EP4320026A1

EP4320026A1 - Method for autonomously driving an actuator of a device

Info

Publication number: EP4320026A1
Application number: EP22710413.0A
Authority: EP
Inventors: Anh-Lam Do
Original assignee: Renault SAS; Nissan Motor Co Ltd
Current assignee: Ampere SAS; Nissan Motor Co Ltd
Priority date: 2021-04-06
Filing date: 2022-03-09
Publication date: 2024-02-14
Also published as: FR3121410A1; WO2022214268A1; FR3121410B1; CN117120323A; JP2024514548A; KR20230166124A

Abstract

The invention relates to a method for autonomously driving an actuator of an automotive device (10), said actuator being intended to have an influence on the trajectory of said device, the method comprising steps of: - acquiring parameters relating to the trajectory of the device; and - a computer (13) calculating a setpoint for driving said actuator as a function of said parameters, by means of a controller associated with at least one saturation function for an output of the controller. According to the invention, the controller satisfies a model of said at least one saturation function per nonlinear sector.

Description

DESCRIPTION

TITLE OF THE INVENTION: AUTONOMOUS CONTROL METHOD OF AN ACTUATOR OF A DEVICE

AUTOMOTIVE

TECHNICAL FIELD OF THE INVENTION

The present invention generally relates to automating the trajectory tracking of automotive devices.

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

[0003] It relates more particularly to a method for autonomously controlling an actuator of an automotive device which is suitable for influencing the trajectory of said device, comprising the steps of:

- acquisition of parameters relating to the trajectory of the aircraft, and

- calculation by a computer of a control setpoint of said actuator according to said parameters, by means of a controller associated with at least one function of saturation of an output of the controller.

[0004] It also relates to a device equipped with a computer adapted to implement this method.

[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] For the sake of securing motor vehicles, they are currently equipped with driving 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] There are, however, situations in which these emergency braking systems do not make it possible to avoid the collision or cannot be used (for example if a vehicle is closely following the motor vehicle).

[0009] For these situations, automatic avoidance systems (better known by the abbreviation AES, standing for "Automatic Evasive Steering" or "Automatic Emergency Steering") have been developed which make it possible to avoid the obstacle by deflecting the vehicle from its trajectory, either by acting on the steering of the vehicle, or by acting on the vehicle's differential braking system. It will be noted that the obstacle can be in the same lane as the vehicle or in an adjacent lane, in which case it is detected that this obstacle can be found within a short time in the trajectory of the vehicle.

[0010] It happens, however, that the AES system imposes a limit trajectory on the vehicle in terms of controllability, which does not allow the driver to regain control of driving the vehicle in complete safety.

[0011] We then know from document FR3099450 a solution consisting in 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 regain control during the avoidance procedure. For this, the controller limits the amplitude and the 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 a performance (i.e. good tracking of the avoidance trajectory) that can sometimes be improved because the LPV modeling used (linear with variable parameter) is conservative and does not describe not explicitly the typical characteristics of saturations.

PRESENTATION OF THE INVENTION

In order to remedy the aforementioned drawback of the state of the art, the present invention proposes a control method as defined in the introduction, in which the controller satisfies a modeling of said at least one saturation function by nonlinear sector.

[0013] In other words, the controller is synthesized on the basis of a non-linear sector approach, so as to be able to guarantee not only the stability of the automobile apparatus in all situations, but also a good performance from as the situation permits.

[0014] Thus, the invention proposes a more appropriate technique for modeling the saturation functions. This technique indeed has many advantages compared to the solution described in the document FR3099450.

[0015] As has been mentioned, it first of all ensures good performance, that is to say good position and heading tracking, which allows the vehicle to follow the trajectory of the vehicle with greater precision. reference calculated to avoid the obstacle.

[0016] The claimed solution also ensures great stability as long as the disturbances have a bounded 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 know quickly whether the avoidance trajectory calculated can be performed dynamically by the vehicle, so as to activate the AES function only when this is the case.

The invention also proposes to synthesize the controller by separating the stability conditions and those of performance. More precisely, in linear mode (when the controller is not saturated), the controller guarantees performance (which implies stability). In saturation mode (when the controller is saturated), this controller seeks to stabilize the closed-loop system. Thus the controller does not always seek to guarantee stability and performance at the same time, whatever the operating mode, which makes it possible to obtain better performance in certain operating modes.

[0018] In other words, in the event of saturation, the controller mainly seeks to guarantee the stability of the system. In the absence of saturation (which is statistically generally the case), it also seeks to guarantee performance, i.e. good avoidance trajectory tracking. It thus makes it possible to obtain better results than those obtained by the methods proposed in the prior art, where stability always took precedence over performance.

[0019] According to the invention, the controller operates even if the initial states of the vehicle when the AES function is triggered are not adversely affected (initial heading, initial yaw rate, etc.), which happens when the vehicle has already a certain dynamic (for example because it is in a bend when the AES obstacle avoidance function is triggered), 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.

The invention also proposes an automatic calculation of the gains of the corrector used in the control law of the vehicle, which makes it possible to reduce the design time of this control law.

The proposed controller is optimal and consistent with the controllability limits specific to the vehicle, because the constraints on the steering angle and on the steering speed are taken into account beforehand in the synthesis of the controller.

[0022] The robustness of the controller is also guaranteed for part of the obstacle avoidance trajectory curvatures (as long as the energy required to follow this trajectory remains limited), taking into account the saturation conditions of the actuator ( related to the controllability of the vehicle by the driver).

