Path approximation for planar motion of a ground vehicle

• US 8,606,498 B2
• Filed: 02/15/2008
• Issued: 12/10/2013
• Est. Priority Date: 02/16/2007
• Status: Active Grant

• Current Assignee: Javad Gnss
• Original Assignee: Javad GNSS, Inc.
• Inventors: Pesterev, Alexander V., Rapoport, Lev B., Tkachenko, Michael
• Primary Examiner(s): Zeender, Ryan
• Assistant Examiner(s): ORTIZ ROMAN, DENISSE Y
• Application Number:
  US12/070,333
• Publication Number:
  US 20080208454A1
• Time in Patent Office: 2,125 Days
• Field of Search: None
• US Class Current: 701/400
• CPC Class Codes: G01C 21/16 by integrating acceleration or speed, i.e. inertial navigation
• CPC Class Codes: G01C 21/26 specially adapted for navigation in a road network

Abstract

The generation of a planar trajectory for use by a vehicle in guiding its position is described. The trajectory is generated by identifying points representing the trajectory, fairing the identified points to generate a set of faired points, and computing a set of polynomial segments from the faired points. The segments form a curve representing the trajectory, where the curve is C²-smooth, and the curve does not exceed the steering capability of the vehicle. The segments may comprise cubic B-spline segments. If the identified points are not substantially equidistant, then an auxiliary curve approximating the trajectory is generated, and a set of substantially equidistant points on the auxiliary curve is selected as the identified points.

Claims

1. A computer-implemented method for generating a planar trajectory for use by a vehicle in guiding its position, the method comprising:

(a) determining whether a plurality of points representing the trajectory are at least substantially equidistant;

(b) if the plurality of points are determined to not be at least substantially equidistant;

generating an auxiliary curve approximating the trajectory;

identifying a plurality of substantially equidistant points from the auxiliary curve; and

fairing the identified plurality of substantially equidistant points to generate a plurality of faired points;

(c) if the plurality of points are determined to be at least substantially equidistant, fairing the plurality of points to generate the plurality of faired points; and

(d) computing by a processor, a plurality of polynomial segments from the plurality of faired points, wherein the polynomial segments form a curve representing the trajectory, the curve is C²-smooth, and the curve does not exceed the steering capability of the vehicle.

2. The method of claim 1, wherein the polynomial segments comprise cubic B-spline segments.

3. The method of claim 1, wherein distances between neighboring points of the plurality of substantially equidistant points are within 5% of each other.

4. The method of claim 3, wherein the polynomial segments comprise cubic B-spline segments.

5. The method of claim 1, further comprising:

identifying a segment associated with a current position;

computing a trajectory deviation value based upon a distance of the current position from the segment; and

providing a course correction signal for the vehicle based upon the trajectory deviation value.

6. The method of claim 5, wherein computing the trajectory deviation value comprises:

identifying coordinates of the current position;

computing the trajectory deviation value associated with the distance of the current position from the associated segment based upon a point of intersection between the normals of the endpoints of the segment and a line projected between the current position and the point of intersection.

7. A non-transitory computer-readable storage medium comprising computer-executable instructions for representing a planar trajectory for use by a vehicle in guiding its position, the instructions for:

(a) determining whether a plurality of points representing the trajectory are at least substantially equidistant;

(b) if the plurality of points are determined to not be at least substantially equidistant;

generating an auxiliary curve approximating the trajectory;

identifying a plurality of substantially equidistant points from the auxiliary curve; and

fairing the identified plurality of substantially equidistant points to generate a plurality of faired points;

(c) if the plurality of points are determined to be at least substantially equidistant, fairing the plurality of points to generate the plurality of faired points; and

(d) computing a plurality of polynomial segments from the plurality of faired points, wherein the polynomial segments form a curve representing the trajectory, the curve is C²-smooth, and the curve does not exceed the steering capability of the vehicle.

8. The computer-readable storage medium of claim 7, wherein the polynomial segments comprise cubic B-spline segments.

9. The computer-readable storage medium of claim 7, wherein distances between neighboring points of the plurality of substantially equidistant points are within 5% of each other.

10. The computer-readable storage medium of claim 9, wherein the polynomial segments comprise cubic B-spline segments.

11. The computer-readable storage medium of claim 7, further comprising instructions for:

identifying a segment associated with a current position;

computing a trajectory deviation value based upon a distance of the current position from the segment; and

providing a course correction signal for the vehicle based upon the trajectory deviation value.

12. The computer-readable storage medium of claim 11, wherein computing the trajectory deviation value comprises:

identifying coordinates of the current position;

computing the trajectory deviation value associated with the distance of the current position from the associated segment based upon a point of intersection between the normals of the endpoints of the segment and a line projected between the current position and the point of intersection.

13. A navigation apparatus for use with a vehicle, the apparatus comprising:

the computer-readable medium of claim 7;

processing logic for executing instructions stored on the computer-readable medium; and

a directional control apparatus for controlling the direction of vehicle movement based upon the curve formed by the computed segments.

14. A vehicle for following a trajectory, the vehicle comprising:

the navigation apparatus of claim 13;

a navigation signal receiver coupled to the processing logic; and

an inertial sensor coupled to the processing logic.