Dynamic observer for the estimation of vehicle lateral velocity
View Patent ↗A system and method for estimating vehicle lateral velocity that defines a relationship between front and rear axle lateral forces and front and rear axle side-slip angles. The method includes providing measurements of vehicle yaw-rate, lateral acceleration, longitudinal speed, and steering angle. The method also includes using these measurements to provide a measurement of the front and rear axle forces. The method calculates a front axle lateral velocity and a rear axle lateral velocity, and calculates a front axle side-slip angle based on the rear axle lateral velocity and a rear axle side-slip angle based on the front axle lateral velocity. The method then estimates front and rear axle forces, and selects a virtual lateral velocity that minimizes an error between the estimated and measured lateral axle forces. The method then provides an estimated vehicle lateral velocity using the selected virtual lateral velocity.
1. A non-transitory computer-readable storage medium with an executable program stored theron, wherein the program instructs a controller to estimate a lateral velocity of a vehicle by performing the following steps:
providing measurements of vehicle yaw-rate, lateral acceleration, longitudinal speed, and steering angle;
providing measured front axle lateral forces and rear axle lateral forces based on the measurements of vehicle yaw-rate, lateral acceleration and steering angle;
calculating a front axle lateral velocity and a rear axle lateral velocity;
calculating a front axle side-slip angle based on the rear axle lateral velocity and a rear axle side-slip angle based on the front axle lateral velocity;
estimating front and rear axle lateral forces;
selecting a virtual lateral velocity that minimizes an error between the estimated and measured lateral axle forces; and
providing and estimate vehicle lateral velocity using the selected virtual lateral velocity.
2. The method according to claim 1 wherein calculating the front and rear axle lateral velocities includes using the equations:
v y F =v x tan({circumflex over (α)} F table +δ)− ar
v y R =v x tan({circumflex over (α)} R table +δ)+ br
where varibles with ^ are estimates, v y F is the front axle lateral velocity, v y R is the rear axle lateral velocity, v x is the vehicle foreward, α F is a front axle slide-silp angle, α R is a rear axle slide-slip angle, δ is a vehicle steering angle, r is vehicle yaw-rate, a and b are the longitudinal distances of the front and rear axles from the center of gravity and variables with table incorporate table data that are fit using a hyperbolic tangent function.
3. The method according to claim 1 wherein calculating the front axle side-slip angle and the rear axle side-slip angle includes using the equations:
α
^
F
=
tan
-
1
(
v
^
y
-
a
r
^
v
^
x
)
-
δ
α
^
R
=
tan
-
1
(
v
^
y
-
b
r
^
v
^
x
)
where variables with ^ are estimates, α F is the front axle side-slip angle, α R is the rear axle side-slip angle, v y is the vehicle lateral velocity, v x is the vehicle forward speed, r is the vehicle yaw-rate, δ is the vehicle steering angle and a and b are the longitudinal distances of the front and rear axles.
4. The method according to claim 1 wherein estimating the front and rear axle forces includes using the equations:
F
y
F
v
y
R
=
c
table
F
μ
^
tan
h
(
d
table
F
μ
^
α
^
F
v
R
y
)
F
y
R
v
y
F
=
c
table
R
μ
^
tan
h
(
d
table
R
μ
^
α
^
R
v
F
y
)
where variables with ^ are estimates, F y v F R y is the front axle force, F y v R F y is the rear axle force, μ is the surface coefficient of friction, c tableF and d tableF are the front tire parameters, c tableR and d tableR are the rear tire parameters, v R y is the vehicle lateral velocity at the front axle and v F y is the vehicle lateral velocity at the rear axle.
5. The method according to claim 1 wherein selecting the virtual lateral velocity includes using the equation:
v
y
virtual
=
{
v
y
R
if
F
y
F
-
F
y
F
v
y
R
<
F
y
R
-
F
y
R
v
y
F
v
y
F
if
F
y
R
-
F
yR
v
y
F
<
F
y
F
-
F
y
F
v
y
R
Where v y virtual is the selected virtual lateral velocity, v y R is the vehicle lateral velocity of the rear axle, v y F is the vehicle lateral velocity of the front axle, F y F is the lateral force at the front axle, F y R is the lateral force at the rear axle, F y v F R y is the front axle force and F y v R F y is the rear axle force.
6. The method according to claim 1 wherein estimating the vehicle lateral velocity includes using the equation:
v
^
.
y
=
F
⋒
y
F
m
+
F
⋒
y
R
m
-
v
x
r
^
+
K
11
(
r
-
r
^
)
+
K
12
(
v
y
VIRTUAL
-
v
^
y
)
where variables with ^ are estimates, v y is the vehicle lateral velocity, v y VIRTUAL is the virtual lateral velocity, m is the mass of the vehicle, F y F is the force at the front axle of the vehicle , F y R is a force at the rear axle of the vehicle, v x is the forward vehicle speed, r is the vehicle aw-rate and K 11 and K 12 are gains.
7. The method according to claim 4 wherein the surface coefficient of friction is estimated.
8. The method according to claim 6 wherein estimating the lateral velocity includes using a Luenberger observer.
9. The method according to claim 7 wherein the surface coefficient of friction is estimated using the measured yaw-rate, steering angle, vehicle speed, and the front and rear axle forces.
10. A non-transitory computer-readable storage medium with an executable program stored thereon, wherein the program instructs a controller to estimate a lateral velocity of a vehicle by performing the following steps:
providing measurements of vehicle yaw-rate, lateral acceleration and steering angle;
providing measured front axle lateral forces and rear axle lateral forces based on the measurements of vehicle yaw-rate, lateral acceleration and steering angle;
calculating a front axle lateral velocity and a rear axle lateral velocity;
calculating a front axle side-slip angle based on the rear axle lateral velocity and a rear axle side-slip angle based on the front axle lateral velocity;
estimating front and rear axle lateral forces including using an estimated surface coefficient of friction;
selecting a virtual lateral velocity that minimizes an error between the estimated and measured lateral axle forces; and
providing an estimated vehicle lateral velocity using the selected virtual lateral velocity, wherein estimating the lateral velocity includes using a Luenberger observer.
11. The method according to claim 10 wherein estimating the front and rear axle forces includes using the equations:
F
y
F
v
y
R
=
c
table
F
μ
^
tan
h
(
d
table
F
μ
^
α
^
F
v
R
y
)
F
y
R
v
y
F
=
c
table
R
μ
^
tan
h
(
d
table
R
μ
^
α
^
R
v
F
y
)
where variables with ^ are estimates, F y v F R y is the front axle force, F y v R F y is the rear axle force, μ is the surface coefficient of friction, c tableF and d tableF are the front tire parameters, c tableR and d tableR are the rear tire parameters, v R y is the vehicle lateral velocity at the front axle, and v F y is the vehicle lateral velocity at the rear axle.