METHOD FOR AUTONOMOUSLY DRIVING AN AUTOMOBILE DEVICE

Abstract

The invention relates to a method for autonomously controlling actuators of an automotive device (10), comprising steps of: - acquiring a reference trajectory that said automotive device must follow, - determining a nominal value of at least one parameter allowing the automotive device to follow the reference trajectory, - determining a current value of each of said parameters when said automotive device follows the reference trajectory, - determining a difference in values ​​between the current value and the nominal value of each of said parameters, then - calculating by a computer a control instruction for each actuator, as a function of each difference in values, by means of a corrector. According to the invention, the corrector comprises a trajectory corrector and a movement regulator, where the trajectory corrector calculates a longitudinal speed difference and a yaw speed difference. Figure for the abstract: Fig.1

Description

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

[0001] The present invention generally relates to the automation of the tracking of trajectories of automotive devices.

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

[0003] It relates more particularly to a method for autonomously controlling actuators of an automotive device which are adapted to influence the trajectory and speed of said automotive device, comprising steps of: - acquisition of a reference trajectory that said automotive device must follow, - determination of a nominal value of at least one parameter allowing the automotive device to follow the reference trajectory, - determination of a current value of each parameter when said automotive device follows the reference trajectory, - determination of a difference in values ​​between the current value and the nominal value of each parameter, then

[0004] - calculation by a computer of a control instruction for each actuator, in function of each difference in values, using for this a mathematical object hereinafter called “corrector”.

[0005] It also relates to a device equipped with a computer adapted to implement this method.

[0006] It also relates to a method for synthesizing such a corrector.

[0007] It applies more particularly, but not exclusively, to the following of an obstacle avoidance trajectory by a motor vehicle. State of the art

[0008] In an effort to make motor vehicles safer, they are currently being equipped with driving assistance systems or autonomous driving systems.

[0009] 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.

[0010] However, there are situations in which these emergency braking systems do not allow collision to be avoided or are not usable (for example if a machine is following closely behind the motor vehicle).

[0011] For these situations, automatic avoidance systems (better known by the abbreviation AES, from the English "Advanced Evasive Steering" or "Automatic Emergency Steering") have been developed which make it possible to avoid the obstacle by diverting the vehicle from its trajectory, either by acting on the steering of the vehicle, or by acting on the differential braking system of the vehicle. It will be noted that the obstacle may be in the same lane as the vehicle or in an adjacent lane, in which case it is detected that this obstacle may be located within a short time on the trajectory of the vehicle.

[0012] However, it happens that the AES system imposes a limit trajectory on the vehicle in terms of controllability and which does not necessarily allow the driver to regain control of driving the vehicle safely.

[0013] The problem is in fact that so-called “high dynamic” avoidance maneuvers, i.e. for which the acceleration experienced by the vehicle exceeds a threshold of, for example, 0.3g, are likely to generate instabilities and trajectory tracking defects, so much so that they prove difficult to control. Presentation of the invention

[0014] In order to overcome 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.

[0015] More particularly, the invention proposes a control method as defined in the introduction, in which the corrector is used to jointly calculate an exclusively lateral control instruction for the automotive device and an exclusively longitudinal control instruction for the automotive device.

[0016] In the case where the device considered is a motor vehicle, the exclusively lateral steering instruction will be a steering instruction for the vehicle's steered wheels, and the exclusively longitudinal steering instruction will be a traditional braking instruction for the vehicle's wheels (therefore we are not talking about differential braking allowing the vehicle to be braked and turned).

[0017] Thus, the invention makes it possible to control the dynamics of the device (here the vehicle) not only laterally in relation to the trajectory that it must take, but also longitudinally, via a single corrector.

[0018] In other words, when this method 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.

[0019] This solution makes it possible to guarantee better tracking of the obstacle avoidance trajectory and better vehicle stability.

[0020] The corrector obtained is in fact capable of guaranteeing the stability and performance of a modeling of the dynamics of the vehicle by 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 field of use.

[0021] More particularly, the invention proposes a piloting method as defined in the introduction, in which the corrector comprises a trajectory corrector and a movement regulator, and in which the method comprises steps of:

[0022] - calculation by the trajectory corrector, as a function of the value deviations, of a deviation longitudinal speed and a yaw speed deviation of said motor vehicle from the reference trajectory; then

[0023] - calculation by the motion regulator, depending on the speed difference longitudinal and yaw rate deviation, a steering angle and a torque for each actuator of said automotive device to achieve the longitudinal speed and yaw rate calculated by the trajectory corrector.

[0024] The corrector is here divided into two parts: the trajectory corrector and the motion regulator. This separation makes the implementation of the corrector more modular and scalable, and independent of the actuators installed on the vehicle, which allows easy updating of the trajectory corrector and therefore of the corrector.

[0025] The generation of the instructions is here based on the longitudinal speed difference and the yaw speed difference.

[0026] The constraints of the corrector synthesis are different because the corrector is divided into two parts: the possible dynamics of the motion regulator must be taken into account when synthesizing the trajectory corrector. The motion regulator must be 10 times faster than the trajectory corrector, due to the use in the automatic community for nested loops. Therefore the maximum dynamics of the trajectory corrector must be constrained.

