Methods and apparatus for estimating bank angle using steering-rack force

1 . A vehicle comprising:

a steering rack;

an axle;

an inertial measurement unit (IMU);

data processing hardware; and

memory hardware in communication with the data processing hardware and storing instructions that, when executed by the data processing hardware, cause the data processing hardware to perform operations comprising:

obtaining a measured position of the steering rack;

determining, based on the measured position of the steering rack, an estimate of a lateral force in the axle;

determining, using the IMU, a measurement of the lateral force in the axle;

determining a difference between the estimate of the lateral force in the axle and the measurement of the lateral force in the axle; and

determining, based on the difference, an estimate of a bank angle of a surface on which the vehicle is situated.

2 . The vehicle of claim 1 , wherein determining, based on the measured position of the steering rack, the estimate of the lateral force in the axle comprises:

determining, based on the measured position of the steering rack, an estimate of a steering-rack force load; and

determining, based on the estimate of the steering-rack force load, the estimate of the lateral force in the axle.

3 . The vehicle of claim 1 , wherein determining the estimate of the lateral force in the axle is based on a mathematical steering compliance model representing a first relationship between a steering-rack force and a lateral acceleration.

4 . The vehicle of claim 3 , wherein the mathematical steering compliance model also represents a second relationship between a traction force and a lateral acceleration, and a third relationship between a normal force and a lateral acceleration.

5 . The vehicle of claim 1 , wherein:

the vehicle further comprises a motor configured to operate the steering rack; and

determining, based on the measured position of the steering rack, the estimate of the lateral force in the axle comprises:

obtaining a measurement of a motor current of the motor;

determining, based on the measurement of the motor current, an estimate of a steering-rack force load; and

determining, based on the estimate of the steering-rack force load, the estimate of the lateral force in the axle.

6 . The vehicle of claim 1 , wherein determining, using the IMU, the measurement of the lateral force in the axle comprises:

obtaining, using the IMU, a lateral acceleration; and

determining, based on the lateral acceleration, the measurement of the lateral force in the axle.

7 . The vehicle of claim 1 , wherein the operations further comprise:

obtaining a measurement of an environmental condition;

determining that the measurement of the environmental condition satisfies a criterion; and

based on determining that the measurement of the environmental condition satisfies the criterion, adjusting the estimate of the bank angle.

8 . The vehicle of claim 7 , wherein:

determining that the measurement of the environmental condition satisfies a criterion comprises determining that a windy condition is present; and

adjusting the estimate of the bank angle comprises discarding the estimate of the bank angle.

9 . A computer-implemented method executed by data processing hardware that causes the data processing hardware to perform operations comprising:

obtaining a measured position of a steering rack;

determining, based on the measured position of the steering rack, an estimate of a lateral force in an axle;

determining, using an inertial measurement unit (IMU), a measurement of the lateral force in the axle;

determining a difference between the estimate of the lateral force in the axle and the measurement of the lateral force in the axle; and

determining, based on the difference, an estimate of a bank angle of a surface.

10 . The computer-implemented method of claim 9 , wherein determining, based on the measured position of the steering rack, the estimate of the lateral force in the axle comprises:

determining, based on the measured position of the steering rack, an estimate of a steering-rack force load; and

determining, based on the estimate of the steering-rack force load, the estimate of the lateral force in the axle.

11 . The computer-implemented method of claim 9 , wherein determining the estimate of the lateral force in the axle is based on a mathematical steering compliance model representing a first relationship between a steering-rack force and a lateral acceleration.

12 . The computer-implemented method of claim 11 , wherein the mathematical steering compliance model also represents a second relationship between a traction force and a lateral acceleration, and a third relationship between a normal force and a lateral acceleration.

13 . The computer-implemented method of claim 9 , wherein determining, based on the measured position of the steering rack, the estimate of the lateral force in the axle comprises:

obtaining a measurement of a motor current of a motor configured to operate the steering rack;

determining, based on the measurement of the motor current, an estimate of a steering-rack force load; and

determining, based on the estimate of the steering-rack force load, the estimate of the lateral force in the axle.

14 . The computer-implemented method of claim 9 , wherein determining, using the IMU, the measurement of the lateral force in the axle comprises:

obtaining, using the IMU, a lateral acceleration; and

determining, based on the lateral acceleration, the measurement of the lateral force in the axle.

15 . The computer-implemented method of claim 9 , wherein the operations further comprise:

obtaining a measurement of an environmental condition;

determining that the measurement of the environmental condition satisfies a criterion; and

based on determining that the measurement of the environmental condition satisfies the criterion, adjusting the estimate of the bank angle.

16 . The computer-implemented method of claim 15 , wherein:

determining that the measurement of the environmental condition satisfies a criterion comprises determining that a windy condition is present; and

adjusting the estimate of the bank angle comprises discarding the estimate of the bank angle.

17 . A vehicle comprising:

a steering rack;

a motor configured to operate the steering rack; an axle;

an inertial measurement unit (IMU);

data processing hardware; and

memory hardware in communication with the data processing hardware and storing instructions that, when executed by the data processing hardware, cause the data processing hardware to perform operations comprising:

obtaining a measured position of the steering rack;

obtaining a measurement of a motor current of the motor;

determining, based on the measured position of the steering rack and the measurement of the motor current, an estimate of a steering-rack force load; and

determining, based on the estimate of the steering-rack force load, an estimate of a lateral force in the axle;

obtaining, using the IMU, a lateral acceleration;

determining, based on the lateral acceleration, a measurement of a lateral force in the axle;

determining a difference between the estimate of the lateral force in the axle and the measurement of the lateral force in the axle; and

determining, based on the difference, an estimate of a bank angle of a surface on which the vehicle is situated.

18 . The vehicle of claim 17 , wherein determining the estimate of the lateral force in the axle is based on a mathematical steering compliance model representing a first relationship between a steering-rack force and a lateral acceleration.

19 . The vehicle of claim 17 , wherein the operations further comprise:

obtaining a measurement of an environmental condition;

determining that the measurement of the environmental condition satisfies a criterion; and

based on determining that the measurement of the environmental condition satisfies the criterion, adjusting the estimate of the bank angle.

20 . The vehicle of claim 19 , wherein:

determining that the measurement of the environmental condition satisfies a criterion comprises determining that a windy condition is present; and

adjusting the estimate of the bank angle comprises discarding the estimate of the bank angle.