Method for controlling a wheeled vehicle in low grip conditions

Abstract

A method of controlling a vehicle having wheels provided with tires supported on a surface, the method using as a side slip angle (β) of each tire relative to the surface ij ) is a model of the physical behavior of each tire as a function of the tire pressure. This model is obtained by implementing an adaptive algorithm that selectively applies an affine model (Z1), a DUGOFF model (Z2) or a constant model (Z3).

Description

Background of the Invention

[0002] The present invention relates to the field of wheeled vehicles, such as land vehicles and in particular off-road vehicles, including also flying machines when taxiing.

[0003] There are automatic control methods for wheeled vehicles that utilize control relationships that rely on a linear model of the behavior of the tires relative to the ground. The driving limit is determined by the maximum lateral force exerted by each of the tires on the ground, using the formula: F ymax =μ ymax F z , where μ ymax is the maximum lateral friction coefficient, which depends on the materials of the ground and the tire, and F z is the vertical force exerted on the tire corresponding to the weight of the vehicle supported by the tire, which is adjusted by the weight transfer caused by the vehicle tilting sideways on turns or inclined ground and tilting longitudinally when accelerating or decelerating. The coefficient of friction varies roughly in the following ranges: 0.9 to 1 for dry asphalt; 0.5 to 0.8 for wet asphalt; 0.2 to 0.3 for snow; and 0.15 to 0.2 for ice. These control methods are effective when the vehicle is moving on the ground without slipping, as occurs when the vehicle is moving at a speed that is appropriate to the radius of curvature of the path followed and the grip of the vehicle's tires on the ground. In this ideal situation, the sideslip angle β, that is, the angle between the direction in which the tire is pointing and the tire's travel vector relative to the ground, is small and therefore has a great influence on the lateral force F. y Related, the tire can transmit the lateral force F according to the linear relationship y , until it reaches a maximum force F that conforms to the linear model on which these control relations depend ymax However, it will be appreciated that the vehicle may quickly deviate from this ideal condition, for example if the properties of the ground surface change and / or its path changes and / or its speed changes. However, outside this ideal condition, the behavior of the tire relative to the ground surface, and therefore the change in lateral force relative to the sideslip angle β, is not linear.

[0004] Therefore, current control methods are generally not suitable for off-road vehicles or high-speed driving.

[0005] It is not possible to conceive of building vehicle control relationships on a model that represents the nonlinear behavior of tires, such as the pacejka model. In particular, the optimal use of this model requires the definition of a large number of empirical parameters, which is difficult to implement in real time.

[0006] Purpose of the Invention

[0007] A particular object of the invention is to improve the control method of a wheeled vehicle, in particular when the tires exhibit non-linear behavior. Summary of the invention

[0008] To this end, according to the invention, there is provided a method of controlling a vehicle whose wheels are provided with tires resting on a surface, the method using as a side slip angle (β) of each tire relative to the surface ij ) is a function of the lateral force (F y ) is obtained by identifying a first linear variation region, a second linear-to-nonlinear transition region, and a third nonlinear variation region in the curve; and, for each tire, performing the following steps:

[0009] Operate in real time to define a set of successive lateral force values Each value corresponds to a sideslip angle, and determining whether the value varies according to a first region, a second region, or a third region;

[0010] When the values ​​vary according to the first region, an affine model is applied;

[0011] When the values ​​vary according to the second region, the DUGOFF model is applied; and

[0012] When the values ​​vary according to the third region, a constant model is applied.

[0013] The so-called "DUGOFF" model is a relatively simple model for modeling the tire relative to the ground, but it is still effective because it considers the lateral force (F y ) is associated with a finite number of parameters, specifically the longitudinal stiffness of the tire (written as C σ ), longitudinal slip rate (written as σ x ), cornering stiffness coefficient (written as C β ), vertical force (F z ), maximum lateral friction coefficient (μ ymax ) and the sideslip angle (β). Again, in the case of pure lateral slip, the first two parameters can be neglected. Nevertheless, it has been found that the model is unnecessarily complex on the linear portion of the curve plotting the lateral force as a function of the sideslip angle, and that it converges slowly or to incorrect values ​​on the non-linear portion. In the present invention, the DUGOFF model is used to estimate the value of the lateral force on the most efficient portion of the curve, while on other portions of the curve the lateral force is estimated by more appropriate methods.

