CN117957162A - Method for autonomously controlling an actuator of a device - Google Patents

Abstract

The invention relates to a method for autonomously controlling at least one actuator of a vehicle device, said actuator being intended to influence the trajectory of the vehicle device, comprising the following steps: -obtaining parameters (V _y,r,Ψ_L,y_L,δ,M_z,Y_ref) related to the trajectory of the vehicle device and to the speed (V) of the vehicle device, and-using the controller (K) causing the computer to calculate a control setpoint (M _{z_ref},δ_ref) for each actuator from these parameters. According to the invention, the controller used varies according to the speed of the vehicle.

Description

Method for autonomously controlling an actuator of a device

Technical Field

The present invention relates generally to automation of trajectory compliance in automotive equipment.

The invention has particularly advantageous application in the context of motor vehicle steering assistance, but can also be applied in the field of aeronautics or robotics.

The invention relates more particularly to a method for autonomously controlling at least one actuator of a vehicle device, which is capable of affecting the trajectory of said vehicle device, comprising the steps of:

-acquiring parameters related to the trajectory of the vehicle device, and

-Calculating, using a computer, a control setpoint for each actuator in accordance with said parameters, using a controller.

The invention also relates to a device provided with a computer capable of implementing the method.

The invention has more particular, but not exclusive, application to obstacle avoidance trajectory following of a motor vehicle.

Background

In order to make motor vehicles safer, such vehicles are currently equipped with a driving assistance system or an autonomous driving system.

Such systems comprise, in particular, automatic emergency braking systems (more known by the abbreviation AEB thereof) designed to avoid any collision with obstacles on the path taken by the vehicle by simply acting on the conventional braking system of the motor vehicle.

However, in some cases, these emergency braking systems cannot avoid a collision or cannot be used (e.g., if there is a vehicle immediately behind the motor vehicle).

For such a situation, an automatic avoidance steering or automatic emergency steering system (which is more known by the abbreviation AES) has been developed and allows avoidance of an obstacle by deviating the vehicle from its trajectory (by acting on the vehicle steering system of the vehicle or by acting on the differential braking system of the vehicle). It should be noted that the obstacle may be on the same lane as the vehicle or on an adjacent lane, in which case detection of the obstacle may soon occur on the trajectory of the vehicle.

However, AES systems sometimes impose trajectories on the vehicle that are at a controllability limit and do not allow the driver to fully safely re-control the vehicle.

Document FR3099450 thus describes a solution that involves using a controller to generate a control setpoint that allows the vehicle to remain controllable by the driver of the vehicle in the event that the driver wishes to obtain a re-control during the avoidance process. To this end, the controller limits the magnitude and rate of the direction change imposed on the motor vehicle by a hyperbolic tangent function. While this solution works well in many configurations, its performance (i.e., correctly following the back-off trajectory) does leave room for improvement.

More specifically, it is desirable to find a solution that guarantees the performance and robustness of the vehicle in terms of stability when the vehicle speed changes, which is particularly reflected in:

correctly follow heading and positioning along the entire avoidance trajectory,

Good stability.

Disclosure of Invention

To this end, the invention proposes a control method as defined in the introduction, wherein the controller used varies as the speed of the vehicle (which here means the speed of the vehicle relative to the road, which speed may have a longitudinal component along the axis of the vehicle as well as a transverse component) varies.

More specifically, the controller constantly changes as the vehicle speed changes.

Thus, by means of the invention, the controller used will be different regardless of the vehicle speed, and this will allow the control law of the actuator to be adapted to the dynamics of the vehicle best. Such a solution works well. In particular, the more suitable the controller is for this situation (i.e. the fewer unexpected events that must be considered), the more room it has to control the vehicle and this will enable it to avoid obstacles in the safest and most comfortable way for the passengers.

This solution proves to be particularly important in the context of using differential braking (in addition to steering). This is because in this context the vehicle speed is changing (decreasing) along the entire avoidance trajectory and this has a significant impact on the behavior of the vehicle.

Other features of the invention provide other advantages.

Thus, the solution described below will allow for hybrid control of steering and differential braking. In particular, the calculation of the (raw before saturation) steering set point is not only based on the dynamic variables of the vehicle, the measured steering angle and the saturated steering set point, but also on the saturated yaw moment set point and the measured (or estimated) yaw moment, and vice versa. This allows for good agreement between the two command set points (because the two command set points are interdependent).

The structure of the proposed controller is simple, which means that the controller is inexpensive to use, in particular in terms of computational power.

The optimization of the controller is simple because this involves only solving a system of linearization matrix inequalities that have previously set values for certain parameters (minimum and maximum vehicle speeds in the case of AES functionality, minimum and maximum curvatures … of the avoidance trajectory).

The controller may vary with the curvature of the avoidance trajectory so as to be well suited for this situation.

The controller is capable of maximizing the performance and robustness of the effective trajectory of the vehicle within the controllability limits of the vehicle.

As already mentioned, the method used yields good performance, i.e. correct following of the position and heading, allowing the vehicle to follow with higher accuracy the avoidance trajectory that has been calculated for avoidance of the obstacle.

The claimed solution also provides a great stability as long as the energy of the disturbance is limited, in particular as long as the curvature of the trajectory to be followed remains within acceptable boundaries. In other words, this solution makes it possible to quickly determine whether the calculated avoidance trajectory can be dynamically implemented by the vehicle, so that the AES function is only activated if this is indeed the case.

More specifically, if the characteristics of the track exceed a predetermined threshold, it may be specified that the AES function is not activated. The idea is thus not to deactivate the AES function afterwards, but to pre-select whether to activate it, thus making it possible to predict instances where the system may be unstable and instances where the resulting trajectory will be too imperfect (too much overshoot, too much oscillations, etc.).

According to the invention, the controller operates, even if the initial state of the vehicle is non-zero (initial heading, initial yaw rate, etc.) at the moment of triggering the AES function, which is what happens when the vehicle already has some dynamic behavior (for example because the vehicle is turning at the moment of triggering the AES obstacle avoidance function), something other than the solution described in document FR 3099450. To achieve this result, the controller is synthesized to take into account the initial state of the vehicle.

