Method for controlling a wheeled vehicle in low-grip conditions
A method of controlling a vehicle having wheels provided with tires resting on a surface, the method using a model of the physical behavior of each tire as a function of a sideslip angle (β ij ) for each tire relative to the surface. The model is obtained by implementing an adaptive algorithm that selectively applies an affABREGEine model (Z1), a DUGOFF model (Z2), or a constant model (Z3).
1. A method of controlling a vehicle having wheels provided with tires resting on a surface, the method using a model of the physical behavior of each tire as a function of a sideslip angle for each tire relative to the surface, the method being characterized in that the model is obtained by defining a theoretical curve for variation of the lateral force exerted by a tire on the surface as a function of its sideslip angle by identifying in the curve a first zone of linear variation, a second zone of linear-to-nonlinear transition, and a third zone of nonlinear variation; and, for each tire, executing the steps of:
acting in real time to define a group of successive lateral force values, each corresponding to a sideslip angle and determining whether said values are varying in accordance with the first zone, the second zone, or the third zone;
applying an affine model when the values are varying in accordance with the first zone;
applying a DUGOFF model when the values are varying in accordance with the second zone; and
applying a constant model when the values are varying in accordance with the third zone.
2. The method according to claim 1 , wherein the affine model has the form:
F yij *=α 1 β ij +b 1
where F yij * is the value of the lateral force of each tire, a 1 is the slope of the curve in the zone and b 1 is the intercept.
3. The method according to claim 1 , wherein the DUGOFF model has the form:
F yij *=F yij dug
where:
F yij * is the lateral force of each tire;
F
y
ij
dug
=
{
C
β
ij
tan
(
β
ij
)
i
f
λ
≥
1
C
β
ij
tan
(
β
ij
)
(
2
-
λ
)
λ
if
λ
<
1
;
λ
=
μ
y
ij
max
F
Z
ij
2
C
β
ij
❘
"\[LeftBracketingBar]"
tan
(
β
ij
)
❘
"\[RightBracketingBar]"
;
C βij is the cornering stiffness coefficient of each tire;
μ ymaxij is the maximum lateral friction coefficient of each tire; and
β ij is the sideslip angle of each tire.
4. The method according to claim 1 , wherein the constant model has the form:
F yij *=b 2
where F yij * is the lateral force of each tire and b 2 is the maximum lateral force in the third zone.
5. The method according to claim 1 , wherein
application of each of the models consists in finding the cornering stiffness coefficient and the maximum lateral friction coefficient for each tire that minimizes the difference between the lateral force values obtained for each tire with each model and the values of the group of values.
6. The method according to claim 5 , wherein application of the affine model implements the least squares method.
7. The method according to claim 5 , wherein application of the DUGOFF model includes implementing a Levenberg Marquardt optimization algorithm.
8. The method according to claim 1 , wherein the group of lateral force values is modified by adding a value if:
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 (ϵ 1 ); and/or
no value has been added or a length of time longer than a first time threshold (i).
9. The method according to claim 1 , wherein the group of lateral force values is modified by subtracting a value if:
the difference between the first sideslip angle of the group values and the last sideslip angle β(k) of the group of values is greater than a second angle threshold (ϵ 2 ), then the first value is deleted;
a value has been in the window for a length of time longer than a second time threshold then the first value is deleted; and/or
the group has a number of values that is greater than a predetermined threshold number, then at least one value is deleted and preferably every other value is deleted.
10. The method according to claim 1 , wherein the model for application is determined by calculating the slope of the curve and by applying the values of the group of the affine model, with the transition from one zone to another being determined as a function of the values of the slope and of the ordinate.