[0014] Other characteristics and advantages of the invention will become apparent upon reading the following description of a particular and non-limiting implementation of the invention.

[0015] BRIEF DESCRIPTION OF THE DRAWINGS

[0016] With reference to the accompanying drawings, in which:

[0017] · Figure 1 The operation of the algorithm of the present invention is shown and includes a description of how the lateral force varies with the sideslip angle;

[0018] · Figure 2 It is a plan view of a wheeled vehicle;

[0019] · Figure 3 shows a simplified vehicle moving relative to the ground with its front wheels grouped together as a single front wheel and its rear wheels grouped together as a single rear wheel; and

[0020] · Figure 4 The data required for estimating the cornering stiffness coefficient and the maximum lateral friction coefficient in the implementation of the present invention are shown.

[0021] Detailed description of the invention

[0022] The present invention is applied below to a vehicle having four steerable wheels.

[0023] With reference to the accompanying drawings, given a general reference 1, the vehicle comprises a body 2 standing on the ground via four steerable wheels, namely: a left front wheel fl, a right front wheel fr, a left rear wheel rl and a right rear wheel rr. In conventional manner, each wheel comprises a rim surrounded by a tire and the wheel can be steered relative to the body 2 by means of a motor device 3 connected to an electronic control unit 4, which is also connected to a motor device 5 for driving the wheel in rotation and a brake system 6 for braking the rotation of the wheel.

[0024] The control unit 4 is also connected to sensors including an inertial measurement unit 7, which in a conventional manner comprises an accelerometer and a gyroscope for determining the attitude of the vehicle 1 and the speeds and accelerations to which it is subjected. Thus, the control unit 4 receives in particular the speed of the vehicle 1 along its longitudinal axis (x), the speed of the vehicle 1 along its transverse axis (y) and the yaw speed of the vehicle 1. Other sensors can be envisaged for the application under consideration, and in particular sensors measuring the speed of rotation of each wheel, sensors measuring the orientation (or heading angle) of each wheel, pressure sensors for each tire, temperature sensors for each tire, ... Such sensors and how they are used are known and are not described in more detail herein.

[0025] The control unit 4 is a computer unit that executes a program including instructions for executing the method of the present invention. The control method of the present invention is based on the cornering stiffness coefficient Cβ of each of the wheels fl, fr, rl, rr relative to the ground.ij and the maximum lateral friction coefficient μ ymaxij By using this control relationship, the control unit 4 can control the motor device 3, the motor device 5 and the brake device 6 so as to keep the vehicle 1 on the desired path.

[0026] Cornering stiffness coefficient C for each wheel βij and the maximum lateral friction coefficient μ ymaxij The estimate of is obtained by executing an adaptive algorithm that performs the following steps for each wheel:

[0027] A theoretical curve ( ) of the lateral force exerted by the tire on the surface as a function of the sideslip angle β is defined by identifying a first zone Z1 in which the variation is linear, a second zone Z2 of linear-to-nonlinear transition and a third zone Z3 in which the variation is nonlinear. Figure 1 );

[0028] Operate in real time to define a set of successive lateral force values Each value corresponds to a sideslip angle β, and it is determined whether the value varies according to the first zone Z1, the second zone Z2 or the third zone Z3;

[0029] When the lateral force value is in the first zone Z1, the affine estimation model is applied;

[0030] When the lateral force value is in the second zone Z2, the DUGOFF model is applied; and

[0031] When the lateral force value is in the third zone Z3, the constant model is applied.