Other advantageous and non-limiting features of the method according to the invention, considered alone or in any technically possible combination(s), are as follows:

-the automotive device is a vehicle comprising wheels, a power steering actuator and a differential brake actuator;

-the controller comprises a plurality of components for determining a control setpoint of the power steering actuator and a control setpoint of the differential brake actuator;

-the controller comprises a plurality of components including at least one state return gain to be applied to said parameter and at least one saturation compensation gain to be applied to the value of the control setpoint determined in the previous iteration;

The controller may be written in the form of a sum of a plurality of products of a speed-dependent variable and a speed-independent local controller;

Each local controller is determined for a determined value of a vector of two variation (schedule) parameters, one of which is preferably equal to the speed V of the vehicle and the other of which is preferably equal to the inverse of said speed;

-the controller conforms to at least one saturation function modeled in nonlinear sectors;

the saturation function conforms to the set point amplitude limiter model and can be expressed in the form:

ψ₁(x)＝sat_η(K(ρ).x)-K(ρ).x

The saturation function conforms to a model that limits the control set point variation and can be expressed in the form:

ψ₂(x)＝sat_v(A₁x+B₁sat_η(K(ρ).x))-(A₁x+B₁sat_η(K(ρ).x))

Where K is the controller, sat _v is the amplitude limiting function, A1 and B1 are the predetermined matrices, and x is the state vector of the automotive device including the parameters;

-the controller conforms to the modeling of the device, wherein one output to be minimized is a function of the trajectory following error and the heading angle error;

-providing for calculating a parameter related to the curvature of the trajectory and then providing for performing said calculating step under conditions in which said parameter lies within a predetermined interval;

-calculating a control setpoint for the power steering actuator from a control setpoint previously calculated for the differential brake actuator;

-calculating a control setpoint for the differential brake actuator based on a control setpoint previously calculated for the power steering actuator.

The invention also proposes an automotive device comprising at least one actuator capable of affecting the trajectory of said device and a computer for controlling said actuator, programmed to implement the method as defined hereinabove.

Naturally, the various features, variants and forms of embodiment of the invention can be combined with each other in various combinations, as long as these features, variants and forms are not mutually incompatible or mutually exclusive.

Detailed Description

The following description, with reference to the accompanying drawings, given by way of non-limiting example, will make it easy to understand the content of the invention and how it may be implemented.

In the drawings:

Fig. 1 is a schematic top view of a motor vehicle travelling along a road and suitable for implementing the method according to the invention;

FIG. 2 is a graph illustrating parameters used in the context of the method of FIG. 1;

FIG. 3 is a schematic top view of the motor vehicle of FIG. 1 depicted in four successive positions on the obstacle avoidance trajectory;

FIG. 4 is a diagram illustrating a polyhedron used in the context of the method of FIG. 1;

FIG. 5 is a diagram illustrating a closed loop transfer function for controlling the motor vehicle of FIG. 1;

FIG. 6 is a graph illustrating the saturated polyhedron and suction domain of a controller used in the context of the method of FIG. 1, and an example of how the vehicle state changes in the absence of a disturbance;

FIG. 7 is a graph similar to the graph of FIG. 4, but showing an example of a change in vehicle state in the presence of a disturbance;

Fig. 8 is a diagram illustrating a method for selecting an appropriate controller in the context of the method of fig. 1.

Fig. 1 depicts a motor vehicle 10 comprising, in a conventional manner, a chassis defining a cabin, two steered front wheels 11 and two non-steered rear wheels 12. Alternatively, the two rear wheels may also be steered by an adaptive control law.

The motor vehicle 10 includes a conventional steering system that is capable of acting on the orientation of the front wheels 11 to enable steering of the vehicle. The conventional steering system includes, among other things, a steering wheel connected to a link for pivoting the front wheels 11. In the example considered, the conventional steering system also comprises an actuator able to act on the orientation of the front wheels according to the orientation of the steering wheel and/or according to a request received from the computer 13. For this purpose, the actuator may act on the steering column of the vehicle (which column is fixed to the steering wheel) or on the steering rack (which steering rack connects the steering column to the steering wheel). Of course, the actuator may be implemented in different ways.

In addition to this, the motor vehicle comprises a differential braking system which can act in different ways on the rotational speed of the front wheels 11 (and, where applicable, of the rear wheels 12) in order to slow down the motor vehicle while steering it. In the example considered, the differential braking system comprises at least one actuator, formed for example by a controlled differential or an electric motor located at the wheels of the vehicle.

Thus, the computer 13 is intended to control the power steering actuators as well as the actuators of the differential brake system. To this end, the computer includes at least one processor, at least one memory, and various input and output interfaces.

The computer 13 is able to receive input signals originating from various sensors by means of its input interface.

These sensors include, for example:

A device capable of recognizing the position of the vehicle relative to the lane in which it is travelling, such as a front-facing camera,

A device capable of detecting an obstacle 20 (fig. 3) located on the trajectory of the motor vehicle 10, such as a RADAR or LIDAR remote detector,

At least one transverse device capable of observing the environment along the side of the vehicle, such as a RADAR or LIDAR remote detector,

A device capable of determining the yaw rotation rate (about a vertical axis) of the motor vehicle 10, such as a gyroscope,

Steering wheel position and angular velocity sensor, and

-A sensor capable of estimating the yaw moment experienced by the vehicle.

In fact, a sensor for measuring the yaw moment is not actually provided here. In contrast, a low-order computing unit capable of estimating a yaw moment from a braking torque applied to wheels of a vehicle is provided.

The computer 13 is able to transmit the setpoint to the power steering actuator and to the actuator of the differential braking system by means of its output interface.

Thus, it can force the vehicle to follow a predefined avoidance trajectory T0 to avoid the obstacle 20 (see fig. 3).

The computer 13 stores data by means of its memory, which is used in the context of the method described below.

The memory stores, inter alia, a computer application consisting of a computer program comprising instructions that, when executed by a processor, enable the computer to perform the method described below.

Before describing the method, different variables to be used will be introduced, some of which are shown in fig. 1 and 2.

The total mass of the motor vehicle will be denoted "m" and expressed in kg.

The moment of inertia of a motor vehicle about a vertical axis passing through its center of gravity CG will be denoted "J" and expressed in N.m units.

The distance between the center of gravity CG of the vehicle and the front axle will be denoted as "l _f" and will be expressed in meters.

The distance between the center of gravity CG and the rear axle will be denoted "l _r" and will be expressed in meters.

The cornering stiffness coefficient of the front wheel will be denoted as "C _f" and will be expressed in units of N/rad.

The cornering stiffness coefficient of the rear wheel will be denoted as "C _r" and will be expressed in units of N/rad.

These cornering stiffness coefficients of the wheels are concepts well known to those skilled in the art. For example, the cornering stiffness coefficient of the front wheel is thus the cornering stiffness coefficient that implements equation F _f＝2.C_f.α_f, where F _f is the cornering force of the front wheel and α _f is the cornering angle of the front wheel.

The steering angle of the steered front wheels with respect to the longitudinal axis A1 of the motor vehicle 10 will be denoted "delta" and expressed in rad.

The variable delta _ref expressed in rad will refer to the saturated steering angle set point, as will be transmitted to the power steering actuator.

