Vehicle lateral velocity and surface friction estimation using force tables
View Patent ↗A system and method for estimating vehicle lateral velocity and surface coefficient of friction using front and rear axle lateral force versus side-slip angle tables and sensor measurements. The sensor measurements include lateral acceleration, yaw-rate, longitudinal speed and steering angle of the vehicle. The method includes calculating front and rear axle lateral forces and front and rear side-slip angles on the axles of the vehicle. The method also includes identifying two equations from the calculated lateral forces and the vehicle measurements. The method provides tables that identify a relationship between the calculated front and rear axle lateral forces and the front and rear side-slip angles, and determines the vehicle lateral velocity and surface coefficient of friction from the tables.
1. A method for estimating lateral velocity of a vehicle and surface coefficient of friction, said method comprising:
calculating front and rear axle lateral forces on the vehicle;
calculating front and rear side-slip angles on axles of the vehicle;
identifying two equations from the calculated lateral forces and vehicle measurements;
providing tables that identify a relationship between the calculated front and rear axle lateral forces and the front and rear side-slip angles; and
estimating vehicle lateral velocity and surface coefficient of friction from the tables.
2. The method according to claim 1 wherein calculating the front and rear axle lateral forces includes using vehicle lateral acceleration, yaw-rate, longitudinal speed, and steering angle measurements.
3. The method according to claim 2 wherein the front and rear axle lateral forces are calculated using the equation:
[
F
yF
F
yR
]
=
[
1
m
cos
δ
1
m
a
l
z
cos
δ
-
b
l
z
]
-
1
[
a
y
,
compensated
r
.
]
where F yF is the front axle force, F yR is the rear axle force, m is vehicle mass, I is the moment of inertia, r is vehicle yaw-rate, a ycompensated is vehicle lateral acceleration compensated for gravity due to vehicle roll, δ is the steering angle and a and b are the longitudinal distances of the front and rear axles.
4. The method according to claim 2 wherein the lateral acceleration measurement is compensated for a vehicle roll motion.
5. The method according to claim 1 wherein calculating the front and rear axle side-slip angles includes calculating the front and rear axle side-slip angles based on a kinematic relationship between lateral velocity and axle side-slip angles.
6. The method according to claim 5 wherein calculating the front and rear axle side-slip angles includes using the equations:
α
F
=
tan
-
1
(
v
y
,
compensated
+
ar
v
x
)
-
δ
α
R
=
tan
-
1
(
v
y
,
compensated
-
br
v
x
)
where α F is the front axle side-slip angle, α R is the rear axle side-slip angle, ν y is vehicle lateral velocity, r is vehicle yaw-rate, ν x is vehicle forward speed, δ is vehicle steering angle, and a and b are the longitudinal distances of the front and rear axles.
7. The method according to claim 1 wherein the two equations are:
F
yF
=
f
tableF
(
α
F
,
μ
)
=
f
tableF
(
tan
-
1
(
v
y
+
ar
v
x
)
-
δ
,
μ
)
F
yR
=
f
tableR
(
α
R
,
μ
)
=
f
tableR
(
tan
-
1
(
v
y
-
br
v
x
)
,
μ
)
where F yF is the front axle force, F yR is the rear axle force, α F is the front axle side-slip angle, α R is the rear axle side-slip angle, μ is surface coefficient of friction, ν y is the vehicle lateral velocity, δ is vehicle steering angle, ν x is vehicle forward speed and a and b are the longitudinal distances of the front and rear axles.
8. The method according to claim 1 further comprising preventing estimating of the lateral velocity and the coefficient of friction for an unrealistic solution by solving the two equations with a constraint based on a kinematic relationship between the lateral acceleration and the rate of change of lateral velocity.