[0032] The theoretical curve is Figure 1 , to illustrate the operation of the adaptive algorithm of the present invention. It can be subdivided into three sections A, B and C, corresponding to the linear condition, the transition condition and the nonlinear condition respectively. The figure also shows a first zone Z1, a second zone Z2 and a third zone Z3, which are not completely consistent with these three sections.

[0033] Next, how to determine the successive lateral force values These values ​​are used as inputs to the model (and hence they are called “input values”), and they are written as These input values ​​are determined in real time so that at any time there is available a set of values ​​relating to the time preceding the moment in question.

[0034] As input values ​​it would be possible to use the measurement of the lateral forces on each tyre: however, in order to make the measurement usable it would be necessary to resort to complex measurement methods requiring extensive calculations. This is why it is preferred to estimate the input values ​​in the manner explained below.

[0035] Estimating the lateral force input requires estimating the sideslip angle and normal force at each wheel.

[0036] Estimate the sideslip angle for each of the wheels according to the following formula:

[0037]

[0038]

[0039]

[0040]

[0041] in:

[0042] l f is the distance between the vehicle’s center of gravity and the front axle;

[0043] l r is the distance between the vehicle’s center of gravity and the rear axle;

[0044] ·e f is the front track;

[0045] ·e r is the rear track;

[0046] ·V x is the longitudinal velocity of the center of gravity;

[0047] ·V y is the lateral velocity of the center of gravity;

[0048] · is the angular velocity in yaw; and

[0049] ·δ fl ,δ fr ,δ rl ,δ rr is the heading angle of the wheel.

[0050] The various speeds and accelerations are provided by the inertial unit 7 or they are calculated from measurements provided by said inertial unit 7. The heading angles of the wheels are determined by the control relationship of the driver's actions or they are provided by dedicated sensors. The other parameters are constant characteristics of the vehicle 1 .

[0051] The normal force at each wheel (taking into account the weight transfer during the acceleration, braking and leaning phases of the vehicle) is determined as follows:

[0052]

[0053]

[0054]

[0055]

[0056] Where: m is the mass of the vehicle, g is the acceleration due to gravity, h is the height of the center of gravity, a x is the longitudinal acceleration of the center of gravity, and a y is the lateral acceleration of the center of gravity. The first parameter is a constant property of the vehicle or it can be measured by a sensor, and the acceleration due to gravity depends on the geographical area and can be measured.

[0057] Estimate the longitudinal force F for each tire xpij is possible:

[0058]

[0059] Among them:

[0060] · is the torque of the wheel under consideration;

[0061] I r is the moment of inertia of the wheel under consideration (same for all wheels in this example);

[0062] · is the angular velocity of the wheel under consideration; and

[0063] ·r ij is the effective radius of the tire on the wheel under consideration. In this example, since the model has been used to determine the cornering stiffness coefficient C βij and the maximum lateral friction coefficient μ ymaxij , so the input value of the lateral force can be estimated without the aid of a model. For example, the method described by J. Yang et al., "Estimate Lateral Tire Force Based on Yaw Moment without Using Tire Model", ISRN Mechanical Engineering Volume 2014, Hindawi Publishing Corporation may be used.

[0064] Initially calculate the yaw moment M at the center of gravity G of each of the wheels G and the center of gravity G ij Yaw moment M Gij :

[0065]

[0066]

[0067] In this pair of equations:

[0068] · is the acceleration vector at G;

[0069] · is the vertical axis attached to the vehicle;

[0070] ·T x including terms dependent on longitudinal forces (as described in the previous clause); and

[0071] ·T y Include terms that depend on lateral forces (as described in the above clauses).

[0072] The subscript i indicates the front wheel (i=f) or the rear wheel (i=r), and the subscript j indicates the left wheel (j=l) or the right wheel (j=r).

[0073] By expressing this pair of equations in matrix form, we can obtain the following result:

[0074]

[0075] in:

[0076]

[0077] F ypf Corresponding to the total lateral force on the front axle, F ypr Corresponds to the total lateral force on the rear axle. Symbol ·, as in M·, T y · and T x · is used to simplify the expression in order to avoid repeating the equation: and in this example, G or G can be used, depending on whether the center of gravity of the vehicle 1 or the center of gravity of each of the wheels is concerned. ij replace.

