FR3135685A1 - Method for autonomously controlling an automobile device - Google Patents

Abstract

The invention relates to a method for autonomously controlling actuators of an automobile device (10) which are adapted to influence the trajectory and speed of said automobile device, comprising steps of: - acquisition of a reference trajectory that said automobile device must follow, - determination of a nominal value of at least one parameter allowing the automobile device to follow the reference trajectory, - determination of a current value of each of said parameters when said automobile device follows the trajectory of reference, - determination of a difference in values between the current value and the nominal value of each of said parameters, then - calculation by a computer of a control setpoint for each actuator, according to each difference in values, by means of 'corrector. According to the invention, the corrector makes it possible to jointly calculate an exclusively lateral control instruction for the automobile device and an exclusively longitudinal control instruction for the automobile device. Figure for abstract: Fig.1

Description

Method for autonomously controlling an automobile device Technical field of the invention

The present invention generally relates to the automation of tracking the trajectories of automobile devices.

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

It relates more particularly to a method for autonomously controlling actuators of an automobile device which are adapted to influence the trajectory and speed of said automobile device, comprising steps of:
- acquisition of a reference trajectory that said automobile device must follow,
- determination of a nominal value of at least one parameter allowing the automobile device to follow the reference trajectory,
- determination of a current value of each parameter when said automobile device follows the reference trajectory,
- determination of a difference in values between the current value and the nominal value of each parameter, then
- calculation by a calculator of a control instruction for each actuator, according to each difference in values, using for this a mathematical object hereinafter called "corrector".

It also concerns a device equipped with a computer adapted to implement this process.

It also relates to a method for synthesizing such a corrector.

It applies more particularly, but not exclusively, to following an obstacle avoidance trajectory by a motor vehicle.

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 English "Automatic Emergency Braking"), designed to avoid any collision with obstacles located in the lane taken by the vehicle. vehicle, by simply acting on the conventional braking system of the motor vehicle.

However, there are situations in which these emergency braking systems do not prevent a collision or are not usable (for example if a vehicle is closely following the motor vehicle).

For these situations, automatic avoidance systems have been developed (better known by the abbreviation AES, from English “Advanced Evasive Steering” or “Automatic Emergency Steering”) 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. Note that the obstacle may be in the same lane as the vehicle or in an adjacent lane, in which case it is detected that this obstacle may be found in the path of the vehicle within a short time.

However, it happens that the AES system imposes on the vehicle a limiting trajectory in terms of controllability and which does not necessarily allow the driver to regain control over driving the vehicle in complete safety.

The problem is in fact that so-called “high dynamic” avoidance maneuvers, that is to say for which the acceleration experienced by the vehicle exceeds a threshold of, for example, 0.3 g, are likely to generate instabilities. and trajectory tracking defects, so that they prove difficult to control.

Presentation of the invention

In order to remedy the aforementioned drawback of the state of the art, the present invention proposes a solution making it possible to couple the lateral and longitudinal controls of the vehicle to ensure precise and stable steering of the vehicle during high dynamic maneuvers, and in particular during obstacle avoidance maneuvers.

More particularly, according to the invention, we propose a control method as defined in the introduction, in which the corrector is used to jointly calculate an exclusively lateral control instruction of the automobile device and an exclusively longitudinal control instruction of the automotive device.

In the case where the device considered is a motor vehicle, the exclusively lateral steering instruction will be a steering instruction for the steering wheels of the vehicle, and the exclusively longitudinal steering instruction will be a traditional braking instruction for the wheels of the vehicle (we do not therefore not talking about differential braking allowing the vehicle to be braked and turned).

Thus, the invention makes it possible to control the dynamics of the device (here the vehicle) not only laterally in relation to the trajectory it must take, but also longitudinally, via a single corrector.

In other words, when this process is implemented on a motor vehicle in order to avoid an obstacle, it is possible to control the steering and braking (or acceleration) of the vehicle jointly.

This solution ensures better tracking of the obstacle avoidance trajectory and better vehicle stability.

The corrector obtained is in fact capable of guaranteeing the stability and performance of vehicle dynamics modeling using a closed-loop system, for a very large set of reference trajectories at different speeds. Thanks to the invention, it is therefore not necessary to calculate and develop a corrector for each trajectory, the corrector once correctly calibrated being valid for a fairly wide range of use.

In this regard, this corrector is calculated offline (during the design of the vehicle) and it is then on-board the vehicle, so that no new summary calculation of the corrector on the vehicle is necessary.

The invention is thus easy to implement.

Preferably, said automobile device is a vehicle which comprises at least one wheel adapted to be steered in a variable direction, at least one power steering actuator, at least one braking actuator and at least one vehicle propulsion actuator. Therefore, the lateral steering instruction is transmitted to said at least one power steering actuator to steer said at least one wheel, and the longitudinal steering instruction is transmitted to said at least one braking actuator or to said at least one propulsion actuator to brake or accelerate the vehicle

The invention also relates to a method for developing a corrector with a view to its use in a control method as mentioned above, in which it is planned to:
- model the automobile device in a non-linear form,
- linearize said model in a linear form with varying parameters,
- synthesize a corrector which ensures monitoring of reference trajectories,
and in which the model is linearized in polytopic form.