The variable delta _K expressed in rad will be referred to as the unsaturated steering angle set point. At this stage, it may be provided that only the concept of saturation will be associated with the limits of the steering angle, steering rate, which are not necessarily complied with by the variable δ _K, but will be complied with by the variable δ _ref.

The variable delta _sat expressed in rad will be referred to as the half-saturated steering angle set point. This variable is derived from the unsaturated setpoint δ _K and is saturated only in terms of steering angle. The saturation set point delta _ref will be calculated based on this semi-saturation set point delta _sat.

The orthogonal reference frame of the vehicle (as defined herein when the vehicle is on a horizontal surface) will have the vehicle center of gravity CG as its origin. The abscissa axis X _v of the orthogonal reference frame will be oriented along the longitudinal axis A1 of the motor vehicle 10, and the ordinate axis Y _v of the orthogonal reference frame will be oriented laterally toward the left hand side of the vehicle. The vertical axis through the center of gravity will be denoted as Z _v.

The yaw moment applied by the differential braking system about axis Z _v expressed in N.m will be denoted as M _z.

The variable M _{z_ref} expressed in N.m units will represent the yaw moment set point to be applied to the wheels using the differential braking device.

The variable M _zK expressed in N.m units will represent the unsaturated yaw moment. At this stage, it may be provided that only the concept of saturation will be associated with the limits of yaw moment and yaw moment variation, which are not necessarily complied with by the variable M _zK, but will be complied with by the variable M _{z_ref}.

The variable M _{z_sat} expressed in rad will be referred to as the semi-saturated yaw moment set point. The variable is derived from variable M _zK and is saturated only in amplitude. The saturation set point M _{z_ref} will be calculated based on this semi-saturation set point M _{z_sat}.

The yaw rate of the vehicle (about a vertical axis passing through its center of gravity CG) will be denoted "r" and expressed in rad/s.

The relative heading angle between the longitudinal axis A1 of the vehicle and the tangent to the avoidance trajectory T0 (the desired trajectory of the vehicle) will be denoted as "ψ _L" and will be expressed in rad.

At a viewing distance "ls" in front of the vehicle, the lateral offset between the longitudinal axis A1 of the motor vehicle 10 (through the center of gravity CG) and the evasion trajectory T0 will be denoted as "y _L" and expressed in meters.

At a viewing distance "ls" in front of the vehicle, a set point for the lateral offset between the longitudinal axis A1 of the motor vehicle 10 (through the center of gravity CG) and the avoidance trajectory T0 will be denoted as "y _L-ref" and expressed in meters.

The trajectory following error will be denoted as "e _yL" and will be expressed in meters. The trajectory following error will be equal to the difference between the lateral offset set point y _L-ref and the lateral offset y _L.

The above-mentioned viewing distance "ls" will be measured from the center of gravity CG and expressed in meters.

The slip angle of the motor vehicle 10 (the angle that the motor vehicle's velocity vector makes with the longitudinal axis A1 of the vehicle) will be denoted "β" and expressed in rad.

The speed of the motor vehicle will be denoted "V" and expressed in units of m/s.

The lateral speed of the motor vehicle corresponding to the projection of the vehicle speed vector on axis Y _v will be denoted as "V _y".

The constants "ζ" and "ω" will represent the dynamic characteristics of the steering angle of the front wheels of the vehicle.

The constant "g" will be the gravitational acceleration expressed in m.s ^-2 units.

The steering rate will represent the rotational angular velocity of the steering front wheel.

The method according to the invention aims at allowing the vehicle to autonomously follow the evasion trajectory T0 as precisely as possible. The method is implemented when the autonomous obstacle avoidance AES function has been triggered and then the avoidance trajectory T0 has been calculated. It should be noted that the manner in which the AES function is triggered and the dodging trajectory T0 is calculated does not strictly form part of the subject matter of the present invention, and will therefore not be described here.

The method is intended to be cyclically implemented in successive "iterations" (in this example, the iterations have a duration of about 10 ms).

Here, it should be noted that the trajectory following is intended to be performed autonomously by the computer 13, but the trajectory following also needs to be able to be interrupted at any time in order to allow the driver to re-control the vehicle. This trajectory following is also required to be able to be used as a driving aid when the driver is holding the steering wheel but does not apply the torque to the steering wheel that is required to avoid the obstacle.

Before describing the method to be performed by the computer 13 in order to implement the invention itself, a first part of this explanation will describe the calculations that lead to the invention in order to allow a comprehensive understanding of where and on what these calculations originate.

The aim of this first part of the explanation is to effectively describe how a controller can be synthesized, which, once implemented in the computer 13, will enable the vehicle to be controlled in such a way that it follows the avoidance trajectory T0 in a stable and well behaved manner.

It will be considered herein that the dynamic behavior of the vehicle can be modeled by the following equation 1.

[ Equation 1]

The model is a classical bicycle model.

It should be noted from this equation that the term γ _ref of the curvature of the avoidance trajectory T0 makes it possible to take into account the trajectory of the vehicle (and thus the curvature of the road) when modeling the dynamic behavior of the vehicle.

It should also be noted from this equation that in the preliminary state vector used, the first state variable will be the lateral velocity V _y. Alternatively, a slip angle β will be used. However, the use of the lateral velocity V _y will be preferred, as this will make it possible to reduce the number of varying (scheduling) parameters in the non-linear model described below.

The steering of the front wheels 11 can be modeled simply using the following formula:

[ equation 2]

Differential braking in itself exhibits a dynamic behavior that can be modeled using the differential equation:

[ equation 3]

In this equation, τ is the dynamic characteristic of the yaw moment.

These three equations make it possible to express a new model of the behavior of the vehicle.

[ Equation 4]

The curvature change of the avoidance trajectory T0 may also be modeled using the following equation.

[ Equation 5]

In this equation, the variable ω _f represents the dynamics of the curvature change of the trajectory, and the term w refers to a random input that is assumed to be finite.

This equation (e.g. equation 3) makes it possible to model the curvature change of the trajectory in the form of a low-pass filter.

Thus, the two previous equations make it possible to express a rich model of the vehicle:

[ equation 6]

In this new model, it can be noted that the speed V of the vehicle is involved. This speed in fact proves to be an important parameter to consider, since the differential braking system will have an influence not only on the trajectory of the vehicle but also on its speed. The vehicle speed will also depend on other factors such as the braking or acceleration set point imposed on the vehicle by the driver or by the computer 13.

In order to synthesize a robust trajectory following controller in terms of stability and performance (which will be described in more detail below), it is therefore important to take into account speed changes of the vehicle.

Here, the idea is therefore to restate the above equation 6 as an LPV (linear parameter variation) model, which would then make it simpler to find a controller that would need to be optimized for that LPV model.

The modified model is as follows.

