FR3099450A1 - Autonomous control method of an actuator of an automotive device - Google Patents

Abstract

The invention relates to a method for autonomous piloting of an actuator of an automobile device (10) which is adapted to influence the trajectory of said device, comprising steps of: - acquisition of parameters relating to the trajectory of the device, and - calculation by a computer of a new control instruction of said actuator as a function of said parameters. According to the invention, the new piloting setpoint is determined by means of a controller which satisfies a pilot setpoint amplitude limiter model and a pilot setpoint variation limiter model. Figure for the abstract: Fig. 2

Description

Autonomous control method of an actuator of an automotive device

Technical field of the invention

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

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.

It relates more particularly to a method for autonomously controlling an actuator of an automotive device which is adapted to influence the trajectory of said device, comprising steps of:
- acquisition of parameters relating to the trajectory of the aircraft, and
- Calculation by a computer of a new setpoint for controlling said actuator as a function of said parameters.

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

State of the art

In order to make motor vehicles safer, they are currently equipped with driver assistance systems or autonomous driving systems.

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 path taken by the vehicle, by simply acting on the conventional braking system of the motor vehicle.

However, there are situations in which these emergency braking systems cannot avoid a collision or cannot be used (for example if a machine is following the motor vehicle closely).

For these situations, automatic avoidance systems (better known by the abbreviation AES, 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.

However, this AES system sometimes imposes a limiting trajectory on the vehicle in terms of controllability, which does not allow the driver to regain control of driving the vehicle with full control.

Presentation of the invention

In order to remedy the aforementioned drawback of the state of the art, the present invention proposes to use a controller suitable for developing a control setpoint which limits the amplitude and the speed of the change of direction imposed on the automotive device. .

More particularly, according to the invention, a steering method is proposed as defined in the introduction, in which the new steering setpoint is determined by means of a controller which satisfies a steering setpoint amplitude limiting model and a control setpoint variation limiter model.

Thus, thanks to the invention, the control setpoint is determined natively to restrict the amplitude and the speed of variation of the control setpoint.

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

In this particular case, the steering angle is therefore directly calculated so as not to be able to vary too quickly and so as not to exceed an amplitude threshold, which will allow the driver of the vehicle to be able to regain control of the driving the vehicle in complete safety and which will make it possible not to exceed the trajectory following capabilities of the vehicle.

The invention applies particularly to the case where the trajectory of the vehicle is an avoidance trajectory of an obstacle located on the road taken by the vehicle. In this particular case, the vehicle must react quickly and safely, following the desired trajectory with a low response time.

Other advantageous and non-limiting characteristics of the control method in accordance with the invention, taken individually or according to all the technically possible combinations, are the following:
- the controller satisfies a behavioral matrix model of the device which takes account of the slope of the road;
- the behavioral matrix model of the device considers the inclination as a disturbance of unknown value;
- provision is made to determine an unsaturated steering angle setpoint for each steered wheel which satisfied neither the steering setpoint amplitude limiting model nor the steering setpoint variation limiting model;
- the steering set point amplitude limiter model is defined by a subsidiary closed-loop controller which outputs a semi-saturated steering angle set point and whose direct chain transfer function includes a hyperbolic tangent function of the the difference between the unsaturated steering angle setpoint and the semi-saturated steering angle setpoint;
- the control setpoint variation limiter model is defined by a subsidiary closed loop controller which outputs said new control setpoint and whose direct chain transfer function comprises a hyperbolic tangent function of the difference between the semi setpoint -saturated with steering angle and said new steering setpoint;
- provision is made to calculate the value of a first parameter using the hyperbolic tangent function of the difference between the unsaturated steering angle set point and the semi-saturated steering angle set point, to calculate the value of a second parameter using the hyperbolic tangent function of the difference between the semi-saturated steering angle setpoint and the new steering setpoint, to compare the values of the first and second parameters with thresholds predetermined and, depending on the result of said comparison, to continue or interrupt said process;
- provision is made to determine whether the pair formed by the values of the first and second parameters is included in a predetermined zone and, depending on the result of said comparison, to continue or interrupt said method;
- the values of the first and second parameters are calculated using the following mathematical expressions:
, with And Or :
- η is a steering angle threshold,
- α _r and α _s are predetermined adjustment constants,
- δ _K is the unsaturated steering angle setpoint,
- δ _sat is the semi-saturated steering angle setpoint, and
- δ _ref is the new control setpoint;