[0027] In other words, the invention is based on the modularity of the control law: in fact, by separating the trajectory corrector and the position regulator, the architecture is more modular and more scalable. With the invention, the trajectory corrector is independent of the actuators present on the vehicle and the motion regulator is independent of the vehicle's reference trajectory.

[0028] While an LMI region is often used to bound the dynamics of a corrector, this technique is usually used to bound slow dynamics and damping coefficients. In the case of the invention, fast dynamics must also be bounded: this is linked to the fact that the invention is based on cascaded loops. This therefore facilitates the integration of different position regulators. All this is achieved in the context of a robust control that allows us to carry out the synthesis of the trajectory corrector independently of that of the position regulator.

[0029] In this regard, this corrector is calculated offline during the design of the vehicle or during updates to the control methods, and it is then installed on the vehicle, so that no new synthesis calculation of the corrector on the vehicle is necessary.

[0030] The invention is thus easy to implement. The static gain of the trajectory corrector does not require discretization of the trajectory corrector.

[0031] Preferably, said automotive 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.

[0032] The invention also relates to a method for developing a corrector for use in a piloting method as mentioned above, in which it is provided to: - model the automotive device in a non-linear form, - linearize said model in a linear form with varying parameters, - synthesize a corrector which ensures tracking of reference trajectories, and in which the model is linearized in polytopic form.

[0033] Other advantageous and non-limiting characteristics of this method according to the invention, taken individually or in all technically possible combinations, are the following:

[0034] - the modeling of the automotive device in non-linear form is derived of force balance equations applying to the automobile device;

[0035] - the forces acting on the automotive apparatus comprising reaction forces normal that the ground exerts on at least two wheels of the motor vehicle, said normal reaction forces are modeled by a variable load transfer model between the two wheels, which depends on the dynamics of the automotive device; - the forces acting on the motor vehicle comprising normal reaction forces as well as longitudinal and lateral friction forces that the ground exerts on wheels of the motor vehicle, to linearize said model, the motor vehicle is modeled in the form of a closed-loop system, said normal reaction forces and longitudinal and lateral friction forces being used as input to the system and dependent on the output of said system;

[0036] - a part of the forces applied to the automotive device saturating beyond of 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;

[0037] - to linearize said model in a linear form with varying parameters, it is planned to determine a linearized model involving two state matrices, having an affine dependence on variable parameters;

[0038] - the synthesis of the trajectory corrector from convex optimization criteria under linear matrix inequality constraints, including:

[0039] - the dynamic constraint in the Hoo sense of the calculation of the speed difference longitudinal and yaw rate deviation of said automotive device;

[0040] - the constraint of the dynamics in the H2generated sense of the calculation of the speed difference longitudinal and yaw rate deviation of said automotive device;

[0041] - the synthesis of the trajectory corrector for a minimization of a function of the cost of the dynamics of the calculation of the longitudinal speed deviation and the yaw speed deviation of said automotive device subject to said constraints of said linear matrix inequalities.

[0042] The invention also proposes an automotive 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 provided to control each actuator and programmed for this purpose to implement a method as mentioned above.

[0043] Of course, the various features, variants and embodiments of the invention may be combined with each other in various combinations to the extent that they are not incompatible or mutually exclusive. Detailed description of the invention

[0044] The description which follows with reference to the appended drawings, given as non-limiting examples, will make it clear what the invention consists of and how it can be implemented.

[0045] In the attached drawings:

[0046] [Fig.l] is a schematic top view of a motor vehicle traveling on a road;

[0047] [Fig.2] is a representation of the bicycle model used to model the motor vehicle of [Fig.l];

[0048] [Fig.3] is a graph illustrating the range of variation of the longitudinal and lateral forces acting on the tires of the vehicle of [Fig.l];

[0049] [Fig.4] is a diagram of the hierarchical architecture modeling the decision and control logic of the motor vehicle of [Fig.l];

[0050] [Fig.5] is a graph illustrating a region in which the dynamics of the closed loop of [Fig.4] is bounded.

[0051] [Fig.6] is a diagram of the architecture used in a simulation of a trajectory corrector of the motor vehicle of [Fig.l].

[0052] [Fig.7] is a graph illustrating the simulation results in a high dynamic maneuver of the motor vehicle of [Fig.l].

[0053] In [Fig.l], a motor vehicle 10 is shown, conventionally comprising a chassis which delimits in particular a passenger compartment and an engine compartment, two front steered wheels 11, and two rear non-steered wheels 12. As a variant, these two rear wheels could also be steered with an adaptation of the control law.

[0054] This motor vehicle 10 comprises a conventional steering system making it possible to act on the orientation of the steered wheels so as to be able to turn the vehicle. This conventional steering system notably comprises a steering wheel connected to connecting rods in order to pivot the steered wheels. In the example considered, it also comprises at least one actuator making it possible to act on the orientation of the steered 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 power steering actuator can, for this purpose, act on the steering column of the vehicle (which is fixed to the steering wheel) or on a rack (which connects the steering column to the steered wheels). Of course, the actuator could be positioned differently.

[0055] The motor vehicle also comprises a conventional braking system for braking the 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 comprises several in order to be able to adjust the braking force exerted on each wheel as needed.

[0056] The motor vehicle finally comprises a powertrain, comprising in particular a propulsion actuator making it possible to control this group in order to accelerate the motor vehicle 10.

