Method for synthesizing an infinite H-type controller for a vehicle motion control system

Abstract

The invention relates to a method for synthesizing a type controller for a vehicle motion control system, comprising the steps of: modeling a generalized system (501) to be controlled, defining controlled inputs and outputs of the generalized system, and calculating the controller (502) by type synthesis, wherein the modeling of the generalized system to be controlled includes: generating a reference yaw rate using a first vehicle model (504), generating an effective yaw rate using a second vehicle model (503) different from the first, calculating a difference (ε(t)) between the reference and effective yaw rates, and using this difference as an input to the high-level controller during synthesis. The invention also relates to the use of the controller in a vehicle. Figure for the abstract: Fig. 5

Description

Title of the invention: Method for synthesizing an infinite H-type controller for a vehicle motion control system. Technical field

[0001] The invention is in the field of motor vehicle actuator control, and relates more specifically to a method of synthesis (or definition) of an infinite H-type controller (or for a vehicle motion control system (in English “Vehicle Motion Control”, VMC), the vehicle comprising at least one actuator.

[0002] The invention also relates to a vehicle using the synthesized controller. Previous technique

[0003] An actuator is a device that can be installed in a vehicle and whose role is to convert an electrical command signal into an action. The invention relates to the control of such actuators in a vehicle. It is described in the context of a motor vehicle, but is generally applicable to any type of vehicle (motorcycle, airplane, boat, etc.). For illustrative purposes, it is subsequently described in the specific case of controlling the rear wheel steering for a four-wheel steering (4WS) motor vehicle and controlling the differential braking. However, the invention is not limited to these actuators and can be applied mutatis mutandis to any actuator in the vehicle, for example, a longitudinal speed actuator (engine).

[0004] In four-wheel steering vehicles, the steering of the two rear wheels is typically implemented by a single actuator, but can also be implemented by two separate actuators, each acting on one of the two rear wheels. For differential braking, each brake of the vehicle is controlled by a dedicated actuator, in order to adjust the braking pressure between the right and left wheels, for example for ABS functions (an acronym derived from the German "Antiblockiersystem," or anti-lock braking system).

[0005] Figure 1 shows the block diagram of a motion control system 100 for controlling the rear wheel steering angle and differential braking of a motor vehicle according to the state of the art. Such a system transforms a steering wheel angle command 5f and a vehicle speed command Vx into actions of vehicle actuators, in this example, wheel braking actuators and a rear wheel steering actuator. The objective is to optimize the vehicle's stability and maneuverability by coordinating the use of differential braking and the rear steering system. However, the invention applies identically to the control of the various actuators of a vehicle.

[0006] The motion control system relies on a reference model 101, which models the vehicle's chassis dynamics, to determine a reference yaw rate V'rej corresponding to the time derivative of the reference yaw angle ^ref (the desired yaw angle). The calculations are performed based on the steering wheel angle setpoint ôf, the vehicle speed setpoint, and possibly other inputs, such as an estimate of the road friction coefficient. The reference model used for a motor vehicle is typically the bicycle model, shown in [Fig. 2], where the wheels of the same wheel set are modeled as a single wheel located on the axis of the vehicle's center of gravity. This bicycle model allows the vehicle's chassis dynamics to be modeled in order to deduce the setpoints to be applied to the various actuators. It uses: af and ar: the drift angles of the front and rear wheels; Caf, Car: the cornering rigidity of the front and rear tires; Oops; front wheel angle; Fyf, Fyr; the lateral forces applied to the front and rear wheels; Vx; the longitudinal velocity vector; Iz: moment of inertia; Af; the mass of the vehicle; fi: the drift of the vehicle, which is also the angle of the velocity vector with respect to the axis of the vehicle; : the yaw angle of the vehicle; / / , lr: the distance between the center of gravity and the front (respectively rear) axle of the vehicle; Mz: the moment of the yaw.

[0007] The matrix state-space representation of the bicycle model can be defined as :

[0008] '0 ar ■ F r MVX IfCgf Ô f + 0' .L . M z

[0009] where: - the state variables are the drift fi of the vehicle and the yaw rate V', - the command input is the yaw moment Mz.

[0010] Returning to Figure 1, a high-level software controller 102 determines a yaw moment Mz from the difference between the reference yaw rate Wref and the effective yaw rate V of the vehicle (i.e., the difference between the target yaw rate and that of the vehicle).