[0023] As will clearly appear in the remainder of the description, the method for estimating the stability zone in which the controller must remain consists here of an estimation of a basin of attraction. This method guarantees stability if the initial state of the vehicle, when the AES function is activated, meets certain criteria. The method according to the invention offers good results in terms of vehicle stability, performance (good trajectory following), tolerance to data measurement delays used in the context of the invention.

Other advantageous and non-limiting characteristics of the process according to the invention, taken individually or in all technically possible combinations, are as follows:

- the device is a motor vehicle which is suitable for driving on the road and which comprises at least one steered wheel, in which said actuator is adapted to control the steering of said steered wheel, and in which the steering setpoint is a saturated setpoint steering angle of said steering wheel;

- the saturation function satisfies a control setpoint amplitude limiting model and is expressed in the form: ^(x) = sa^iKx - Kx, with K the controller, sat _n an amplitude limiting function, and x a state vector of said device;

- the saturation function satisfies a control setpoint variation limiting model and is expressed in the form: i/> ₂ (x) = sat _v (A^ + B^aίhίKc)) - (A^ + B^aίhίKc )), with K the controller, sat _v an amplitude limiting function, A1 and B1 predetermined matrices, and x a state vector of said device;

- given a basin of attraction located in at least one polyhedron defined according to the modeling of said at least one saturation function, in the absence of disturbance, the controller guarantees that a state vector of said device has successive values over time which remain in the basin of attraction and which converge asymptotically towards the origin in a predetermined time;

- given a basin of attraction located in at least one polyhedron defined according to the modeling of said at least one saturation function, in the presence of a disturbance whose energy is less than a predetermined threshold, the controller guarantees that a state vector of said device has successive values over time which remain in the basin of attraction;

- the output to be minimized is expressed in the form \ z = e _VL + a _y . y _ί with e _yi _ the trajectory tracking error, Yi_ the heading angle error and a _y an adjustment coefficient which varies over time;

- in the absence of saturation of the controller output, the controller guarantees that the synthesis of the H norm applied to the controller is less than a predetermined scalar;

- one of said parameters is a variable which depends on the curvature of the trajectory;

- said basin of attraction is defined by means of a Lyapunov function, disturbances which apply to said device and a term which depends on said at least a saturation function;

- the controller satisfies a modeling of said device in which an output to be minimized is a function of a path tracking error and a heading angle error;

- the size of the trajectory tracking error and the size of the heading angle error in the calculation of the piloting instruction vary over time.

Preferably, provision is made to deactivate the controller: n as soon as the initial values of a state vector of said device do not belong to a first predetermined space, or n when said initial values do not belong to the first space and that the instantaneous values of said state vector do not belong to a second predetermined space.

[0027] This controller deactivation method is determined based on the stability zone and on vehicle state parameters (drift angle, yaw rate, heading angle, lateral position, steering wheel angle, steering wheel speed and curvature of the trajectory to be followed). The deactivation conditions enacted make it possible to guarantee the correct operation of the controller and to diagnose abnormal situations (risk of vehicle instability, failure of sensors, actuators, unforeseen vehicle/driver behavior, etc.).

The invention also relates to 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, programmed to implement a method according to one of the preceding claims.

Of course, the different characteristics, variants and embodiments of the invention can be associated with each other in various combinations insofar as they are not incompatible or exclusive of each other.

DETAILED DESCRIPTION OF THE INVENTION

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

[0031] In the accompanying drawings:

[0032] [Fig. 1A] is a schematic top view of a motor vehicle traveling on a road and which is adapted to implement a method according to the invention; [0033] [Fig. 1B] is a homologous view of FIG. 1A;

[0034] [Fig. 2] is a schematic perspective view of the motor vehicle of the FIG. 1A, represented in four successive positions situated along an obstacle avoidance trajectory;

[0035] [Fig. 3] is a diagram illustrating the closed-loop transfer function used to drive the motor vehicle of FIG. 1A;

[0036] [Fig. 4] is a graph illustrating the saturation polyhedra and the basin of attraction of the controller used in the context of the invention, and an example of variation in the state of the vehicle in the absence of disturbance,

[0037] [Fig. 5] is a graph similar to that of FIG. 4, on which the example of variation in the state of the vehicle is represented in the event of the presence of a disturbance; [0038] [Fig. 6] is a graph illustrating the influence of a setting on the performance of the controller; and

[0039] [Fig. 7] is a graph illustrating a vehicle steering algorithm according to a method according to the invention.

In Figure 1A, there is shown a motor vehicle 10 conventionally comprising a frame which delimits a passenger compartment, two front wheels 11 steered, and two rear wheels 12 not steered. As a variant, these two rear wheels could also be steered with an adaptation of the control law.

This motor vehicle 10 comprises a conventional steering system making it possible to act on the orientation of the front wheels 11 so as to be able to turn the vehicle. This conventional steering system comprises in particular a steering wheel connected to connecting rods in order to cause the front wheels 11 to pivot. In the example considered, it also comprises an actuator making it possible to act on the orientation of the front wheels according to the orientation of the steering wheel and/or according to a request received from a computer 13.

[0042] In addition, it may possibly be provided that this motor vehicle includes a differential braking system making it possible to act differently on the speeds of rotation of the front wheels 11 (and if necessary on those of the rear wheels 12) so as to slow down the motor vehicle by turning it. This differential braking system comprises for example a controlled differential or electric motors placed at the wheels of the vehicle.

[0043] In the remainder of this presentation, the steering system considered will be formed by the conventional steering system alone. Alternatively, it could be formed by the combination of the conventional steering system and the differential braking system. The computer 13 is then provided to control the power steering actuator. It comprises for this purpose at least one processor, at least one memory and various input and output interfaces.

