Methods and systems for calibration of multiple lidar devices with non-overlapping fields of view

1. A method of calibration of a first lidar device and a second lidar device from a plurality of lidar devices that are mounted on a vehicle, the method comprising:

receiving lidar returns recorded by the first lidar device and the second lidar device as the vehicle moves along a path in an environment according to a predetermined path pattern;

determining, based on a first subset of the lidar returns that are recorded by the first lidar device, positions of the vehicle along the path with respect to a world coordinate system;

determining a subset of pairs of the positions of the vehicle, wherein each pair from the subset of pairs includes a first position and a second position of the vehicle, and wherein a first field of view of the first lidar device when the vehicle is located at the first position at a first time overlaps with a second field of view of the second lidar device when the vehicle is located at the second position at a second time;

determining, for each pair from the subset of pairs of the positions, an estimate of transformation between the first subset of the lidar returns recorded by the first lidar device when the vehicle was located at the first position and a second subset of the lidar returns recorded by the second lidar device when the vehicle was located at the second position to produce a plurality of estimates of transformations for the pairs of the positions; and

determining, based on the plurality of estimates of the transformations, an extrinsic calibration transformation that transforms a position of the second lidar device on the vehicle into a calibrated position of the second lidar device that allows to obtain a consistent view of the world between the first lidar device and the second lidar device.

2. The method of claim 1 , wherein the determining, for each pair from the subset of pairs of the positions, the estimate of the transformation includes:

converting the first subset of the lidar returns into a converted first subset of the lidar returns in a first lidar coordinate system of the first lidar device when the vehicle was located at the second position; and

converting the second subset of the lidar returns into a converted second subset of the lidar returns in the first lidar coordinate system when the vehicle was located at the second position.

3. The method of claim 2 , wherein the converting the first subset of the lidar returns includes converting the first subset of the lidar returns from the first lidar coordinate system when the vehicle was located at the first position, and wherein the converting the second subset of the lidar returns includes converting the second subset of the lidar returns from a second lidar coordinate system when the vehicle was located at the second position.

4. The method of claim 2 , wherein the determining the estimate of the transformation includes:

calculating, based on the converted first subset of the lidar returns and the converted second subset of the lidar returns, the estimate of the transformation.

5. The method of claim 1 , wherein the determining the subset of pairs of the positions of the vehicle includes:

pairing distinct ones of the positions of the vehicle to obtain a set of pairs of the positions, wherein each one from the set of pairs includes a third position of the vehicle and a fourth position of the vehicle;

generating for each pair from the set of pairs a first bounding box representative of a third field of view of the first lidar device when the vehicle is located at the third position and a second bounding box representative of a fourth field of view of the second lidar device when the vehicle is at the fourth position; and

responsive to determining that the first bounding box and the second bounding box overlap above a predetermined threshold, adding the pair including the third position of the vehicle and the fourth position of the vehicle to the subset of pairs of the positions of the vehicle.

6. The method of claim 1 , further comprising:

determining an intrinsic calibration transformation that allows to produce lidar returns for the second and the first lidar devices with similar intensity values.

7. The method of claim 6 , wherein the determining the intrinsic calibration transformation includes:

transforming based on the extrinsic calibration transformation a third subset of the lidar returns recorded by the second lidar device to obtain a calibrated third subset of the lidar returns;

aggregating the calibrated third subset of the lidar returns with a fourth subset of the lidar returns recorded by the first lidar device into a three-dimensional grid of cells that is representative of the environment; and

determining the intrinsic calibration transformation based on lidar returns from the third subset and the fourth subset that hit a same cell in the three-dimensional grid of cells.

8. A non-transitory computer-readable storage medium that provides instructions, which when executed by a processor cause said processor to perform operations for calibration of a first lidar device and a second lidar device from a plurality of lidar devices that are mounted on a vehicle, the operations comprising:

receiving lidar returns recorded by the first lidar device and the second lidar device as the vehicle moves along a path in an environment according to a predetermined path pattern;

determining, based on a first subset of the lidar returns that are recorded by the first lidar device, positions of the vehicle along the path with respect to a world coordinate system;

determining a subset of pairs of the positions of the vehicle, wherein each pair from the subset of pairs includes a first position and a second position of the vehicle, and wherein a first field of view of the first lidar device when the vehicle is located at the first position at a first time overlaps with a second field of view of the second lidar device when the vehicle is located at the second position at a second time;

determining, for each pair from the subset of pairs of the positions, an estimate of transformation between the first subset of the lidar returns recorded by the first lidar device when the vehicle was located at the first position and a second subset of the lidar returns recorded by the second lidar device when the vehicle was located at the second position to produce a plurality of estimates of transformations for the pairs of the positions; and

determining, based on the plurality of estimates of the transformations, an extrinsic calibration transformation that transforms a position of the second lidar device on the vehicle into a calibrated position of the second lidar device that allows to obtain a consistent view of the world between the first lidar device and the second lidar device.