[0078] The lateral force input value for each wheel is calculated by distributing the vertical force as follows:

[0079]

[0080] For model selection purposes, the input values ​​are inserted into the algorithm in the form of a sliding window. A sliding window is actually a window containing the data. A group of , where 1≤K≤N, where N is the empirically determined maximum window size, and t is time. Windows are used to accumulate values ​​over time to avoid estimation bias, but it is also necessary to limit the number of accumulated values ​​to limit computation time and load. The use of windows is based on thresholds ∈1, ∈, τ1, and τ2 in the following way, so that:

[0081] - A value is added to the window if:

[0082] The difference between the most recent sideslip angle β(k) in the window and the current sideslip angle β(k+1) is greater than a first angle threshold ∈1; and / or

[0083] no value has been added for a time exceeding a first time threshold τ1; and

[0084] - The window will be refreshed if:

[0085] If the difference between the first sideslip angle β(1) and the last sideslip angle β(N) in the window is greater than the second angle threshold ∈2, the first value is deleted; and / or

[0086] a value has been present in the window for a time period longer than a second time threshold τ2, then the first value is deleted; and / or

[0087] - The window contains a number of data items equal to a predetermined number threshold, then the values ​​are deleted, in this example preferably every other value is deleted.

[0088] The slope of the curve is calculated by applying the values ​​of each group to the affine model, determining the model to be applied, and determining the transition from one zone to another based on the values ​​of the slope and intercept. Specifically, the slope value represents a straight line in the first zone Z1, drops to 0 in the second zone Z2, and is smaller and negative in the third zone Z3.

[0089] Application of the model to seek the selection of the cornering stiffness coefficient C βij and the maximum lateral friction coefficient μ ymaxij , to minimize the estimated lateral force With input value The error between .

[0090] The affine model is written as follows:

[0091]

[0092] It can be understood that a1 represents the slope of the curve in the area Z1, and b1 represents the intercept (ie, the lateral force value when the sideslip angle is zero).

[0093] Application of the affine model advantageously involves a least squares solution using:

[0094]

[0095] in:

[0096] The affine model is only used to determine the cornering stiffness coefficient C βij , and can therefore be updated.

[0097] DUGOFF will longitudinal force F x and the lateral force F y The definition is as follows:

[0098]

[0099]

[0100] The parameter f(λ) is given by:

[0101]

[0102]

[0103] In these formulas:

[0104] σ x is the longitudinal slip rate;

[0105] C σ is the longitudinal stiffness;

[0106] C β is the cornering stiffness coefficient;

[0107] F z is the normal force; and

[0108] μ max is the maximum ground-tire friction coefficient.

[0109] By neglecting the longitudinal slip, a simplified DUGOFF model is obtained, which is preferably used in this example:

[0110]

[0111] in

[0112]

[0113] The subscript i designates the front wheel (i=f) or the rear wheel (i=r), and the subscript j designates the left wheel (j=l) or the right wheel (j=r).

[0114] The application of the DUGOFF model involves implementing the Levenberg Marquardt optimization algorithm. Order:

[0115]

[0116] Therefore, the cornering stiffness coefficient C of each tire relative to the ground is βij and the maximum lateral friction coefficient μ ymaxij Both are used to model the characteristics of the interaction between the tire and the ground, and can therefore be updated by applying this model.

[0117] This ultimately led to:

[0118]

[0119] When the value of the lateral force to be estimated is located in the third zone Z3, applying the constant model includes giving a predetermined value to the estimation of the lateral force, and is written as follows:

[0120]

[0121] In this equation, It corresponds to the maximum lateral force value in zone Z3, namely:

[0122]

[0123] The maximum lateral friction coefficient μ of each tire relative to the ground ymaxij The value of is determined and updated using the model.