[0045] Thanks to its input interfaces, the computer 13 is suitable for receiving input signals from different sensors.

Among these sensors, provision is made, for example:

- a device such as a front camera, making it possible to identify the position of the vehicle in relation to its traffic lane,

- a device such as a RADAR or LIDAR remote sensor, making it possible to detect an obstacle 20 lying in the path of the motor vehicle 10 (FIG. 2),

- at least one lateral device such as a RADAR or LIDAR remote sensor, allowing observation of the environment on the sides of the vehicle,

- a device such as a gyrometer, making it possible to determine the speed of rotation in yaw (around a vertical axis) of the motor vehicle 10, and

- a steering wheel position and angular speed sensor.

[0047] Thanks to its output interfaces, the computer 13 is suitable for transmitting a setpoint to the power steering actuator.

It thus makes it possible to force the vehicle to follow an avoidance trajectory T0 of the obstacle 20 (see FIG. 2).

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

It stores in particular a computer application, consisting of computer programs comprising instructions whose execution by the processor allows the implementation by the computer of the method described below.

Before describing this process, the various variables which will be used can be introduced, some of which are illustrated in FIGS. 1A and 1B.

[0052] The total mass of the motor vehicle will be denoted "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 denoted "J" and will be expressed in N.m.

The distance between the center of gravity CG and the front axle of the vehicle will be denoted “I _f ” and will be expressed in meters.

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

The drift stiffness coefficient of the front wheels will be denoted “C _f ” and will be expressed in N/rad.

The coefficient of drift stiffness of the rear wheels will be denoted “C _r ” and will be expressed in N/rad.

[0058] These wheel drift stiffness coefficients are notions that are well known to those skilled in the art. By way of example, the drift stiffness coefficient of the front wheels is thus the one which makes it possible to write the equation F _f = 2.C _f .a _f , with F _f the lateral force of slip of the front wheels and a _f the angle of drift of the front wheels.

The steering angle that the front steered wheels make with the longitudinal axis A1 of the motor vehicle 10 will be denoted “d” and will be expressed in rad.

The variable δ _ref , expressed in rad, will designate the saturated steering angle setpoint, as it will be transmitted to the power steering actuator.

The variable dk, 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 dk, but which would be with the variable δ _ref . The variable δ _sat , expressed in rad, will designate the semi-saturated steering angle setpoint. It comes from the unsaturated setpoint dk and is saturated in steering angle only. The saturated setpoint ô _ref will be calculated on the basis of this half-saturated setpoint ô _sat .

[0063] The reference point of the vehicle will here originate from its center of gravity CG. 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 yaw rate of the vehicle (around the vertical axis passing through its center of gravity CG) will be denoted “r” and will be expressed in rad/s.

The relative angle of heading between the longitudinal axis A1 of the vehicle and the tangent to the avoidance trajectory T0 (desired trajectory of the vehicle) will be denoted “Yi_” and will be expressed in rad.

[0066] The lateral difference 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 "Is" located at the front of the vehicle, will be noted “yi_” and will be expressed in meters.

The lateral deviation setpoint 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 "Is" located in front of the vehicle, will be noted "yi_- _ref " and will be expressed in meters. The trajectory tracking error will be denoted “e _yi _” and will be expressed in meters. It will be equal to the difference between the lateral deviation setpoint yi_- _ref and the lateral deviation yi_.

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

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 denoted “b” and will be expressed in rad. The speed of the motor vehicle will be denoted "V" and will be expressed in m/s.

The constants “x” and “w” will represent dynamic characteristics of the steering angle of the front wheels of the vehicle. The constant “oo _f ” will represent a dynamic characteristic of a bounded arbitrary disturbance “w” applied to the vehicle.

The constant “g” will be the acceleration due to gravity, expressed in ms ² .

[0075] The steering speed will designate the angular steering speed of the steered front wheels.

The method according to the invention is provided to enable the vehicle to follow the avoidance trajectory T0 as precisely as possible, in autonomous mode. This process is implemented when the AES automatic obstacle avoidance function is triggered and an avoidance trajectory T0 has been calculated. It will be noted that the manner of triggering the AES function and of calculating the avoidance trajectory T0 is not strictly speaking the subject of the present invention, and will therefore not be described here. This method is designed to be implemented in a loop, during successive “time steps”.

[0077] It will be noted here that trajectory tracking is provided 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 required on the steering wheel to avoid the obstacle.

[0078] Before describing the process which will be executed by the computer 13 to implement the invention itself, we can in a first part of this presentation describe the calculations which made it possible to lead to the invention, so as to fully understand where these calculations come from and on what springs they are based.

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 make it possible to control the vehicle in such a way that it follows the avoidance trajectory T0 in a stable and efficient manner.

It will be considered here that the dynamic behavior of the vehicle can be modeled by means of the following Mathl equation.

[0081] [Math 1]

This model is an improved bicycle model.

The term oo _f is used to model the dynamics of the curvature of the avoidance trajectory T0 to be followed (which is calculated elsewhere and is therefore already known).

The term p _ref of curvature of the avoidance trajectory T0 then makes it possible to take account of the trajectory of the vehicle (and therefore of the curvature of the road) in the modeling of the dynamic behavior of the vehicle.

[0086] However, this model does not in itself make it possible to limit the steering angle and the steering speed of the front wheels 11 of the vehicle. However, such a limitation is particularly important to ensure that the driver of the vehicle is able to regain control of the vehicle at any time.

