Method for autonomously controlling an actuator of a device

Abstract

The invention relates to a method for autonomously controlling at least one actuator of an automotive device, said actuator being intended to have an influence on the trajectory of the automotive device, the method comprising steps of: - acquiring parameters (Vy, r, ΨL, yL, δ, Mz, Yref) relating to the trajectory of the automotive device and to the speed (V) of the automotive device, and - having a computer calculate a control setpoint (Mz_ref, δref) for each actuator, as a function of the parameters, using a controller (K). According to the invention, the controller used varies according to the speed of the vehicle.

Description

DESCRIPTION TITLE OF THE INVENTION: METHOD FOR AUTONOMOUSLY CONTROLLING AN ACTUATOR OF A DEVICE TECHNICAL FIELD OF THE INVENTION

[0001] The present invention relates generally to the automation of trajectory tracking 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 at least one actuator of an automotive device which is adapted to influence the trajectory of said automotive device, comprising steps of: - acquisition of parameters relating to the trajectory of the automotive device, and - calculation by a computer of a control instruction for each actuator, as a function of said parameters, using a controller.

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

[0005] It applies more particularly, but not exclusively, to the following of an obstacle avoidance trajectory by a motor vehicle. STATE OF THE ART

[0006] In an effort to make motor vehicles safer, they are currently being equipped with driver assistance systems or autonomous driving systems.

[0007] 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.

[0008] However, there are situations in which these emergency braking systems do not prevent a collision or cannot be used (for example, if a vehicle is following closely behind the motor vehicle).

[0009] For these situations, automatic avoidance systems (better known by the abbreviation AES, from the English "Automatic 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 path within a short time.

[0010] However, it may happen that the AES system imposes a limiting trajectory on the vehicle in terms of controllability, which does not allow the driver to regain control of the vehicle's driving safely.

[0011] Document FR3099450 then discloses a solution consisting of using a controller which makes it possible to generate a steering instruction such that the vehicle remains controllable by the driver of the vehicle if the latter wishes to take back control during the avoidance procedure. To do this, the controller limits the amplitude and speed of the change of direction imposed on the motor vehicle, by means of hyperbolic tangent functions. This solution, although effective in many configurations, has performance (i.e. good tracking of the avoidance trajectory) which can sometimes be improved.

[0012] More specifically, we wish to find a solution guaranteeing the performance and robustness of the vehicle's stability when its speed changes, which translates in particular into: - good tracking of heading and position throughout the avoidance trajectory, - good stability. PRESENTATION OF THE INVENTION

[0013] To this end, the invention proposes a control method as defined in the introduction, in which the controller used varies according to the speed of the vehicle (here we are talking about the speed of the vehicle relative to the road, which may have a longitudinal component in the axis of the vehicle and a lateral component).

[0014] More precisely, the controller varies continuously depending on the vehicle speed.

[0015] Thus, thanks to the invention, the controller used will not be the same regardless of the vehicle speed, which will allow the actuator control law to be best adapted to the vehicle dynamics. This solution proves to be effective. Indeed, the more the controller is adapted to the situation (i.e. the fewer eventualities it has to consider), the more latitude it will have to control the vehicle, which will allow it to avoid the obstacle in the safest and most comfortable way for the passengers.

[0016] This solution is particularly important when using differential braking (in addition to steering). In this case, the vehicle's speed always changes (decreases) along the avoidance trajectory, which has a significant impact on its behavior.

[0017] Other features of the invention will provide other advantages.

[0018] Thus, the solution described below will allow mixed control of steering and differential braking. In fact, the steering input (raw, before saturation) is not only calculated from the vehicle's dynamic variables, the measured steering angle and the saturated steering input, but also from the saturated yaw moment input and the measured (or estimated) yaw moment. And vice versa. This allows for good consistency between the two control inputs (they are mutually dependent on each other).

[0019] The structure of the proposed controller is simple, so that it is inexpensive to use in terms of computing power in particular.

[0020] Its development is simple since it simply consists of solving a system of linearized matrix inequalities, having previously fixed values ​​for certain parameters (minimum and maximum speeds of the vehicle within the framework of the AES function, minimum and maximum curvatures of the avoidance trajectory, etc.).

[0021] This controller can vary depending on the curvature of the avoidance path, so as to be well adapted to the situation.

[0022] This controller allows to maximize the performance and robustness of the vehicle's effective trajectory, within the vehicle's controllability limits.

[0023] As mentioned, the method used ensures good performance, i.e. good position and heading tracking, which allows the vehicle to follow with greater precision the avoidance trajectory calculated to avoid the obstacle.

[0024] The claimed solution also ensures high stability as long as the disturbances have a limited energy, that is to say in particular as long as the trajectory to be followed has a curvature remaining within acceptable limits. In other words, this solution makes it possible to quickly know whether the calculated avoidance trajectory can be dynamically achieved by the vehicle, so as to only activate the AES function when this is the case.

[0025] More precisely, if a characteristic of the trajectory exceeds a predetermined threshold, it may be planned not to activate the AES function. The idea is therefore not to deactivate the AES function a posteriori, but to choose whether or not to activate it a priori, which makes it possible to anticipate cases where the system would be potentially unstable and cases where the trajectory produced would be too imperfect (with too much overshoot, too large oscillations, etc.).

[0026] According to the invention, the controller operates even if the initial states of the vehicle at the time of triggering the AES function are non-zero (initial heading, initial yaw rate, etc.), which happens when the vehicle already has a certain dynamic (for example because it is in a bend at the time of triggering the AES obstacle avoidance function), which is not the case with the solution described in the document FR3099450. To achieve this result, the controller is synthesized by considering the initial states of the vehicle.

[0027] Other advantageous and non-limiting characteristics of the method according to the invention, taken individually or in all technically possible combinations, are as follows: - said automotive device is a vehicle which comprises wheels, a power steering actuator and a differential braking actuator; - the controller comprises several components making it possible to determine a control setpoint for said power steering actuator and a control setpoint for said differential braking actuator; - the controller comprises several components, including at least one state feedback gain to be applied to said parameters, and at least one saturation compensation gain to be applied to a value of the control setpoint which has been determined at a previous time step; - the controller is written in the form of a sum of several 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 variant parameters, one of said variant parameters being preferably equal to the speed V of the vehicle and the other of said variant parameters being preferably equal to the inverse of said speed; - the controller satisfies a modeling of at least one saturation function per non-linear sector; - the saturation function satisfies a setpoint amplitude limiting model and is expressed in the form:; - the saturation function satisfies a limiting model of variation of the control setpoint and is expressed in the form: with K the controller, satν an amplitude limiting function, A1 and B1 predetermined matrices, and x a state vector of said automotive device comprising said parameters; - the controller satisfies a modeling of said device in which an output to be minimized is a function of a trajectory tracking error and a heading angle error; - it is planned to calculate a parameter relating to the curvature of said trajectory then it is planned to implement said calculation step only on condition that said parameter is included in a predetermined interval; - the control instruction of said power steering actuator is calculated as a function of a control instruction of the differential braking actuator calculated previously; - the control instruction of said differential braking actuator is calculated as a function of a control instruction of the power steering actuator calculated previously.