[0011] A command allocation unit 103 implements a command allocation method to distribute the yaw moment Mz into forces to be applied to the differential braking actuators of the four wheels (with here Fx fi, Fx_ fr, Fx and Fxrr the braking forces respectively associated with the front left, front right, rear left and rear right wheels) and to the actuator controlling the steering of the rear wheels (Fy,^, taking into account limitations of the chassis 104.

[0012] Low-level software controllers 106 and 107 translate these force commands into braking accelerations Mbrake for each of the four wheels, and rear wheel steering angle ^r, respectively. Sensors positioned on the vehicle 108 measure the vehicle's motion, in particular the effective yaw rate V of the vehicle. This yaw rate is compared to the reference yaw rate Vref, and the difference is transmitted to the high-level controller 102 for the next iteration.

[0013] Thus, the system in Figure 1 operates in a closed loop to optimally allocate commands to the differential braking and rear wheel steering actuators, the goal being for the vehicle to maintain a reference yaw rate Vyef-

[0014] The present invention relates to an improvement of the high-level software controller block 102, which receives as input the difference between the reference yaw rate and the effective yaw rate 7' of the vehicle. In state-of-the-art motion control calculation methods, this controller is implemented by a PID (Proportional, Integral, Derivative) type controller, tuned using parameter tables based on the vehicle's longitudinal speed and lateral acceleration, obtained from exhaustive tests and fine-tuned on the vehicle by performance specialists at the desired yaw rate.

[0015] One object of the invention is to improve the robustness of the high-level PID software controller, while making it faster and providing better tracking performance. Summary of the invention

[0016] To this end, the present invention describes a method for synthesizing an infinite H-type controller, or for a vehicle motion control system, the synthesis method comprising: - a modeling step of a generalized system to be controlled p(s), - a step of defining the inputs of said generalized system, - a step of defining controlled outputs z(f) of the generalized system, - a calculation step of the controller k(s) Pæ" a synthesis of type Hx.

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[0024] The distinctive feature of the synthesis process according to the invention is that the modeling of the generalized system to be controlled p(g) includes: - the generation of a reference yaw rate ÿ'ref using a first vehicle modeling model, - the generation of an effective yaw rate using a second vehicle modeling model, the first and second modeling models being different, - the calculation of a difference between the reference yaw rate and the effective yaw rate W, and the use of this difference as input to the high-level controller K(s) during synthesis. More specifically, the calculation step of a high-level controller by an Hx-type synthesis includes the determination of the high-level controller Rfy that minimizes the influence of the inputs of the generalized system on the outputs z(t) of the generalized system. According to one embodiment, the second vehicle modeling model is a bicycle model. According to a compatible embodiment of the preceding one, the first vehicle modeling model is a bicycle model modified to make one or more vehicle parameters variable. Advantageously, the output of the high-level controller ^(s) is a yaw moment Mz of the vehicle. According to a particular embodiment in which the Hx-type controller is configured to control a differential brake actuator and a rear-wheel steering actuator, a matrix state-space representation of the first vehicle modeling model is: * ref MVX Tz MVl C. .7" -jC J- . f rej1 / rear.reprj-e f [Æ f '"J Cafe MVS 10 ,1 IL with : - Prefer the vehicle's drift, - ^ref the vehicle's yaw, - Cafref ct ^arref 'cs rigidities in turns respectively front and rear, _ fref ct fref 'a distance between the center of gravity and the front and rear axles respectively, - M is the mass of the vehicle, - Vx is the longitudinal velocity vector of the vehicle, - the moment of inertia of the vehicle, - &rref the angle of the rear wheel of the vehicle, - Mz the yaw moment of the vehicle.

[0025] Advantageously, the second vehicle modeling model takes as input a 5f steering angle of the front wheels of the vehicle calculated from the yaw moment Mz.

[0026] The invention also addresses a computer program comprising program code instructions for the execution of the first, second, third and fourth steps of a method for synthesizing a controller of type according to the invention when the program is executed on a computer, as well as a computer-readable recording medium comprising the computer program.

[0027] The invention also relates to a vehicle comprising a motion control system with:

[0028] computing means configured to implement: - a reference model configured to generate a reference yaw rate V'ref for the vehicle to follow, - a high-level controller configured to determine a yaw moment Mz from the difference between said reference yaw rate and an effective yaw rate V of the vehicle, - a command allocation unit configured to transform the yaw moment Mz into force commands to be applied to at least one actuator, - at least one low-level controller configured to translate force commands into movement of at least one actuator, and - at least one sensor configured to measure the vehicle's effective yaw rate 7', the high-level controller of the vehicle being developed by a synthesis process of an Hx type controller according to the invention.