[0087] Such limitations can be expressed using the following equation, by saturation in steering speed:

[0088] [Math 2]

[0089] \S _ref \£v

[0090] As well as using the following equation, by saturation in steering amplitude:

[0091] [Math 3]

[0092] | S _re f | < h

In the Math 2 equation, the coefficient u is a constant which represents the steering speed 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 0.0491 Rad/s, which corresponds to 0.785 Rad/s at the level of the steering wheel (i.e. 45°/s) if the steering reduction coefficient is equal to 16 .

[0094] In the Math 3 equation, the coefficient h is a constant which represents the steering angle 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 0.0328 Rad, which corresponds in our example to 0.524 Rad at the steering wheel (i.e. 30°).

The constraint expressed by the Math 3 equation makes it possible to limit the torque exerted by the power steering actuator so that an average driver can manually compensate for this torque.

[0096] Indeed, the greater the steering angle, the greater the force applied by the power steering actuator. This limitation thus ensures that the user can regain control of the vehicle without having to counteract too much effort. This angle will then depend on the force applied by the type of actuator chosen.

It will be noted that the aforementioned values are given by way of example and could alternatively be reduced (for example 25°/s and 20° to ensure greater comfort). According to the invention, it is desired to limit the angle and the steering speed of the steered wheels 11 not by imposing a sudden threshold, but rather by gradually saturating the setpoint amplitude and the setpoint variation.

In Figure 3, there is shown the control architecture used to control the power steering actuator so that it follows the avoidance trajectory T0 while respecting the aforementioned constraints.

In this figure, a controller K has been shown which makes it possible to calculate an unsaturated steering angle dk setpoint. This controller K advantageously comprises an adder which outputs the unsaturated steering angle setpoint dk and which receives as input a state feedback term (coming from a state feedback block K _p ) which depends on the state of the vehicle, and a saturation compensation term (resulting from a saturation compensation block K _a ) which depends on the saturated steering angle setpoint δ _ref calculated at the previous time step.

The saturation compensation term makes it possible to reinforce the stability of the controller in nonlinear mode, that is to say in cases where the control of the power steering actuator is saturated in amplitude or in speed.

The block SAT1 represented in FIG. 3 illustrates the saturation in amplitude of the unsaturated steering angle dk setpoint. It receives as input the output of the controller K and it provides as output a semi-saturated steering angle setpoint δ _sat . We observe that this block operates in an open loop.

The set of blocks SAT2 illustrates the saturation in speed of the semi-saturated steering angle setpoint δ _sat . It receives this semi-saturated setpoint as input and it supplies the saturated steering angle setpoint δ _ref as output. We observe that it is a closed loop. In this set of blocks SAT2, corresponding to a “pseudo rate limiter” function, an adder is therefore provided at the input which makes it possible to calculate the difference D between the semi-saturated steering angle setpoint δ _sat and the saturated setpoint steering angle δ _ref at the previous time step. It comprises a multiplier block making it possible to multiply this difference by a parameter l, a saturation block making it possible to not exceed the derivative of the saturated steering angle setpoint δ _ref according to the equation Math2 and an integrator block making it possible to obtain the saturated steering angle setpoint δ _ref (via a Laplace transform).

The parameter l represents the dynamics of the SAT2 blocks (for our application, we can consider l=500), and the larger l is, the closer this pseudo rate limiter is to a "rate-limiter" function.

In FIG. 3, the block P _sy s represents the open loop system which describes the dynamics of the vehicle and the behavior of the power steering actuator. It is observed that this block receives as input a disturbance w and the saturated steering angle setpoint d _GQί . It outputs an output vector y and an error z. According to an advantageous characteristic, this error z to be minimized is a function of the trajectory tracking error e _yi _ and of the relative heading angle between the longitudinal axis A1 of the vehicle and the tangent to the trajectory d avoidance T0 (denoted below heading error Yi_), which we know should be minimized. We can then write:

[0108] [Math 4]

[0109] z = e _yL + a^. xp _L

In this equation, the term ay is an adjustment coefficient which makes it possible to adjust the error which it is primarily desired to minimize (heading-angle tracking error or position tracking error) . It will be seen later in this presentation how the value of this adjustment coefficient is chosen. This choice of error z at the output makes it possible to guarantee both correct position tracking and correct heading tracking.

The output vector y is here considered equal to a preliminary state vector x _p , all the elements of which can be measured or estimated while driving, and which can be written in the form:

[0112] [Math 5]

[0113] c _r = (br ip _L e _yL ddp _ref ) ^T

The objective is then to determine the form of the controller K which is a state feedback regulator making it possible to calculate the unsaturated steering angle setpoint dk on the basis of the preliminary state vector x _p .

It will be noted that one of the parameters of this state vector (the state variable p _ref ) depends on the curvature of the avoidance trajectory T0. The dynamics (ie the derivative) of the curvature is assumed to be known (since the avoidance trajectory T0 is known). By integrating this dynamic into the model of the vehicle, we therefore obtain an augmented system so the curvature becomes a state (which is an input of the controller K). In this way, the curvature compensation is treated in a more precise way (via the knowledge of the dynamics of the curvature) than it would be if we used a more classic method (of the "FeedForward" type) which considers static or slightly varying curvatures.

To understand how to determine a controller K which is suitable both in terms of 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 d _GQί , dk setpoints are equal).