[0057] The computer 13 is then designed to control the power steering actuator, the braking actuators and the actuator of the powertrain. For this purpose, it comprises at least one processor, at least one memory and various input and output interfaces.

[0058] Thanks to its input interfaces, the computer 13 is adapted to receive input signals coming from different sensors.

[0059] Among these sensors, it is for example planned: - a device such as a front camera, making it possible to locate the position of the vehicle in relation to its lane, - a device such as a RADAR or LIDAR remote sensor, 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 sensor, allowing observation of 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 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 bank angle and the slope of the road, etc.

[0060] Thanks to its output interfaces, the computer 13 is adapted to transmit an instruction to the power steering actuator, to the powertrain actuator and to the braking actuators.

[0061] 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.

[0062] Thanks to its memory, the computer 13 stores data used in the context of the method described below.

[0063] 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.

[0064] Before describing this method, we can introduce the different variables that will be used, some of which are illustrated in Figures 1 and 2.

[0065] The total mass of the motor vehicle will be noted “m” and will be expressed in kg.

[0066] The center of gravity of the vehicle will be noted “CG”.

[0067] Here we will mainly consider an orthogonal reference frame (CG, X, Y, Z) attached to the vehicle. Its origin is the same as the center of gravity CG. The X axis corresponds to the longitudinal axis of the vehicle. The Y axis corresponds to the lateral axis facing towards the left of the vehicle. In practice, this Z axis is the axis normal to the road.

[0068] The vertical moment of inertia of the motor vehicle around the Z axis will be noted “Izz” and will be expressed in Nm

[0069] 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. Generally, in the following, the index f will be associated with the front wheels.

[0070] The distance between the center of gravity CG and the rear axle will be noted "lr" and will be expressed in meters. In the following, the index r will be associated with the rear wheels.

[0071] The lateral moment of inertia of a wheel of the motor vehicle will be noted “Iwy” and will be expressed in Nm

[0072] The effective radius of a wheel will be noted “re” and will be expressed in meters.

[0073] The coefficient of friction between the ground and a tire will be noted p.

[0074] The air density coefficient will be noted p.

[0075] The aerodynamic drag coefficient of the vehicle will be noted Cd.

[0076] The frontal surface of the vehicle will be noted Af.

[0077] The lateral stiffness of the front wheel tires will be noted caf.

[0078] The lateral stiffness of the rear wheel tires will be noted as r.

[0079] The longitudinal stiffness of the front wheel tires will be noted cK f.

[0080] The longitudinal stiffness of the rear wheel tires will be noted c^.

[0081] The coefficient of the rolling resistance forces of the front wheels will be noted fr f.

[0082] The coefficient of the rolling resistance forces of the rear wheels will be noted fr r.

[0083] The height of the center of inertia CG of the vehicle above the ground will be noted h.

[0084] The torque distribution rate between the front and rear wheels will be noted kT.

[0085] The longitudinal slip rate of a tire will be noted K.

[0086] The lateral slip angle of a tire will be noted a.

[0087] The acceleration of Earth's gravity will be noted g.

[0088] The steering angle that the front steered wheels make with the longitudinal axis X of the motor vehicle 10 will be noted “ôf” and will be expressed in rad.

[0089] The steering angle that the rear wheels make with the longitudinal axis X of the motor vehicle 10 will be noted “ôr” and will be expressed in rad. It will be noted 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 ôf.

[0090] The torque at the front drive wheels will be noted rwf.

[0091] The torque at the rear wheels will be noted rwr. 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: rwr = 0.3. rwf

[0092] The road's slope angle (i.e. its angle of inclination to the right or left) will be noted 0x and will be expressed in degrees, in the trigonometric sense.

[0093] The slope angle of the road will be noted 0y and will be expressed in degrees. It will be positive if the road goes uphill and negative otherwise.

[0094] The vehicle's yaw rate (around the Z axis) will be noted as "r" and will be expressed in rad / s.

[0095] The longitudinal speed of the vehicle, along the X axis, will be noted v and will be expressed in m / s.

[0096] The lateral speed of the vehicle, along the Y axis, will be noted u and will be expressed in m / s.

[0097] The speed of rotation of the front wheels of the vehicle, around the axis of rotation of these wheels, will be noted cowf and will be expressed in rad / s.

[0098] The rotation speed of the rear wheels of the vehicle, around the axis of rotation of these wheels, will be noted cow r and will be expressed in rad / s.

[0099] The relative heading angle between the X axis and the tangent to the reference trajectory T0 will be noted “W” and will be expressed in rad.

[0100] Therefore, the yaw angle error between the vehicle heading and the tangent to the reference trajectory T0 will be noted Arp.

[0101] The longitudinal position error between the vehicle and the reference trajectory T0 will be noted xL.

[0102] The lateral position error between the vehicle and the reference trajectory T0 will be noted yL.

[0103] These two errors can be expressed at the level of the center of gravity CG of the vehicle.

[0104] The method according to the invention is designed to allow the vehicle to follow the reference trajectory T0 as precisely as possible, in autonomous mode (without driver intervention).

[0105] 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 will be noted that the manner 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.

[0106] Given 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 deviations between the current values ​​of these parameters and the nominal values ​​along the reference trajectory T0 are minimal.

