Techniques for maintaining vehicle formations

1. A method of maintaining vehicle formation, the method comprising:

receiving a desired formation distance between a lead vehicle and a follower vehicle;

receiving a pre-planned path for the follower vehicle;

defining a dynamic zone around a current position of the lead vehicle, the dynamic zone having a first boundary extending along a first arc of a first circle and a second boundary extending along a second arc of a second circle, the first circle encompassing the second circle and the dynamic zone comprising an area between the first boundary and the second boundary, the first boundary characterized by a first radius from the current position of the lead vehicle, the first radius being substantially equal to the desired formation distance, and the second boundary characterized by a second radius from the current position of the lead vehicle, the second radius being shorter than the first radius;

determining a next speed of the follower vehicle based on a current position of the follower vehicle with respect to the first boundary of the dynamic zone, so as to cause the follower vehicle to maintain the desired formation distance from the lead vehicle;

determining a commanded curvature of the follower vehicle based on the current position of the follower vehicle with respect to the pre-planned path, so as to cause the follower vehicle to follow the pre-planned path while maintaining the desired formation distance from the lead vehicle; and

outputting the next speed and the commanded curvature to a control system of the follower vehicle for navigation of the follower vehicle.

2. The method of claim 1 wherein the desired formation distance comprises a desired radial distance.

3. The method of claim 1 wherein the first boundary of the dynamic zone is centered around the current position of the lead vehicle.

4. The method of claim 3 wherein the first arc of the first circle encompasses a central angle that is equal to or less than 180 degrees.

5. The method of claim 4 wherein the first arc of the first circle is substantially a semicircle, and a diameter of the semicircle is substantially normal to a current heading of the lead vehicle.

6. The method of claim 4 wherein the dynamic zone is behind the lead vehicle in a pull mode.

7. The method of claim 6 wherein determining the next speed of the follower vehicle comprises:

in response to determining that the current position of the follower vehicle is located inside the dynamic zone, determining the next speed of the follower vehicle to be less than a current speed of the follower vehicle; and

in response to determining that the current position of the follower vehicle is located outside the dynamic zone, determining the next speed of the follower vehicle to be greater than a current speed of the follower vehicle.

8. The method of claim 4 wherein the dynamic zone is in front of the lead vehicle in a push mode.

9. The method of claim 8 wherein determining the next speed of the follower vehicle comprises:

in response to determining that the current position of the follower vehicle is located inside the dynamic zone, determining the next speed of the follower vehicle to be greater than a current speed of the follower vehicle; and

in response to determining that the current position of the follower vehicle is located outside the dynamic zone, determining the next speed of the follower vehicle to be less than a current speed of the follower vehicle.

10. The method of claim 1 further comprising:

defining a dynamic geo-fence around the current position of the lead vehicle; and

in response to determining that the current position of the follower vehicle is outside the dynamic geo-fence, sending a command to the control system of the follower vehicle to cause the follower vehicle to stop.

11. The method of claim 10 wherein the dynamic geo-fence encompasses the dynamic zone and comprises

a third boundary defined by a third arc about the current position of the lead vehicle, the third arc having a third arc radius that is greater than the first radius of the dynamic zone.

12. The method of claim 11 wherein each of the first arc and the third arc comprises a semicircle.

13. A method of maintaining vehicle formation, the method comprising:

receiving a desired formation distance between a lead vehicle and a follower vehicle;

defining a dynamic zone around a current position of the lead vehicle, the dynamic zone having a first boundary extending along a first arc of a first circle and a second boundary extending along a second arc of a second circle, the dynamic zone comprising an area between the first boundary and the second boundary, the first boundary characterized by a first radius from the current position of the lead vehicle, the first radius being substantially equal to the desired formation distance, and the second boundary characterized by a second radius from the current position of the lead vehicle, the second radius being shorter than the first radius;

determining a next speed and a commanded curvature of the follower vehicle based on the current position of the follower vehicle with respect to the first boundary of the dynamic zone and a path of the lead vehicle, so as to cause the follower vehicle to follow the path of the lead vehicle while maintaining the desired formation distance from the lead vehicle; and

outputting the next speed and the commanded curvature to a control system of the follower vehicle for navigation of the follower vehicle.

14. The method of claim 13 wherein the desired formation distance comprises a desired radial distance.

15. The method of claim 13 wherein the first boundary of the dynamic zone is centered around the current position of the lead vehicle.

16. The method of claim 15 wherein the first arc of the first circle is substantially a semicircle, and a diameter of the semicircle is substantially normal to a current heading of the lead vehicle.

17. The method of claim 15 wherein the dynamic zone is behind the lead vehicle in a pull mode, and determining the next speed of the follower vehicle comprises:

in response to determining that the current position of the follower vehicle is located inside the dynamic zone, determining the next speed of the follower vehicle to be less than a current speed of the follower vehicle; and

in response to determining that the current position of the follower vehicle is located outside the dynamic zone, determining the next speed of the follower vehicle to be greater than a current speed of the follower vehicle.

18. The method of claim 15 wherein the dynamic zone is in front of the lead vehicle in a push mode, and determining the next speed of the follower vehicle comprises:

in response to determining that the current position of the follower vehicle is located inside the dynamic zone, determining the next speed of the follower vehicle to be greater than a current speed of the follower vehicle; and

in response to determining that the current position of the follower vehicle is located outside the dynamic zone, determining the next speed of the follower vehicle to be less than a current speed of the follower vehicle.

19. The method of claim 13 further comprising:

defining a dynamic geo-fence around the current position of the lead vehicle; and

in response to determining that the current position of the follower vehicle is outside the dynamic geo-fence, sending a command to the control system of the follower vehicle to cause the follower vehicle to stop.

20. The method of claim 19 wherein the dynamic geo-fence encompasses the dynamic zone and comprises

a third boundary defined by a third arc about the current position of the lead vehicle, the third arc having a third arc radius that is greater than the first radius of the dynamic zone.