We can write our system in a generic form:

[0118] [Math 6] c _r = A _p . _xp + _Bp . u _p + B _w . w iip = — Aiip + Aii _j(

In this equation:

- the term u _p is the saturated control input, here equal to the saturated steering angle set point ô _ref ,

- the term UK is the unsaturated command input, here equal to the unsaturated steering angle set point dk,

- w is the disturbance, assumed to be bounded,

- A _p is a dynamic matrix,

- B _p is a control matrix and

- B _w is a disturbance matrix.

We can write these three matrices in the following form.

[0122] [Math 7]

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:

[0129] [Math 10] [0130] u _K = K. x [0131] With [0132] [Math 11] = ¾w]

[0133]\ ^K

( x [Xp u _p ]T

[0134] x is the state vector increased by the saturated steering angle setpoint δ _ref which will be considered later in this presentation. Its parameters will be called state variables.

The term U _K is, in our application, considered equal to the unsaturated steering angle dk setpoint.

We can now describe the system Psys in closed loop, that is to say in non-linear mode with saturation (case where the saturated and unsaturated steering angle d _{G ί} , dk setpoints are unequal).

On the basis of the Math 6 and Math 10 equations, we can write:

[0138] [Math 12]

[0139] x = (A + BA _t + BB _± K)x + BB^^x) + Bp ₂ (x)

In this equation, the terms x, A, B, Ai and Bi are defined as follows:

[0141] [Math 13]

[0143][Math 14]

A 0144] _p B

[ A = p 0 0 .

[0145] [Math 15]

[0146] fl = [°]

I is the identity matrix.

[0148] [Math 16]

[0149] A = [0 -2]

[0150][Math 17]

[0151] B _± = l

To take into account the controllability constraints as defined in the Math 2 and Math 3 equations, two new saturation functions Yi(c) and 4(x) have been introduced, which represent the overrun of the limits of the command input not saturated.

[0153] We then seek to model the saturation functions via modeling by non-linear sectors (from the English "dead-zone nonlinearity"), on the basis of work disclosed in the referenced document: "Alessandra Palmeira, Joâo 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”.

[0154] The two saturation functions Yi(c) and 4 (x) can therefore be defined as follows: [0155] [Math 18]

In these two equations, a saturation function denoted satro(f) is used, which can be defined as follows:

[0160]

[0161]

It will therefore be noted that these two saturation functions Yi(c), Y2(c) have zero values in unsaturated mode and non-zero values otherwise.

To model the controllability limits of the system, two polyhedra can be defined, one of which, denoted Si(x,q), models the behavior of the saturation in amplitude and the other, denoted 82(c,Yi ,n) models the behavior of velocity saturation. These two polyhedrons can be modeled in the following form:

[0164][Math 21]

[0165] X^c,h) = {xe R ⁿ , \ (K — G _x ) | £ h }

[0166] [Math 22]

[0167] S ₂ (x,\p ₁ ,v) = {xe R ⁿ , ip _t e R ^m , \(A _t + B _t K - G ₂ )x + (B _t - G ₃ )^ ₁ ( x)| £v}

These models involve matrices Gi, G2 and G3. These matrices have the same dimension as that of the controller K. They illustrate the deviation that is authorized to exceed the saturation constraints.

By way of illustration, the matrix G1 could be considered equal to the product of the matrix K by a scalar ak. Then the math equation 21 could be rewritten in a form involving the term (1-ak), which will therefore constitute an adjustment of the allowed overshoot. This overshoot could for example be set to 10%. To adjust this excess, it will be necessary to do road tests.

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, the conservatism of a solution such as the one described in the previous paragraph will be avoided.

[0171] First, it can be assumed that during operation of the closed-loop system (as defined in Math Equation 12), the state vectors x and the variable Yi are found in these two polyhedra, so that we can write:

[0172] [Math 23]

G01731 i ^{xe Si} M ^{1 J} {(. ^c ,y _ί ) e S ₂ (.x,ip ₁ ,v)

These two polyhedra are represented here in FIGS. 4 and 5 and therefore represent, as will be clearly described above, the two spaces within which the stability and the performance of the system are guaranteed.

It will be noted at this stage that these figures illustrate two-dimensional graphics, simplifying the solution described above with a view to making it more understandable.

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

In practice, here, the state vector comprises eight state variables. A representation of the invention should therefore be drawn in eight dimensions.

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

[0179] [Math 24]

[0180]

It will be noted here that these scalar quantities Ui and l^ are introduced here simply to facilitate the subsequent calculations (according to the S-procedure).

To sum up, the Math equations 21 and 22 are two saturation models, respectively in amplitude and speed, which, as long as they remain valid within the meaning of the Math equation 23, make it possible to ensure that the equations Math 24 are too. We can then use these models for the synthesis (that is to say the optimization) of the main gain K _p of the state feedback linked to the state variables of the open loop system P and of the gain K _a for compensation of saturations (or “anti-windup gain”) of the controller K. The closed-loop equation Math 12 and the representation of the Psys system represented in FIG. 3 make it possible to write:

[0185][Math 25]

In this equation, z is the error of the system considered, with z=e _yi _ +ai_.Yi_. The matrix Cz is then expressed as follows:

[0189] [Math 26] [0190] c _z = [0 0 a _y 1 0 0 0 0]

We assume that the disturbance w is limited in energy, that is to say bounded, so that we can write:

[0192] [Math 27]

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

[0195] Therefore, in equation Math 27, where the term w represents the curvature of the avoidance trajectory, the maximum value w _max of this curvature is known (since we know the dynamic limits of the vehicle and therefore the curvature maximum that the vehicle can follow in complete safety and in fact taxable by trajectory planning). Therefore, the parameter o can be defined as:

[0196] [Math 28]

In this equation, the TAES time corresponds 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.