[0028] The invention also proposes an automotive device comprising at least one actuator which is adapted to influence the trajectory of said device and a computer for controlling said actuator, which is programmed to implement a method as defined above.

[0029] Of course, the various features, variations 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

[0030] 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.

[0031] On the attached drawings:

[0032] [Fig.1] is a schematic top view of a motor vehicle traveling on a road and which is suitable for implementing a method according to the invention;

[0033] [Fig.2] is a graph illustrating parameters used in the process of Figure 1;

[0034] [Fig.3] is a schematic top view of the motor vehicle of Figure 1, shown in four successive positions located along an obstacle avoidance path;

[0035] [Fig.4] is a diagram illustrating a polytope used in the process of Figure 1;

[0036] [Fig.5] is a diagram illustrating the closed-loop transfer function used to control the motor vehicle of Figure 1;

[0037] [Fig. 6] is a graph illustrating saturation polyhedra and a basin of attraction of the controller used in the method of Figure 1, and an example of variation of the state of the vehicle in the absence of disturbance,

[0038] [Fig.7] is a graph similar to that of Figure 4, on which the example of variation in the state of the vehicle is represented in the event of the presence of a disturbance;

[0039] [Fig.8] is a diagram illustrating a method of selecting a suitable controller within the framework of the method of Figure 1.

[0040] In Figure 1, a motor vehicle 10 is shown, conventionally comprising a chassis which delimits a passenger compartment, two front steering wheels 11, and two 12 non-steering rear wheels. Alternatively, these two rear wheels could also be steered with an adaptation of the control law.

[0041] This motor vehicle 10 comprises a conventional steering system for acting on the orientation of the front wheels 11 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 front wheels 11. In the example considered, it also comprises an actuator for acting on the orientation of the front 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 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 implemented in a different manner.

[0042] In addition, the motor vehicle comprises a differential braking system making it possible to act differently on the rotation speeds of the front wheels 11 (and where appropriate on those of the rear wheels 12) so as to slow down the motor vehicle by making it turn. In the example considered, this differential braking system comprises at least one actuator formed for example by a controlled differential or by electric motors placed at the level of the wheels of the vehicle.

[0043] The computer 13 is then designed to control the power steering actuator and the differential braking system actuator. For this purpose, it comprises at least one processor, at least one memory and various input and output interfaces.

[0044] Thanks to its input interfaces, the computer 13 is adapted to receive input signals from different sensors.

[0045] Among these sensors, the following are provided, for example: - a device such as a front camera, making it possible to locate the position of the vehicle relative to its traffic lane, - a device such as a RADAR or LIDAR remote sensor, making it possible to detect an obstacle 20 located on the trajectory of the motor vehicle 10 (figure 3), - at least one lateral device such as a RADAR or LIDAR remote sensor, making it possible to observe 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, - a steering wheel position and angular speed sensor, and - a sensor making it possible to estimate the yaw moment experienced by the vehicle.

[0046] In practice, no sensor is provided for measuring the yaw moment. Instead, a low-level calculation unit is provided, which is capable of estimating the yaw moment based on the braking torques applied to the vehicle's wheels.

[0047] Thanks to its output interfaces, the calculator 13 is adapted to transmit a instruction to the power steering actuator and the differential braking system actuator.

[0048] It thus makes it possible to force the vehicle to follow an avoidance trajectory T0 of the obstacle 20 which will have been defined beforehand (see figure 3).

[0049] Thanks to its memory, the computer 13 stores data used in the process described below.

[0050] 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.

[0051] Before describing this process, we can introduce the different variables that will be used, some of which are illustrated in Figures 1 and 2.

[0052] The total mass of the motor vehicle will be noted “m” and will be expressed in kg.

[0053] The inertia of the motor vehicle around a vertical axis passing through its center of gravity CG will be noted “J” and will be expressed in Nm

[0054] The distance between the center of gravity CG and the front axle of the vehicle will be noted “lf” and will be expressed in meters.

[0055] The distance between the center of gravity CG and the rear axle will be noted “lr” and will be expressed in meters.

[0056] The front wheel drift stiffness coefficient will be noted “Cf” and will be expressed in N / rad.

[0057] The rear wheel drift stiffness coefficient will be noted “Cr” and will be expressed in N / rad.

[0058] These wheel drift stiffness coefficients are concepts well known to those skilled in the art. For example, the front wheel drift stiffness coefficient is thus the one that allows the equation Ff = 2.Cf.αf to be written, with Ff the lateral sliding force of the front wheels and αf the front wheel drift angle.

[0059] The steering angle that the front steered wheels make with the longitudinal axis A1 of the motor vehicle 10 will be noted “δ” and will be expressed in rad.

[0060] The variable ^ ref , expressed in rad, will designate the saturated steering angle setpoint, as it will be transmitted to the power steering actuator.

[0061] The variable ^K, expressed in rad, will designate the unsaturated steering angle setpoint. At this stage, we can only specify that the concept of saturation will be linked to steering angle and steering speed limits which would not necessarily be respected with the variable ^K, but which would be with the variable ^ref.

[0062] The variable ^sat, expressed in rad, will designate the semi-saturated steering angle setpoint. It comes from the unsaturated setpoint ^ K and is saturated in steering angle only. The saturated instruction ^ ref will be calculated on the basis of this semi-saturated setpoint ^ sat .

[0063] The vehicle's orthogonal reference frame (defined here when the vehicle is on a horizontal surface) will have its center of gravity CG as its origin. Its abscissa Xv will be oriented along the longitudinal axis A1 of the motor vehicle 10, and its ordinate Yv will be oriented laterally, on the left side of the vehicle. The vertical axis passing through the center of gravity will be noted ZV.

[0064] The yaw moment exerted by the differential braking system around the ZV axis, expressed in Nm, will be noted Mz.

[0065] The variable Mz_ref, expressed in Nm, will designate the yaw moment setpoint to be applied to the wheels using the differential braking means.

