On-board road friction estimation
A road friction coefficient of a vehicle is estimated by obtaining substantially contemporaneous values associated with a steering angle for a steered axle of the vehicle, a lateral acceleration, a yaw acceleration, an alignment torque and an axle load on the steered axle; estimating a lateral tire force on the basis of the steering angle, lateral acceleration, and yaw acceleration; deriving a pneumatic trail from the alignment torque and estimated lateral tyre force; and estimating a road friction coefficient from the lateral tire force, the axle load, and the pneumatic trail. In embodiments, the derivation of the road friction coefficient includes evaluating a nonlinear function of the pneumatic trail.
1. A method of estimating a road friction coefficient of a vehicle, the method comprising:
obtaining substantially contemporaneous values associated with a steering angle (δ) for a steered axle of the vehicle, a lateral acceleration (a y ), a yaw acceleration (dω z /dt), an alignment torque (M z ), and an axle load (m f ) on the steered axle;
estimating a lateral tire force (F y ) on the basis of the steering angle, lateral acceleration, and yaw acceleration;
deriving a pneumatic trail (t p ) from the alignment torque (M z ) and the estimated lateral tire force (F y ); and
estimating a road friction coefficient (μ) from the lateral tire force, the axle load, and the pneumatic trail,
wherein the method further comprises at least one of:
i) estimating the road friction coefficient by evaluating a predetermined nonlinear function of the pneumatic trail, wherein the nonlinear function is at least equal to any of:
F
y
m
f
g
tanh
3
a
-
9
t
p
2
a
,
F
y
m
f
g
arc
tanh
3
a
-
9
t
p
2
a
,
F
y
m
f
g
2
a
3
a
-
9
t
p
or scaled versions thereof, where g is gravitational acceleration, 2a is a tyre contact length, F y is lateral tyre force and t p is the pneumatic trail;
ii) deriving a tolerance range (μ − , μ + ) associated with the road friction coefficient; and
iii) evaluating the lateral tire force and alignment torque with respect to threshold values (F y,lim , M z,lim ) for the lateral tire force and the alignment torque.
2. The method of claim 1 , wherein the derivation of the pneumatic trail further comprises correcting for a caster trail (t c ) of the vehicle.
3. The method of claim 1 , wherein the evaluation provides a reliability appraisal of the estimated road friction coefficient.
4. The method of claim 1 , further comprising controlling the vehicle based on the estimated road friction coefficient.
5. The method of claim 4 , wherein the controlling further comprises taking a safety-relevant action in the vehicle in response to an evaluation of the estimated road friction coefficient.
6. The method of claim 1 , which is implemented in one or more of: a vehicle, a vehicle enabled for autonomous driving, an autonomous vehicle, a processing unit receiving data from a vehicle.
7. A vehicle comprising:
sensors including a steering angle sensor, a position and orientation sensor, a steering actuator, and an axle load estimator; and
processing circuitry including:
a lateral tire force estimator configured to:
receive a steering angle from the steering angle sensor as well as a lateral acceleration and yaw acceleration from the position and orientation sensor, and
estimate, based thereon, a lateral tire force,
a pneumatic trail estimator configured to:
receive a control signal controlling the steering actuator as well as the estimated lateral tire force, and
estimate, based thereon, a pneumatic trail, and
a road friction estimator configured to:
receive an axle load from the axle load estimator as well as the estimated lateral tire force and pneumatic trail, and
estimate, based thereon, a road friction coefficient,
wherein at least one of:
i) the processing circuitry further includes at least one post-processing unit configured to:
derive a tolerance of the road friction coefficient, and/or
evaluate current lateral tyre force and alignment torque with respect to threshold values (F y,lim , M z,lim ) for the lateral tire force and the alignment torque, or
ii) the road friction estimator is further configured to estimate the road friction coefficient by evaluating a predetermined nonlinear function of the pneumatic trail, wherein the nonlinear function is at least equal to any of;
F
y
m
f
g
tan
h
3
a
-
9
t
p
2
a
,
F
y
m
f
g
arc
tan
h
3
a
-
9
t
p
2
a
,
F
y
m
f
g
2
a
3
a
-
9
t
p
or scaled versions thereof, where g is gravitational acceleration, 2a is a tyre contact length, F y is lateral tyre force and t p is the pneumatic trail.
8. The vehicle of claim 7 , wherein the position and orientation sensor includes an inertial sensor.
9. The vehicle of claim 7 , wherein the pneumatic trail estimator is configured to derive an alignment torque from the control signal controlling the steering actuator.
10. A computer program comprising instructions which, when the program is executed by a computer, cause the computer to carry out the method of claim 1 .