this reference trajectory T0 to be followed as best as possible.

[0335] To do this, it begins by calculating the parameters which constitute the measurement vector y (Δv Δu Δr XL yL. Δψ ).

[0336] More precisely, knowing the nominal values ​​x0, y0, 0, v0, u0, r0 of the parameters which theoretically allow the motor vehicle 10 to follow the reference trajectory T0, and knowing the current values ​​x, y, , v, u, r of these same parameters while the vehicle follows the reference trajectory T0 (i.e. the measured or estimated values ​​of these parameters), the computer 13 can calculate the deviations Av, Δu, Δr, xL, yL, AΨ between the current and nominal values ​​of these parameters.

[0337] Then, taking into account the Math33 equation, it can use the K corrector to determine the values ​​of the desired control instructions δf, Twf.

[0338] Finally, these steering and braking (or acceleration) angle instructions will be transmitted to the actuators to steer and brake or accelerate the wheels of the motor vehicle 10.

[0339] This process is then repeated in a loop, along the entire reference trajectory T0.

[0340] The present invention is in no way limited to the embodiment described and shown, but those skilled in the art will be able to provide any variation in accordance with the invention.

Claims

DEMANDS 1. A method for autonomously controlling actuators of an automotive device (10) adapted to influence the trajectory and speed of said automotive device (10), comprising the steps of: - acquisition of a reference trajectory (T0) that said automotive device (10) must follow, - determination of a nominal value (x0, y0, 0, v0, u0, r0) of at least one parameter enabling the automotive device (10) to follow the reference trajectory (T0), - determination of a current value (x, y, , v, u, r) of each parameter when said automotive device (10) follows the reference trajectory (T0), - determination of a difference in values ​​(Δv, Δu, Δr, xL, yL, ΔΨ) between the current value (x, y, , v, u, r) and the nominal value (x0, y0, ψ0, v0, u0, r0) of each parameter, then - calculation by a computer (13) of a control setpoint (δf, T Wf) for each actuator, as a function of each difference in values ​​(Δv, Δu, Δr, xL, yL, Δψ), by means of a controller (K), characterized in that the controller (K) allows joint calculation of an exclusively lateral control setpoint (δ f ) of the automotive device (10) and an exclusively longitudinal piloting instruction (T Wf ) of the automotive device (10).

2. A steering method according to claim 1, wherein, said automotive device (10) being a vehicle which includes at least one wheel (11, 12) adapted to be steered in a variable direction, at least one power steering actuator, at least one braking actuator and at least one vehicle propulsion actuator, the lateral steering command is transmitted to said at least one power steering actuator to steer said at least one wheel, and the longitudinal steering command is transmitted to said at least one braking actuator and / or to said at least one propulsion actuator to brake or accelerate the vehicle.

3. Method for developing a corrector (K) for use in a control process according to one of claims 1 and 2, wherein it is provided that: - model the automotive device (10) in a non-linear form, - linearize said model in a linear variable parameter (LPV) form, - synthesize a compensator (K) which ensures a reference trajectory follower (T0), and in which the compensator (K) is synthesized by considering a finite number of points defined by distinct values ​​of variable parameters.

4. A method of preparation according to claim 3, wherein it is provided that steps consisting of: 51 - acquire a validation grid composed of several points, 52 - create an initial points grid that is less dense than the validation grid, 53 - synthesize a first corrector (K) with the first grid, 54 - determine if the first corrector (K) is valid over the entire validation grid, then: o if the first corrector (K) is valid over the entire validation grid, the corrector (K) is considered equal to the first corrector (K), o otherwise, another grid denser than the first grid is generated and then steps S3 and S4 are repeated with this other grid.

5. Method of development according to claim 4, wherein the first grid comprises, for a major part of the variable parameters, only the maximum and minimum limits of variation of these variable parameters, said limits being determined for two extreme reference trajectories.

6. Method of development according to any one of claims 3 to 5, wherein the modeling of the automotive device (10) in non-linear form is derived from equilibrium equations of the forces acting on the automotive device (10).

7. Method of development according to claim 6, wherein, the forces acting on the automotive device (10) comprising normal reaction forces as well as longitudinal and lateral friction forces which the ground exerts on wheels of the automotive device (10), to linearize said model in a linear form with variable parameters, a thresholding function (Φ) is applied to the normal reaction forces and to the longitudinal and lateral friction forces.

8. Method of development according to any one of claims 6 and 7, wherein, considering the model of control inputs of the actuators, to linearize said model in a linear form with variable parameters, a saturation function (o) is applied to the control inputs.

9. A method of fabrication according to any one of claims 3 to 8, wherein the variable parameters are the longitudinal acceleration of the automotive device (10), its speed longitudinal (v), its lateral speed (u), its yaw rate (r), its heading angle (ψ) and a steering angle (δf).

10. Method of preparation according to any one of claims 3 to 9, wherein the corrector (K) includes an "anti-windup".

11. Method of preparation according to any one of claims 3 to 10, wherein the regulator (K) is synthesized from constrained convex optimization criteria linear matrix inequalities (LMI), at least one of the constraints including: - minimizing performance in the H∞ sense of the relationship between a disturbance applied to the automotive device (10) and a position and / or yaw error of the automotive device (10), - minimizing performance in the generalized H2 sense of the relationship between a disturbance applied to the automotive device (10) and a control signal (Z2) of the automotive device (10), - taking into account amplitude saturations of the actuators.

12. Automotive device (10) comprising at least one actuator which is adapted to influence the trajectory of said device (10), at least one actuator which is adapted to influence the speed of said device (10) and a computer (13) for controlling said actuators, characterized in that the computer (13) is programmed to implement a method according to one of claims 1 and 2.

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