The invention also proposes a method for developing a controller with a view to its use in an autonomous piloting method as mentioned above, in which it is planned to:
- acquire a behavioral matrix model of the device,
- determine at least part of the coefficients of the matrices of the behavioral matrix model,
- deduce therefrom a controller which satisfies the monitoring of a trajectory to be taken, a piloting setpoint amplitude limiting model and a piloting setpoint variation limiting model.

Preferably, the controller is determined taking into account the influence of the cant on the trajectory of the aircraft.

The invention also relates to an automotive device comprising at least one actuator which is suitable for influencing the trajectory of said device and a computer for controlling said actuator, programmed to implement a method as mentioned above.

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.

On the attached drawings:

is a schematic top view of a motor vehicle traveling on a road, on which the trajectory that this vehicle must take is represented;

is a schematic perspective view of the motor vehicle of FIG. 1, represented in four successive positions located along an obstacle avoidance path;

shows cross-sectional views of two roads with a cant;

is a graph illustrating the variations of a saturation function of a steering angle;

is a graph illustrating the variations of a saturation function of a steering speed;

is a diagram illustrating the closed-loop transfer functions used to implement the saturation functions of FIGS. 4 and 5;

is a diagram illustrating the closed-loop transfer function used to drive the motor vehicle of FIG. 1;

is a graph illustrating the parameters making it possible to stabilize the closed loop illustrated in FIG. 7;

is a graph illustrating, in a first case, the stability and performance zones of a parameter θυη used to control the motor vehicle;

is a graph illustrating, in a second scenario, the stability and performance zones of a parameter θυη used to control the motor vehicle;

is a graph illustrating a vehicle steering algorithm according to a method according to the invention.

In Figure 1, there is shown a motor vehicle 10 conventionally comprising a chassis 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.

In addition, provision could possibly be made for this motor vehicle to include a differential braking system making it possible to act differently on the speeds of rotation of the front wheels 11 (and on those of the rear wheels 12) so as to slow down the motor vehicle by doing so turn. This differential braking system comprises for example a controlled differential or electric motors placed at the wheels of the vehicle.

In the remainder of this description, 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.

Thanks to its input interfaces, the computer 13 is suitable for receiving input signals originating from various sensors.

Among these sensors, it is for example provided:
- 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, making it possible to observe the environment on the sides of the vehicle,
- a device such as a gyrometer, making it possible to determine the speed of rotation in yaw (around a vertical axis) of the motor vehicle 10, and
- a steering wheel position and angular speed sensor.

Thanks to its output interfaces, the computer 13 is suitable for transmitting a setpoint to the power-assisted steering actuator.

It thus makes it possible to force the vehicle to follow an avoidance trajectory T0 of the obstacle 20.

Thanks to its memory, the computer 13 stores data used in the context of the method described below.

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

Before describing this process, we can introduce the different variables that will be used, some of which are illustrated in Figure 1.

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

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 noted " _lf " and will be expressed in meters.

The distance between the center of gravity CG and the rear axle will be noted "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 drift stiffness coefficient of the rear wheels will be denoted “C _r ” and will be expressed in N/rad.

These wheel drift stiffness coefficients are notions well known to those skilled in the art. By way of example, the coefficient of drift stiffness of the front wheels is thus the one which makes it possible to write the equation F _f = 2.C _f .α _f , with F _f the lateral sliding force of the front wheels and α _f the drift angle 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 “δ” 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-assisted steering actuator.

The variable δ _K , expressed in rad, will designate the unsaturated steering angle setpoint. At this stage, it will only be possible to 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 δ _K , 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 δ _K summer st saturated in steering angle only. The saturated set point δ _ref will be calculated on the basis of this half-saturated set point δ _sat .