[0124] Calculate the sideslip angle β that constitutes the threshold at which the affine model is no longer valid th is favorable. Theoretically, in the first region, the affine model and the DOGOFF model (where λ ≥ 1) should be consistent. Therefore, the ratio p is essentially equal to 1, so:

[0125] F lin corresponds to the lateral force obtained by the linear model, such that:

[0126]

[0127] F yDugNL Corresponds to the lateral force obtained by the DUGOFF model with λ < 1.

[0128] It is considered that when p is greater than or equal to 1.05 (determined empirically), the threshold β is reached. th . Then the following is obtained:

[0129]

[0130] The equation is solved as follows:

[0131]

[0132] in

[0133]

[0134] Then choose a smaller value as the threshold, that is:

[0135]

[0136] In this example, the estimated value of the lateral force is used in the control relationship u to help steer the vehicle. The control relationship u implemented by the electronic control unit 4 is (T ω , δ f , δ r ) T The electronic control unit 4 is enabled to control the electric machine device 3 , the electric machine device 4 and / or the brake system 6 in such a way that the torque of the wheels and their heading angles are adjusted in order to keep the vehicle 1 on a desired path.

[0137] In practice, the control relationship seeks to reduce the difference between the actual position of vehicle 1 associated with reference frame [c] and the position of a reference vehicle associated with reference frame [d] ideally placed along the path. Vehicle 1 and the reference vehicle and their respective positions (X, Y, ψ) T and (X d , Y d , ψ d ) T In the same inertial reference frame [i]. ψd is the transformation matrix between reference frames [d] and [i], Rψ d is the transformation matrix between reference frames [c] and [i] such that:

[0138]

[0139] The longitudinal, lateral and yaw errors along the path are written in reference frame [i] as e = (e X , e Y , e ψ ) T and in the reference frame [c] is x1, such that:

[0140] as well as

[0141]

[0142]

[0143]

[0144] By using the signs for the longitudinal, lateral, and yaw velocities of the actual vehicle and the reference vehicle, respectively and And by differentiating the error along the path, we get the following:

[0145]

[0146] By projecting equation (2) into the reference frame [c], we obtain the following:

[0147]

[0148] Distinguish e1 and e2 and give

[0149]

[0150]

[0151] in:

[0152]

[0153] It is then necessary to model the dynamic behavior of the vehicle 1. For simplicity, the four-wheeled vehicle 1 is reduced to a vehicle with two wheels, namely the front wheel f and the rear wheel r (see Figure 3 ), and the center of gravity is assumed to be relatively low so as to make it possible to neglect rolling and pitching motions. These simplifications are taken into account so as not to harm the modeling of the dynamic behavior of the vehicle with the help of the following equations:

[0154] in:

[0155] F xf is the longitudinal force of the front wheel; F xr is the longitudinal force on the rear wheel;

[0156] F yf is the lateral force on the front wheel;

[0157] F yr is the lateral force on the rear wheel; and

[0158] Iz is the moment of inertia in yaw about the vertical axis, along with the other parameters mentioned above.

[0159] The forces and moments in the above equations are expressed in reference frame [c] as follows:

[0160]

[0161] In the tire's reference frame, the longitudinal force is defined as follows:

[0162]

[0163] The coefficient p is a coefficient of the distribution of the total torque Tω, which lies in the range of 0 (for torque transmitted via the rear wheels only) to 1 (for torque transmitted via the front wheels only), and is set to 0.5 in this example.