[0066] The variable MzK, expressed in Nm, will designate the unsaturated yaw moment setpoint. At this stage, we can only specify that the concept of saturation will be linked to limits of yaw moment and yaw moment variation which would not necessarily be respected with the variable M zK , but which would be with the variable M z_ref .

[0067] The variable Mz_sat, expressed in Nm, will designate the semi-saturated yaw moment setpoint. It comes from the variable MzK and is saturated in amplitude only. The saturated setpoint Mz_ref will be calculated on the basis of this semi-saturated setpoint Mz_sat.

[0068] The vehicle's yaw rate (around the vertical axis passing through its center of gravity CG) will be noted "r" and will be expressed in rad / s.

[0069] The relative heading angle between the longitudinal axis A1 of the vehicle and the tangent to the avoidance trajectory T0 (desired trajectory of the vehicle) will be noted “Ψ L » and will be expressed in rad.

[0070] The lateral deviation between the longitudinal axis A1 of the motor vehicle 10 (passing through the center of gravity CG) and the avoidance trajectory T0, at a sighting distance “ls” located in front of the vehicle, will be noted “y L » and will be expressed in meters.

[0071] The lateral deviation instruction between the longitudinal axis A1 of the motor vehicle 10 (passing through the center of gravity CG) and the avoidance trajectory T0, at a sighting distance “ls” located in front of the vehicle, will be noted “y L-ref » and will be expressed in meters.

[0072] The trajectory tracking error will be noted as “e yL » and will be expressed in meters. It will be equal to the difference between the lateral deviation setpoint yL-ref and the lateral deviation yL.

[0073] The aforementioned aiming distance “ls” will be measured from the center of gravity CG and will be expressed in meters.

[0074] The drift angle of the motor vehicle 10 (angle that the speed vector of the motor vehicle makes with its longitudinal axis A1) will be noted “β” and will be expressed in rad.

[0075] The speed of the motor vehicle will be noted “V” and will be expressed in m / s.

[0076] The lateral speed of the motor vehicle, corresponding to the projection of the vehicle speed vector on the Yv axis, will be noted “Vy”.

[0077] The constants “ξ” and “ω” will represent dynamic characteristics of the steering angle of the vehicle’s front wheels.

[0078] The constant "g" will be the acceleration of gravity, expressed in ms -2 .

[0079] The steering speed will refer to the angular steering speed of the front steered wheels.

[0080] The method according to the invention is designed to allow the vehicle to follow the avoidance trajectory T0 as precisely as possible, in autonomous mode. This method is implemented when an AES function for automatic obstacle avoidance has been triggered and then an avoidance trajectory T0 has been calculated. It will be noted that the manner of triggering the AES function and calculating the avoidance trajectory T0 is not strictly speaking the subject of the present invention, and will therefore not be described here.

[0081] This process is intended to be implemented in a loop, during successive “time steps” (here these time steps have a duration of approximately 10ms).

[0082] It should be noted here that the trajectory tracking is intended to be operated autonomously by the computer 13, but that it must also be able to be interrupted at any time to allow the driver to regain control of the vehicle. It must also be able to be used as an aid for the driver when the latter is holding the steering wheel but is not exerting the torque that would be required on the steering wheel to avoid the obstacle.

[0083] Before describing the process which will be executed by the calculator 13 to implement the invention itself, we can in a first part of this presentation describe the calculations which 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.

[0084] 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 which, once implemented in the computer 13, will allow the vehicle to be piloted so that it follows the avoidance trajectory T0 in a stable and efficient manner.

[0085] Here we will consider that the dynamic behavior of the vehicle can be modeled using the following equation Math.1.

[0088] This model is a classic bicycle model.

[0089] It should be noted that the term γref of curvature of the avoidance trajectory T0 makes it possible to take into account the trajectory of the vehicle (and therefore the curvature of the road) in the modeling of the dynamic behavior of the vehicle.

[0090] It should also be noted that in the preliminary state vector used, the first state variable will be the lateral velocity Vy. Alternatively, the drift angle β could have been used. However, the use of the lateral velocity Vy will be preferred because it will reduce the number of varying parameters in the nonlinear model described below.

[0091] The steering of the front wheels 11 of the vehicle can be modeled simply by the following formula:

[0094] Differential braking presents a dynamic that can be modeled by the following differential equation:

[0095] [Math.3]

[0096] ^̇ ^ = −^^ ^ + ^^ ^_^^^

[0097] In this equation, τ is a dynamic characteristic of the yaw moment.

[0098] These three equations make it possible to write a new model of the vehicle's behavior.

[0101] We can also model the variation in curvature of the avoidance trajectory T0 by the equation below.

[0102] [Math.5]

[0103] ^̇ ^^^ = −^ ^ ^ ^^^ + ^ ^ ^

[0104] In this equation, the variable ωf represents a dynamic characteristic of the variation of the curvature of the trajectory. As for the term ^, it is a random input assumed to be bounded.

[0105] This equation (like equation Math.3) allows us to model the variation of the curvature of the trajectory in the form of a low-pass filter.

[0106] The two previous equations therefore make it possible to write a model of the enriched vehicle:

[0109] On this new model, we can see that the vehicle's speed V is involved. Speed ​​is indeed important to take into account since the differential braking system will have an influence not only on the vehicle's trajectory but also on its speed. The vehicle's speed will also depend on other factors such as the braking or acceleration instructions imposed on the vehicle by the driver or by the computer 13.

[0110] For the synthesis of a trajectory tracking controller (which will be described in more detail below) that is robust in terms of stability and performance, it is therefore important to take into account the change in vehicle speed.

[0111] Here, the idea is to reformulate the aforementioned Math.6 equation into an LPV (Linear Parameter Variant) model, which will then make it easier to find a controller that will need to be optimized for this LPV model.

[0112] This improved model is as follows.

[0115] In this equation, the term ρ1 / v is equal to the inverse of the speed V (i.e. 1 / V) and the term ρv is equal to the speed V. These two terms are commonly called "variant parameters". Their vector ρ is then written in the form (ρv, ρ1 / v).

[0116] The state vector xp is defined as follows.

[0117] [Math.8] ^

[0118] ^ ^ = ^ ^ ^ ^ ^ ^ ^ ^ ^̇ ^ ^ ^ ^ ^^^ ^

[0119] As for the up vector, it is written as follows.

[0120] [Math.9]

[0121] ^ ^ = (^ ^^^ ^ ^_^^^ )

[0122] The matrices used are written as follows.