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

- the modeling of the automobile device in nonlinear form comes from balance equations of forces applying to the automobile device;

- the forces applying to the automobile device comprising normal reaction forces that the ground exerts on at least two wheels of the automobile device, said normal reaction forces are modeled by a variable load transfer model between the two wheels, which depends on the dynamics of the automobile device;
- the forces applying to the automobile device including normal reaction forces as well as longitudinal and lateral friction forces that the ground exerts on the wheels of the automobile device, to linearize said model, the automobile device is modeled in the form of a closed-loop system, said normal reaction forces and longitudinal and lateral friction being used as input to the system and depending on the output of said system;

- part of the forces applying to the automobile device saturating beyond a predefined threshold, during the linearization of said model, a linearized saturation function is used in the form of a straight line having a variable slope;

- to linearize said model in a linear form with varying parameters, it is planned to determine a linearized model involving three state matrices having an affine dependence on parameters varying over time, then to write this linearized model in polytopic form involving only two state matrices, having an affine dependence on variable parameters;

- at least part of the time-varying parameters are chosen from the terms of the three state matrices, the other terms of the state matrices being considered invariable over time;
- the number of time-varying parameters chosen is between 6 and 10, limits included;

- the regulator is synthesized from convex optimization criteria under linear matrix inequalities constraints, at least one of the constraints comprising:

¤ the minimization of the performance in the H∞ sense of the relationship between a disturbance applying to the automobile device and a position and/or yaw error of the automobile device,

¤ the minimization of performance in the generalized H2 sense of the relationship between a disturbance applying to the automobile device and a control signal of the automobile device,

¤ taking into account amplitude saturations of the actuators.

The invention also proposes an automobile device comprising at least one actuator which is adapted to influence the trajectory of said device, at least one actuator which is adapted to influence the speed of said device and a computer which is intended to control each actuator and programmed for this purpose to implement a process such as aforementioned.

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

Detailed description of the invention

The description which follows with reference to the appended drawings, given as non-limiting examples, will make it clear what the invention consists of and how it can be carried out.

On the attached drawings:

is a schematic top view of a motor vehicle traveling on a road;

is a representation of the bicycle model used to model the motor vehicle of the ;

is a graph illustrating the range of variation of the longitudinal and lateral forces exerted on the tires of the vehicle of the ;

is a block diagram of a closed loop modeling the dynamics of the motor vehicle of the ;

illustrates two other block diagrams modeling the dynamics of the motor vehicle of the ;

is a block diagram of another closed loop modeling the dynamics of the motor vehicle of the ;

is a graph illustrating a region in which the closed loop dynamics of the is bounded.

On the , we have shown a motor vehicle 10 conventionally comprising a chassis which delimits in particular a passenger compartment and an engine compartment, two front steering wheels 11, and two rear non-steering wheels 12. Alternatively, these two rear wheels could also be steered with an adaptation of the control law.

This motor vehicle 10 includes a conventional steering system making it possible to act on the orientation of the steering wheels so as to be able to turn the vehicle. This conventional steering system notably includes a steering wheel connected to rods in order to rotate the steering wheels. In the example considered, it also comprises at least one actuator making it possible to act on the orientation of the steering wheels as a function of the orientation of the steering wheel and/or as a function of a request received from a computer 13. This actuator power steering can, for this, act on the steering column of the vehicle (which is attached to the steering wheel) or on a rack (which connects the steering column to the steering wheels). Of course, the actuator could be positioned differently.

The motor vehicle also includes a conventional braking system making it possible to brake all four wheels so as to slow down the motor vehicle. In the example considered, this conventional braking system comprises at least one braking actuator. Here, it has several to be able to adjust the braking force exerted on each wheel if necessary.

The motor vehicle finally comprises a powertrain, including in particular a propulsion actuator making it possible to control this group in order to accelerate the motor vehicle 10.

The computer 13 is then designed to control the power steering actuator, the braking actuators and the powertrain actuator. To this end, it comprises at least one processor, at least one memory and different input and output interfaces.

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

Among these sensors, for example:
- a device such as a front camera, making it possible to identify the position of the vehicle in relation to its lane,
- a device such as a RADAR or LIDAR remote detector, making it possible to detect an obstacle located in the path of the motor vehicle 10,
- at least one lateral device such as a RADAR or LIDAR remote detector, making it possible to observe the environment on the sides of the vehicle,
- a device such as a gyrometer, making it possible to determine the yaw rotation speed (around a vertical axis) of the motor vehicle 10, and
- various sensors making it possible to estimate, for example, the longitudinal and lateral speed of the vehicle, the rotation speeds of the front and rear wheels of the vehicle, the steering angle of the front wheels, the tilt angle and the slope of the road, etc.

Thanks to its output interfaces, the computer 13 is adapted to transmit a setpoint to the power steering actuator, the powertrain actuator and the braking actuators.

It thus makes it possible to force the vehicle to follow a reference trajectory T0 which will have been defined beforehand. This reference trajectory T0 is for example an obstacle avoidance trajectory.

Thanks to its memory, the computer 13 stores data used as part of the process described below.

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

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

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

The center of gravity of the vehicle will be noted “CG”.

We will mainly consider here an orthogonal marker (CG, X, Y, Z) attached to the vehicle. Its origin is confused with the CG center of gravity. The X axis corresponds to the longitudinal axis of the vehicle. The Y axis corresponds to the side axis facing the left of the vehicle. In practice, this Z axis is the axis normal to the road.

The vertical moment of inertia of the motor vehicle around the Z axis will be noted “I _zz ” and will be expressed in Nm

The distance between the center of gravity CG and the front axle of the vehicle will be noted “l _f ” and will be expressed in meters. Generally speaking, in the following, the index f will be associated with the front wheels.

The distance between the center of gravity CG and the rear axle will be noted “l _r ” and will be expressed in meters. In the following, the index r will be associated with the rear wheels.

The lateral moment of inertia of a wheel of the motor vehicle will be noted “I _wy ” and will be expressed in Nm

The effective radius of a wheel will be noted “r _e ” and will be expressed in meters.

The coefficient of friction between the ground and a tire will be noted μ.

The air density coefficient will be denoted ρ.