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

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 “ls” situated at the front of the vehicle, will be denoted “ y _L ” 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 "ls" located in front of the vehicle, will be noted "y _{L -ref} " and will be expressed in meters.

The trajectory tracking error will be denoted “e _yL ” and will be expressed in meters. It will be equal to the difference between the lateral deviation setpoint y _{L -ref} and the lateral deviation y _L .

The aforementioned aiming distance "ls" 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 “β” and will be expressed in rad.

The speed of the motor vehicle along the longitudinal axis A1 will be denoted "V" and will be expressed in m/s.

P and Q will be matrices of appropriate dimensions, positive and symmetric, such that Q = P ^-1 . The exact expression of these matrices will appear more clearly on reading the rest of this presentation.

The constants “ξ” and “ω” will represent dynamic characteristics of the steering angle of the front wheels of the vehicle.

The constant “ω _f ” will represent a dynamic characteristic of an arbitrary disturbance “w” bounded applied to the vehicle.

The constant "g" will be the acceleration due to gravity, expressed in ms ^-2 .

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

Finally, the variable “Φ _r ” will correspond to the cant angle of the road, expressed as a percentage. To clearly illustrate this angle, there is shown in Figure 3 two sectional views of two roads 31, 32.

As a hypothesis, these roads are supposed to be straight and notably flat. They extend along a main axis. The cross-sectional views are then represented in a section plane orthogonal to this longitudinal axis. The cant angle therefore makes it possible to characterize the amplitude according to which the road 31, 32 is leaning to one side or the other. This angle is negative when Route 31 leans to the left. It is positive when Route 32 is leaning to the right.

Before describing the process which will be executed by the computer 13 to implement the invention, 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 do these calculations come from and on what springs they are based.

It will be considered here that the dynamic behavior of the vehicle can be modeled by means of the following equation Math1.

This model is an improved bicycle model.

It makes it possible to take into account the cant angle Φ _r in the form of an unknown disturbance which influences the dynamics of the vehicle, which proves to be particularly advantageous insofar as this angle is difficult to measure or calculate.

However, it 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.

Such limitations can be expressed using the following Math2 equation:

As well as using the following Math3 equation:

In the Math 2 equation, the coefficient υ 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 .

In the Math 3 equation, the coefficient η 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°).

In practice, the greater the steering angle, the greater the force applied by the power steering actuator. This limitation will ensure 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.

The aforementioned values could alternatively be lower (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 using a setpoint amplitude limiter and a setpoint variation limiter.

With reference to FIG. 6, we can first describe the angle limiter L1 which will be used here to modify the unsaturated steering angle setpoint δ _K in order to generate the semi-saturated steering angle setpoint δ _sat .

This angle limiter L1 is particular in the sense that it forms a subsidiary controller in closed loop which comprises:
- a transfer function in direct chain equal to the product of the constant η (to respect the condition enacted by equation Math 3) and of a corrector which is a hyperbolic tangent function of Δ ₁ .α _s ,
- an indirect chain transfer function (or "feedback chain") equal to one.

In this figure 6, the coefficient Δ ₁ corresponds to the difference between the variables δ _sat and δ _K . The coefficient α _s is a constant between 0 and infinity, which is the one and only parameter making it possible to play on the rapid or flexible nature of the angle limiter L1.

As shown in Figure 4, the use of such a subsidiary controller not only makes it possible to properly limit the steering angle δ over time, but also to ensure continuity of the variation of the semi-saturated setpoint d steering angle δ _sat .

Curve D1 thus shows that this setpoint variation can be smooth and flexible (with a low coefficient α _s ), or faster as shown by curve D2 (curve D3 corresponds to an infinite coefficient α _s ).

This steering angle limiter L1 has the advantage of being simple to develop since it suffices to adjust the coefficient α _s . It ensures continuous and smooth control (infinitely differentiable). Above all, it can be directly taken into account in the dynamic behavior model of the vehicle defined by equation Math 1, with a view to calculating a vehicle steering angle setpoint.

An example of a value for the coefficient α _s is 3000 Rad ^-1 .