[0131] [Math.14]

[0133] It should be noted that these equations are well defined and explained in the paper “M. Corno, G. Panzani, F. Roselli, M. Giorelli, D. Azzolini and SM Savaresi, "An LPV Approach to Autonomous Vehicle Path Tracking in the Presence of Steering Actuation Nonlinearities," in IEEE Transactions on Control Systems Technology, doi: 10.1109 / TCST.2020.3006123”.

[0134] At this point, the equation Math.7 can be rewritten using a very particular form, namely in the form of a polytopic LPV system. To do this, we assume that the vehicle speed is limited between two minimum limits Vmin and maximum Vmax.

[0135] The vector of variant parameters ρ is then bounded by the contour of the geometric figure represented in Figure 4, called polytope P1. This polytope is presented here in the form of a triangle. The vertices ρ1, ρ2, ρ3 of this polytope P1 are defined by the following equations.

[0138] As will become clear in the rest of this presentation, the idea of ​​this polytope consists of taking into account the fact that the controller K (which will allow the calculation of the instructions to be transmitted to the actuators) will depend on the speed, and that it will be easier to calculate it by means of an approximation resulting from the theory of projection onto a closed convex space.

[0139] Now the function ρ, illustrated in Figure 4, is a curve C1 which varies between the ends ρ1 and ρ3. The convex space chosen to frame this curve C1 in the tightest possible way is then the polytope P1. We are in fact trying to frame the curve in a tight way so as not to increase the number of eventualities taken into account, which would make the controller too conservative. The triangle shape is the one which allows us to obtain the best results.

[0140] The chosen theory will therefore make it possible to calculate the controller K for any speed V between two minimum limits V min and maximum V max , depending on the three values ​​of this controller K at the vertices ρ1, ρ2, ρ3 of this polytope P1. It is then appropriate simply to determine these three values ​​of this controller K.

[0141] In practice, it is possible to rewrite the equation Math.7 as follows:

[0142] [Math.16]

[0143] ^̇ ^ = ^ ^ ( ^ ) ^ ^ + ^ ^ ^ ^ + ^ ^ ^

[0144] With

[0145] [Math.17]

[0146] ^ ^ = ^ ^^^ ^^ ^^ ^ ( ) ^ ^ + ^ ^ ^ ^ + ^ ^ ^ ^

[0147] Or

[0160] However, this model does not in itself limit the steering angle and steering speed of the front wheels 11 of the vehicle, as well as the amplitude of the yaw moment applied by the differential braking and the speed of variation of this yaw moment. However, such limitations are particularly important, in particular to ensure that the driver of the vehicle is able to regain control of the vehicle at any time.

[0161] Such limitations can be expressed using the following equations.

[0162] For the steering speed limitation, we can write.

[0165] For the limitation in amplitude of the steering angle, we can write.

[0168] In the equation Math.24, the coefficient υ δis a constant that represents the steering speed not to be exceeded. This constant is defined either by calculation or following a test campaign carried out on a test vehicle. For example, it is equal to 0.0491 Rad / s, which corresponds to 0.785 Rad / s at the steering wheel (i.e. 45° / s) if the steering gear ratio is equal to 16.

[0169] In equation Math.25, the coefficient η δ is a constant that represents the steering angle not to be exceeded. This constant is defined either by calculation or following a test campaign carried out on a test vehicle. For example, it is equal to 0.0328 Rad, which in our example corresponds to 0.524 Rad at the steering wheel (i.e. 30°).

[0170] The constraint expressed by the equation Math.25 limits the torque exerted by the power steering actuator so that an average driver can manually compensate for this torque.

[0171] Indeed, the greater the steering angle, the greater the force applied by the power steering actuator. This limitation ensures that the user can regain control of the vehicle without having to counteract excessive force. This angle will then depend on the force applied by the type of actuator chosen.

[0172] The constraint expressed by the equation Math.24 allows the driver not to be surprised by not varying the steering wheel orientation too quickly.

[0173] It should be noted that the above values ​​are given as an example and could alternatively be lower (for example 25° / s and 20° to ensure greater comfort).

[0174] For the limitation in speed of variation of the yaw moment, we can write. in amplitude of the yaw moment, we can write.

[0180] In the equation Math.26, the coefficient is a constant that represents the variation in the yaw moment not to be exceeded. This constant is defined either by calculation or at the end of a test campaign carried out on a test vehicle. It is, for example, equal to 2500 Nm / s.

[0181] In equation Math.27, the coefficient η M is a constant that represents the yaw moment not to be exceeded. This constant is defined either by calculation or at the end of a test campaign carried out on a test vehicle. It is, for example, equal to 2000Nm.

[0182] These two equations allow the driver to regain control of the steering of the vehicle in a controllable manner, at all times. In particular, they help to limit the surprise effect that would be due to sudden lateral acceleration.

[0183] According to the invention, we wish to limit these four parameters not by imposing a sudden threshold, but rather by gradually saturating their values. Above all, we wish to take these four parameters into account in the synthesis of the controller, so that it presents a more stable and more pleasant behavior for the vehicle passengers.

[0184] Figure 5 shows the control architecture used to control the power steering actuator and the differential braking actuator, so that the vehicle follows the avoidance trajectory T0 as best as possible while respecting the aforementioned constraints.

[0185] In this figure, a controller K is represented as depending on the speed V of the vehicle and as being composed of two components, one (denoted K Mz ) associated with differential braking and the other (noted K δ ) associated with power steering.

[0186] These two components allow respectively to calculate an unsaturated yaw moment setpoint MzK and an unsaturated steering angle setpoint ^K.

[0187] Each of these two components advantageously includes a summer which provides the unsaturated setpoint as output and which receives as input a state feedback term (from a state feedback block K Mz p , K δ p ) which depends on the state of the vehicle, and a saturation compensation term (from a saturation compensation block K Mz aw , K δ aw ) which depends on the saturated yaw moment Mz_ref or steering angle ^ref setpoint calculated at the previous time step.

[0188] The saturation compensation term helps to enhance the stability of the controller in non-linear mode, i.e. in cases where the control of the power steering or yaw moment actuator is saturated in amplitude or speed.

[0189] The SAT1 block shown in Figure 5 illustrates the amplitude saturation of the unsaturated steering angle setpoint ^K. It receives as input the output of the corresponding component of the controller K and provides as output a semi-saturated steering angle setpoint ^ sat . We observe that this block operates in open loop.

[0190] The SAT2 block illustrates the amplitude saturation of the unsaturated yaw moment setpoint MzK. It receives as input the output of the corresponding component of the K controller and provides as output a semi-saturated yaw moment setpoint Mz_sat. We observe that this block also operates in open loop.