[0199] Given the controllability limits that it is desired to impose, w _max being the curvature of the most dynamic reference trajectory that the AES function can achieve, this maximum curvature can be estimated as a function of the steering angle maximum (imposed by the Math 3 controllability constraint). Therefore, we can also write:

[0200][Math 29]

In this equation, the term k is the understeer gradient, which is calculated as follows:

[0203]

[0204]

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

[0206] [Math 31]

[0207] V t ) = x ^T Px

[0208] It is also possible to define a second Lyapunov function V _Y (t) for the performance conditions: [0209] [Math 32]

[0210] n _g( ) = c ^t R _gc

In these two equations, the matrices P and P _Y are positive and symmetric definite.

The advantage of the first 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.

[0213] The idea here is then to use this first derivative function, by subtracting from it a term which takes into account the disturbances and another term which takes into account the saturation (within the meaning of equation Math 24), and to ensure that this set is always strictly negative, which we can write:

[0214][Math 33]

[0215] V(t)-W ^T . W - 2. ip U ₁ (ip ₁ + G _x x) - 2. ip U ₂ (ip ₂ + G ₂ x + G 3^) < 0

This condition relating to the first Lyapunov function V(t) guarantees stability with the presence or absence of the disturbance and with the presence of the saturation of the actuator.

In Figures 4 and 5, the two polyhedrons are shown ensuring the stability and performance of the system. We will then look for a space located simultaneously in these two polyhedra. It could for example be the intersection of these two spaces. [0218] However, here, we prefer to model this space in the form of an ellipse called the basin of attraction. This basin of attraction e is here defined in the form:

[0219] [Math 34]

[0220] e(R,m) = {xe R ⁿ ,x ^T Px < m ^-1 }

[0221] In addition to the stability condition relating to the first Lyapunov function V(t) defined by Math 33, 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 be guaranteed).

To guarantee performance, one could also define a second space, on the basis of the second Lyapunov function V _Y (t), but it is preferable here to use another model (the Hinfini model, which will be mentioned below ).

The basin of attraction e is therefore a space of stability (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, insofar as they have been initialized in this space (even if the system is subject to disturbances and saturations of the actuators).

[0224] Taking into account the equations Math 21, Math 22 and Math 34, there has been shown schematically in FIGS. 4 and 5 the spaces in which the state variables of the system can change.

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

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 e (which ensures stability) and converge asymptotically towards the origin (which ensures performance), in particular within a predefined time.

In Figure 4, the case of no disturbance has been considered. In this case, the space of the initial conditions of the system, denoted Eo, and the estimate Ei of the basin of attraction e merge. We observe that the trajectory T1 of the state vector x from any initial situation does indeed converge towards the origin.

The second objective is that in the presence of disturbance, the controller K guarantees that the trajectories of the state variables of the closed-loop system remain in the basin of attraction e (which ensures stability) whatever the disturbance w, provided that the latter is limited in energy (within the meaning of equation Math 27). In FIG. 5, this case has been considered where a disturbance occurs. In this case, the space of the initial conditions of the system, denoted Eo, are necessarily contained in the estimate Ei of the basin of attraction e. We observe that the trajectory T2 of the state variables, when it starts from any initial situation contained in the space Eo, remains well contained inside the basin of attraction e.

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

It will be recalled that this synthesis consists in finding the controller K which is such that the norm H of the term Fi(P _sys , K) is minimum, with:

[0232] [Math 35]

[0233] z = F^P _sys .K w

We can write this equation in the following form:

[0235][Math 36]

[0236] V _y (t) + z ^T z — y ² w ^T w < 0

It will be noted here that y is the norm H of the transfer function of w -> z.

This synthesis implies good rejection of the disturbance w and good tracking of the reference trajectory (with an error z close to zero).

In practice, to satisfy these three objectives, several methods could be used, for example a method based on the resolution of the Riccati equations or a method using the Youla parametrization.

But the method used here is preferably the use of Finsler's lemma applied to linear matrix inequalities (LMI) to reduce conservatism (LMI relaxation), this Finsler's lemma being applied in particular to the both stability (Math equation 33) and performance (Math equation 35). It is thus carried out on the basis of convex optimization criteria under constraints of linear matrix inequalities (the linearity of the terms of the matrices used ensuring that the mathematical problem can be solved without requiring too great a computational load).

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

For predefined positive reals ei and £2, if there exist matrices of appropriate dimensions R, Q, Q, Q _Y , L1, L2, T 1 , T2 and a scalar £3 such that the problem of optimization is feasible, we therefore obtain a controller K which satisfies the three aforementioned objectives.

These matrices are calculated as a function of the matrix P (see Math equation 42). The matrix inequalities used here are five in number and are defined by the following inequalities, in which y is to be minimized.

[0245][Math 37]

[0255] In these inequalities, a matrix of the form is written under X y forms L* W-

The matrices R, Q, Q, Q _Y , Li, L2, T 1 , T2 are expressed here in the following form:

[0257][Math 42]

In these equations, J is a non-singular matrix.

[0260] The controller K is defined by the equation:

[0261][Math 43]

[0262] K = R.Q ^{~ 1}

The speed V of the vehicle is assumed to be constant (therefore all the matrices of the system are considered constant).

The four inequalities Math 37 to Math 40 make it possible to ensure that the dynamics of the closed loop remain limited, that is to say that the system remains stable in the absence or in the presence of a disturbance ( the first two conditions are therefore fulfilled).