Given the shape of this steering angle limiter L1, we can write the equation Math4:

As shown in figure 6, the steering speed limiter L2 is also particular in the sense that it forms a subsidiary controller in closed loop which comprises:
- a transfer function in direct chain equal to the product of the constant υ (to respect the condition enacted by the equation Math 2), of an integrator in 1/s, and of a corrector which is a hyperbolic tangent function of Δ ₂ .α _r ,
- an indirect chain transfer function (or "feedback chain") equal to one.

It receives as input the semi-saturated steering angle setpoint δ _sat and transmits as output the saturated steering angle setpoint δ _ref .

In this figure, the coefficient Δ ₂ corresponds to the difference between the variables δ _ref and δ _sat . The coefficient α _r is a constant comprised between 0 and infinity, which is the only parameter making it possible to play on the rapid or flexible nature of the steering speed limiter L2.

As shown in FIG. 5, the use of such a corrector makes it possible not only to effectively limit the steering angle variations over time, but also to ensure continuity of the variation of the saturated angle setpoint steering angle δ _ref .

Curve C1 thus shows that this setpoint variation can be smooth and flexible (with a low coefficient α _r ), or faster as shown by curve C2 (curve C3 corresponds to an infinite coefficient α _r ).

This steering speed limiter L2 has the advantage of being simple to develop since it suffices to adjust the coefficient α _r . It ensures continuous and smooth control (infinitely differentiable). Above all, it can be directly taken into account in the dynamic behavior model of the vehicle defined by equation Math 1, with a view to calculating a vehicle steering angle setpoint.

For this, given the shape of this steering speed limiter L2, we can write the equation Math5:

A controllability model of the vehicle which is pseudo-linear is thus obtained.

We can now introduce some variables to simplify the expressions of the Math 4 and Math 5 equations in order to represent the complete model in a quasi-linear way (i.e. in an LPV way, from the English "Linear Parameter Varying") , in a form of state representation.

The Math 4 equation can be written as a Math6 equation:

with

We can then introduce the following parameter θ _η :

Then rewrite the Math 6 equation as the following Math9 equation:

For its part, the Math 5 equation can be written in the form of a Math10 equation:

We can then introduce the following parameter θ _υ :

Then rewrite the Math 10 equation, i.e. the controllability model, in the form of the following Math12 equation:

The Math 9 and Math 12 equations make it possible to write:

We can then introduce the following parameter θ _υη :

And then can we write the following Math15 equation:

This Math 15 equation is characteristic of a state representation and it shows that the complete angle limiter and steering speed model is quasi-linear as a function of the exogenous parameters θ _υη and θ _υ (which parameters are computable when the vehicle is moving).

We can then enrich the bicycle model of the Math 1 equation with this state representation to obtain a new model which is written in the form of the following Math16 equation:

In figure 7, the behavioral model of the vehicle has been represented in the form of a closed loop, where P represents the model of the vehicle given by equation Math 16.

In this loop, the L1 and L2 models are represented as a single L3 model.

The model P of the vehicle receives as input the saturated steering angle setpoint δ _ref and the disturbances denoted w and Φ _r .

It outputs an output vector y and an error z, which is here formed by the trajectory tracking error e _yL which we know should be minimized.

Based on this model P and thanks to the measurement results provided by sensors, it is possible to obtain the output vector y, here considered equal to a state vector x, all of whose elements are measurable or estimable in rolling, which can be written in the form:

The objective is then to determine the form of the controller K which is the state feedback making it possible to calculate the unsaturated steering angle setpoint δ _K on the basis of this state vector x. Thanks to the quasi-linear controllability model, this determination of the controller K can be done without having to map it by means of a multitude of tests.

To understand how to determine a controller K that is suitable both in terms of stability and speed, we can write our behavioral model in a generic form:

In this equation (see figure 7), u=δ _ref is the control input, W is the disturbance, y is the measurement (system state vector), and z=e _{yL_Ctrl} is the output to be minimized. Note that this output e _{yL_Ctrl} is equal to the sum of the trajectory tracking error e _yL and the product (l _ctrl – l _s ). Ψ _L , with l _ctrl a predetermined control distance.