[ Equation 7]

In this equation, term ρ _1/v is equal to the inverse of speed V (i.e., 1/V), and term ρ _v is equal to speed V. These two terms are commonly referred to as "variation parameters" or "scheduling parameters". Their vector ρ is then written into a form (ρ _v,ρ_1/v).

The state vector x _p is defined as follows.

[ Equation 8]

As for vector u _p, it can be written as:

[ equation 9]

u_p＝(δ_ref M_{z_ref})

The matrix used itself can be expressed as follows:

[ equation 10]

[ Equation 11]

[ Equation 12]

[ Equation 13]

[ Equation 14]

It should be noted that these equations are well defined and explained in the following documents: M.Corno, G.Panzani, F.Roselli, M.Giorelli, D.Azzolini and s.m. savaresi, entitled LPV method for autonomous vehicle path tracking in the presence of steering actuation nonlinearity "An LPV Approach to Autonomous Vehicle Path Tracking in the Presence of Steering Actuation Nonlinearities[ ", IEEE control systems technology journal, doi:10.1109/tcst.2020.3006123.

At this stage, equation 7 can be rewritten using a very specific form (i.e., in the form of a polyhedral LPV system). For this reason, it is assumed that the vehicle speed is limited between two boundaries (minimum limit V _min and maximum limit V _max).

The varying parameter vector ρ is then delimited by the contour of the geometric figure depicted in fig. 4 (called polyhedron P1). The polyhedron here takes the form of a triangle. The vertices ρ ₁、ρ₂ and ρ ₃ of the polyhedron P1 are defined by the following equations.

[ Equation 15]

As will become clear in the rest of this explanation, the concept of this polyhedron is to take into account the fact that: the controller K (which enables calculation of the set point to be transmitted to the actuator) will depend on the speed and this will be easier to calculate by the approximation created by the theory of projection onto the closed convex space.

Now, the function ρ shown in fig. 4 is a curve C1 that varies between the extremum values ρ ₁ and ρ ₃. The convex space chosen to surround the curve C1 as closely as possible is then a polyhedron P1. In particular, the aim is to closely enclose the curve so as not to increase the number of unexpected events considered, since doing so would make the controller too conservative. The triangle shape is the shape that yields the best results.

Thus, the theory chosen makes it possible to calculate the controller K for any velocity V lying between two boundaries from the three values of the controller K at the vertices ρ ₁、ρ₂ and ρ ₃ of the polyhedron P1: minimum limit V _min and maximum limit V _max. All that is then required is to determine only the three values of the controller K.

In practice, equation 7 can be rewritten as follows:

[ equation 16]

Wherein,

[ Equation 17]

Wherein,

[ Equation 18]

[ Equation 19]

[ Equation 20]

[ Equation 21]

[ Equation 22]

[ Equation 23]

However, the model itself cannot limit the steering angle and the steering rate of the front wheels 11 of the vehicle, or the magnitude of the yaw moment applied by the differential brake and the rate at which the yaw moment changes. However, such limitations prove particularly important, especially for ensuring that the driver of the vehicle will be able to re-control the vehicle at any time.

This limitation can be expressed using the following equation.

To limit the steering rate, one can express

[ Equation 24]

In order to limit the steering angle amplitude, it can be expressed that

[ Equation 25]

|δ_ref|≤η_δ

In equation 24, the coefficient v _δ is a constant representing the steering rate that must not be exceeded. The constant is defined by calculation or after a test activity performed on the test vehicle. For example, this constant is equal to 0.0491rad/s, which corresponds to 0.785rad/s (i.e., 45 °/s) at the steering wheel if the steering gear ratio is 16.

In equation 25, the coefficient η _δ is a constant representing the steering angle that must not be exceeded. The constant is defined by calculation or after a test activity performed on the test vehicle. For example, the constant is equal to 0.0328rad, which in this example corresponds to 0.524rad (i.e., 30 °) at the steering wheel.

The constraint expressed in equation 25 makes it possible to limit the torque applied by the power steering actuator so that an average driver can manually cancel out the torque.

Specifically, the greater the steering angle, the greater the force applied by the power steering actuator. Thus, this limitation ensures that the user will be able to re-control the vehicle without having to apply excessive reactive torque. The angle will then depend on the force applied by the selected type of actuator.

The constraint expressed in equation 24 ensures that the driver is not surprised by too fast a change in the orientation of the steering wheel.

It should be noted that the above values are given by way of example and may alternatively be lower (e.g. 25 °/s and 20 ° in order to ensure greater comfort).

In order to limit the rate of change of yaw moment, it can be expressed that

[ Equation 26]

To limit the magnitude of the yaw moment, it can be expressed that

[ Equation 27]

|M_{z_rer}|≤η_M

In equation 26, the coefficient v _M is a constant representing the yaw moment variation that must not be exceeded. The constant is defined by calculation or after a test activity performed on the test vehicle. For example, the constant is equal to 2500Nm/s.

In equation 27, the coefficient η _M is a constant representing the yaw moment that must not be exceeded. The constant is defined by calculation or after a test activity performed on the test vehicle. For example, the constant is equal to 2000Nm.

These two equations allow the driver to re-control the steering of the vehicle in a controlled manner at any time. They make it possible in particular to limit the few minutes surprise that a sharp lateral acceleration would lead to.

According to the invention, it is desirable to limit these four parameters not by imposing a sudden threshold but by gradually saturating their values. Most importantly, it is desirable to consider these four parameters in the composition of the controller so that the behavior of the controller is more stable and pleasing to the vehicle occupants.

Fig. 5 depicts a control architecture for controlling the power steering actuator and the differential braking actuator such that the vehicle follows the evasion trajectory T0 as closely as possible while conforming to the aforementioned constraints.

The figure indicates the controller K as being dependent on the vehicle speed V and is made up of two components, one of which (denoted K _Mz) is associated with differential braking and the other (denoted K _δ) is associated with power steering.

These two components respectively make it possible to calculate the unsaturated setpoint of the yaw moment M _zK and the unsaturated setpoint of the steering angle delta _K.

Each of these two components advantageously comprises a summer that supplies the unsaturation set point at the output and receives the following at the input: a state return item (derived from the state return unit K _Mz ^p,K_δ ^p) depending on the state of the vehicle; and a saturation compensation term (derived from the saturation compensation unit K _Mz ^aw,K_δ ^aw) that depends on the saturation yaw moment set point M _{z_ref} or the saturation steering angle set point delta _ref calculated in the previous iteration.

In the nonlinear mode, i.e. in instances where the power steering actuator or yaw moment actuator commands are saturated in magnitude or in rate, the saturation compensation term enhances the stability of the controller.

The unit SAT1 indicated in fig. 5 shows the amplitude saturation of the unsaturated steering angle set point delta _K. The unit receives as input the output from the corresponding component of the controller K and supplies as output the half-saturated steering angle set point δ _sat. It can be observed that the cell operates in open loop.