[0107] 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 x0 and the current value x), - the lateral position of the vehicle (the nominal value of which is noted y0 and the current value y), - the vehicle's heading angle (the nominal value of which is noted Wo and the current value - the longitudinal speed v of the vehicle (the nominal value of which is noted v0 and the current value v), - the lateral speed u of the vehicle (the nominal value of which is noted u0 and the current value u), - the yaw rate r of the vehicle (the nominal value of which is noted r0 and the current value r).

[0108] These parameters are determined in an absolute reference frame initialized at the start of the maneuver (which corresponds in practice to the reference frame attached to the vehicle at the moment the maneuver begins).

[0109] The calculation of the nominal values ​​is considered known here.

[0110] At this stage, it can be noted that if the reference trajectories are provided by a trajectory planner (DPL, from the English “Decision and Planning”), the latter can also calculate the nominal instructions ôffl and rwf0.

[0111] If a trajectory planner is not available, from said reference trajectories T0, it is possible to calculate the nominal commands from the following expressions:

[0112] [Math.0] ...... / ■).. Z i-Sz. / \ .. . . , > 2-.-,-, / ( / — \ (.^7 + J . ■> — .7 ... . . . r... . . ... ... . , . . H- pCd A / V" 4- ... - i 4- Cf} 4- 77^ i-Uy 4-

[0113] In this equation, the term p' refers to the radius of curvature of the reference trajectory T0.

[0114] Before describing the method that will be executed by the computer 13 to implement the invention itself, we can in a first part of this presentation describe the calculations that made it possible to arrive at the invention, so as to clearly understand where these calculations come from and on what springs they are based. We will explain in particular how the corrector K is synthesized which will make it possible to calculate vehicle control instructions as a function of measured data.

[0115] The idea of ​​the first part of the presentation is in fact to describe the way in which it is possible to synthesize a controller which, once implemented in the computer 13, will allow the vehicle to be driven so that it follows the reference trajectory TO in a stable and efficient manner.

[0116] Firstly, we can model the vehicle as well as the forces which act on it and which we wish to take into account in order to control the vehicle.

[0117] It will be considered here that the dynamic behavior of the vehicle can be modeled using a non-linear bicycle model.

[0118] In such a model, the two wheels of the front axle are considered to be merged, and the same applies to the two rear wheels. The vehicle chassis is modeled by a body that connects the two wheel models.

[0119] 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 speak of "rear wheel", in the singular, we will designate this modeling of the two rear wheels by a single wheel.

[0120] We will then consider, for each wheel, an orthogonal reference frame (Ow, xw, yw, zw) attached to this wheel. Its origin is the same as the geometric center of this wheel. The yw axis corresponds to the axis of rotation of the wheel. The xw axis corresponds to the axis of the wheel orthogonal to the aforementioned axis and to the Z axis. Finally, the zw axis is considered parallel to the Z axis.

[0121] At this stage, it can be noted that when in an equation or a reference, a term relates in a similar and obvious way to the front wheel or to the rear wheel, it can be written without the index "f" or "r". For example, we will speak for simplification of the orthogonal reference frame (Ow, xw, yw, zw) associated with each wheel, whereas we could write these reference frames more laboriously in the form (Ow r, xw r, yw r, zw r ) and (Ow f, xw f, yw f, zw f).

[0122] The dynamic parameters of the vehicle taken into account, that is to say the parameters characterizing its movements, are as follows: - the longitudinal translational movement of the vehicle body along the X axis, - the lateral translational 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 Yw f, and - the rolling movement of the rear wheel around its axis of rotation Yw r.

[0123] The dynamic parameters of the vehicle neglected in the following are the following: - the vertical translational 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.

[0124] 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 rate r of the vehicle, and - the rotation speeds cowf and cowr of the front and rear wheels.

[0125] The state of the vehicle system can then be noted: x = [vur cowf cowr]T

[0126] The inputs of this vehicle system are: - the steering angle ôf of the front wheel, - the rwf torque at the front wheel, - the 0x slope angle of the road, - the slope angle 0y of the road.

[0127] The input of the vehicle system will then be noted: u = [ôf rwf 0x 0y]T

[0128] In the following, we will speak of control inputs to designate the pair (ôf, rwf) and of disturbance inputs to designate the pair (0x, 0y).

[0129] The forces acting on the vehicle system are partly shown in [Fig.2] and are all listed below: - the weight of the vehicle, with its three components (Px, Py, Pz) in the frame of reference (CG, X, Y, Z), - the normal reaction forces oriented along the Z axis (modeling the support of the wheels against the ground) and noted Nf for the front wheel and Nr for the rear wheel, - the longitudinal friction forces of the tires on the ground, noted Fxf for the front wheel and Fxr for the rear wheel, expressed in the reference (Ow, xw, yw, zw) attached to the corresponding wheel, - the lateral friction forces of the tires on the ground, noted Fyf for the front wheel and Fyr for the rear wheel, expressed in the reference frame (Ow, xw, yw, zw) attached to the corresponding wheel, - the rolling resistance forces of the tires, noted Rxf for the front wheel and RXI for the rear wheel, expressed in the reference (Ow, xw, yw, zw) 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.

[0130] 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 frame (CG, X, Y, Z), so that we can write:

[0131] [Math.l]

[0132] These equations can be simplified by considering the steering angle at the rear wheels to be zero, in particular here where only the front wheels of the vehicle are steered.

[0133] The vehicle system is considered in equilibrium so that the resultant and the resulting moment of the external forces are zero.