The aerodynamic drag coefficient of the vehicle will be denoted C _d .

The frontal surface of the vehicle will be noted Af.

The lateral stiffness of the front wheel tires will be noted c _αf .

The lateral stiffness of the rear wheel tires will be noted c _{α r} .

The longitudinal stiffness of the front wheel tires will be noted c _{K f} .

The longitudinal stiffness of the rear wheel tires will be noted c _Kr .

The coefficient of the rolling resistance forces of the front wheels will be denoted f _{r f} .

The coefficient of the rolling resistance forces of the rear wheels will be denoted f _{r r} .

The height of the center of inertia CG of the vehicle above the ground will be denoted h.

The torque distribution rate between the front and rear wheels will be noted k _τ .

The longitudinal slip rate of a tire will be noted κ.

The lateral slip angle of a tire will be noted α.

The acceleration of the earth's gravity will be denoted g.

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

The steering angle that the rear wheels make with the longitudinal axis X of the motor vehicle 10 will be denoted “δ _r ” and will be expressed in rad. Note here that in the following, this angle will be zero. Alternatively, it could be non-zero and be expressed as a function of the steering angle δ _f .

The torque at the front drive wheels will be noted τ _wf .

The torque at the rear wheels will be noted τ _wr . It will be noted here that in the following, this torque will be expressed as a function of the torque at the front drive wheels. For example, we could write: τ _wr = 0.3. _τwf

The angle of inclination of the road (that is to say its angle of inclination towards the right or the left), will be noted θ _x and will be expressed in degrees, in the trigonometric direction.

The angle of slope of the road will be noted θ _y and will be expressed in degrees. It will be positive if the road goes up and negative otherwise.

The yaw speed of the vehicle (around the Z axis) will be denoted “r” and will be expressed in rad/s.

The longitudinal speed of the vehicle, along the X axis, will be noted v and will be expressed in m/s.

The lateral speed of the vehicle, along the Y axis, will be noted u and will be expressed in m/s.

The speed of rotation of the front wheels of the vehicle, around the axis of rotation of these wheels, will be noted ω _wf and will be expressed in rad/s.

The speed of rotation of the rear wheels of the vehicle, around the axis of rotation of these wheels, will be noted ω _{w r} and will be expressed in rad/s.

The relative heading angle between the X axis and the tangent to the reference trajectory T0 will be noted “Ψ” and will be expressed in rad.

As a result, the yaw angle error between the vehicle heading and the tangent to the reference trajectory T0 will be noted Δψ.

The longitudinal position error between the vehicle and the reference trajectory T0 will be noted x _L.

The lateral position error between the vehicle and the reference trajectory T0 will be noted y _L.

These two errors can be expressed at the level of the CG center of gravity of the vehicle.

The method according to the invention is intended to allow the vehicle to follow the reference trajectory T0 as precisely as possible, in autonomous mode (without driver intervention).

This method is for example implemented when an AES automatic obstacle avoidance function has been triggered and then a reference trajectory T0 has been calculated. It should be noted that the way of triggering the AES function and calculating the reference trajectory T0 is not strictly speaking the subject of the present invention, and will therefore not be described here.

Taking into account this trajectory T0, it is possible to calculate the nominal values of parameters allowing the motor vehicle 10 to follow this trajectory exactly. In the following, the objective will be to ensure that the vehicle follows this trajectory exactly, that is to say that the differences between the current values of these parameters and the nominal values along the reference trajectory T0 are minimal.

The parameters used to describe the trajectory that the vehicle must follow are here:
- the longitudinal position of the vehicle (the nominal value of which is noted x ₀ and the current value x),
- the lateral position of the vehicle (the nominal value of which is noted y ₀ and the current value y),
- the heading angle of the vehicle (the nominal value of which is noted Ψ ₀ and the current value Ψ),
- the longitudinal speed v of the vehicle (the nominal value of which is noted v ₀ and the current value v),
- the lateral speed u of the vehicle (the nominal value of which is noted u ₀ and the current value u),
- the yaw speed r of the vehicle (the nominal value of which is denoted r ₀ and the current value r).

These parameters are determined in an absolute reference initialized at the start of the maneuver (which corresponds in practice to the reference attached to the vehicle at the moment the maneuver begins).

The calculation of the nominal values is here considered known.

At this stage, we can note that if the reference trajectories are provided by a trajectory planner (DPL, from English “Decision and Planning”), the latter can also calculate the nominal instructions δ _f0 and τ _wf0 .

If we do not have a trajectory planner, from said reference trajectories T0, we are able to calculate the nominal commands from the following expressions:

In this equation, the term ρ’ refers to the radius of curvature of the reference trajectory T0.

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 arrive at the invention, so as to clearly understand where these calculations come from and what sources they rely on. In particular, we will explain how the corrector K is synthesized which will make it possible to calculate vehicle control instructions based on measured data.

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 so that it follows the reference trajectory T0 in a stable and efficient manner.

Firstly, we can model the vehicle as well as the forces which act on it and which we wish to take into account to control the vehicle.

We will consider here that the dynamic behavior of the vehicle can be modeled using a non-linear bicycle model.

In such a model, the two wheels of the front axle are considered to be the same, and the same goes for the two rear wheels. The chassis of the vehicle is modeled by a body which connects the two wheel models.

In the following, when we speak of “front wheel”, in the singular, we will designate this modeling of the two front wheels by a single wheel. In the same way, when we talk about “rear wheel”, in the singular, we will designate this modeling of the two rear wheels by a single wheel.

We will then consider, for each wheel, an orthogonal reference frame (O _w , x _w , y _w , z _w ) attached to this wheel. Its origin is confused with the geometric center of this wheel. The y _w axis corresponds to the axis of rotation of the wheel. The x _w axis corresponds to the axis of the wheel orthogonal to the aforementioned axis and to the Z axis. Finally, the z _w axis is considered parallel to the Z axis.