[0029] In one embodiment, this is a four-wheel drive vehicle comprising a differential braking actuator and a rear wheel steering actuator. Brief description of the drawings

[0030] The invention will be better understood and other features, details and advantages will become clearer from the following description, given by way of non-limiting reason, and from the accompanying figures, given by way of example.

[0031] [Fig.1] Fig.1 represents a block diagram of a motion control system for controlling the steering angle of the rear wheels and differential braking of a motor vehicle according to the state of the art.

[0032] [Fig.2] Fig.2 represents the linear bicycle model, widely used in the prior art.

[0033] [Fig.3] Figure 3 represents the functional synthesis diagram of an Hx type controller, known from the prior art.

[0034] [Fig.4] Figure 4 represents a synoptic diagram of a synthesis process for an Hx type controller according to the invention.

[0035] [Fig.5] Figure 5 represents the elements implemented by the synthesis process of a high-level controller of type Hx according to the invention, in an embodiment aimed at controlling actuators of the differential braking and the orientation of the rear axle of the vehicle.

[0036] [Fig.6] Figure 6 compares the yaw moment calculated by a high-level controller defined by an Hx-type synthesis process according to the state of the art and according to the invention. Description of the implementation methods

[0037] One way to improve the performance of the high-level software controller 102 in Figure 1 is to replace it with an infinite H-type controller, which represents a modern alternative to PID-type controllers. The principle of an Hx controller is well known and described, for example, in the thesis by Moad Kissai: “Optimal Coordination of Chassis Systems for Vehicle Motion Control”, Automatic Control Engineering, Université Paris Saclay (COmUE), 2019.

[0038] A robust controller must guarantee the performance and stability of the system despite varying operating conditions and model uncertainties (e.g., variations in vehicle mass). The H» control specifically aims for robustness by minimizing the / / « norm, which corresponds to the maximum singular value of the system's frequency response. This represents the worst-case gain, i.e., the most amplified disturbance in the system across all frequencies:

[0039] ||G( / W)|| -PCiâxGijtv) œ

[0040] with G(jœ) the system gain on all frequencies.

[0041] In control, the generalized system is an extended representation of a system that includes not only the dynamics of the system to be controlled, but also the weights and models of external signals, such as disturbances and noise. The generalized system is used to formulate robust control problems, such as Hx control.

[0042] Figure 3 represents the elements required for the synthesis (or development) of a high-level controller of the type, namely: - p($) the modeling of the generalized system, that is to say the system with control, in which weightings can be used to increase or decrease the weights of inputs / outputs, - x(s) The high-level controller of the system (i.e., box 102 in Figure 1), which aims to stabilize the generalized system P^)- This is the controller that will be implemented in block 102 of system 100 in [Fig. 1] in vehicles, - the inputs of the generalized system, for example the reference that the The controller must monitor disturbances and noise. - z(t) the controlled outputs of the system, i.e., estimators of the controller's quality, used during synthesis to constrain the performance of the controller K(s)-

[0043] The main objective of the synthesis is to determine the stabilization controller which, based on the information measured in jQ) by the generalized system P(s), generates the control signal minimizing the influence of undesirable signals on the controlled variable ^). This is done by minimizing the norm Hx of the closed-loop transfer function below a specified optimal value F. This objective can be formulated as follows:

[0044] K (s) - argminy si. I1 T^s) II < y Kl si "

[0045] where st means "subject to", or "under constraint that" in French.

[0046] The closed-loop transfer function T7Jj) includes the system contributions to control 6(^), the controller k(s} as well as the weighting functions that define the performance and robustness requirements.

[0047] The performance models define the desired performance criteria, such as tracking accuracy, disturbance rejection, and noise attenuation. These criteria are translated into weighting functions that penalize deviations from the desired performance.

[0048] The use of an Hx type controller instead of the high-level software controller 102 of [Fig.1] improves the robustness of the motion control calculation, its speed and tracking accuracy compared to a PID controller.

[0049] Once the generalized system pfy and the inputs outputs and t( / ) are defined, the synthesis can be done in the usual way for a person skilled in the art.