[0134] We can therefore write the following three equations:

[0135] [Math.2] w (ù - r = 2 ? - 2 .FF,, - 2 / 2, ; - 2 - 2 R.,.;; - 2 - B - / m+ r <2 = 2 + 2Fra;ï. - 2 - 2<;ï;î. + 2 EÎSff 4- 2¾ - / ¾ / , R = {2 to -4 3.F^f — 2 Ç — [2.F,,,, 4- 2 £2.,,,. -2.^^..12,.,

[0136] 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.

[0137] We can also write the equations of motion for rolling wheels:

[0138] [Math.3] M - 2F = ■-■ --.Fc.

[0139] Note that the disturbance inputs (angles of deflection towards 0X and slope 0y of the road) will be used to calculate the Px, Py, Pz components of the weight.

[0140] The longitudinal and lateral friction forces produced by the tires of a wheel are proportional respectively to the longitudinal slip rate K and to the lateral slip angle a of the tires. We can then write:

[0141] [Math.4] / \. <: ~ 1 p. To , fï ) K I = tÿ, ( / i. JV, ) (X

[0142] In these equations, the hat "A" indicates that this is the input to the saturation function.

[0143] The coefficients cK* and ca* vary non-linearly according to the dynamics of the vehicle, in particular according to the longitudinal and lateral sliding of the tires, the normal reaction force N exerted on the tire and the friction coefficient q between the tire and the ground.

[0144] They are expressed here in the form:

[0145] [Math.5]

[0146] In these equations, the terms K* and a* can be written as follows:

[0147] [Math.6]

[0148] The longitudinal slip rate and the lateral slip angle for both wheels are expressed as:

[0149] [Math.7]

[0150] And:

[0151] [Math. 8] .. ti -F f rr Qf 'L — -----i- ? 3 — f. r = to:f. —------:—

[0152] 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.

[0153] As shown in [Fig.3], this saturation can be modeled in the form of an ellipse, which shows that the total maximum force that the tire is capable of supporting follows the perimeter of an ellipse. In other words, the longitudinal Fx and lateral Fy components of the forces always remain inside an ellipse and are at their maximum equal to thresholds Fxmax and Fymax.

[0154] 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:

[0155] [Math.9]

[0156] The normal reaction forces N which are exerted on the tires are here modeled 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 even its lateral speed). It is understood that the stresses which are exerted vertically on the front wheels are stronger than those which are exerted on the rear wheels in the event of braking. This is the reason why this variable load transfer model between the front wheel and the rear wheel is considered.

[0157] For example, we can write these forces in the following form:

[0158] [Math. 10]

[0159] In these equations, the function d is calculated as follows:

[0160] [Math. 11] (àf .dy} ™ / f 'h ty f- 2 / yf CQS df 2 , / yy CGS> dy

[0161] 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 resulting moments of the external forces around the X and Y axes are equal.

[0162] The rolling resistance force Rx of a wheel is considered proportional to the normal reaction force N, so that we can write:

[0163] [Math. 12]

[0164] Since the aerodynamic drag force is mainly oriented along the longitudinal axis X of the vehicle, its components along the Y and Z axes are neglected here. The remaining component, along the X axis, is then expressed in the form:

[0165] [Math. 13]

[0166] At this stage, the entire vehicle model considered is therefore well defined.

[0167] We can now explain how this model, non-linear by nature, can be linearized along the reference trajectory T0.

[0168] To do this, we introduce a function f which depends on the state of the vehicle system, its derivative and its input. Taking into account the equations Math2 and Math3, we can then write:

[0169] [Math. 14]

[0170] It can be noted here that because of the non-linear dependence links between the longitudinal and lateral reaction forces Fxf, F^, Fyf, Fyr with respect to the normal reaction forces Nf, Nr, it is not possible to obtain an explicit form of the derivative of the state x (i.e. of the dynamics) of the vehicle system.

[0171] In the Mathl4 equation, we then isolate these forces in order to write:

[0172] [Math. 15]

[0173] Using the above equations and in particular the Math4 equation, it is possible to develop the term M as follows:

[0174] [Math. 16]

[0175] In this equation, to take into account the saturation of the tire friction forces, saturation functions o have been introduced, which can be written in the form of the following vector:

[0176] [Math. 17] r | a (¼ (x ; x, u)) I I ! { ? s - _ •> •, €7 I U'-j Xs U. <T ? 3 (h) = I ’• ——' I (7 (&5 (x, x, u. a)) | a (to g (x, x, u, ^)}

[0177] In this equation, we introduced the input h before saturation, whose vector can be written:

[0178] [Math. 18]

[0179] Thus, the term M can be reformulated as follows:

[0180] [Math. 19] —— eos th -i siisA (} * ■ • - “777 / rf 0 0 F _ i — 0 i> 77-7 C(!êU7 — ces § <7 ih 1 ■ü 0 0 0 0 0 (J i) ü ü

[0181] Therefore, the Mathl5 and Mathl9 equations allow us to write our modeling of the vehicle system in the form:

[0182] [Math.20] X = $ (x, U.) + Sh (u) £F (h)

[0183] [Fig.4] then represents the closed loop in the form of a block diagram expressed by this equation. We observe that the normal reaction forces to the wheels and the longitudinal and lateral friction forces of the tires of the wheels, represented by the vector o(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 therefore be possible to describe this situation in the form of a simple equation (Math23 below).