At this stage, we can note that when in an equation or a reference, a term relates in a similar and obvious way to the front wheel or the rear wheel, we can write it without an “f” or “r” index. As an example, we will speak by simplification of the orthogonal reference frame (O _w , x _w , y _w , z _w ) associated with each wheel, whereas we could write these references in a more laborious manner in the form (O _{w r} , x _{w r} , y _{w r} , z _{w r} ) and (O _{w f} , x _{w f} , y _{w f} , z _{w f} ).

The dynamic parameters of the vehicle taken into account, that is to say the parameters characterizing its movements, are as follows:
- the longitudinal translation movement of the vehicle body along the X axis,
- the lateral translation movement of the vehicle body along the Y axis,
- the yaw movement of the vehicle body around the Z axis,
- the rolling movement of the front wheel around its axis of rotation Y _{w f} , and
- the rolling movement of the rear wheel around its axis of rotation Y _{w r} .

The dynamic parameters of the vehicle neglected in the following are the following:
- the vertical translation movement of the vehicle body along the Z axis, and
- the rolling and pitching movements of the vehicle body around the X and Y axes.

In view of the movements considered, the state variables of the vehicle system are:
- the longitudinal speed v of the vehicle,
- the lateral speed u of the vehicle,
- the yaw speed r of the vehicle, and
- the rotation speeds ω _wf and ω _wr of the front and rear wheels.

The state of the vehicle system can then be noted: x = [vur ω _wf ω _wr ] ^T

The inputs to this vehicle system are:
- the steering angle δ _f of the front wheel,
- the torque τ _wf at the front wheel,
- the slope angle θx of the road,
- the slope angle θy of the road.

The input of the vehicle system will then be noted: u = [δf τ _wf θx θy] ^T

In the following, we will talk about control inputs to designate the torque (δ _f , τ _wf ) and disturbance inputs to designate the torque (θx, θy).

The forces acting on the vehicle system are partly represented on the and are all listed below:
- the weight of the vehicle, with its three components (P _x , P _y , P _z ) in the reference frame (CG, X, Y, Z),
- the normal reaction forces oriented along the Z axis (modeling the support of the wheels against the ground) and noted N _f for the front wheel and N _r for the rear wheel,
- the longitudinal friction forces of the tires on the ground, noted F _xf for the front wheel and F _xr for the rear wheel, expressed in the mark (O _w , x _w , y _w , z _w ) attached to the corresponding wheel,
- the lateral friction forces of the tires on the ground, noted F _yf for the front wheel and F _yr for the rear wheel, expressed in the mark (O _w , x _w , y _w , z _w ) attached to the corresponding wheel,
- the rolling resistance forces of the tires, noted R _xf for the front wheel and R _xr for the rear wheel, expressed in the mark (O _w , x _w , y _w , z _w ) attached to the corresponding wheel and which form the friction forces of the wheels on their axes (they apply to the center of the wheel), and
- aerodynamic drag forces.

The axis of rotation of a wheel is not necessarily parallel to the Y axis. The longitudinal and lateral friction forces of the tires then each have a longitudinal component and a lateral component in the reference frame (CG, X, Y, Z), so that we can write:

These equations can be simplified by considering the steering angle at the rear wheels to be zero, particularly here where only the front wheels of the vehicle are steered.

The vehicle system is considered in equilibrium so that the resultant and the resulting moment of the external forces are zero.

We can therefore write the following three equations:

The first equation is the resultant of the forces along the X axis, the second is the resultant of the forces along the Y axis and the third is the resultant of the moment around the Z axis.

We can also write the equations of motion for the rolling of the wheels:

Note that the disturbance inputs (angles of slope θ _x and slope θ _y of the road) will be used to calculate the components P _x , P _y , P _z of the weight.

The longitudinal and lateral friction forces produced by the tires of a wheel are proportional to the longitudinal slip rate κ and the lateral slip angle α of the tires, respectively. We can then write:

In these equations, the hat “^” indicates that this is the input to the saturation function.

The coefficients c _κ * and c _α * vary non-linearly depending on the dynamics of the vehicle, in particular depending on the longitudinal and lateral sliding of the tires, the normal reaction force N acting on the tire and the coefficient of friction μ between the tire and ground.

They are expressed here in the form:

In these equations, the terms κ* and α* can be written as follows:

The longitudinal slip rate and the lateral slip angle for the two wheels are expressed in the form:

And :

The longitudinal and lateral friction forces produced by the tires of a wheel, as expressed by the Math4 equations, can increase indefinitely. But in reality, we see that they saturate.

As shown in the , this saturation can be modeled as an ellipse, which shows that the total maximum force the tire is capable of withstanding follows the perimeter of an ellipse. Otherwise formulated, the longitudinal Fx and lateral Fy components of the forces always remain inside an ellipse and are maximally equal to thresholds F _xmax and F _ymax .

Here, to simplify the equations, we consider that the ellipse is a circle, so that the two aforementioned thresholds are equal. These thresholds are proportional to the normal reaction force N, so that we can write:

The normal reaction forces N which are exerted on the tires are modeled here by a variable load transfer model between the front wheel and the rear wheel, which depends on the dynamics of the vehicle (in particular its longitudinal acceleration, or also its its lateral speed). We understand in fact that the stresses exerted vertically on the front wheels are greater than those exerted on the rear wheels in the event of braking. This is why we consider this model of variable load transfer between the front wheel and the rear wheel.