C _y is the identity matrix, Cz is an error vector, A is a dynamic matrix, B _u is a control matrix and B _w is a disturbance matrix, which can be written in the form of an equation Math19:

of a Math20 equation:

of a Math21 equation:

and a Math22 equation:

The controller K, which is defined as a static state feedback, can be expressed in the form:

Before describing how to find an optimal K controller, we can first make some observations about the parameters θ _η and θ _υ .

These two parameters are known because they can be calculated when the vehicle is moving. However, these limits impose sometimes average performance on the K controller, so that the avoidance trajectory risks being followed with a significant deviation. We therefore prefer to restrict the range of these values to consider only the usual driving conditions, which will make it possible to better follow the avoidance trajectory initially planned, even if it means deactivating the controller if we leave this range of values. We can then introduce the following constraint in the form of the Math24 equation:

As well as the following constraint in the form of the equation Math25:

We can then write the equation Math26:

With :

The equations Math 24 and Math 26 then make it possible to delimit a performance zone C _performance inside which the performance of the controller K in terms of trajectory following will be guaranteed.

This performance zone C _performance has been represented in FIGS. 9 and 10, FIG. 9 corresponding to the scenario in which θ _{η_min} ≥ θ _{υ _min} and FIG. 10 corresponding to the scenario in which θ _{η_min} <θ _{υ _min} .

To find an optimal controller K, one can then use different methods.

The method used here is that of linear matrix inequalities. It is thus carried out using convex optimization criteria under constraints of linear matrix inequalities.

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.

The matrix inequalities used here are four in number and are defined by the following inequalities.

1st inequality Math28:

2nd inequality Math29:

Math30 3rd inequality:

Math31 4th inequality:

In these inequalities, a matrix of the form is written in the form .

The controller K is defined by the equation Math 32:

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

The index i is a natural number which takes the successive values 1, 2, 3 and 4 and which corresponds to each vertex of the polygon defined by the performance zone C _performance . Thus, we can write:

Term A ₁ :

Term A ₂ :

Term A ₃ :

Term A ₄ :

Term B _u1 :

Term B _{u 2} :

Term B _{u 3} :

Term B _{u 4} :

It will be noted that the constraints defined by the Math 2 and Math 3 equations are taken into account thanks to the parameters θ _{υ η_min} and θ _{υ _min} , and that the cant is taken into account in the disturbance matrix B _w .

The three inequalities Math 28, Math 29 and Math 30 ensure that the dynamics of the closed loop remain limited. Indeed, as shown in Figure 8, thanks to these constraints, the poles of the closed loop find themselves bounded in a zone Z1 defined by a radius γ, a minimum distance from the imaginary axis μ, and an angle d opening φ.

This method is effective when it comes to determining the steering wheel angle at all times in a reasonable way (and manageable by a driver with average skills) and in a way that the actuator can perform. These constraints also ensure the stability of the closed loop.

The objective here is to minimize the radius γ in this zone Z1.

The fourth inequality Math 31 guarantees stability and robust T0 avoidance trajectory tracking performance. Indeed, thanks to this condition, the impact of the disturbance on trajectory tracking is minimized, which can be written:

In this equation, γ _opt is the optimal value of γ, as calculated using the first three matrix inequalities.

Once the controller K has been obtained, the unsaturated steering angle set point δ _K can be calculated using the following formula:

The values θ _{υ _m in} , θ _{υ _max} , θ _{η _m in} and θ _{η _ max} have been introduced into the three matrix inequalities.

The values of the parameters θ _υ , θ _η , which are related to the deviation between the angles δ _K and δ _ref , reflect the level of violation by the controller K of the controllability limits stated by the equations Math 2 and Math 3.

When the parameter θ _υ is equal to 1 and the parameter θ _η is equal to θ _{η_max} , the unsaturated steering angle δ _K calculated by the controller K does not exceed the controllability limits stated by the equations Math 2 and Math 3.

When the parameter θ _υ and/or the parameter θ _η is close to zero, the unsaturated steering angle δ _K calculated by the controller K is too large and/or too dynamic and it does not respect the stated controllability limits by the Math 2 and Math 3 equations. There is then a possible risk of vehicle instability.