[0191] The SAT3 block set illustrates the speed saturation of the semi-saturated steering angle setpoint ^ sat . It receives this semi-saturated instruction as input and provides the saturated steering angle instruction as output ^ ref . We observe that this is a closed loop.

[0192] The SAT4 block set illustrates the velocity saturation of the semi-saturated yaw moment setpoint M z_sat It receives this semi-saturated setpoint as input and provides the saturated yaw moment setpoint M as output. z_ref . We observe that this is also a closed loop.

[0193] In each of these two sets of blocks SAT3, SAT4, corresponding to "pseudo rate limiter" functions, an adder is therefore provided as input which allows the calculation of the difference ^ between the semi-saturated setpoint and the saturated setpoint at the previous time step. It includes a multiplier block allowing this difference to be multiplied by the parameter λ, a saturation block allowing the derivative of the saturated setpoint to not be exceeded and an integrator block allowing the saturated setpoint to be obtained (via a Laplace transform).

[0194] The parameter λ represents the dynamics of the SAT3 and SAT4 blocks (for our application, we can consider λ = 500), and the larger λ is, the closer this pseudo rate limiter is to a “rate-limiter” function.

[0195] In Figure 5, the Psys block represents the open-loop system that describes the vehicle dynamics, the behavior of the power steering actuator, the behavior of the differential braking actuator, and the positioning of the vehicle relative to the avoidance trajectory T0.

[0196] We observe that this block receives as input the disturbance w, the saturated yaw moment setpoint M z_ref , and the saturated steering angle instruction ^ ref . It provides as output an output vector y and an error z.

[0197] The output vector y corresponds in practice to the state vector xp introduced previously.

[0198] The error z has a value that we seek to minimize.

[0199] This error z is here a function of the trajectory tracking error eyL and the relative heading angle between the longitudinal axis A1 of the vehicle and the tangent to the avoidance trajectory T0 (hereinafter denoted heading error ΨL), which we know should be minimized. We can then write:

[0200] [Math.28]

[0201] ^ = ^ ^^ + ^ ^ . ^ ^

[0202] In this equation, the term ^ Ψ is an adjustment coefficient that allows the adjustment of the error that we want to minimize as a priority (heading-angle error or position-tracking error). We will see in the rest of this presentation how the value of this adjustment coefficient is chosen. This choice of output z error makes it possible to guarantee both good position tracking and good heading tracking.

[0203] The objective is then to determine the form of the controller K which is a regulator of the state feedback allowing the calculation of the unsaturated yaw moment setpoint M zK and the unsaturated steering angle setpoint ^K based on the preliminary state vector xp, taking into account the vehicle speed V.

[0204] To understand how to determine a K controller that is suitable in terms of both stability and performance, we can first describe the Psys system when it operates in open loop, that is to say in linear mode, without saturation (case where the saturated and unsaturated steering angle setpoints ^ ref , ^ K are equal and where the saturated and unsaturated yaw moment setpoints Mz_ref, MzK are also equal).

[0205] We can write our system in a generic form:

[0208] Given the equation Math.28, the matrix C pz is known. Note that the principal matrices A p , command B p and disturbance Bw are deduced from the equation Math.6.

[0209] The controller K, for which we are looking for the optimal gains that meet our control criteria, which is defined as a static state feedback regulator, can be expressed in the form:

[0210] [Math.30]

[0211] ^ ^ = ^(^). ^

[0212] In this equation, the term x is the state vector augmented by the saturated steering angle and saturated yaw moment setpoints. It will be this augmented state vector that will be considered in the remainder of this presentation. It can be written as follows.

[0213] [Math.31]

[0214] ^ = [^^ ^^]^

[0215] For the reasons mentioned above with reference to Figure 5, the state feedback gain to be optimized forms a 2x2 matrix whose terms depend on the speed V of the vehicle and which is expressed as follows:

[0218] As explained above, the controller K can be expressed in terms of its values ​​at the vertices ρ1, ρ2, ρ3 of the polytope. More precisely, it can be written in the following polytopic form:

[0219] [Math.33]

[0220] ^ ( ^ ) = ^ ^^ ^ ^ + ^ ^^ ^ ^ + ^ ^^ ^ ^

[0221] In this equation, the terms α1, α2, α3 are defined by equations Math.21 to Math.23.

[0222] The K matrices ρ1 , K ρ2 , K ρ3 , on the basis of which the controller K can be calculated, must be determined by an optimization proposed in the following paragraphs.

[0223] Here, the idea is to synthesize not an infinite number of K controllers, but a reduced number of them (equal to three). The values ​​of the other controllers can then be interpolated according to those of these three matrices, via the aforementioned convex combination.

[0224] We can now describe the Psys system in a closed loop, that is to say in non-linear mode with saturation (case where the saturated and non-saturated setpoints are unequal).

[0225] Based on equations Math.29 and Math.30, we can write:

[0228] In this equation, the terms A, B, A1 and B1 are defined as follows:

[0231] [Math.36]

[0232] ^ = ^0^ ^

[0233] I is the identity matrix.

[0234] [Math.37]

[0235] ^ ^ = [ 0 −Λ ]

[0236] [Math.38]

[0240] To take into account the controllability constraints as defined in equations Math.24 to Math.27, two new saturation functions Ψ1(x) and Ψ2(x) have been introduced, which represent the exceeding of the limits of the unsaturated control input.

[0241] The two saturation functions Ψ1(x) and Ψ2(x) can therefore be defined as follows:

[0242] [Math.40]

[0246] In these two equations, we use a saturation function denoted satf0(f), which can be defined as follows:

[0249] We will therefore note that these two saturation functions Ψ1(x), Ψ2(x) have zero values ​​in unsaturated mode and non-zero otherwise.

[0250] We then seek to model the saturation functions via a modeling by non-linear sectors (from the English "dead-zone nonlinearity"), on the basis of works disclosed in the referenced documents: - "S. Tarbouriech, G. Garcia, JM Gomes da Silva Jr., and I. Queinnec, Stability and Stabilization of Linear Systems with Saturating Actuators, 1st ed. London: Springer, 2011", and - "Alessandra Palmeira, João Manoel Gomes da Silva Jr, Sophie Tarbouriech, I. Ghiggi. Sampled-data control under magnitude and rate saturating actuators. International Journal of Robust and Nonlinear Control, Wiley, 2016, 26 (15), pp.3232 – 3252".