[0184] The linearization of the model expressed by the equation Math20 along the reference trajectory T0 can then be written as follows:

[0185] [Math.21] Ax = Sîtjâu -t- (Ah) Ah — CÙAX + Di'jAu -j- lLA)<ï(Ahj

[0186] In these equations, the index "0" refers to the aforementioned nominal values. The vertical bar refers to the Jacobian at a given point.

[0187] Note that the second equation (Ah) is formed based on the same method as the first equation.

[0188] We use the logistic function o as the saturation function. This function is in fact ideal in our situation since it has a slope equal to 1 at the origin (where it varies in a substantially linear manner) and then it saturates beyond a certain threshold.

[0189] This saturation function o can then be written in the following form:

[0190] [Math.22]

[0191] In this equation, us and are respectively the upper bound and the lower bound of saturation.

[0192] It is then possible to linearize the logistic function by a straight line centered on the origin and having a variable slope, which allows us to write:

[0193] [Math.23] Aa (h) «

[0194] In this equation, the Ko matrix is ​​a diagonal matrix with the slope coefficients of the saturated forces along the diagonal. Using this approximation, the following linearized model can be obtained:

[0195] [Math.24] W) ML * mil O) ••

[0196] In these equations, I is the identity matrix.

[0197] It can be noted that this linearized model no longer depends on the saturated inputs. Thus, the linearization of the saturation functions using a straight line with variable slope allows us to reduce the time-varying matrices, which is useful for the definition of the LPV model described below.

[0198] The present invention describes a method for obtaining a trajectory corrector for controlling a vehicle in high dynamic maneuvers. The decision-making and control logic of an autonomous vehicle is composed of:

[0199] — a trajectory planner that generates a reference trajectory of the vehicle open loop,

[0200] — a closed-loop control function, which must realize the trajectory of reference and which is itself composed of two elements:

[0201] — a trajectory corrector, which calculates the longitudinal and transverse speed deviations vehicle yaw relative to the reference trajectory to eliminate position and yaw angle errors (combined longitudinal and lateral controls),

[0202] — a motion controller that calculates the steering angle and torque of the wheels to achieve the longitudinal and yaw speed at the output of the trajectory regulator.

[0203] [Fig.4] represents the hierarchy of decision and control logic. The invention describes a method for synthesizing the trajectory corrector.

[0204] First of all we initially describe the non-linear model used for the synthesis of the trajectory corrector. This model is used for the definition of a polytopic LPV model.

[0205] For the synthesis of the trajectory regulator, we seek to define the dynamics of the absolute position error and yaw angle of the vehicle relative to the reference trajectory. This dynamic is expressed by:

[0206] [Math.25]

[0207] where is the absolute longitudinal error, ™ -Hn -- -n one is the absolute lateral error, vl M 0 - / \« is the yaw angle error.

[0208] The variables and are respectively the longitudinal speed of the Kl \ L / ÇT) ( f / vehicle and yaw angle calculated by the trajectory planner.

[0209] 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 tracking on the vehicle. This combination of equations then makes it possible to ensure good control of the vehicle along the reference trajectory T0.

[0210] 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.

[0211] An LPV model allows a system to be represented in linear form with varying parameters.

[0212] 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 much as possible in order to reduce the complexity of the optimization problem, i.e. to limit the number of solutions to be tested to synthesize the corrector K and thus reduce the necessary calculation time.

[0213] To model our system in this way, we consider two distinct vectors, namely a first vector Au for the control inputs and a second vector Aw for the disturbance inputs.

[0214] The control inputs are: - the deviation of the vehicle's longitudinal speed from the reference longitudinal speed necessary to eliminate position and angle errors, - the deviation of the vehicle's yaw rate from the reference yaw rate necessary to eliminate position and angle errors.

[0215] The signals and w, / , represent disturbance inputs generics.

[0216] For the synthesis of the corrector, we consider and UHO as variable parameters. Table 1 shows the variation range considered for the two parameters.

[0217] [Tableauxl] Parameter P. -1 A yvdi) -0.2617 0.2618 9.5808 23.261

[0218] It will be noted in this table that the bar under the variable parameter p; indicates that it is the lower threshold of this parameter, and that the bar above the variable parameter p; indicates that it is the upper threshold.

[0219] By calling p the vector of variable parameters, the Math25 model of position and yaw angle errors can be expressed as a state representation of the model by:

[0220] [Math.26] x = 4 (p) x 4- w 4" (p) u

[0221] Or and where "read

[0222]

[0223]

[0224]

[0225]

[0226]

[0227]

[0228]

[0229] vectors " And ' represent the vectors of the measured and controlled outputs respectively. The matrices 4 [pï and depend affinely on the variable parameters, that is, elements of the vector p . The LPV Math26 model can be represented then with the polytopic approach. The variation space of the variable parameters is therefore defined by a polytope and the state representation of the system inside this polytope can be expressed by a convex combination of its vertices: [Math.27] Or y are the vertices of the polytope 4 ■ cl are the values ​​of the matrices .4 (p)et r> 4 at the top 7 of the polytope. The matrices of the model given by the first expression of the Math26 equation depend on the state variables and the inputs of the system, and more particularly on: - the longitudinal acceleration dv / dt of the vehicle, - its longitudinal speed v, - its lateral speed u, - its yaw speed r, - its yaw angle rp,

[0230] - its rotation speeds at the wheels cowf and cowr, and

[0231] - its steering angle ôf.