For example, we can write these forces in the following form:

In these equations, the function d is calculated as follows:

These equations are obtained here by considering that the vehicle system is in equilibrium so that the resultant of the external forces along the Z axis and the moments resulting from the external forces around the X and Y axes are zero.

The rolling resistance force R _x of a wheel is considered proportional to the normal reaction force N, so that we can write:

The aerodynamic drag force being mainly oriented along the longitudinal axis X of the vehicle, its components along the axes Y and Z are neglected here. The remaining component, along the X axis, is then expressed in the form:

At this stage, the entire vehicle model considered is therefore well defined.

We can now explain how this model, non-linear by nature, can be linearized along the reference trajectory T0.

To do this, we introduce a function f which depends on the state of the vehicle system, its derivative and its input. Given the Math2 and Math3 equations, we can then write:

We can note here that because of the non-linear dependence links between the longitudinal and lateral reaction forces F _xf , F _xr , F _yf , F _yr in relation to the normal reaction forces N _f , N _r , it will not be is not possible to obtain an explicit form of the derivative of the state x (i.e. the dynamics) of the vehicle system.

In the Math14 equation, we then isolate these forces in order to write:

By using the aforementioned equations and in particular the Math4 equation, it is possible to develop the term M as follows:

In this equation, to take into account the saturation of tire friction forces, we introduced saturation functions σ, which can be written in the form of the following vector:

In this equation, we introduced the input h before saturation, whose vector can be written:

Thus, the term M can be reformulated as follows:

Consequently, the Math15 and Math19 equations allow us to write our modeling of the vehicle system in the form:

There then represents in the form of a block diagram the closed loop expressed by this equation. We observe that the normal reaction forces at the wheels and the longitudinal and lateral tire friction forces of the wheels, represented by the vector σ(h), are looped on this model of the dynamics of the state of the vehicle system, since they appear at the input of this system and they depend only on the vector h at the output of this system. It will also be possible to describe this situation in the form of a simple equation (Math23 below).

The linearization of the model expressed by the Math20 equation along the reference trajectory T0 can then be written as follows:

In these equations, the index “0” refers to the aforementioned nominal values. The vertical bar refers to the Jacobian at a given point.

Note that the second equation (Δ h ) is formed based on the same method as the first equation.

We use the logistic function as saturation function σ. This function is indeed ideal in our situation since it has a slope equal to 1 at the origin (where it varies in a substantially linear manner) then it saturates beyond a certain threshold.

This saturation function σ can then be written in the following form:

In this equation, u _s and ℓ _s are the upper bound and the lower bound of saturation, respectively.

It is then possible to linearize the logistic function by a line centered on the origin and having a variable slope, which allows us to write:

In this equation, the matrix K _σ is a diagonal matrix with the slope coefficients of the forces saturated along the diagonal. Thanks to this approximation we can obtain the following linearized model:

In these equations, I is the identity matrix.

It can be noted that this linearized model no longer depends on saturated inputs. Thus, the linearization of the saturation functions using a line with variable slope allows us to reduce the time-varying matrices, which is useful for the definition of the LPV model described below.

Here we add to the dynamics of the linearized model given by the Math24 equations the dynamics of the absolute longitudinal position x _L and lateral y _L and yaw angle Δψ errors of the vehicle system:

Thus, the Math24 equations make it possible to take into account the dynamic characteristics of the vehicle, while the Math25 equations make it possible to impose good trajectory following on the vehicle. This combination of equations then ensures good control of the vehicle along the reference trajectory T0.

At this stage, the model being linearized and extended to the Math23 and Math24 equations, we wish to transform it into a polytopic LPV model.

An LPV model makes it possible to represent a system in linear form with varying parameters.

The variation space of these parameters is, in a polytopic LPV model, represented by a convex hull (the polytope). The idea is to restrict the size of this polytope as best as possible so as not to be too conservative (i.e. not to excessively limit the possible solutions for synthesizing the corrector K).

To model our system in this way, we consider two distinct vectors, namely a first vector Δ u for the control inputs and a second vector Δ w for the disturbance inputs. We therefore express our linearized model by:

Note here that the order of the system n (i.e. the dimension of the square matrix A(t)) is equal to 8, that the number of disturbance entries m _w is equal to 2, and that the number of measurement inputs m _u is equal to 2.

In this model, the matrices A(t), B _w (t) and B _u (t) vary over time because they depend on the state variables and inputs of the vehicle system along the reference trajectory T0.

To represent the model given by the equation above in polytopic LPV form, it is necessary to choose variable parameters which are such that the matrices of the linearized model are affine with respect to these parameters.

The most logical choice would be to use the state variables and the inputs of the reference trajectory T0 as variable parameters of the LPV model. Unfortunately, time-varying matrices do not depend affinely on the reference trajectory variables, so in this case they cannot be chosen as variable parameters with the polytopic approach.

This is the reason why we choose here, as variable parameters, terms (a ₁₁ , a ₁₂ …) of the matrices A(t), B _w (t) and B _u (t) which are variable over time .

On the other hand, a total of twenty terms are variable over time for the matrices of the linearized model considered. Twenty represents a high number of variable parameters for a polytopic LPV model.

Therefore it is preferable to reduce, if possible, the number of variable parameters.

At this stage, we can notice that the matrices of the linearized model given by the Math21 equation (without linearization of the saturation functions) have a total of forty-eight time-varying terms. Indeed, the model information is distributed in six time-varying matrices, instead of two for the model given by the Math24 equation. It is for this reason that it is preferable to use the model given by the Math24 equation in order to develop a polytopic LPV model.

To further reduce the number of parameters, we chose to consider a subset of the time-varying terms of the linearized model matrices and to approximate the remaining elements with a constant value. In particular, we chose the eight terms of the matrices A(t), Bw(t) and Bu(t) which have the most impact on the dynamics of the vehicle model as variable parameters.