The unit SAT2 shows the amplitude saturation of the unsaturated yaw moment set point M _zK. The unit receives as input the output from the corresponding component of the controller K and supplies as output the semi-saturated yaw moment set point M _{z_sat}. It can be observed that the unit also operates in open loop.

The set of units SAT3 shows the rate saturation of the half-saturated steering angle set point delta _sat. The set of cells receives the semi-saturated set point as an input and the set of cells supplies a saturated steering angle set point delta _ref as an output. It can be observed that this is a closed loop.

The set of units SAT4 shows the rate saturation of the half-saturated yaw moment set point M _{z_sat}. The set of units receives the semi-saturated set point as input and the set of units supplies the saturated yaw moment set point M _{z_ref} as output. It can be observed that this is also a closed loop.

In each of the two sets of cells SAT3, SAT4 corresponding to the "pseudo rate limiter" function, a summer is thus provided at the input that makes it possible to calculate the difference delta between the half-saturated set point and the saturated set point in the previous iteration. The unit comprises a multiplier unit capable of multiplying the offset by a parameter lambda, a saturation unit ensuring that the derivative of the saturation set point is not exceeded, and an integration unit for obtaining the saturation set point (via a laplace transform).

The parameter λ represents the dynamic behaviour of the units SAT3 and SAT4 (for this application λ=500 may be considered) and the larger the value of λ, the more closely the behaviour of the pseudo rate limiter corresponds to the behaviour of the rate limiter.

In fig. 5, unit P _sys represents an open loop system describing the dynamic behavior of the vehicle, the behavior of the power steering actuator, the behavior of the differential brake actuator, and the positioning of the vehicle relative to the avoidance trajectory T0.

It can be observed that this unit receives as inputs the disturbance w, the saturated yaw moment set point M _{z_ref} and the saturated steering angle set point delta _ref. The unit delivers as output an output vector y and an error z.

The output vector y corresponds in effect to the state vector x _p described above.

The error z has as such a value to be minimized.

The error z is here a function of the trajectory following error e _yL and the relative heading angle between the longitudinal axis A1 of the vehicle and the tangent to the avoidance trajectory T0 (hereinafter referred to as heading error ψ _L), which is known to need to be minimized.

Thus, it can be written as:

[ equation 28]

In this equation, the term α _ψ is an adjustment coefficient for adjusting an error (heading follow (or heading angle) error or position follow error) to be minimized as a priority. How the value of the adjustment coefficient is selected will be seen later in this explanation. This choice of output error z makes it possible to ensure both correct position compliance and correct heading compliance.

The aim is therefore to determine the form of the controller K, which is a state return regulator capable of calculating the unsaturated yaw moment setpoint M _zK and the unsaturated steering angle setpoint δ _K based on the preliminary state vector x _p, taking into account the vehicle speed V.

To understand how to determine a suitable controller K both in terms of stability and in terms of performance, it is possible to first describe a system Psys operating in open loop, i.e. in linear mode without saturation (a scenario where the saturated and unsaturated steering angle setpoints δ _ref、δ_K are equal and the saturated and unsaturated yaw moment setpoints M _{z ref}、M_zK are also equal).

The system can be expressed herein in a general form:

[ equation 29]

z＝C_pz·x_p

y＝x_p

Given the content of equation 28, matrix C _pz is known. It should be noted that principal component matrix A _p, command B _p, and perturbation B _w can be derived from equation 6.

Controller K (for which we are seeking optimal gain to meet control criteria and which is defined as a static return regulator) can itself be expressed in the form:

[ equation 30]

u_K＝K(ρ).x

In this equation, the term x is a state vector augmented by a saturated steering angle set point and a saturated yaw moment set point. The amplified state vector will be considered in the rest of the explanation. The amplified state vector can be expressed as follows.

[ Equation 31]

x＝[x_p u_p]^T

For the reasons mentioned above with reference to fig. 5, the state-return gains to be optimized form a 2x2 matrix whose entries depend on the vehicle speed V and which can be expressed as:

[ equation 32]

As already explained above, the controller K may be expressed as a function of its values at the vertices ρ ₁、ρ₂ and ρ ₃ of the polyhedron. The controller may be more specifically expressed in the form of the following polyhedron:

[ equation 33]

K(ρ)＝K^ρ1α₁+K^ρ2α₂+K^ρ3α₃

In this equation, the term α ₁、α₂、α₃ is defined by equations 21 to 23.

The matrix K ^ρ1、K^ρ2、K^ρ3 (on the basis of which the controller K can be calculated) must itself be determined by the optimization method set forth in the following paragraph.

Here, therefore, the idea is to synthesize not an infinite number of controllers K but a reduced number of (three) controllers. Via the foregoing convex combinations, the values of the other controllers can then be interpolated as a function of the values of the three matrices.

The system Psys can now be described when operating in closed loop, i.e. in a nonlinear mode with saturation (a scenario where the saturation and the unsaturation set points are not equal).

Given the contents of equations 29 and 30, it can be written as:

[ equation 34]

In this equation, terms A, B, A ₁ and B ₁ are defined as follows:

[ equation 35]

[ Equation 36]

I is the identity matrix.

[ Equation 37]

A₁＝[0 -Λ]

[ Equation 38]

B₁＝Λ

[ Equation 39]

To take into account the controllability constraints as defined in equations 24 to 27, two new saturation functions ψ ₁ (x) and ψ ₂ (x) have been introduced, which represent that the unsaturated command inputs exceed the limits.

Thus, two saturation functions ψ ₁ (x) and ψ ₂ (x) can be defined:

[ equation 40]

ψ₁(x)＝sat_η(K(ρ).x)-K(ρ).x

[ Equation 41]

ψ₂(x)＝sat_v(A₁x+B₁sat_η(K(ρ).x))-(A₁x+B₁sat_η(K(ρ).x))

In both equations, a saturation function denoted as sat _f0 (f) is used, which can be defined as:

[ equation 42]

It should be noted, therefore, that the two saturation functions ψ ₁ (x) and ψ ₂ (x) take on zero values in unsaturated mode, otherwise take on non-zero values.

The objective is then to model the saturation function by using nonlinear sector ("dead zone nonlinearity") modeling based on the work disclosed in the reference:

S.Tarbouriech, G.Garcia, J.MGomes da Silva Jr, and I.Queinnec, titled "Stability and Stabilization of LINEAR SYSTEMS WITH Saturating Actuators [ stability and stabilization of Linear System with saturation actuator ]", 1 st edition, london: schpranger 2011, and

-Alessandra Palmeira，Manoel Gomes da Silva Jr, sophie Tarboureich, and i.ghiggi, entitled "Sampled-data control under magnitude and rate saturating actuators [ sample data control under magnitude and rate saturation actuator ]", journal of international robust and nonlinear control, wiley,2016, 26 (15), pages 3232-3252.