[0232] At this stage of the description, we wish to explain how to synthesize the corrector K.

[0233] The Math26 model ignores the dynamics of the velocity loop. For hierarchical control to be effective, it is therefore necessary for the velocity loop to be considerably faster than the position loop, so that its behavior is transparent to the trajectory corrector (about ten times faster).

[0234] For the trajectory corrector, we chose to use a Hoo / H2-generalized static corrector with placement of the poles through an LMI region: the method used is preferably the use of linear matrix inequalities (from the English Linear Matrix Inequalities LMI). It is carried out from convex optimization criteria under constraints of linear matrix inequalities (the linearity of the terms of the matrices used ensuring that the mathematical problem can be solved without requiring too much computational load).

[0235] A static corrector was chosen instead of a dynamic corrector because we want to limit the fastest dynamics of the position loop. This is an important aspect to simplify the synthesis of the motion regulator.

[0236] Indeed, the faster dynamics of the position loop constrains us on the slower dynamics of the motion regulator, which must increase in speed with the faster dynamics of the position loop.

[0237] The synthesis of the trajectory corrector is then done by guaranteeing that the set of poles of the closed position loop are placed inside an LMI region (a region of the complex plane).

[0238] If a static corrector is used, only the poles of the system must be moved, being the only ones to exist. In the case of a dynamic corrector, also the poles of the corrector must be placed inside the closed-loop LMI region. This makes finding a solution more difficult and in particular often requires relaxing the constraints on the LMI region, by using a larger region.

[0239] We call the desired static gain K. This corrector here presents a static gain, that is to say a matrix of scalars.

[0240] 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.

[0241] In this method, the corrector will be used to calculate, from a measurement vector y (i.e. from measured or calculated data), the vectors of the control inputs of the system are therefore calculated by:

[0242] [Math.28] ayr * / \11 ™ A v •"••••' AX / u111j> X x JJ? Jt-

[0243] An LMI A region was used to bound the closed loop dynamics. The LMI A region used for the corrector synthesis is shown in [Fig.5] and the following values ​​were chosen:

[0244] -2 = -1.3, - 2 = -4.5, and - 0 = 0.6435 rad.

[0245] This limits the placement of the closed-loop poles of all LTI systems in the polytopic domain.

[0246] This is therefore useful for imposing limits on the slowest and fastest dynamics of the closed loop. Limiting the slowest dynamics is important in the context of emergency maneuvers, for which the system must converge as quickly as possible. In addition, the LMI region also allows for a minimum damping > çmin = 0.6 of the poles of the LTI realizations.

[0247] For the synthesis of the corrector we consider the following theorem:

[0248] Considering an LMI region defined by:

[0249] [Math.29] D = {s £ C: l +■ sM 4- < 0}

[0250] 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.

[0251] Thus, if there exist matrices of appropriate dimensions Q (of dimension nxn and such that Q = QT >0) .... wx«, and Y (of dimension muxn), and scalars strictly positive and y2g such that the optimization problem below is feasible, we therefore obtain a controller K which satisfies our objectives.

[0252] The matrix inequalities used here are four in number and are defined by the following inequalities (for all i ranging from 1 to Np).

[0253] [Math.29]

[0254] Note that in these inequalities Yj are the rows of the matrices Y.

[0255] The first of these inequalities imposes a bound on the norm H , which is then less than yœ. This amounts to minimizing the performance in the sense H, of the relationship between a disturbance and a position and / or yaw error.

[0256] The second and third inequalities impose a bound on the generalized H2 norm which is then less than y2 g- This amounts to minimizing the performance in the generalized H2 sense of the relationship between a disturbance and a control signal.

[0257] The fourth inequality allows the poles to be placed in the LMI A region of the complex plane.

[0258] All poles of all LTI realizations of the closed loop in the polytopic domain are in region A

[0259] Then, the corrector K can then be calculated using the following equation:

[0260] [Math.30] K = Y Q1

[0261] and stabilizes the polytopic system.

[0262] In other words, thus, when the four inequalities are satisfied, the corrector K: - stabilizes the LPV system defined by the Math26 equation, - ensures that the poles of all LTI (linear time invariant) realizations of the closed loop defined by the Math26 equation in the polytopic domain P are in the region A, - ensures that the generalized H , and H2 norms of the closed loop are less than yœ and y2g respectively.

[0263]

[0264]

[0265]

[0266]

[0267]

[0268]

[0269]

[0270]

[0271]

[0272] For the optimization problem, we choose to minimize the following cost function: [Math.31] for which we choose to favor because we want to maximize the robustness of the closed loop as a priority. Finally, the correctors are determined by solving the optimization problem: [Math.32] min {•w3(Æn submitted to Math29. At this stage of the description, we wish to present a simulation result to validate the corrector developed with the above procedure. The simulation was done using the following nonlinear model, which describes the dynamics of the vehicle trajectory: / / Z.- At 7¾? Slli (A 't" Çp j fpSlil Lp A - Ar Or f / ? cl are respectively the longitudinal speed and the reference yaw angle. The inputs of the model are and that is to say the outputs of the corrector of trajectory. This model therefore allows us to evaluate the behavior of the trajectory corrector without using the motion regulator, which is assumed to be perfect in this simulation. Indeed, the motion regulator can be obtained using different methods. The simulation diagram is shown in [Fig.6]. Figure 7 shows the reference signals pQ and , which are those of a high dynamic maneuver, the control signals at the output of the corrector of trajectory, ^7; and Ar, ct the position and yaw errors for a simulation {X yL ct A 76)- The latter considers the following initial conditions: Æ t I ni. y_i, ""lù-Ç™W

[0273] In [Fig.7] we see that the position and yaw errors converge correctly to zero. The behavior of the trajectory corrector is therefore validated.

