Lateral controller for autonomous low-g maneuvering using front and rear steering

1 . A method for operating an autonomous vehicle, comprising:

determining a desired path of the autonomous vehicle in a turn;

calculating a current trajectory for the autonomous vehicle in the turn based on at least a front road wheel angle of a front wheel of the autonomous vehicle and a rear road wheel angle of a rear wheel of the autonomous vehicle;

determining a cross-track error between the desired path and the current trajectory;

determining a heading error between the desired path and the current trajectory;

creating a tracking cost function based on the cross-track error and the heading error;

performing an optimization operation on the tracking cost function to determine a value of at least one of the front road wheel angle and the rear road wheel angle that reduces at least one of the cross-track error and the heading error; and

controlling a steering of the autonomous vehicle based on the value of the at least one of the front road wheel angle and the rear road wheel angle.

2 . The method of claim 1 , further comprising applying a constraint to the optimization operation to limit a rate of change of at least one of the front road wheel angle and the rear road wheel angle.

3 . The method of claim 1 , further comprising determining a plurality of waypoints for the desired path, determining the cross-track error and the heading error for each of the plurality of waypoints, determining a cross-track cost function based on the cross-track errors, determining a heading error cost function based on the heading errors, and creating the tracking cost function by summing the cross-track cost function and the heading error cost function.

4 . The method of claim 3 , further comprising determining the cross-track error and the heading error for a waypoint using a first tangent line to the waypoint and a second tangent line to the current trajectory, wherein the second tangent line intersects the current trajectory at an intersection of the current trajectory and a radial line passing through the waypoint and a center of rotation of the current trajectory.

5 . The method of claim 1 , wherein the current trajectory is a semi-circular arc about a center of rotation.

6 . The method of claim 1 , wherein the desired path is one of: (i) a 90-degree turn; (ii) a U-turn; and (iii) a lane change.

7 . The method of claim 1 , wherein performing the optimization operation further comprises performing a two-dimensional nonlinear optimization operation.

8 . A system for operating an autonomous vehicle, comprising:

a processor configured to:

determine a desired path of the autonomous vehicle in a turn;

calculate a current trajectory for the autonomous vehicle in the turn based on at least a front road wheel angle of a front wheel of the autonomous vehicle and a rear road wheel angle of a rear wheel of the autonomous vehicle;

determine a cross-track error between the desired path and the current trajectory;

determine a heading error between the desired path and the current trajectory;

create a tracking cost function based on the cross-track error and the heading error;

perform an optimization operation on the tracking cost function to determine a value of at least one of the front road wheel angle and the rear road wheel angle that reduces at least one of the cross-track error and the heading error; and

control a steering of the autonomous vehicle based on the value of the at least one of the front road wheel angle and the rear road wheel angle.

9 . The system of claim 8 , wherein the processor is further configured to apply a constraint to the optimization operation to limit a rate of change of at least one of the front road wheel angle and the rear road wheel angle.

10 . The system of claim 8 , wherein the processor is further configured to determine a plurality of waypoints for the desired path, determine the cross-track error and the heading error for each of the plurality of waypoints, determine a cross-track cost function based on the cross-track errors, determine a heading error cost function based on the heading errors, and create the tracking cost function by summing the cross-track cost function and the heading error cost function.

11 . The system of claim 10 , wherein the processor is further configured to determine the cross-track error and the heading error for a waypoint using a first tangent line to the waypoint and a second tangent line to the current trajectory, wherein the second tangent line intersects the current trajectory at an intersection of the current trajectory and a radial line passing through the waypoint and a center of rotation of the current trajectory.

12 . The system of claim 8 , wherein the current trajectory is a semi-circular arc about a center of rotation.

13 . The system of claim 8 , wherein the desired path is one of: (i) a 90-degree turn; (ii) a U-turn; and (iii) a lane change.

14 . The system of claim 8 , wherein the processor is further configured to perform the optimization operation by performing a two-dimensional nonlinear optimization operation.

15 . An autonomous vehicle, comprising:

a first sensor for measuring a front road wheel angle of a front wheel of the autonomous vehicle;

a second sensor for measuring a rear road wheel angle of a rear wheels of the autonomous vehicle;

a processor configured to:

determine a desired path of the autonomous vehicle in a turn;

calculate a current trajectory for the autonomous vehicle in the turn based on at least the front road wheel angle and the rear road wheel angle;

determine a cross-track error between the desired path and the current trajectory;

determine a heading error between the desired path and the current trajectory;

create a tracking cost function based on the cross-track error and the heading error;

perform an optimization operation on the tracking cost function to determine a value of at least one of the front road wheel angle and the rear road wheel angle that reduces at least one of the cross-track error and the heading error; and

control a steering of the autonomous vehicle based on the value of the at least one of the front road wheel angle and the rear road wheel angle.

16 . The autonomous vehicle of claim 15 , wherein the processor is further configured to apply a constraint to the optimization operation to limit a rate of change of at least one of the front road wheel angle and the rear road wheel angle.

17 . The autonomous vehicle of claim 15 , wherein the processor is further configured to determine a plurality of waypoints for the desired path, determine the cross-track error and the heading error for each of the plurality of waypoints, determine a cross-track cost function based on the cross-track errors, determine a heading error cost function based on the heading errors, and create the tracking cost function by summing the cross-track cost function and the heading error cost function.

18 . The autonomous vehicle of claim 17 , wherein the processor is further configured to determine the cross-track error and the heading error for a waypoint using a first tangent line to the waypoint and a second tangent line to the current trajectory, wherein the second tangent line intersects the current trajectory at an intersection of the current trajectory and a radial line passing through the waypoint and a center of rotation of the current trajectory.

19 . The autonomous vehicle of claim 15 , wherein the current trajectory is a semi-circular arc about a center of rotation.

20 . The autonomous vehicle of claim 15 , wherein the desired path is one of: (i) a 90-degree turn; (ii) a U-turn; and (iii) a lane change.