[0164] By using a linear model to calculate the sideslip angle β f , β r The lateral force F of the front and rear tires ypf and F ypr Modeling is performed and the following is obtained:

[0165]

[0166] By assuming the steering angle δ r ,δ f is relatively small, and by injecting equations (7), (8), and (9) into equation (6), we can obtain the following:

[0167]

[0168] in:

[0169]

[0170]

[0171]

[0172] To reduce the complexity of model (10), nonlinear terms and commands are ignored to obtain:

[0173]

[0174] However, since the goal is to control an off-road vehicle, a purely linear model is not sufficient. Therefore, it is necessary to modify the linear model so that it adapts to the nonlinear behavior of the tire: Specifically, it is known that as the sideslip angle increases, the lateral force given by the linear model Greater than the actual front and rear lateral forces In this example, this is actually the lateral force estimated from the DUGOFF model. Therefore, the force To ensure that the assumption that the linear model is valid holds true, write the following:

[0175]

[0176] Since measured values ​​for the actual lateral forces are not available, one must resort to estimates and, in this example, the following estimate is chosen

[0177] For small heading angles, this gives:

[0178]

[0179] As a result, equation system (6) gives:

[0180]

[0181] in:

[0182] g1(x)=g(x)+Δ g

[0183]

[0184]

[0185]

[0186] A solution to the problem of a vehicle with four steerable wheels following a path involves using an expression for the dynamic error vector.

[0187] The control relationship is constructed by a recursive technique called "backstepping" and is based on equations (4) and (5). The control relationship is used to stabilize the error in an asymptotic manner.

[0188] To implement the backstepping technique, the variable e2 in equation (4) is considered to be the control input that adjusts e1 to zero. To do this, let:

[0189]

[0190]

[0191] In the first step of the inverse technique, the first candidate Lyapunov function is selected, that is, by choosing (where K1 is a positive definite diagonal matrix), making its derivative negative. This leads to Since e2 is not a true external control input, the following residual is obtained

[0192]

[0193] in

[0194] Introducing this residual into equation (17) stabilizes ∑1. Equation (17) then becomes:

[0195]

[0196] And the Lyapunov derivative becomes:

[0197]

[0198] In the second step of the backpropagation technique, a candidate Lyapunov function is selected for the dynamic behavior of Z2, namely:

[0199]

[0200] The derivative of this function is:

[0201]

[0202] The derivative is negative by choosing

[0203]

[0204] Where K2 is positive.

[0205] The derivative is It is less than or equal to 0.

[0206] The final command input is the vector u, which appears in equations (12) and (5) middle.

[0207] By equating equations (20) and (5), the following control relationship for adjusting e1 can be obtained:

[0208]

[0209] It can be seen that if g is reversible, then the control relation holds. This gives:

[0210]

[0211] in Serves 10 4 and is greater than the acceleration of the wheel rotation, so

[0212] The dynamic behavior of the system in a closed loop is as follows:

[0213]

[0214] The control relation u expressed in this way takes into account only the linear behavior of the tire.

[0215] In order to adapt the control relationship u to the nonlinear behavior of the tire, the two correction terms Δ + and Δ - is added to the other terms of the relationship.

[0216] The force in equation (16) and Depends on the heading angle δ f and δr , which is the command input, and and The delay value, which is Δ + and Δ - The estimate of is written as and Then the following is obtained:

[0217]

[0218] Where s is the Laplace operator, τ is the delay, and F LP (s) is a low pass filter and f0 is the cutoff frequency of the filter.

[0219] Therefore, it is possible to add Δ to the control relationship u(21) + and Δ - The estimated delay value of and The relation u thus takes the following form:

[0220]

[0221] Thus, the control relationship then has a first part based on the linear model of the tire behavior and a corrected second part subtracted from the first part in order to account for nonlinear effects in the tire behavior. It will be appreciated that by adding a correction term based on the nonlinear model to adjust the control relationship based on the linear model, the preparation of the control relationship is simplified. This applies to any control relationship based on a linear model.

[0222] against and The terms in the expression and Calculated by the above method. Thus, an estimate of the maximum lateral friction coefficient for the front and rear tires is obtained Estimation of the cornering stiffness coefficient

[0223] like Figure 4 As outlined in , the estimation is based on measurements made by the inertial unit 7, such as the angular velocity in yaw Longitudinal and lateral speed V x and V y and the longitudinal and lateral acceleration a x and a y . It also utilizes the torque T provided by the control relationship itself ω , and the heading angle δ f and δ r , and the angular acceleration of the wheel The algorithm takes into account the linear and nonlinear parts of the tire characteristics by using an adaptive algorithm with three regions. Once an estimate of the maximum lateral friction coefficient for the front and rear wheels has been obtained Estimation of the cornering stiffness coefficient These estimates are used in the DUGOFF model to obtain an estimate of the lateral force such that:

[0224]

[0225] in:

[0226]

[0227] Therefore, this gives:

[0228]

[0229] in and

[0230] Naturally, the invention is not limited to the described implementations but covers any variant coming within the scope of the invention as defined by the claims.