[0265] The fifth inequality Math 41 guarantees the performance (within the meaning of the H ⁰⁰ standard) of the closed-loop system when the system is subjected to a disturbance and when the output of the control K is not yet saturated (nor in amplitude , nor in speed, i.e. when the steering instructions ô _ref and dk are equal). This inequality ensures that the third condition is satisfied.

As shown in FIG. 6, several types of controller K can be obtained depending on the chosen value of a _y .

In this figure, it is then observed that it is possible to play on the performance of the controller K by adjusting the value of a _y .

Thus, the adjustment coefficient a _y , when it has a reduced value, makes it possible to obtain a controller K which minimizes the position tracking error (zone ZC1). On the contrary, when it has a high value, it makes it possible to obtain a controller K which minimizes the heading tracking error (zone ZC2). Between these extreme values, it is possible to make a compromise between position tracking and heading tracking (zone ZC3).

At the start of avoidance, the adjustment coefficient a _y will be chosen with a reduced value (less than 20), to minimize the position tracking error and ensure that the vehicle follows the avoidance trajectory T0.

[0270] At the end of avoidance (once the obstacle has been passed), the adjustment coefficient a _y will be chosen with a high value (greater than 20), to minimize the heading tracking error and ensure that the vehicle is positioned parallel to the road.

Thus, by way of example, if the driver wishes to regain control at the end of avoidance, the high value of the adjustment coefficient a _y is such that the saturated steering angle setpoint δ _ref transmitted to the power steering actuator will help the driver stabilize the vehicle.

[0272] Again by way of example, if the driver wishes to regain control at the start of avoidance and if he deviates much further from the obstacle than expected (in the sense of the avoidance trajectory T0), the high value of the adjustment coefficient a _y at the end of avoidance ensures that the saturated steering angle setpoint δ _ref does not unnecessarily bring the vehicle back onto the avoidance trajectory when the latter has been exceeded by a great deal ( which would otherwise be destabilizing for the driver).

[0273] At this stage, it will be noted that Finsler's lemma (within the meaning of the document "Skelton, RE, Iwasaki, T., and Grigoriadis, KM (1998). A Unified Algebraic Approach to Linear Control Design. Taylor and Francis, London”) has been applied to linear matrix inequalities to reduce conservatism. Indeed, two different Lyapunov matrices Q and Q _Y (instead of a single common matrix) were respectively used for the stability and performance criteria.

The proposed method therefore proves to be effective when it comes to determining the steering wheel angle at each instant in a reasonable way (and manageable by a driver with average skills) and in a way that can be carried out by the actuator.

[0275] After solving the linear matrix inequalities, the controller K is recalculated using the following equation:

[0276][Math 44]

[0277] K = RJ ^T [0278] With [0279] [Math 45]

[0280]; = Q ^-1

[0281] Once the controller K has been obtained, the computer can be used to calculate the unsaturated steering angle setpoint dk using the following formula:

[0282][Math 46]

[0283] d _k = K.x

The controller K found during the design of the vehicle can then be implemented in the computers 13 of the motor vehicles 10 of the range. At this stage, it is possible to describe with reference to FIG. 7 the method which will be executed by the computer 13 of one of these motor vehicles to implement the invention. The computer 13 is here programmed to implement this method recursively, that is to say step by step, and in a loop.

For this, during a first step, the computer 13 checks that the autonomous obstacle avoidance function (AES) is activated and that an obstacle avoidance trajectory has been planned.

The computer 13 will then seek to define a steering setpoint for the conventional steering system, namely a saturated steering angle setpoint δ _ref , making it possible to follow this avoidance trajectory T0 as well as possible.

[0289] To do this, he begins by calculating or measuring the parameters which are:

- the measured steering angle d,

- the time derivative of the measured steering angle d,

- the saturated steering angle setpoint δ _ref obtained at the previous time step,

- the yaw rate r,

- the relative heading angle Yi_ _,

- the trajectory tracking error e _yi _,

- the curvature p _ref of the avoidance trajectory,

- the drift angle b.

The computer 13 then uses the controller K stored in its memory. This controller K will therefore make it possible to determine, during a first step, the values of the unsaturated steering angle dk and saturated δ _ref values.

It will be noted that the controller K is synthesized taking into account the saturation functions, so that the setpoints are perfectly adapted to the chosen saturation model.

The saturated steering angle setpoint δ _ref will then be transmitted to the power steering actuator to steer the wheels of the motor vehicle 10.

[0293] It may happen, once the AES function has been activated, that there are anomalies (failure of the sensors, of the power-assisted steering system, behavior of the vehicle and/or of the driver that cannot be managed by the controller K. ..). In this case, provision is made to deactivate the AES function.

The overall control strategy employed can then be described, with reference to figure 7.

The first step E1 occurs when the AES function is activated.

At this instant, the computer 13 acquires the initial state of the vehicle, defined by the state vector x (denoted, at this initial instant, xo). During the second step E2, the computer can, with the aid of the controller K and taking into account the avoidance trajectory to be followed, determine a saturated steering angle setpoint δ _ref . This instruction is sent to the power steering actuator of the motor vehicle 10, which reacts so that the vehicle can be defined by a new state vector x.

The method for calculating the saturated steering angle setpoint δ _ref is then repeated in a loop, at regular time intervals, so that the vehicle follows the avoidance trajectory as well as possible.

In parallel, and here at each new loop, the computer 13 checks whether it is in the presence of an anomaly requiring the deactivation of the AES function.

For this, during a step E3, the computer checks whether two cumulative conditions are fulfilled.