9. The method according to claim 8 wherein the constraint is provided as:
v
·
y
|
measured
-
v
.
y
|
estimated
=
[
v
y
(
k
)
-
v
y
(
k
-
1
)
Δ
t
]
-
[
a
y
,
compensated
-
rv
x
]
<
K
vydot
,
threshold
where ν y is the vehicle lateral velocity, a y is the vehicle lateral acceleration, r is vehicle yaw-rate, ν x is the vehicle forward speed and K νydot,threshold is the threshold that defines the constraint.
10. A method for estimating lateral velocity of a vehicle and estimating surface coefficient of friction, said method comprising:
measuring lateral acceleration, yaw-rate, longitudinal speed, and steering angle of the vehicle;
calculating front and rear axle lateral forces on the vehicle;
calculating front and rear side-slip angles on axles of the vehicle;
providing tables that identify a relationship between the calculated front and rear axle lateral forces and the front and rear side-slip angles; and
determining vehicle lateral velocity and surface coefficient of friction from the tables.
11. The method according to claim 10 wherein the lateral acceleration measurement is compensated for vehicle roll motion.
12. The method according to claim 10 wherein the front and rear axle lateral forces are calculated using the equation:
[
F
yF
F
yR
]
=
[
1
m
cos
δ
1
m
a
l
z
cos
δ
-
b
l
z
]
-
1
[
a
y
,
compensated
r
.
]
where F yF is the front axle force, F yR is the rear axle force, m is vehicle mass, I is the moment of inertia, r is vehicle yaw-rate, a y,compensated is vehicle lateral acceleration compensated for gravity due to vehicle roll, δ is the steering angle and a and b are the longitudinal distances of the front and rear axles.
13. The method according to claim 10 wherein calculating the front and rear axle side-slip angles includes calculating the front and rear axle side-slip angles based on a kinematic relationship between lateral velocity and axle side-slip angles.
14. The method according to claim 13 wherein calculating the front and rear axle side-slip angles includes using the equations:
α
F
=
tan
-
1
(
v
y
,
compensated
+
ar
v
x
)
-
δ
α
R
=
tan
-
1
(
v
y
,
compensated
-
br
v
x
)
where α F is the front axle side-slip angle, α R is the rear axle side-slip angle, ν y is vehicle lateral velocity, r is vehicle yaw-rate, ν x is vehicle forward speed, δ is vehicle steering angle, and a and b are the longitudinal distances of the front and rear axles.
15. The method according to claim 10 further comprising preventing the determining of the lateral velocity and the coefficient of friction for an unrealistic solution using a constraint based on a kinematic relationship between the lateral acceleration and the rate of change of lateral velocity.
16. The method according to claim 15 wherein the constraint is provided as:
v
·
y
|
measured
-
v
.
y
|
estimated
=
[
v
y
(
k
)
-
v
y
(
k
-
1
)
Δ
t
]
-
[
a
y
,
compensated
-
rv
x
]
<
K
vydot
,
threshold
where ν y is the vehicle lateral velocity, a y is the vehicle lateral acceleration, r is vehicle yaw-rate, ν x is the vehicle forward speed and K νydot,threshold is the threshold that defines the constraint.
17. A system for estimating lateral velocity of a vehicle and estimating surface coefficient of friction, said system comprising:
means for measuring a lateral acceleration, yaw-rate, longitudinal speed, and steering angle of the vehicle;
means for calculating front and rear axle lateral forces on the vehicle;
means for calculating front and rear side-slip angles on axles of the vehicle;
means for providing tables that identify a relationship between the calculated front and rear axle lateral forces and the front and rear side-slip angles; and
means for determining vehicle lateral velocity and surface coefficient of friction from the tables.
18. The system according to claim 17 further comprising means for compensating for vehicle roll motion.
19. The system according to claim 17 wherein the means for calculating the front and rear axle side-slip angles includes means for calculating the front and rear axle side-slip angles based on a kinematic relationship between lateral velocity and axle side-slip angles.
20. The system according to claim 17 further comprising means for preventing a determination of the lateral velocity in the coefficient of friction for an unrealistic solution using a constraint based on a kinematic relationship between the lateral acceleration and the rate of change of lateral velocity.