The number eight makes it possible to make a good compromise between the representativeness of the LPV model and the complexity of the synthesis of the corrector K. Following tests, it was in fact demonstrated that the synthesis of the corrector K did not lead to any solution if more than ten variable parameters were used. Then it was found that the performance of the correctors was comparable using eight or ten variable parameters. The choice to use only eight was therefore made.

In practice, we will therefore use eight parameters but alternatively, we could use between six and ten.

These eight variable parameters constitute a vector denoted p . The variation space of this vector p therefore forms our polytope, which is therefore in the form of an eight-dimensional hypercube, with Np = 2 ⁸ vertices.

For the choice of these eight time-varying parameters among the variable terms of the matrices A(t), B _w (t) and B _u (t), we proceeded as follows:
- the variables ψ and v are fundamental to represent the dynamics of the lateral error y _L , expressed by the Math 25 equation, they are therefore selected,
- to find the remaining six parameters, we calculate the product of each term with the state variable or the corresponding input along the reference trajectory T0 and if this product is less than 5% of the dynamics of the variable d state, these terms are excluded, then
- we calculate the coefficient of variation of the remaining terms along the reference trajectory T0 and we select the six time-varying terms having the highest coefficient of variation.

We will then note that for all the other terms of the matrices which have not been selected, we calculate an approximate constant value, for example equal to the average of the term along the reference trajectory T0.

Finally the polytopic LPV model has the following form:

For the synthesis of the LPV corrector with the polytopic approach, it is necessary that the matrix B _u is not dependent on the vector p of the variable parameters. However, in our case, taking into account the variable parameters chosen, the matrix B _u does indeed depend on the vector p . Then, to eliminate this dependence, we add a first order filter F(s) to the input of the vehicle system, as shown in the upper part of the . Here, this filter applies to only one column of the matrix B _u since only this column varies according to the variable parameters.

We can therefore rewrite our model of the vehicle system thus augmented in the way illustrated on the lower part of the (the index “a” refers to the augmented model), which will facilitate the synthesis of the corrector K.

Indeed, using this method, the system input is added to the system state vector and the elements of the matrix B _u which depend on the vector p are then found in the new matrix A _a (p) of the augmented system . In this way, it will be possible to synthesize the LPV corrector with the polytopic approach.

Note that if the filter used as input is fast, the effect of the fictitious dynamics of the input on the representativeness of the model is negligible.

At this stage, we therefore have a polytopic LPV model that can be used for the synthesis of the corrector K.

However, it remains to determine the variation intervals of the polytopic domain considered, which results from a compromise between size (the largest possible to have the greatest chance of synthesizing an effective K corrector in terms of trajectory monitoring), while guaranteeing the controllability of the vehicle.

For this, we arbitrarily considered two distinct T0 reference trajectories, namely:
- a trajectory associated with a change of lane with braking (the vehicle passes from its lane to the immediately neighboring lane while braking), and
- a trajectory associated with a change of two lanes without braking (the vehicle passes from its lane to the immediately neighboring lane then to the next lane, without braking).

These two trajectories symbolize two types of maneuver for which we wish to stabilize the vehicle.

The objective is then to develop a single and unique K corrector which is capable of controlling the vehicle according to these two “extreme” reference trajectories and, therefore, according to all the reference trajectories included between these two trajectories.

The selected variable parameters of the vector p were therefore chosen on the basis of these two reference trajectories. The interval of variable parameters was then selected so as to include the evolution of the variable elements over time along the two obstacle avoidance maneuvers.

We can therefore give an example of the variable parameters p _i of the vector p which are common to the two trajectories for a given vehicle:

Setting at ₂₁ (t) -0.5574 0.6325 at ₂₇ (t) -0.1033 0.0833 at ₃₇ (t) -0.0658 0.0531 ψ(t) -0.2617 0.2618 v(t) 9.5808 23,261 b _u11 (t) -6.2537 7.0035 at ₃₁ (t) -0.0368 0.0551 a ₃₂ (t) 0.2843 1.4152

Note in this table that the bar under the variable parameter p _i indicates that it is the lower threshold of this parameter, and that the bar above the variable parameter p _i indicates that it is the upper threshold .

In other words, in this example which applies to a particular model of motor vehicle, the minimum and maximum values of the variable parameters have been noted when this vehicle follows the two aforementioned reference trajectories.

We can therefore interpret the two avoidance maneuvers chosen as the envelope of the trajectories for which the performance and stability of the closed loop are guaranteed.

At this stage of the description, we wish to explain how to synthesize the corrector K.

This corrector here presents a static gain, that is to say a matrix of scalars.

In this way, it is not necessary to discretize this corrector, which then facilitates the implementation of the method for determining the vehicle control instructions.

In this method, the corrector will be used to calculate, from a measurement vector y (i.e. from measured or calculated data), the control input vector Δu, by means of equation:

In this equation, the matrix K represents the static gain matrix and therefore constitutes the desired corrector. It belongs to the real space of dimension m _u ×p _y , where p _y is the number of measurement inputs (equal to 6).

The measurement vector considered is in fact written in the form:

y = [Δv Δu Δr x _L y _L Δψ] ^T

The closed loop system is expressed in the form:

For the synthesis of the K corrector, we consider the saturation of the control signals. The dynamics of the system is therefore expressed by:

The saturation function σ(Δu) will be treated as a sector nonlinearity.

For the saturation of the vehicle actuators, we consider the following inequalities:
−30 deg ≤ δ _f ≤ 30 deg, and
- 5000Nm ≤ τ _wf ≤ 1230 Nm.

These thresholds are here substantially equal to the maximum capacities of the actuators.