[0251] To model the controllability limits of the system, two polyhedra can be defined, one of which, denoted S1(x,η), models the behavior of saturation in amplitude and the other, denoted S2(x,Ψ1,ν) models the behavior of saturation in velocity. These two polyhedra can be modeled in the following form:

[0256] These models involve matrices G1, G2 and G3. These matrices have the same dimension as that of the controller K. They illustrate the deviation that is allowed to exceed the saturation constraints.

[0257] As an illustration, the matrix G1 could be considered equal to the product of the matrix K by a scalar ^ K . Then the equation Math.44 could be rewritten in a form involving the term (1- ^K), which will therefore constitute a setting of the authorized excess. This excess could for example be set to 10%. To adjust this excess, it will be necessary to carry out road tests.

[0258] However, preferably, this matrix G1 will not be a function of the matrix K. It will have to be optimized not by road tests, but by calculations, for example by the method of linear matrix inequalities. In this way, we will avoid the conservatism of a solution such as that described in the previous paragraph.

[0259] As a first step, it can be assumed that during the operation of the closed-loop system (as defined in equation Math.7), the state vectors x and the variable are found in these two polyhedra, so that we can write:

[0262] These two polyhedra are represented here in figures 6 and 7 and therefore represent, as will be well described above, the two spaces within which the stability and performance of the system are guaranteed.

[0263] It should be noted at this point that these figures illustrate two-dimensional graphs, simplifying the solution described above in order to make it more understandable.

[0264] In other words, this two-dimensional representation would only be valid if the state vector x had only two state variables, one forming the abscissa and the other the ordinate of each of these graphs.

[0265] In practice, here the state vector has ten state variables. A representation of the invention should therefore be plotted in ten dimensions.

[0266] With the assumption made in the above equation, the following inequalities are satisfied for all positive diagonal matrices U1 and U2, which are more precisely here positive scalar quantities:

[0269] It should be noted here that these scalar quantities U1 and U2 are introduced here simply to facilitate subsequent calculations (according to the S-procedure).

[0270] To summarize, equations Math.43 and Math.44 are two saturation models, respectively in amplitude and in speed, which, as long as they remain valid in the sense of equation Math.45, make it possible to ensure that equations Math.46 are also valid.

[0271] These models can then be used for the synthesis (i.e. optimization) of the main gains K δ p , K Mz p of the state feedback linked to the state variables of the open loop system P and the gains K δ aw , K Mz aw compensation of saturations (or “anti-windup gain”) of the K controller.

[0272] The closed-loop Math.34 equation and the representation of the Psys system shown in Figure 5 allow us to write:

[0273] [Math.47]

[0275] We assume that the perturbation w is limited in energy, that is to say bounded, so that we can write:

[0278] This assumption is linked to the fact that the curvature of the trajectory (which is here considered as a disturbance) and the activation duration of the AES function are always bounded.

[0279] So, in the equation Math.48, where the term w is related to the curvature of the avoidance trajectory, the maximum value wmax of this term is known (since we know the dynamic limits of the vehicle and therefore the maximum curvature that the vehicle can follow safely and in fact imposeable by trajectory planning).

[0280] To obtain an optimal solution of the controller K, we first define a Lyapunov function V(t) for the stability conditions:

[0281] [Math.49]

[0282] ^ ( ^ ) = ^ ^ ^^

[0283] In this equation, the matrix P is positive definite and symmetric.

[0284] The interest of this Lyapunov function V(t) is that if its first derivative is strictly negative, it guarantees that the system will always be stable in the absence of disturbance.

[0285] Figures 6 and 7 show the two polyhedra that ensure the stability and performance of the system. We will then look for a space located simultaneously in these two polyhedra. This could, for example, be the intersection of these two spaces.

[0286] However, here, we will prefer to model this space in the form of an ellipse called a basin of attraction. This basin of attraction ε is defined here in the form:

[0287] [Math.50]

[0288] ℰ(^, ^) = {^ ∈ ^ ^ , ^ ^ ^^ ≤ ^ ^^}

[0289] In addition to the stability condition relating to this Lyapunov function V(t), this basin of attraction must be included in the two polyhedra S1 and S2, which respectively model the saturations in amplitude and in speed, to guarantee the stability of the system (which remains the priority to guarantee).

[0290] The basin of attraction ε is therefore a stability space (or invariant space) of the system considered. In other words, it is a space within which the trajectories of the state variables (i.e. the components of the state vector x) remain, provided that they have been initialized in this space (even if the system is subject to disturbances and saturations of the actuators).

[0291] Taking into account the above equations, the spaces in which the state variables of the system can evolve are schematically represented in Figures 6 and 7.

[0292] As can be understood from these figures, the controller K is then synthesized in such a way as to meet three objectives.

[0293] The first objective is that in the absence of disturbance, the controller K guarantees that the trajectories of the state variables of the closed-loop system remain in the basin of attraction ε (which ensures stability) and converge asymptotically towards the origin (which ensures performance), in particular within a predefined time.

[0294] In Figure 6, we considered the case of absence of disturbance. In this case, the space of initial conditions of the system, denoted E0, and the estimate E1 of the basin of attraction ε merge. We observe that the trajectory T1 of the state vector x from any initial situation converges well towards the origin.

[0295] The second objective is that in the presence of a disturbance, the controller K guarantees that the trajectories of the state variables of the closed-loop system remain in the basin of attraction ε (which ensures stability) whatever the disturbance w, provided that the latter is limited in energy (in the sense of equation Math.48).

[0296] In Figure 6, we have considered this case where a disturbance occurs. In this case, the space of initial conditions of the system, noted E0, are necessarily contained in the estimate E1 of the basin of attraction ε. We observe that the trajectory T2 of the state variables, when it starts from any initial situation contained in the space E0, remains well contained inside the basin of attraction ε.

[0297] The third objective is that in linear mode (without saturation in amplitude and speed), the K controller guarantees the performance of the system, which then takes precedence over stability, by ensuring that the synthesis of the H∞ norm is less than a predetermined scalar.

[0298] We will recall that this synthesis consists of finding the controller K which is such that the norm H∞ of the term Fl(Psys, K) is minimum, with:

[0299] [Math.51]

[0300] ^ = ^ ^ ^ ^ ^^^ , ^ ^ . ^

[0301] We can write this equation in the following form:

[0302] [Math.52]

[0303] ^̇ ( ^ ) + ^ ^ ^ − ^ ^ ^ ^ ^ < 0

[0304] We will note here that γ is the H∞ norm of the transfer function from w -> z. In linear mode (without saturation), we will have the guarantee on the performance (with the H∞ norm) thanks to this constraint.