[0050] In practice, it has been found that an Hx-type controller is too powerful to be implemented in a vehicle. For example, in the context of a controller driving differential braking and rear axle control actuators, the yaw moments calculated by the controller and transformed into braking and angle commands by the brick 103 of [Fig. 1], cause excessively abrupt braking of the vehicle to make driving acceptable.

[0051] To address this problem, the inventors have developed a method for synthesizing a high-level Hx-type controller for a vehicle motion control system, described below. Such a controller is robust to disturbances and noise, while exhibiting a sufficiently flexible response to be implemented in a vehicle, particularly a motor vehicle.

[0052] Figure 4 shows a block diagram of a method for synthesizing an Hx-type controller according to the invention. This method includes a first step 401 of modeling a generalized system to be controlled p[g].

[0053] This step consists of describing the generalized system p(^) which will be controlled and stabilized by the controller K(s\). The inventors discovered that if the use of an Hx-type controller is not suitable for controlling a motor vehicle, it is because the reference model is not taken into account during the synthesis of ^($). Indeed, the error c(C) = Wref - W is an input of the generalized system, and the controller does not know its actual dynamics. It therefore tends to oversize its setpoints.

[0054] The invention integrates the reference model (i.e., the model generating the reference yaw rate V!ref) into the generalized system p^), so that the controller has information on the dynamics of the deviation e(t). The setpoint that arrives at the input of the controller is then more realistic with respect to the dynamics achievable by the vehicle.

[0055] The other steps in the process of synthesizing a high-level controller of type Hx according to the invention are the usual steps for this type of controller: - a step 402 for defining the inputs of the generalized system, - a step 403 defining controlled outputs of the generalized system, - a step 404 of calculation of the high-level controller k(s) of type Hx.

[0056] Step 404 can be implemented by following Riccati's equations. Alternatively, matrix calculation tools such as Matlab® software can be used to calculate the high-level stability controller K(s) once the system has been generalized and its inputs / outputs defined.

[0057] Figure 5 shows the elements implemented by the synthesis process of a high-level controller of type Hx according to the invention, in an embodiment a specific device aimed at controlling differential braking and rear axle steering actuators of the vehicle.

[0058]

[0059] The generalized system / »(5) 501 includes a model (7(5) 503) of the vehicle allowing calculation of an effective yaw rate V' of the vehicle. The cfs model is typically a bicycle model as described previously, taking as input the steering angle of the vehicle. It corresponds to the modeling of the behavior of the gearboxes 103 to 107 of [Fig. 1]. The generalized system p(s) 501 also includes a model q 504 configured to calculate a reference yaw rate iprej of the vehicle, which will hereafter be called the reference model. The reference model q differs from the bicycle model. It can, for example, be obtained by making one or more parameters of the bicycle model variable, or by using a model other than the bicycle model. The output iprej of q corresponds to the reference yaw rate calculated by the box 101 in [Fig. 1].

[0060] In the embodiment considered by way of illustration, the reference model is obtained from the bicycle model, by making three parameters variable, selected for their link with differential braking and rear steering control: - the wheelbase ratio (WB); varying the wheelbase ratio, typically between 0.5 and 1.5, allows for the generation of a reference yaw rate that would be typical of a larger or smaller vehicle. This variation is important because it allows the vehicle's behavior to be adapted to its environment: a shorter wheelbase being more suitable for city driving and a longer wheelbase being more suitable for highway driving; - angular dynamics DA; the variation of angular dynamics allows the understeer / oversteer behavior of the vehicle to be varied, which is of interest in case of acceleration or braking in a turn; - the specific front / rear drifts, respectively d}s and d2x: the variation of the specific front / rear drifts allows adjusting the synchronization between the front and rear axles of the vehicle.

[0061] It thus implements a state matrix close to that of the bicycle model, in which the front / rear cornering stiffnesses Caf and Car, and the distance between the center of gravity and the front / rear axle lf and lr are defined as follows:

[0062] lfref-lf*WB

[0063]

[0064] Lref = L*WB

[0065] with L being the wheelbase of the vehicle (i.e., the distance between the front axle and the rear axle), and

[0066] Ml, Ml„ef u]s ~ -Lrct[DA+(Q

[0067] r ar. ref Lfefd7i

[0068] The final state space of the reference model is then defined as:

[0069] C„fnf P ref " MV* ' MVi ' 1 P ref ~MV7 TUI ; jot / -< 1 1 7 1 Wref href-aïreï ' J [ ■ [ ' L ■ hVx LLJ

[0070] where the state variables are the vehicle drift / irej and the yaw rate Wref, and the control input is the yaw moment Mz. The rear wheel angle is ôrjref.