The saturation of the signals Δδ _f and Δτw _f therefore depends on the values of the steering angle δ _f and the torque at the front wheels τ _wf along the reference trajectory T0.

As shown in the , to impose on the closed loop a behavior respecting these saturations, we add to the system the filters W _e (s), W _u (s) and W _d (s). We can then carry out the synthesis using the augmented system G _a (s).

In this new model, z is a variable or vector of variables that measures the performance of the system.

Filters impose frequency behavior (and therefore desired performance) on the closed loop.

To summarize, note that the filter W _d (s) is not used since the reference input is not used in the system. The filters W _e (s) and W _u (s) are then sufficient to adjust the two input-output relationships between the disturbance signals Δ w and the controlled outputs z ₁ and z ₂ (which measure the performance of the system).

The filters W _e (s) and W _u (s) used are:

It then remains to synthesize the corrector K on this basis.

For this, several methods can be used.

The method used is preferably the use of linear matrix inequalities (Linear Matrix Inequalities LMI). It is carried out using convex optimization criteria under the constraints of linear matrix inequalities (the linearity of the terms of the matrices used ensuring that the mathematical problem is possible to solve without requiring too much computational effort).

We then consider the following space:

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

Thus, if there exist matrices of appropriate dimensions Q (of dimension nxn and such that Q = Q ^T >0), Y (of dimension m _u xn), S _u (of dimension m _u xm _u and such that S _u = S _u ^T >0), J _u (of dimension m _u xn) and strictly positive scalars γ _∞ and γ _{2 g} such that the optimization problem below is feasible, we therefore obtain a controller K which satisfies our goals.

The matrix inequalities used here are six in number and are defined by the following inequalities (for all i ranging from 1 to Np).

Note that in these inequalities:
- Y _j and J _uj are the rows of the matrices Y and J _u ,
- _j are the maximum values of the inputs (Δ _f and Δ _wf therefore being the maximum values of Δδ _f and Δτ _wf ).

The first of these inequalities imposes a bound on the norm H _∞ (between the transfers of the disturbance inputs to the controlled outputs z ₁ and z ₂ ). This amounts to minimizing the performance in the H _∞ sense of the relationship between a disturbance and a position and/or yaw error.

The second and third inequalities impose a bound on the norm H ₂ (between the transfers of the disturbance inputs to the controlled output z ₂ ). This amounts to minimizing performance in the _generalized H ₂ sense of the relationship between a disturbance and a control signal.

The fourth inequality allows us to place the poles in the LMI region of the complex plan.

The last two inequalities are used to take into account the saturations of the actuators (as sector nonlinearities) while maximizing the region of attraction of the closed loop.

The corrector K can then be calculated using the following equation:

Note that in this equation, the exponent “+” refers to the Moore–Penrose pseudo-inverse of the matrix C _y .Q.

We can define the space E as follows: E(P, 1) = {x ∈ ⁿ | x ^T.P. x ≤ 1}, where P = Q ^{− 1} . This space is an asymptotic stability region of the closed-loop LPV system with saturated Δu inputs.

Thus, when the six inequalities are satisfied, the corrector K:
- stabilizes the LPV system defined by the Math27 equation in space E,
- ensures that the poles of all LTI realizations (linear invariant with time) of the closed loop defined by the Math30 equation in the polytopic domain P are in the region (see below),
- guarantees that the generalized H _∞ and H ₂ performances of the closed loop are lower than γ _∞ and γ _2g respectively.

The condition given by the last inequality considers that the saturation limits of the orders are symmetrical with respect to zero. In practice, the saturations of Δδ _f and Δτw _f are not symmetrical. For conservatism, the lowest absolute value of the saturation thresholds of Δδ _f and Δτ _wf along the reference trajectories T0 is then selected.

An LMI region was used to bound the dynamics of the closed loop. This region is represented in the and the following values were chosen:
- = -1.5,
- = -500, and
- θ = 0.6435 rad.

Here, the parameter θ maximizes the damping of the poles to limit the oscillations of the system.

The upper threshold of λ ensures that the solution converges quickly (taking into account the reference trajectory T0 which lasts approximately 3 seconds). The lower threshold imposes a limit so that the system does not evolve too quickly.

The values of these three parameters here come from the experience of those skilled in the art (or possibly from road tests).

Finally we therefore choose sub-optimal values for the scalars γ _∞ = 1 and γ _2g = 1.4142 and we find the solution of the corrector by solving the following optimization problem:

respecting Math33 inequalities.

In other words, we maximize the trace of Q to maximize the region of attraction of the closed loop with respect to the saturations of the control inputs.

We recall here that the region of attraction is the region in which the linear system considered necessarily converges towards 0, whatever the starting state included in this region.

To resolve this optimization problem, it is possible to use the YALMIP tool in the MATLAB software, as for example presented in the documents Lofberg 2004 Andersen and Andersen 2000.

We can note the following two observations concerning the implementation of the solution presented in conjunction with other algorithms already present on the motor vehicle (typically the algorithm for maintaining the vehicle in the center of its lane).

First, as long as these other algorithms have a higher dynamic than that of this control and they do not actively intervene on the yaw of the vehicle, there will be no stability problem linked to nested loops and a control of traction (which intelligently distributes torque between the four wheels) could potentially contribute to the stability of the closed loop.

Secondly, the idea of the solution presented here is to do an avoidance and, as such, when this algorithm is activated, the other algorithms present which would be likely to have an influence on the trajectory of the vehicle will be deactivated.

The calculation hypotheses now being well established, we can describe the process which will be executed by the computer 13 of the motor vehicle to implement the invention.

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

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

The computer 13 will then seek to define a control instruction for the conventional steering system and for the conventional braking system, making it possible to follow this reference trajectory T0 as best as possible.