To model the controllability limits of the system, two polyhedrons may be defined, one of which is denoted S ₁ (x, η), modeling the amplitude saturation behaviour and the other of which is denoted S ₂(x,Ψ₁, v), modeling the velocity saturation behaviour. These two polyhedrons can be modeled as follows:

[ Eq.43 ]

S₁(x,η)＝{x∈Rⁿ,|(K(ρ)-G₁(ρ))x|≤η}

[ Equation 44]

S₂(x,ψ₁,v)＝{x∈Rⁿ,ψ₁∈R^m,|(A₁+B₁K(ρ)-G₂(ρ))x+(B₁-G₃(ρ))ψ₁(x)|≤v}

The modeling involves the matrices G ₁、G₂ and G ₃. These matrices are the same size as the matrix of the controller K. They exhibit shifts beyond that permitted by saturated conditions.

By way of illustration, matrix G ₁ can be considered equal to the product of matrix K and scalar a _K. Equation 44 can then be rewritten as a form involving term (1-alpha _K) which would then constitute a setting permitting exceeding the limit. The extent to which this limit can be exceeded can be set to 10%, for example. To set this limit level, a road test will be required.

Preferably, however, the matrix G ₁ will not be a function of the matrix K. It will need to be optimized not by road tests but by calculations (e.g. using the linear matrix inequality method). In this way, the conservation of the solution as described in the previous paragraph will be avoided.

In a first step, it can be assumed that when the system is operating in a closed loop (as defined in equation 7), the state vector x and the variable ψ ₁ lie within the two polyhedrons, so that it can be written as:

[ equation 45]

These two polyhedrons are represented here in fig. 6 and 7, and thus, as clearly described above, represent two spaces within which system stability and performance are guaranteed.

It should be noted that at this stage, these figures show two-dimensional graphs that simplify the solution described above in order to make it easier to understand.

In other words, this two-dimensional representation is valid only if the state vector x contains only two state variables (one forming the abscissa value of each of these graphs and the other forming the ordinate value of each of these graphs).

In practice, here, a state vector includes ten state variables. Thus, the representation of the present invention will need to be drawn in ten dimensions.

Under the assumption of the above equation, the following inequality is satisfied for all of the diagonal facing matrices U ₁ and U ₂, which here are more specifically positive scalar quantities:

[ equation 46]

Here, it should be noted that these scalars U ₁ and U ₂ are simply introduced here to facilitate subsequent computations (using the S program).

In summary, equations 43 and 44 are two saturation models for amplitude saturation and velocity saturation, respectively, which, while still valid within the meaning of equation 45, ensure that equation 46 is equally valid.

These models can then be used to synthesize (i.e., optimize) a state-returned main gain K _δ ^p、K_Mz ^p associated with the state variables of the system P operating in open loop, and a saturation compensation gain ("anti-saturation (anti-windup)" gain) K _δ ^aw、K_Mz ^aw of the controller K.

Equation 34 in closed loop operation and the representation of system Psys as shown in fig. 5 make it possible to write as:

[ equation 47]

z＝C_zx

Assuming that the disturbance w is finite in energy, i.e. bounded by limits, it is possible to write as:

[ equation 48]

This assumption is related to the fact that: the curvature of the trajectory (here considered as a disturbance) and the duration of activating the AES function are always bounded by limits.

Thus, in equation 48 where the term w relates to the curvature of the avoidance trajectory, the maximum value w _max of the term is known (since the dynamic limit of the vehicle and thus the maximum curvature that the vehicle can follow completely safely and thus can be imposed by trajectory planning is known).

To obtain the optimal solution for the controller K, first a lyapunov function V (t) of the stability condition is defined:

[ equation 49]

V(t))＝x^TPx

In this equation, the matrix P is defined as positive and symmetric.

The benefit of this lyapunov function V (t) is that if its first derivative is negative in a strict sense, it ensures that the system will always be stable in the absence of disturbances.

Fig. 6 and 7 depict two polyhedrons that ensure system performance and stability. Thus, space will be sought that is located in both of these polyhedrons. This may be, for example, the intersection of these two spaces.

Here, however, it will be preferable to model this space in the form of an ellipse called an attraction domain. The attraction domain epsilon is defined herein as follows:

[ equation 50]

ε(P,μ)＝{x∈Rⁿ,x^TPx≤μ^-1}

In addition to the stability conditions associated with the lyapunov function V (t), the attraction domain needs to be included in two polyhedrons S1 and S2, which model amplitude and rate saturation, respectively, in order to ensure system stability (which is still a priority to be guaranteed).

Thus, the attraction domain ε is the stability space (or invariance space) of the system involved. In other words, this is the space in which the trajectories of the state variables (i.e. the components of the state vector x) remain, as long as they have been initialized in this space (even if the system is affected by disturbances and saturation of the actuator).

In view of the contents of the above equations, the space in which the system state variables can move has been schematically depicted in fig. 6 and 7.

As understood from the figures, the controller K is then synthesized so as to satisfy three purposes.

The first purpose is that in the absence of disturbances, the controller K should ensure that the trajectory of the state variables of the system operating in closed loop remains within the attraction domain epsilon (which ensures stability) and gradually converges towards the origin (which ensures performance), in particular for a predefined length of time.

Fig. 6 considers the case where no disturbance is present. In this case, the space of the initial conditions of the system (denoted as E ₀) and the estimate of the attraction domain ε E ₁ are identical. It can be seen here that the trajectory T1 of the state vector x from any initial situation does converge towards the origin.

The second purpose is that in the presence of disturbances, the controller K should ensure that the trajectory of the state variable of the system operating in closed loop remains within the attraction domain epsilon regardless of the disturbance w (which ensures stability) as long as the disturbance is energetically limited (within the meaning of equation 48).

Fig. 6 considers the case where no disturbance is present. In this case, the space of the initial conditions of the system (denoted as E ₀) must be contained within the estimate of the attraction domain ε E ₁. It can be seen here that the trajectory T2 of the state variables contained in the space E ₀, starting from any initial situation, does remain within the attraction domain epsilon.

A third objective is that in linear mode (no amplitude or rate saturation) the controller K should guarantee the performance of the system, which in turn is better than stability, by making the synthesis of the norm H-infinity smaller than a predetermined scalar.

Recall that this synthesis involves finding the controller K that minimizes the norms H-infinity of the terms F _l(P_sys, K), where:

[ equation 51]

z＝F_l(P_sys,K).w

The equation can be written in the form:

[ equation 52]

It should be noted here that γ is the norm H infinity of the transfer function of w- > z. In linear mode (no saturation) performance (with norm H-infinity) will be guaranteed due to this constraint.