The first condition is that the initial state vector xo does not belong to the space Eo of the initial conditions of the system. The second condition is that the state vector x (of the considered time step) does not belong to the estimate Ei of the basin of attraction e. These two conditions can be written as follows:

[0302] [Math 47]

[0303] { » « ^E ' ^{= £(P} f - " ⁵

( X e E ₁ = e(R,m ^_1 )

[0304] If these two cumulative conditions are fulfilled, then there is a risk of instability of the system, so that during a step E4, the computer 13 automatically deactivates the AES function.

[0305] Otherwise, during a step E5, the computer decides to maintain the autonomous obstacle avoidance AES function in the activated state, in order to avoid the obstacle.

[0306] Consequently, the computer loops the process back to step E2.

[0307] It should be noted that as a variant, the computer could deactivate the AES function on the basis of the first condition only. It is in fact probable, when this first condition is met, that it is not possible to steer the vehicle so that it follows the avoidance trajectory in complete safety.

[0308] However, here the second condition makes it possible to wait to detect a real instability of the control of the vehicle before deactivating the AES function. It can indeed happen, when the initial state vector is outside the space Eo, that the control of the vehicle remains stable, for example under the action of the wind or because the driver has not let go of the steering wheel. and participates in avoidance.

[0309] It will be noted here that if new road circumstances occur, the change of scene will require a reactivation of the AES function. In case the AES function is not reactivated but if, for various reasons, the process continues, this new scene will impact the controller K during step E3, which may result in the automatic deactivation of the AES function.

The present invention is in no way limited to the embodiment described and shown, but those skilled in the art will know how to make any variant in accordance with the invention.

[0311] Thus, the method can be applied to other types of fields in which a particular trajectory must be followed, for example in aeronautics or robotics (in particular when the robot is small and it is necessary to saturate one of his orders).

Claims

[Claim 1] Method for autonomously controlling an actuator of an automobile device (10) which is adapted to influence the trajectory of said device (10), comprising the steps of:

- acquisition of parameters (b, r, Yi_, e _yi _, d, ô _ref ) relating to the trajectory of the apparatus (10), and of

- calculation by a computer (13) of a control setpoint (ô _ref ) of said actuator according to said parameters (b, r, Yi_, e _yi _, d, p _ref ), by means of a controller (K) associated with at least one saturation function of an output of the controller (K), characterized in that the controller (K) satisfies a modeling of the said at least one saturation function per nonlinear sector.

[Claim 2] Steering method according to claim 1, in which the apparatus (10) is a motor vehicle which is suitable for driving on the road and which comprises at least one steering wheel (11), in which the said actuator is adapted to controlling the steering of said steered wheel (11), and in which the steering setpoint (δ _ref ) is a saturated steering angle setpoint of said steered wheel (11).

[Claim 3] Control method according to one of Claims 1 and 2, in which the saturation function satisfies a control setpoint amplitude limiting model (ô _ref ) and is expressed in the form: yi(c) = sat _v (Kx ) — Kx, with

K the controller, sat _n an amplitude limitation function, and x a state vector of said device (10).

[Claim 4] Control method according to one of Claims 1 to 3, in which the saturation function satisfies a control setpoint variation limiting model (ô _ref ) and is expressed in the form:

K the controller, sat _v an amplitude limiting function, A1 and B1 predetermined matrices, andx a state vector of said device (10).

[Claim 5] Steering method according to one of Claims 1 to 4, in which, given a basin of attraction (e) located in at least one polyhedron defined according to the modeling of the said at least one saturation function, in the absence of disturbance, the controller (K) guarantees that a state vector (x) of said device (10) has successive values over time which remain in the basin of attraction (e) and which converge asymptotically towards the origin in a predetermined time.

[Claim 6] Piloting method according to one of Claims 1 to 5, in which, given a basin of attraction (e) located in at least one polyhedron defined according to the modeling of the said at least one saturation function, in the presence of a disturbance whose energy is less than a predetermined threshold, the controller (K) guarantees that a state vector (x) of said apparatus (10) presents successive values over time which remain in the basin of attraction (e).

[Claim 7] Control method according to one of Claims 1 to 6, in which, in the absence of saturation of the output of the controller (K), the controller (K) guarantees that the synthesis of the norm H applied to the controller (K) is less than a predetermined scalar.

[Claim 8] Piloting method according to one of Claims 1 to 7, in which one of the said parameters (p _ref ) is a variable which depends on the curvature of the trajectory.

[Claim 9] Piloting method according to one of Claims 1 to 8, in which, given a basin of attraction (e) located in at least one polyhedron defined according to the modeling of the said at least one saturation function , said basin of attraction (e) is defined by means of a Lyapunov function (V(t)), disturbances which apply to said apparatus (10) and a term which depends on said at least one function saturation.

[Claim 10] Control method according to one of Claims 1 to 9, in which the controller (K) satisfies a modeling of the said device (10) in which an output (z) to be minimized is a function of a tracking error trajectory (e _yi _) and a heading angle error (Yi_).

[Claim 11] Steering method according to Claim 10, in which the output (z) to be minimized is expressed in the form: with e _yi _ the trajectory tracking error, Yi_ the heading angle error and a _y an adjustment coefficient which varies over time.

[Claim 12] Control method according to one of claims 1 to 11, in which provision is made to deactivate the controller (K):

- as soon as the initial values of a state vector (x) of said device (10) do not belong to a first predetermined space (Eo), or - when said initial values do not belong to the first space (Eo) and the instantaneous values of said state vector (x) do not belong to a second predetermined space (Ei).

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