[0231] In particular, the modeling can be used as a basis for vehicle control relationships, for example for controlling the steering of one or more wheels, and / or for controlling the motor arrangements of one or more wheels, and / or for controlling the brakes of one or more wheels, but can alternatively also be used for the purpose of triggering a warning representative of the operating condition of the vehicle.

[0232] It is not necessary to group the wheels together per axle.

[0233] Several other techniques can also be used to control relationships.

[0234] It is also possible to calculate the critical sideslip angle between the linear region and the nonlinear region as follows:

[0235]

[0236] However, this threshold is larger than the threshold calculated above.

[0237] The vehicle may differ from the one described, for example it may have a different number of wheels.

Claims

1. A method of controlling a vehicle, the wheels of which are provided with tires on a supporting surface, the method using as the sideslip angle (β) of each tire relative to the surface ij ), the method being characterized in that the model is defined by the lateral force (F y ) is obtained by defining the curve by identifying a first linear variation region, a second linear-to-nonlinear transition region and a third nonlinear variation region; and for each tire, performing the following steps: Operate in real time to define a set of successive lateral force values each value corresponds to a sideslip angle, and determining whether the value varies according to the first region, the second region, or the third region; When the value varies according to the first region, applying an affine model; When the value varies according to the second region, applying the DUGOFF model; and When the value varies according to the third region, a constant model is applied.

2. The method according to claim 1, characterized in that The affine model has the following form: in is the value of the lateral force for each tire, a1 is the slope of the curve in the area, and b1 is the intercept.

3. The method according to claim 1 or claim 2, characterized in that: The DUGOFF model has the following form: in: · is the lateral force of each tire; · · is the cornering stiffness coefficient of each tire; · is the maximum lateral friction coefficient of each tire; and β ij is the sideslip angle of each tire.

4. A method according to any preceding claim 1, characterized in that The constant model has the following form: in is the lateral force of each tire and b2 is the maximum lateral force in the third region.

5. A method according to any preceding claim, characterised in that Application of each of the models comprises finding, for each tire, a cornering stiffness coefficient and a maximum lateral friction coefficient that minimizes the difference between the lateral force values ​​obtained with each model and the values ​​of the set of values ​​for each tire.

6. The method according to claim 5, characterized in that The application of the affine model implements the method of least squares.

7. The method according to claim 5 or claim 6, characterized in that: The application of the DUGOFF model includes implementing the Levenberg Marquardt optimization algorithm.

8. A method as claimed in any preceding claim, characterised in that The set of lateral force values ​​is modified by adding a value when: The difference between the most recent sideslip angle of the group and the current sideslip angle β(k+1) is greater than a first angle threshold (∈1); and / or • No value has been added for a time longer than a first time threshold (τ1).

9. A method as claimed in any preceding claim, characterised in that The set of lateral force values ​​is modified by subtracting a value when: If the difference between the first sideslip angle of the set of values ​​and the last sideslip angle β(k) of the set of values ​​is greater than a second angle threshold (∈2), then the first value is deleted; a value has been present in the window for a time period longer than a second time threshold (τ2), then the first value is deleted; and / or The group has a plurality of values ​​greater than a predetermined threshold, at least one value is deleted, and preferably every other value is deleted.

10. A method as claimed in any preceding claim, characterised in that The model to be applied is determined by applying the set of values ​​to the affine model to calculate the slope of a curve, wherein a transition from one region to another is determined based on the slope and the value of the ordinate.

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