When the parameter θ _υ and the parameter θ _η take intermediate values, the unsaturated steering angle δ _K calculated by the controller K may exceed the controllability limits given by the equations Math 2 and Math 3, but the performance of the vehicle is still possibly acceptable and the risk of vehicle instability has not yet been established.

In other words, the choice of the bounds θ _{υ _m in} and θ _{η _m in} has a direct impact on the performance and on the robustness of the controller K.

The smaller the limits θ _{υ _m in} and θ _{η _m in} , the less efficient the controller K is but the more robust it is (which means that the trajectory produced follows the reference trajectory less well). The larger the terminals θ _{υ _m in} and θ _{η _m in} , the more efficient the controller K but the less robust it is. For example, the terminal θ _{η _m in} has the value 0.005 and the terminal θ _{υ _m in} has the value 0.13.

The determination of these bounds therefore requires a compromise between performance and robustness. The determination of these values amounts to imposing a maximum threshold for the difference, in absolute value, between the steering angle setpoints δ _K and δ _sat and between the steering angle setpoints δ _ref and δ _sat .

It will be noted that as the parameters θ _υ and θ _η act on different data (the steering angle and the steering speed), the choices of the two terminals θ _{υ _m in} and θ _{η _m in} can be made independently.

To determine these limits when designing a vehicle, it is possible to determine controllability limit values at the end of a test campaign, then to determine that these limits are 25% higher than the controllability limits.

It will be noted that for each value of the parameters θ _υ and θ _η , the corresponding optimal value γ _opt can be calculated (equation Math 41).

The performance objective will then often be fixed before the optimization, by imposing for example γ _opt = 0.2. If the aforementioned choice of 25% does not allow this condition to be met, it will be important to lower this percentage until this condition is met.

One of the methods consists in fixing beforehand an authorized level of violation of the controllability constraints defined by the equations Math 2 and Math3, by fixing maximum thresholds for the absolute values |δ_K -δ_Sat|and |δ_Sat-δ_ref|, which allows to write:

And to write:

The stability of the model is also an essential criterion, which turns out to be less restrictive than the aforementioned performance criterion.

In other words, the performance and stability of the vehicle are ensured as long as the parameters θ _υ and θ _η respect the conditions stated in the equations Math 24 and Math 26, that is to say as long as they are in the performance zone C _performance illustrated in Figures 9 and 10.

On the other hand, when one and/or the other of the parameters θ _υ and θ _η becomes lower than the minimum limit associated with θ _{υ _min} and θ _{η _min} , the performance is no longer guaranteed but it is not certain that the solution is unstable.

We then introduce, to check the stability of the solution, a fifth inequality:

The idea here will be to find the couplets (θ _υ , θ _η ) which satisfy this fifth inequality. We know that these couplets are in a convex zone whose boundary we will seek to determine. We are working here on a mesh (i.e. a sampling grid) defined by the following value:

and by the following value:

We will then search in this mesh for the couplets (θ ⁱ _υ , θ ^j _η ) such as:

with :

To obtain satisfactory results, this mesh must be carried out with sufficiently large values of N and M. Of course, the couplets (θ ⁱ _υ , θ ^j _η ) chosen must all respect the conditions defined by the equations Math 24 and Math 25.

The set of couplets satisfying the above equations then forms a stability zone C _stability inside which the controller K is stable.

This stability zone C _stability has been represented in FIGS. 9 and 10, FIG. 9 corresponding to the scenario in which θ _{η_min} ≥ θ _{υ _min} and FIG. 10 corresponding to the scenario in which θ _{η_min} <θ _{υ _min} .

These two zones are determined during the design of the vehicle. They are then implemented in the form of maps in the vehicle's computer.

They are represented here in a convex shape, but they could have very different shapes.

In summary, the method for calculating the controller K that is suitable for a particular model of motor vehicle consists in setting values for α_s, α_r, θ_{η_min}, θ_{υ _min}θ_{υ _m ax}and θ _{η_ m ax}.