[0071] Alternatively, the reference model can be adapted to vary only one of these parameters, or to vary other parameters such as, for example, the mass of the vehicle, the drift angles, etc. Any other type of model, for example a four-wheeled vehicle model, allowing the determination of a yaw rate setpoint can be implemented in the generalized system.

[0072] In the embodiment described by way of illustration, the reference model Q takes as input the steering angle 5r of the rear wheels. The type of input depends on the reference model chosen.

[0073] In the embodiment considered by way of illustration, the inputs defined during Step 402 consists of the following: - the 5r steering angle of the rear wheels, - input disturbances

[0074] The controlled outputs defined in step 403 are as follows: the tracking error, which contains the multiplied tracking error by an error weighting function, and the front wheel angle multiplied by a control weighting function.

[0075] In the embodiment considered by way of illustration, it was chosen to emulate The command <5 / is based on the yaw moment command Mz. This choice is linked to the searching for the best possible frequency response.

[0076] The conversion of the yaw moment Mz into the yaw control is done by applying a profit such that:

[0077] / \ ô / — i -------------- M f \ llCaf^CaflyMW}}'™z

[0078] To form the standard structure for the controller H”, the weighting functions VFc(s) > J s ) and yy shown in [Fig. 5] are defined to characterize, respectively, the performance objectives, the limitations of the actuator, and the rejection of disturbances. Their development results from the expertise and know-how of the automation engineer.

[0079] By way of example, these weighting functions can be chosen as follows: - VFX0 is used to filter the output signal zi of weighted yaw rate error. This is the yaw rate tracking performance. The VF(s) weighting can, for example, take the form of a high-pass filter whose cutoff frequency is the attenuation level for low frequencies. This filter's role is to adjust the maximum static error and the maximum amplitude of the controller's sensitivity function. WM(s) is used to filter the z2 signal that attenuates the front wheel angle. This weighting can, for example, take the form of a low-pass filter whose cutoff frequency is the attenuation level for high frequencies and whose maximum value serves as an upper limit for the controller's sensitivity function, in order to prevent actuator saturation. - Wd(s) is used to filter the input disturbance. This weighting for example, it can take the form of a simple gain of 0.01, which impacts the controller's sensitivity functions.

[0080] Figure 6 compares the yaw moment calculated by a high-level controller defined by an Hx-type synthesis method according to the prior art 601 and according to the invention 602, extracted from a set of measurements taken under real-world conditions. It can be observed that the controller 602 synthesized with the reference model exhibits a lower yaw moment amplitude and a slightly slower response compared to the controller 601 synthesized without the reference model, thus offering better tracking performance and energy savings since less yaw moment is required to achieve the same performance.

[0081] While the controller according to the invention may appear to have lower performance compared to a conventional Hx controller, during tests carried out on a vehicle operating under real-world conditions, controller 601 proved too powerful to provide satisfactory driving. Conversely, controller 602, synthesized with the reference model, performed perfectly in the various environments in which it was tested. It proved robust to system variations and different modes driving. The Hx 602 type high-level controller, synthesized taking into account the reference model in the generalized system, is therefore more suitable for implementation in a vehicle than the 601 controller.

[0082] The invention relates to a method for synthesizing an Hx-type controller in which the reference model used to generate the reference is defined within the generalized system p($). The method is implemented on digital computing means, such as, for example, a microprocessor associated with a memory containing the code instructions of the method according to the invention.

[0083] It also relates to a computer program comprising program code instructions for the execution of steps 401 to 404 of the process of synthesizing an Hx type controller according to the invention when said program is executed on a computer.

[0084] It also relates to a computer-readable recording medium on which is recorded a computer program comprising program code instructions for the execution of steps 401 to 404 of the method for synthesizing a type controller according to the invention.