[0274] The calculation hypotheses now being well established, we can describe the method which will be executed by the computer 13 of the motor vehicle to implement the invention.

[0275] The computer 13 is here programmed to implement this method recursively, that is to say step by step, and in a loop.

[0276] For 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.

[0277] 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.

[0278] It begins by calculating the parameters which constitute the measurement vector y (Av Au Ar xL yL Arp).

[0279] More precisely, knowing the nominal values ​​x0, yo, ipo, v0, u0, r0 of the parameters which theoretically allow the motor vehicle 10 to follow the reference trajectory T0, and knowing the current values ​​x, y, rp, v, u, r of these same parameters while the vehicle follows the reference trajectory T0 (i.e. the measured or estimated values ​​of these parameters), the computer 13 can calculate the deviations Av, Au, Ar, xL, yL, Arp between the current and nominal values ​​of these parameters.

[0280] Then, taking into account the Math26 equation, it can use the corrector K which will have been previously stored in its memory in order to determine the values ​​of the pilot instructions ôf, rwf sought.

[0281] Finally, these steering and braking (or acceleration) angle instructions will be transmitted to the actuators to steer and brake or accelerate the wheels of the motor vehicle 10.

[0282] This process is then repeated in a loop, along the entire reference trajectory T0.

[0283] 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 in accordance with the invention.

[0284] It could for example be used in the field of robotics (for example in the field of product transport robots in factories).

Claims

Claims

1. Method for autonomously controlling actuators of an automotive device (10) which are adapted to influence the trajectory and the speed of said automotive device (10), comprising steps of: - acquiring a reference trajectory (T0) that said automotive device (10) must follow, - determining a nominal value (x0, y0, rpo, v0, u0, r0) of at least one parameter allowing the automotive device (10) to follow the reference trajectory (T0), - determining a current value (x, y, % v, u, r) of each parameter when said automotive device (10) follows the reference trajectory (T0), - determining a difference in values ​​(Av, Au, Ar, xL, yL, Arp) between the current value (x, y, % v, u, r) and the nominal value (x0, yo, ipo, v0, u0, r0) of each parameter, then - calculating by a computer (13) of a control instruction (ôf, rwf) for each actuator,by means of a corrector (K) comprising a trajectory corrector and a movement regulator, the corrector (K) making it possible to jointly calculate an exclusively lateral steering setpoint (ôf) of the automotive device (10) and an exclusively longitudinal steering setpoint (rwf) of the automotive device (10), characterized in that the calculation of the steering setpoint comprises steps of: - calculation by the trajectory corrector, as a function of the value deviations (Av, Au, Ar, xL, yL, Arp), of a longitudinal speed deviation and a yaw rate deviation of said automotive device with respect to the reference trajectory (T0); then - calculation by the movement regulator, as a function of the longitudinal speed deviation and the yaw rate deviation, of a steering angle and a torque for each actuator of said automotive device (10) to achieve the longitudinal speed and the yaw rate calculated by the trajectory corrector.,

2. A driving method according to claim 1, wherein said automotive apparatus (10) is a vehicle which comprises at least one wheel (11, 12) adapted to be steered in a variable direction, at least one power steering actuator, at least one actuator braking and at least one propulsion actuator of the vehicle, 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 and / or to said at least one propulsion actuator to brake or accelerate the vehicle.

3. Method for developing a trajectory corrector for use in a piloting method according to one of claims 1 and 2, implemented by a computer (13) and in which it is provided to: - model the automotive device (10) in a non-linear form, - linearize said model in a linear form with varying parameters (LPV), - synthesize a trajectory corrector which ensures reference trajectory tracking (T0), and in which the model is linearized in polytopic form.

4. Method of development according to claim 3, in which, to linearize said model in a linear form with varying parameters, it is provided to determine a linearized model in polytopic form involving only two state matrices (Aa(p), Bu a(p)) having an affine dependence on variable parameters (p;).

5. Method of development according to one of claims 3 to 4, in which the trajectory corrector is synthesized from convex optimization criteria under linear matrix inequality (LMI) constraints, comprising: - the constraint of the dynamics in the H direction, of the calculation of the longitudinal speed deviation and the yaw speed deviation of said automotive device (10), - the constraint of the dynamics in the generalized H2 direction of the calculation of the longitudinal speed deviation and the yaw speed deviation of said automotive device (10).

6. A method of development according to claim 5, wherein the trajectory corrector is synthesized for a minimization of a cost function of the dynamics of the calculation of the longitudinal speed deviation and the yaw speed deviation of said automotive device (10) subject to said constraints of said linear matrix inequalities (LMI).

7. 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 and 2.

Images