It then consists in determining the coefficients of the matrices A _i , Bu _i , then in solving the five inequalities in order to deduce a controller K which ensures good monitoring of the avoidance trajectory T0 and which satisfies the angle limiter model steering and steering speed.

This controller K 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. 11 the process 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 process 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.

If this is the case, it attempts to detect the presence of a possible obstacle lying in the path of the motor vehicle 10. For this, it uses its RADAR or LIDAR remote sensor.

In the absence of an obstacle, this step is repeated in loops.

As soon as an obstacle 20 is detected (see figure 2), the computer 13 plans an avoidance trajectory T0 making it possible to avoid this obstacle 20.

The computer 13 will then seek to define a steering setpoint for the conventional steering system 14, namely a saturated steering angle setpoint δ _ref , making it possible to follow this avoidance trajectory T0 as well as possible.

It begins for this by calculating or measuring the parameters which are:
- the steering angle δ measured,
- the time derivative of the measured steering angle δ,
- the saturated steering angle setpoint δ _ref obtained at the previous time step,
- the yaw rate r,
- the relative heading angle Ψ _L,
- the derivative with respect to time of the lateral deviation setpoint y _L-ref ,
- the trajectory tracking error e _yL ,
- the drift angle β.

The computer 13 then uses the controller K recorded in its memory. This controller K will therefore make it possible to determine, during a step E1, the values of the steering angle setpoints, unsaturated δ _K and saturated δ _ref . On this subject, we can here consider that the controller K enriched with the limiting models L1, L2 forms a large controller.

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

Then, during a second step E2, the computer 13 determines the values of the parameters θ _η , θ _υ . They are generally equal to 1 or close to 1. It may however happen that in the presence of disturbances, they deviate from this value.

Then, during a step E3, it could be provided that the computer 13 checks that the values of the parameters θ _η , θ _υ are respectively greater than the thresholds θ _{η _min} , θ _{υ _min} which have been fixed and which are therefore recorded as constants in its memory to control the performance of the K controller.

However, here, the computer rather checks that the values of the parameters θ _υ , θ _{υ η} are indeed located in the stability zone defined above.

If this is indeed the case, during a step E4, the computer decides to maintain the autonomous obstacle avoidance function in the activated state in order to avoid the obstacle 20.

Otherwise, during a step E5, the computer deactivates this function. Then, one can imagine that the vehicle carries out an emergency braking and/or that it resumes the process of piloting the steering of the vehicle as soon as the stability conditions are again met.

This case can occur in particular in the presence of anomalies (failure of the sensors, of the power-assisted steering system, behavior of the vehicle and/or of the driver not manageable by the K controller, etc.). Thus the invention also makes it possible to detect a possible failure of a sensor.

It will be noted that in the embodiment presented here:
- the design time of the control law can be quickly implemented,
- the proposed controller is optimal and consistent with the controllability limits because the constraints on the steering angle and the steering speed have been taken into account from the synthesis of the controller,
- the controller is robust with respect to the cant of the road, which makes avoidance trajectories safer by preventing the vehicle from passing closer than expected to the obstacle or on the contrary further than expected from the obstacle (depending on the slope direction),
- the use of the parameters θ _υ , θ _η makes it possible to deactivate the controller if necessary if the latter leaves its performance zone or, preferably, if it leaves its stability zone, which makes it possible to guarantee the correct operation of the controller and diagnose abnormal situations.

It should be noted with regard to the cant that it is likely to have a significant impact on the lateral dynamics of the vehicle in general and on the robustness of the avoidance trajectory in particular.

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

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 its commands ).