[0085] Finally, the invention relates to a vehicle, for example a motor vehicle, comprising a motion control system 100 with:

[0086] computing means such as one or more processors, configured to implement: - a reference model 101 configured to generate a reference yaw rate for the vehicle to follow, - a high-level controller 102 configured to determine a yaw moment Mz from a difference between said reference yaw rate ^ref and an effective yaw rate V of the vehicle, - a command allocation unit 103 configured to transform the yaw moment Mz into force commands to be applied to at least one actuator, - at least one low-level controller 105, 106 configured to translate force commands into movement from at least one actuator, And - at least one sensor 107 configured to measure the effective yaw rate 7' of the vehicle, where the high-level controller 102 is developed by a synthesis process of an Hx-type controller according to the invention, wherein the modeling of the generalized system includes the reference model.

[0087] According to a particular embodiment of the invention, the vehicle is a four-wheel drive motor vehicle, the at least one actuator includes a differential braking actuator and a rear wheel steering actuator.

Claims

Demands

1. A synthesis method for an infinite H-type controller, or for a vehicle motion control system (100), the synthesis method comprising: - a step (401) of modeling a generalized system to be controlled (P(s)) - a step (402) of defining inputs of said generalized system, - a step (403) of defining controlled outputs (Z(t)) of the generalized system, - a step (404) of calculating the controller (Kis)) A synthesis of said synthesis method being characterized in that the modeling of the generalized system to be controlled (P(s)) comprises: - the generation of a reference yaw rate using a first vehicle modeling model (504), - the generation of an effective yaw rate V using a second vehicle modeling model (503), the first and second modeling models being different,- the calculation of a difference (g0) between the reference yaw rate Vyef and the effective yaw rate V, and the use of this difference as input to the high-level controller (K(5)) during synthesis.

2. Method of synthesizing an Hx-type controller according to claim 1, wherein the step (404) of calculating a high-level controller (k(s)) in an Hx-type synthesis includes determining the high-level controller (k(s)) that minimizes the influence of the inputs (^)) of the generalized system on the outputs ( z(t ) ) of the generalized system.

3. Method of synthesizing an Hx type controller according to any one of claims 1 to 2, wherein the second vehicle modeling model (503) is a bicycle model.

4.

5.

6. Method for synthesizing a controller of type in which the first vehicle modeling model (504) is a bicycle model modified to make one or more vehicle parameters variable. Method for synthesizing a controller of type in which the output of the high-level controller (£{$)) is a yaw moment Mz of the vehicle. Method for synthesizing an Hx-type controller according to any one of claims 1 to 5 for controlling a differential braking actuator and controlling a rear-wheel steering actuator, wherein a matrix state-space representation of the first vehicle modeling model is: n'f MVX MVÎ 1 PreJ MVX &rnf + 0 nf. — ■ h. £arte-flr / ef + l. lz. A.T. with :

7.

8. - Pref the vehicle's drift, - ^ref the vehicle's yaw, - ct Carref the cornering rigidities respectively front and rear - fref ct fref the distance between the center of gravity and the front and rear axles respectively, - M is the mass of the vehicle, - Vx is the longitudinal velocity vector of the vehicle, - Iz, the moment of inertia of the vehicle, - the angle of the vehicle's rear wheel, - Mz is the yaw moment of the vehicle. A method for synthesizing an H-type controller according to claim 6, wherein the second vehicle modeling model takes as input a 5 / steering angle of the vehicle's front wheels calculated from the yaw moment Mz. A computer program comprising program code instructions for executing the first (401), second (402), third (403), and fourth (404) steps of a method for synthesizing an Hx-type controller according to any one of claims 1 to 7 when said program is executed on a computer.

9. A computer-readable recording medium on which is recorded a computer program comprising program code instructions for executing the first (401), second (402), third (403) and fourth (404) steps of a method for synthesizing an Hx-type controller according to any one of claims 1

10. d / . A vehicle comprising a motion control system (100) with computing means configured to implement: - a reference model (101) configured to generate a reference yaw rate y'ref to be followed by the vehicle, - a high-level controller (102) configured to determine a yaw moment Mz from a difference between said reference yaw rate iprej and an effective yaw rate of the vehicle, - a command allocation unit (103) configured to transform the yaw moment Mz into force commands to be applied by at least one actuator, - at least one low-level controller (105), (106) configured to translate the force commands into motion of at least one actuator, and - at least one sensor (107) configured to measure the effective yaw rate W of the vehicle,the vehicle being characterized in that the high-level controller (102) is developed by a synthesis process of an Hx-type controller according to any one of claims 1 to 7.

11. Four-wheel drive vehicle according to claim 10, comprising a differential braking actuator and a rear wheel steering actuator.

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