[0305] This synthesis involves good rejection of the disturbance w and good monitoring of the avoidance trajectory (with a z error close to zero).

[0306] In practice, to satisfy these three objectives, several methods could be used.

[0307] The method used is preferably the use of linear matrix inequalities (LMI). It is carried out using convex optimization criteria under linear matrix inequality constraints (the linearity of the terms of the matrices used ensures that the mathematical problem can be solved without requiring too much computational work).

[0308] The objective is more precisely to optimize the gains of the closed loop defined by the K controller by playing on the choice of poles.

[0309] More precisely, if there exist matrices of appropriate dimensions R(ρ), Q, L1(ρ), L2(ρ), T1(ρ), T2(ρ) such that the optimization problem below is feasible, we obtain a controller ^ which satisfies the three aforementioned objectives.

[0310] These matrices are calculated based on the matrix P.

[0311] The matrix inequalities used here are three in number and are defined by the following inequalities, in which ^ is to be minimized.

[0318] In these inequalities, i is an integer successively equal to 1 then 2.

[0319] The term X(i) corresponds to row i of the matrix X.

[0320] In these inequalities always, a matrix of the form is written in the form .

[0321] The matrix variables R, Q, L1, L2, T1, T2 are expressed here in the form of matrices of appropriate dimensions.

[0322] Matrix variables are expressed in the following form:

[0323] [Math.56]

[0324]

[0325] To solve the optimization problem below within the framework of the problem as posed, it is necessary to solve the matrix inequalities (LMI) only at each vertex (ρ1, ρ2, ρ3) of the polytope represented in Figure 4, which amounts to solving 9 inequalities.

[0326] At this stage, for the optimization of each of the K terms ρ1 , K ρ2 , K ρ3 , the speed V of the vehicle is assumed to be constant (so all these matrices are considered constant). Indeed, each term is optimized for a given vector ρ, that is to say for a given speed.

[0327] The three inequalities Math.53 to Math.55 ensure that the dynamics of the closed loop remains limited, that is to say that the system remains stable in the absence or presence of a disturbance (the first two conditions are therefore fulfilled).

[0328] The first inequality Math.53 further guarantees the performance (in the sense of the H∞ norm) of the closed-loop system when the system is subjected to a disturbance. This inequality thus ensures that the third condition is met.

[0329] After solving the 9 matrix inequalities, the local controllers at the vertices of the polytope P1 are calculated as follows:

[0336] It is thus possible to obtain the controller K(ρ), since it is the convex combination of these local controllers. More precisely, the controller is determined using equations Math.33 and Math.21 to Math.23.

[0337] At this stage, it can be noted that preferably, the controller K to be used to define the actuator control instructions may depend not only on the speed V of the vehicle, but also on the shape of the avoidance trajectory T0.

[0338] To understand how, it should first be noted that in the equation Math.48, where the term w represents the curvature of the avoidance path, the maximum value w max of this curvature is known (since we know the dynamic limits of the vehicle and therefore the maximum curvature that the vehicle can follow in complete safety and in fact imposeable by trajectory planning). Therefore, the parameter σ can be defined as:

[0341] In this equation, time T AEScorresponds to the maximum activation duration of the AES function, which is generally between 1 and 3 seconds, and corresponds in particular to the duration of the avoidance maneuver.

[0342] When the avoidance trajectory T0 is defined, it is therefore possible to calculate the value of this parameter σ.

[0343] We consider that the maximum interval of curvatures of the avoidance trajectories T0 achievable by the vehicle can be divided into N regular sub-intervals. We can then consider that the term σ belongs to a particular interval, which can be written:

[0344] [Math.61]

[0345] ^ ∈ [^ ^ , ^ ^^^ ]

[0346] With i a natural integer ranging from 1 to N.

[0347] Each interval can be defined by the value of its average, which can be written:

[0348] [Math.62]

[0349] ^^ ^ = ( ^^ + ^ ^^^ ) / 2

[0350] The performance of the controller K depends on the curvature of the avoidance trajectory T0. Indeed, 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.

[0351] In the proposed concept of optimization by linear matrix inequalities, one must fix the term σ (which is inversely proportional to the curvature) to find a controller.

[0352] In other words, the resulting controller is only optimal for a given curvature. However, this controller will be less robust if the vehicle has to follow trajectories with greater curvature, since this will generate risks of instability. Conversely, it will be less efficient (it will present a tracking delay or an overshoot) if the vehicle has to follow trajectories with smaller curvature.

[0353] However, when the AES function is triggered, an avoidance trajectory T0 adapted to the situation is calculated over a fixed time horizon (next 3 seconds).

[0354] Preferably, the controller K can then be synthesized in order to be adapted to the curvature of the avoidance trajectory T0.

[0355] More precisely, it will be possible to synthesize several controllers K(ρ) using the above-mentioned inequalities, each associated with one of the above-mentioned intervals (and more precisely with its average ^^ ^ ). We can then write these controllers in the form K(ρ, ^^ ^ ).

[0356] From then on it will be possible to choose the synthesized controller for the value of ^^ ^ which is closest to the term σ calculated for the avoidance trajectory T0.

[0357] In practice, as shown in Figure 8, a calculation module B1 is adapted to determine the avoidance trajectory T0, which makes it possible to calculate the value of the parameter σ. Then, a switch B2 can select, for the entire avoidance trajectory T0 to be carried out, a controller K(ρ, ^^ ^ ) which will be adapted to the curvature of the trajectory.

[0358] Thus, this controller will depend not only on the speed V of the vehicle but also on the curvature of the avoidance trajectory T0.

[0359] At this point, we can also briefly note that several types of K controller can be obtained depending on the chosen value of αψ. Indeed, it is possible to play on the performance of the K controller by adjusting the value of αψ.

[0360] Thus, the adjustment coefficient αψ, when it has a reduced value, makes it possible to obtain a controller K which minimizes the position tracking error. On the contrary, when it has a high value, it makes it possible to obtain a controller K which minimizes the heading tracking error. At the start of avoidance, the adjustment coefficient will be chosen with a reduced value (less than 20), to ensure that the vehicle follows the avoidance trajectory T0. On the contrary, at the end of avoidance (once the obstacle has been passed), the adjustment coefficient αψ will be chosen with a high value (greater than 20), to ensure that the vehicle returns parallel to the road.