Claims (12)

Method for autonomously controlling an actuator of an automotive device (10) which is adapted to influence the trajectory of said device (10), comprising the steps of:
- acquisition of parameters (β, r, Ψ _L , e _yL , δ, δ _ref ) relating to the trajectory of the device (10), and
- calculation by a computer (13) of a new control setpoint (δ _ref ) of said actuator as a function of said parameters (β, r, Ψ _L , e _yL , δ, δ _ref ),
characterized in that the new control setpoint (δ _ref ) is determined by means of a controller which satisfies a control setpoint amplitude limiting model (L1) and a control setpoint variation limiting model (L2). Method according to the preceding claim, in which the apparatus (10) is a motor vehicle which is adapted to travel on the road and which comprises at least one steering wheel (11), in which the said actuator is adapted to control the steering of the said wheel steering wheel (11), and in which the new steering setpoint (δ _ref ) is a saturated steering angle setpoint for said steering wheel (11). Method according to the preceding claim, in which the controller satisfies a behavioral matrix model of the apparatus (10) which takes account of the slope of the road. Method according to the preceding claim, in which the behavioral matrix model of the apparatus (10) considers the slope as a disturbance of unknown value. Method according to one of Claims 2 to 4, in which provision is made to determine an unsaturated steering angle setpoint (δ _K ) for each steered wheel (11) which satisfied neither the setpoint amplitude limiting model control (L1), nor the control setpoint variation limiter model (L2), and in which the control setpoint amplitude limiter model (L1) is defined by a subsidiary closed-loop controller which outputs a semi-saturated steering angle setpoint (δ _sat ) and whose direct chain transfer function comprises a hyperbolic tangent function of the difference (Δ ₁ ) between the unsaturated steering angle setpoint (δ _K ) and the semi-saturated steering angle setpoint (δ _sat ). Method according to claim 5, in which the control setpoint variation limiting model (L2) is defined by a subsidiary closed-loop controller which outputs said new control setpoint (δ _ref ) and whose chain transfer function direct comprises a hyperbolic tangent function of the difference (Δ ₂ ) between the semi-saturated steering angle setpoint (δ _sat ) and said new steering setpoint (δ _ref ). Method according to claim 6, in which it is provided:
- calculating the value of a first parameter (θ _η ) using the hyperbolic tangent function of the difference (Δ ₁ ) between the unsaturated steering angle setpoint (δ _K ) and the semi-saturated setpoint steering angle (δ _sat ),
- calculating the value of a second parameter (θ _υ ) using the hyperbolic tangent function of the difference (Δ ₂ ) between the semi-saturated steering angle set point (δ _sat ) and the new piloting (δ _ref ),
- comparing the values of the first and second parameters (θ _η , θ _υ ) with predetermined thresholds (θ _{η _min} , θ _{υ _min} ) and
- Depending on the result of said comparison, continuing or interrupting said process. Method according to claim 6, in which it is provided:
- calculating the value of a first parameter (θ _η ) using the hyperbolic tangent function of the difference (Δ ₁ ) between the unsaturated steering angle setpoint (δ _K ) and the semi-saturated setpoint steering angle (δ _sat ),
- calculating the value of a second parameter (θ _υ ) using the hyperbolic tangent function of the difference (Δ ₂ ) between the semi-saturated steering angle set point (δ _sat ) and the new piloting (δ _ref ),
- determining whether the pair formed by the values of the first and second parameters (θ _η , θ _υ ) is included in a predetermined zone (C _stability , C _performance ) and
- Depending on the result of said comparison, continuing or interrupting said process. Method according to one of the two preceding claims, in which the values of the first and second parameters (θ _η , θ _υ ) are calculated by means of the following mathematical expressions:
, with ,

Or :
- η is a steering angle threshold,
- α _r and α _s are predetermined adjustment constants,
- δ _K is the unsaturated steering angle setpoint,
- δ _sat is the semi-saturated steering angle setpoint, and
- δ _ref is the new control setpoint. Method for developing a controller with a view to its use in an autonomous piloting method in accordance with one of the preceding claims, in which provision is made for:
- acquiring a behavioral matrix model of the device (10),
- determining at least part of the coefficients of the matrices (A _i , B _i ) of the behavioral matrix model,
- deducing therefrom a controller which satisfies the monitoring of a trajectory to be taken, a piloting setpoint amplitude limiting model (L1) and a piloting setpoint variation limiting model (L2). Generation method according to the preceding claim, in which the controller is determined taking into account the influence of the cant on the trajectory of the device (10). Automotive device (10) comprising at least one actuator which is suitable for influencing 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 Process according to one of Claims 1 to 9.