This synthesis implies a proper suppression of the disturbance w and a proper follow of the avoidance trajectory (error z close to zero).

In fact, there are a number of methods that can be used in order to meet these three objectives.

The method used is preferably to use a Linear Matrix Inequality (LMI). The method is performed based on a convex optimization criterion with linear matrix inequality constraints (the linearity of the terms in the matrix used ensures that mathematical problems can be solved without excessive computational effort).

More specifically, the objective is to optimize the gain of the closed loop defined by the controller K by altering the selection of poles.

Specifically, if matrices R (ρ), Q, L ₁(ρ)、L₂(ρ)、T₁(ρ)、T₂ (ρ) having suitable dimensions exist, so that the following optimization problem is possible, a controller K satisfying the aforementioned three purposes is obtained.

These matrices are calculated from the matrix P.

The matrix inequality used here is three and is defined by the inequality below, where γ is to be minimized.

[ Eq.53 ]

[ Equation 54]

[ Equation 55]

In these inequalities, i is an integer that is in turn equal to 1 and then equal to 2.

Item X _(i) corresponds to the ith row of matrix X.

Still in these inequalities, in the form ofMatrix is write-formed/>

Matrix variables R, Q, L ₁、L₂、T₁、T₂ are expressed herein as a form of a matrix of suitable size.

The matrix variables are expressed in the following form:

[ equation 56]

In order to solve the following optimization problem in the context of the problem as stated, it is only necessary to solve the matrix inequality (LMI) for each vertex (ρ ₁,ρ₂,ρ₃) of the polyhedron depicted in fig. 4, which amounts to solving 9 inequalities.

At this stage, to optimize each of the terms K ^ρ1、K^ρ2、K^ρ3, it is assumed that the vehicle speed V is constant (so that all of these matrices are thus considered constant). Specifically, each term is optimized for a determined vector ρ, i.e. for a determined speed.

The three inequalities in equations 53-55 ensure that the dynamic range of the closed loop remains limited, i.e., the system remains stable in the absence or presence of disturbances (thus meeting the first two conditions).

The first inequality in equation 53 also ensures the performance (in the sense of the norm H-infinity) of a system operating in a closed loop when the system is affected by disturbances. The inequality thus ensures that the third condition is met.

Once the 9 matrix inequalities have been solved, the local controller at the vertices of the polyhedron P1 is calculated as follows:

[ equation 57]

K^ρ1＝R(ρ₁)Q^-1

[ Equation 58]

K^ρ2＝R(ρ₂)Q^-1

[ Equation 59]

K^ρ3＝R(ρ₃)Q^-1

The controller K (p) can thus be obtained because it is a convex combination of these local controllers. More specifically, equations 33 and 21 to 23 are used to determine the controller.

At this stage, it may be noted that the controller K to be used for defining the control set point of the actuator may preferably depend not only on the vehicle speed V but also on the form of the avoidance trajectory T0.

In order to understand what is, it must first be noted that in equation 48 where the term w represents the curvature of the avoidance trajectory, the maximum value w _max of this curvature is known (since the dynamic limits of the vehicle and thus the maximum curvature that the vehicle can follow completely safely and thus can be imposed by the trajectory planning is known). Thus, the parameter σ can be defined as:

[ equation 60]

In this equation, the time T _AES corresponds to the maximum duration of activation of the AES function (which is typically between 1 second and 3 seconds), and in particular to the duration of the back-off strategy.

When the avoidance trajectory T0 has been defined, the value of this parameter σ can thus be calculated.

The maximum interval of curvature of the avoidance trajectory T0 that the vehicle can achieve may be decomposed into N uniform subintervals. Thus, the term σ can be considered as belonging to one particular interval, and this can be written as:

[ equation 61]

σ∈∈[o,0+1]

Where i is a natural integer ranging from 1 to N.

Each interval may be defined by its mean, which may be written as:

[ equation 62]

The performance of the controller K depends on the curvature of the avoidance trajectory T0. Specifically, the smaller the curvature (i.e., the larger the radius of curvature at each point of the trajectory), the easier it is to follow the avoidance trajectory T0.

In the proposed concept of optimization using a linear matrix inequality, it is necessary to fix the term σ (which is inversely proportional to the curvature) in order to find the controller.

In other words, the obtained controller is optimal for only one considered curvature. However, if the vehicle has to follow a trajectory of a large curvature, the controller will be less robust, as this will lead to a risk of instability. Conversely, if the vehicle is caused to follow a trajectory of smaller curvature, the controller will not perform as well (there will be a follow-on delay or overshoot).

Now, when the AES function is triggered, the avoidance trajectory T0 suitable for this case is calculated for a fixed time expectation (next 3 seconds).

Preferably, the controller K may then be synthesized so as to fit the curvature of the avoidance trajectory T0.

More specifically, it will be possible to synthesize a plurality of controllers K (ρ) using the aforementioned inequalities, each controller being in communication with one of the aforementioned intervals (and more specifically with the mean thereof) And (5) associating. These controllers can then be write shaped/>

Then will be able to select a targetIs closest to the term σ calculated for the avoidance trajectory T0.

In fact, as shown in fig. 8, the calculation module B1 is able to determine the avoidance trajectory T0, so that the value of the parameter σ can be calculated. Thereafter, switch B2 will be able to select the controller that will be appropriate for the curvature of the trajectory for the entire avoidance trajectory T0 to be created

Thus, the controller will depend not only on the vehicle speed V but also on the curvature of the avoidance trajectory T0.

At this stage, it may also be briefly noted that there are a plurality of types of controllers K that can be obtained, depending on the selected value of α _ψ. Specifically, the performance of the controller K may be modified by adjusting the value of α _ψ.

Thus, the adjustment coefficient α _ψ makes it possible to obtain the controller K that minimizes the position follow error when the value is low. In contrast, when its value is high, the adjustment coefficient makes it possible to obtain the controller K that minimizes the heading-following error. At the start of the avoidance, the adjustment coefficient α _ψ will be selected to have a low value (below 20) to ensure that the vehicle is properly following the avoidance trajectory T0. In contrast, at the end of the avoidance maneuver (once the obstacle has been passed), the adjustment coefficient α _ψ will be selected to have a high value (above 20) to ensure that the vehicle is indeed repositioned parallel to the road.

Thus, for example, if the driver wishes to gain control again at the beginning of the avoidance maneuver and bypass the obstacle farther than expected (within the meaning of the avoidance maneuver T0), a high value for the adjustment coefficient α _ψ at the end of the avoidance maneuver means that the setpoint will not unnecessarily return the vehicle to the avoidance maneuver when the maneuver has been overshot too much (as otherwise this would be uncomfortable for the other driver).