[0361] Thus, for example, if the driver wishes to take back control at the start of avoidance and he deviates much further from the obstacle than planned (in the sense of the avoidance trajectory T0), the high value of the adjustment coefficient at the end of avoidance ensures that the instructions do not unnecessarily bring the vehicle back onto the avoidance path when it has been exceeded by a lot (which would otherwise be destabilizing for the driver).

[0362] 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.

[0363] The computer 13 is programmed here to implement this process recursively, that is to say step by step, and in a loop.

[0364] To do this, during a first step, the computer 13 checks that the autonomous obstacle avoidance (AES) function can be activated and that an obstacle avoidance trajectory has been planned by the block B1.

[0365] It then calculates the parameter σ to choose a controller K(ρ, ^^ ^ ) adapted to the curvature of this trajectory.

[0366] At this stage, and preferably, we can predict that if the parameter σ exceeds a predetermined threshold, the computer stops the process and does not activate the AES function. In this case, it is considered that the process will not allow safe avoidance.

[0367] Otherwise, the AES function is enabled.

[0368] The computer 13 will then seek to define a control instruction for the conventional steering system and another for the differential braking system, allowing this avoidance trajectory T0 to be followed as best as possible.

[0369] To do this, he begins by calculating or measuring the parameters which are: - the measured steering angle ^, - the yaw moment M z estimated, - the derivative with respect to time of the measured steering angle ^, - the lateral speed Vy, - the yaw rate r, - the relative heading angle Ψ L,- the lateral gap y L , - the curvature γref of the avoidance trajectory, - the saturated steering angle setpoint δref obtained at the previous time step, and - the saturated yaw moment setpoint Mz_ref obtained at the previous time step.

[0370] The calculator 13 then acquires the equations of the matrices K ρ1 , K ρ2 , K ρ3 , which are obtained using the data recorded in its memory and correspond to the adjustment coefficient chosen and to the curvature of the avoidance trajectory T0.

[0371] The controller K is then calculated as a function of the speed V of the vehicle, by first determining the values ​​of the coefficients α1, α2, α3.

[0372] This controller K will then make it possible to determine the values ​​of the unsaturated steering angle setpoints ^K and saturated ^ref and the values ​​of the unsaturated yaw moment setpoints M zKand saturated M Z_ref .

[0373] Note that the K matrices ρ1 , K ρ2 , K ρ3 of the K controller are synthesized taking into account the saturation functions, so that the instructions are perfectly adapted to the chosen saturation model.

[0374] Finally, the saturated steering angle instruction ^ ref will be transmitted to the power steering actuator to steer the wheels of the motor vehicle 10. In the same way, the saturated yaw moment setpoint Mz_ref will be transmitted to the differential braking system actuator to brake the wheels of the motor vehicle 10.

[0375] This process is then repeated in a loop, along the entire avoidance trajectory T0.

[0376] The present invention is in no way limited to the embodiment described and represented, but those skilled in the art will be able to make any variation in accordance with the invention.

[0377] Thus, the process can be applied to other types of fields in which a particular trajectory must be followed, for example in aeronautics or robotics (particularly when the robot is small and one of its commands must be saturated).

Claims

CLAIMS

1. Method for autonomously controlling at least one actuator of an automotive device (10) which is adapted to influence the trajectory of said automotive device (10), comprising steps of: - acquisition of parameters (V y , r, Ψ L , y L , ^, M z , γ ref ) relating to the trajectory of the automotive device (10) and the speed (V) of said automotive device (10), and - calculation by a computer (13) of a piloting instruction (M z_ref , ^ ref ) for each actuator, depending on said parameters (V y , r, Ψ L , y L , ^, M z , γ ref ), using a controller (K), characterized in that the controller (K) used varies according to the speed (V) of the vehicle and comprises several components, including at least one state feedback gain (KMz p , Kδ p) to be applied to said parameters (Vy, r, ΨL, yL, ^, Mz, γref), and at least one saturation compensation gain (K Mz aw , K δ aw ) to be applied to a value of the steering setpoint which was determined at a previous time step.

2. Steering method according to the preceding claim, in which, said automotive apparatus (10) being a vehicle which comprises wheels (11, 12), a power steering actuator and a differential braking actuator, the controller (K) comprises several components making it possible to determine a steering setpoint for said power steering actuator and a steering setpoint for said differential braking actuator.

3. Steering method according to one of the preceding claims, in which the controller (K) is written in the form of a sum of several products of a variable (α1, α2, α3) dependent on the speed (V) and a local controller (Kρ1 , K ρ2 , K ρ3 ) independent of the speed (V).

4. Control method according to claim 3, in which each local controller (K ρ1 , K ρ2 , K ρ3 ) is determined for a determined value of a vector (ρ) of two variant parameters, one of said variant parameters being preferentially equal to the speed V of the vehicle and the other of said variant parameters being preferentially equal to the inverse of said speed.

5. Control method according to one of the preceding claims, in which the controller (K) satisfies a modeling of at least one saturation function by non-linear sector.

6. Control method according to the preceding claim, in which the saturation function satisfies a setpoint amplitude limiting model and is expressed in the form: K the controller, sat ηan amplitude limiting function, and x a state vector of said automotive device (10) comprising said parameters.

7. Control method according to one of the two preceding claims, in which the saturation function satisfies a control setpoint variation limiting model (^ref) and is expressed in the form: K the controller, satν an amplitude limiting function, A1 and B1 predetermined matrices, and x a state vector of said automotive apparatus (10) comprising said parameters.

8. A driving method according to one of the preceding claims, wherein the controller (K) satisfies a modeling of said apparatus (10) in which an output (z) to be minimized is a function of a trajectory tracking error (e yL ) and a heading angle error (Ψ L).

9. Piloting method according to one of the preceding claims, in which, said automotive device (10) being a vehicle, a trajectory (T0) that the vehicle must follow being planned, it is planned to calculate a parameter (σ) relating to the curvature of said trajectory (T0) then it is planned to implement said calculation step only on condition that said parameter is included in a predetermined interval.

10. A driving method according to one of the preceding claims, wherein, said automotive apparatus (10) being a vehicle which comprises wheels (11, 12), a power steering actuator and a differential braking actuator, the driving setpoint of said power steering actuator is calculated as a function of a driving setpoint of the differential braking actuator calculated at a previous time step and / or the driving setpoint of said differential braking actuator is calculated as a function of a driving setpoint of the power steering actuator calculated at a previous time step.

11. An automotive apparatus (10) comprising at least one actuator which is adapted to influence the trajectory of said apparatus (10) and a computer (13) for driving said actuator, characterized in that the computer (13) is programmed to implement a method according to one of the preceding claims.

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