To do this, it begins by calculating the parameters which constitute the measurement vector y (Δv Δu Δr x _L y _L Δψ).

More precisely, knowing the nominal values x ₀ , y ₀ , ψ ₀ , v ₀ , u ₀ , r ₀ of the parameters which theoretically allow the motor vehicle 10 to follow the reference trajectory T0, and knowing the current values x, y, ψ, v, u, r of these same parameters while the vehicle follows the reference trajectory T0 (that is to say the measured or estimated values of these parameters), the calculator 13 can calculate the deviations Δv, Δu, Δr, xL, yL, Δψ between the current and nominal values of these parameters.

Then, taking into account the Math29 equation, it can use the corrector K which will have been previously stored in its memory in order to determine the values of the desired control instructions δ _f , τ _wf .

Finally, these steering angle and braking (or acceleration) instructions will be transmitted to the actuators to steer and brake or accelerate the wheels of the motor vehicle 10.

This process is then repeated in a loop, all along the reference trajectory T0.

The present invention is in no way limited to the embodiments described and represented, but those skilled in the art will be able to make any variation conforming to the invention.

It could, for example, be used in the field of robotics (for example in the field of robots for transporting products in factories).

Claims (11)

Method for autonomously controlling actuators of an automobile device (10) which are adapted to influence the trajectory and speed of said automobile device (10), comprising steps of:
- acquisition of a reference trajectory (T0) that said automobile device (10) must follow,
- determination of a nominal value (x ₀ , y ₀ , ψ ₀ , v ₀ , u ₀ , r ₀ ) of at least one parameter allowing the automobile device (10) to follow the reference trajectory (T0) ,
- determination of a current value (x, y, ψ, v, u, r) of each parameter when said automobile device (10) follows the reference trajectory (T0),
- determination of a difference in values (Δv, Δu, Δr, x _L , y _L , Δψ) between the current value (x, y, ψ, v, u, r) and the nominal value (x ₀ , y ₀ , ψ ₀ , v ₀ , u ₀ , r ₀ ) of each parameter, then
- calculation by a calculator (13) of a control setpoint (δ _f , τ _wf ) for each actuator, according to each difference in values (Δv, Δu, Δr, x _L , y _L , Δψ), by means a corrector (K),
characterized in that the corrector (K) makes it possible to jointly calculate an exclusively lateral control instruction (δ _f ) of the automobile device (10) and an exclusively longitudinal control instruction (τ _wf ) of the automobile device (10) . Control method according to claim 1, in which, said automobile device (10) being a vehicle which comprises at least one wheel (11, 12) adapted to be turned in a variable direction, at least one power steering actuator, at least a braking actuator and at least one vehicle propulsion actuator, the lateral steering instruction is transmitted to said at least one power steering actuator to steer said at least one wheel, and the longitudinal steering instruction is transmitted to said at least one actuator braking and/or auditing at least one propulsion actuator to brake or accelerate the vehicle. Control method according to one of claims 1 and 2, in which, before the acquisition step, it is planned to:
- model the automobile device (10) in a non-linear form,
- linearize said model in a linear form with varying parameters (LPV),
- synthesize said corrector (K) which ensures reference trajectory monitoring (T0), and in which the model is linearized in polytopic form. Control method according to claim 3, in which the modeling of the automobile device (10) in non-linear form comes from force balance equations applying to the automobile device (10). Control method according to claim 4, in which, the forces applying to the automobile device (10) comprising normal reaction forces that the ground exerts on at least two wheels of the automobile device (10), said forces normal reaction are modeled by a variable load transfer model between the two wheels, which depends on the dynamics of the automotive device (10). Control method according to one of claims 4 and 5, in which, the forces applying to the automobile device (10) comprising normal reaction forces as well as longitudinal and lateral friction forces that the ground exerts on wheels of the automobile device (10), to linearize said model, the automobile device (10) is modeled in the form of a closed loop system, said normal reaction forces and longitudinal and lateral friction being used as input of the system and dependent on the output of said system. Control method according to one of claims 4 to 6, in which, part of the forces applying to the automobile device (10) saturating beyond a predefined threshold, during the linearization of said model, we use a saturation function (σ) linearized in the form of a straight line with a variable slope. Control method according to one of claims 3 to 7, in which, to linearize said model in a linear form with varying parameters, it is planned to determine a linearized model involving three state matrices (A(t), B _w (t), B _u (t)) having an affine dependence on time-varying parameters (p _i ), then writing this linearized model in polytopic form involving only two state matrices (A _a (p ), B _wa (p)) having an affine dependence on variable parameters (p _i ). Control method according to claim 8, in which at least part of the time-varying parameters (p _i ) are chosen from the terms of the three state matrices (A(t), B _w (t), B _u ( t)), the other terms of the state matrices being considered invariable over time, and in which the number of time-varying parameters (p _i ) chosen is between 6 and 10, limits included. Control method according to one of claims 3 to 9, in which the regulator (K) is synthesized from convex optimization criteria under linear matrix inequalities (LMI) constraints, at least one of the constraints comprising:
- the minimization of the performance in the sense H _∞ of the relationship between a disturbance applying to the automobile device (10) and a position and/or yaw error of the automobile device (10),
- the minimization of the performance in the _generalized H ₂ sense of the relationship between a disturbance applying to the automobile device (10) and a control signal of the automobile device (10),
- taking into account amplitude saturations of the actuators. Automotive apparatus (10) comprising at least one actuator which is adapted to influence the trajectory of said apparatus (10), at least one actuator which is adapted to influence the speed of said apparatus (10) and a computer (13) for controlling said actuators, characterized in that the computer (13) is programmed to implement a method according to one of claims 1 to 10.