Now that the calculation assumptions have been clearly established, it is possible to describe the method to be performed by the computer 13 of the motor vehicle in order to implement the invention.

Here, the computer 13 is programmed to implement the method in a recursive manner (i.e. in an iterative manner) cyclically.

To do so, in a first step, the computer 13 verifies that an autonomous obstacle avoidance function (AES) can be activated and that an obstacle avoidance trajectory has been planned by unit B1.

The computer then calculates the parameter sigma to select a controller suitable for the curvature of the trajectory

At this stage, and preferably, it may be provided that if the parameter σ exceeds a predetermined threshold, the computer keeps the process and does not activate the AES function. In particular, in such eventualities, it is considered that the process will not be able to achieve obstacle avoidance entirely safely.

If not, the AES function is activated.

The computer 13 will then try to define one control setpoint of the conventional steering system and another control setpoint of the differential braking system, which control setpoints enable the avoidance trajectory T0 to be followed as closely as possible.

To this end, it starts with calculating or measuring the following parameters:

The measured steering angle delta is used to measure the steering angle,

The estimated yaw moment M _z,

The derivative of the measured steering angle delta with respect to time,

The transverse velocity V _y is set at,

The yaw rate r is chosen to be the same,

The relative heading angle ψ _L,

-A side slip yL,

The curvature gamma _ref of the avoidance trajectory,

-Saturated steering angle set point delta _ref obtained in previous iteration, and

The saturated yaw moment set point M _{z_ref} obtained in the previous iteration.

The computer 13 then obtains the equations for the matrices K ^ρ1、K^ρ2、K^ρ3 obtained from the data stored in its memory and corresponding to the selected adjustment coefficients a _ψ and the curvature of the avoidance trajectory T0.

The controller K is then calculated from the vehicle speed V by determining the value of the coefficient α ₁、α₂、α₃ in advance.

The controller K will then make it possible to determine the values of the unsaturated steering angle set point δ _K and the saturated steering angle set point δ _ref and the values of the unsaturated yaw moment set point M _zK and the saturated yaw moment set point M _{z_ref}.

It should be noted that the matrix K ^ρ1、K^ρ2、K^ρ3 of the controller K is synthesized taking into account the saturation function so that the set point fits perfectly into the selected saturation model.

Eventually, the saturated steering angle set point δ _ref will be transmitted to the power steering actuator to turn the wheels of the motor vehicle 10. Likewise, the saturated yaw moment set point M _{z_ref} will be transmitted to the actuators of the differential braking system in order to brake the wheels of the motor vehicle 10.

The method is then repeated cyclically along the entire avoidance trajectory T0.

The invention is not in any way limited to the embodiments described and shown, but a person skilled in the art will know how to vary this embodiment in any way according to the invention.

Thus, the method may be applied in other types of fields where a specific trajectory is to be followed, such as in aeronautics or robotics (especially when the robot is small and needs to saturate one of its commands).

Claims (11)

1. A method for autonomous control of at least one actuator of an automotive device (10), the at least one actuator being capable of affecting a trajectory of the automotive device (10), the method comprising the steps of:

-acquiring a parameter (V _y,r,Ψ_L,y_L,δ,M_z,γ_ref) related to the trajectory of the vehicle device (10) and to the speed (V) of said vehicle device (10), and

-Calculating, using a computer (13), a control setpoint (M _{z_ref},δ_ref) for each actuator from said parameter (V _y,r,Ψ_L,y_L,δ,M_z,γ_ref), using a controller (K), characterized in that the controller (K) used varies with the speed (V) of the vehicle and comprises a plurality of components including at least one state return gain (K _Mz ^p,K_δ ^p) to be applied to said parameter (V _y,r,Ψ_L,y_L,δ,M_z,γ_ref) and at least one saturation compensation gain (K _Mz ^aw,K_δ ^aw) to be applied to the value of the control setpoint determined in the previous iteration.

2. The control method according to the preceding claim, wherein the automotive device (10) is a vehicle comprising wheels (11, 12), a power steering actuator and a differential brake actuator, the controller (K) comprising a plurality of components for determining a control setpoint of the power steering actuator and a control setpoint of the differential brake actuator.

3. Control method according to one of the preceding claims, wherein the controller (K) can be written in the form of the sum of the products of a variable (α ₁,α₂,α₃) dependent on the speed (V) and a local controller (K ^ρ1,K^ρ2,K^ρ3) independent of the speed (V).

4. A control method according to claim 3, wherein each local controller (K ^ρ1,K^ρ2,K^ρ3) is determined for a determined value of a vector (p) of two varying (scheduling) parameters, one of which is preferably equal to the speed V of the vehicle and the other of which is preferably equal to the inverse of said speed.

5. Control method according to one of the preceding claims, wherein the controller (K) corresponds to at least one saturation function modeled by a nonlinear sector.

6. Control method according to the preceding claim, wherein the saturation function conforms to a set point amplitude limiter model and can be expressed in the form:

psi ₁(x)＝sat_η (K (ρ). X) -K (ρ). X, wherein,

K is the controller, sat _η is the amplitude limiting function, and x is the state vector of the vehicle device (10) including the parameter.

7. Control method according to one of the two preceding claims, wherein the saturation function conforms to a model of the limit control setpoint variation (δ _ref) and can be expressed in the form:

ψ₂(x)＝sat_v(A₁x+B₁sat_η(K(ρ).x))-(A₁x+B₁sat_η(K(ρ).x)), Wherein,

K is the controller, sat _v is the amplitude limiting function, A1 and B1 are predetermined matrices, and x is the state vector of the automotive device (10) including the parameter.

8. Control method according to one of the preceding claims, wherein the controller (K) complies with a modeling of said device (10), wherein one output (z) to be minimized is a function of a trajectory following error (e _yL) and a heading angle error (ψ _L).

9. The control method according to one of the preceding claims, wherein in case the automotive device (10) is a vehicle and in case a trajectory (T0) to be followed by the vehicle has been planned, it is provided to calculate a parameter (σ) related to the curvature of the trajectory (T0) and then to implement the calculating step under the condition that the parameter lies within a predetermined interval.

10. Control method according to one of the preceding claims, wherein, in the case where the automotive device (10) is a vehicle comprising wheels (11, 12), a power steering actuator and a differential brake actuator, the control setpoint of the power steering actuator is calculated from the control setpoint of the differential brake actuator determined in the previous iteration and/or the control setpoint of the differential brake actuator is calculated from the control setpoint of the power steering actuator determined in the previous iteration.

11. An automotive device (10) comprising at least one actuator capable of affecting the trajectory of said device (10) and a computer (13) for controlling said actuator, characterized in that the computer (13) is programmed to implement the method according to one of the preceding claims.