9. The non-transitory computer-readable storage medium of claim 8 , wherein the determining, for each pair from the subset of pairs of the positions, the estimate of the transformation includes:

converting the first subset of the lidar returns into a converted first subset of the lidar returns in a first lidar coordinate system of the first lidar device when the vehicle was located at the second position; and

converting the second subset of the lidar returns into a converted second subset of the lidar returns in the first lidar coordinate system when the vehicle was located at the second position.

10. The non-transitory computer-readable storage medium of claim 9 , wherein the converting the first subset of the lidar returns includes converting the first subset of the lidar returns from the first lidar coordinate system when the vehicle was located at the first position, and wherein the converting the second subset of the lidar returns includes converting the second subset of the lidar returns from a second lidar coordinate system when the vehicle was located at the second position.

11. The non-transitory computer-readable storage medium of claim 9 , wherein the determining the estimate of the transformation includes:

calculating, based on the converted first subset of the lidar returns and the converted second subset of the lidar returns, the estimate of the transformation.

12. The non-transitory computer-readable storage medium of claim 8 , wherein the determining the subset of pairs of the positions of the vehicle includes:

pairing distinct ones of the positions of the vehicle to obtain a set of pairs of the positions, wherein each one from the set of pairs includes a third position of the vehicle and a fourth position of the vehicle;

generating for each pair from the set of pairs a first bounding box representative of a third field of view of the first lidar device when the vehicle is located at the third position and a second bounding box representative of a fourth field of view of the second lidar device when the vehicle is at the fourth position; and

responsive to determining that the first bounding box and the second bounding box overlap above a predetermined threshold, adding the pair including the third position of the vehicle and the fourth position of the vehicle to the subset of pairs of the positions of the vehicle.

13. The non-transitory computer-readable storage medium of claim 8 , wherein the operations further comprise:

determining an intrinsic calibration transformation that allows to produce lidar returns for the second and the first lidar devices with similar intensity values.

14. The non-transitory computer-readable storage medium of claim 13 , wherein the determining the intrinsic calibration transformation includes:

transforming based on the extrinsic calibration transformation a third subset of the lidar returns recorded by the second lidar device to obtain a calibrated third subset of the lidar returns;

aggregating the calibrated third subset of the lidar returns with a fourth subset of the lidar returns recorded by the first lidar device into a three-dimensional grid of cells that is representative of the environment; and

determining the intrinsic calibration transformation based on lidar returns from the third subset and the fourth subset that hit a same cell in the three-dimensional grid of cells.

15. A computing device for calibration of a first lidar device and a second lidar device from a plurality of lidar devices that are mounted on a vehicle, the computing device comprising:

a non-transitory computer-readable storage medium to store instructions; and

a processor coupled with the non-transitory computer readable storage medium to process the stored instructions to perform the following operations of:

receiving lidar returns recorded by the first lidar device and the second lidar device as the vehicle moves along a path in an environment according to a predetermined path pattern,

determining, based on a first subset of the lidar returns that are recorded by the first lidar device, positions of the vehicle along the path with respect to a world coordinate system,

determining a subset of pairs of the positions of the vehicle, wherein each pair from the subset of pairs includes a first position and a second position of the vehicle, and wherein a first field of view of the first lidar device when the vehicle is located at the first position at a first time overlaps with a second field of view of the second lidar device when the vehicle is located at the second position at a second time,

determining, for each pair from the subset of pairs of the positions, an estimate of transformation between the first subset of the lidar returns recorded by the first lidar device when the vehicle was located at the first position and a second subset of the lidar returns recorded by the second lidar device when the vehicle was located at the second position to produce a plurality of estimates of transformations for the pairs of the positions, and

determining, based on the plurality of estimates of the transformations, an extrinsic calibration transformation that transforms a position of the second lidar device on the vehicle into a calibrated position of the second lidar device that allows to obtain a consistent view of the world between the first lidar device and the second lidar device.

16. The computing device of claim 15 , wherein the determining, for each pair from the subset of pairs of the positions, the estimate of the transformation includes:

converting the first subset of the lidar returns into a converted first subset of the lidar returns in a first lidar coordinate system of the first lidar device when the vehicle was located at the second position; and

converting the second subset of the lidar returns into a converted second subset of the lidar returns in the first lidar coordinate system when the vehicle was located at the second position.

17. The computing device of claim 16 , wherein the converting the first subset of the lidar returns includes converting the first subset of the lidar returns from the first lidar coordinate system when the vehicle was located at the first position, and wherein the converting the second subset of the lidar returns includes converting the second subset of the lidar returns from a second lidar coordinate system when the vehicle was located at the second position.

18. The computing device of claim 16 , wherein the determining the estimate of the transformation includes:

calculating, based on the converted first subset of the lidar returns and the converted second subset of the lidar returns, the estimate of the transformation.

19. The computing device of claim 15 , wherein the determining the subset of pairs of the positions of the vehicle includes:

pairing distinct ones of the positions of the vehicle to obtain a set of pairs of the positions, wherein each one from the set of pairs includes a third position of the vehicle and a fourth position of the vehicle;

generating for each pair from the set of pairs a first bounding box representative of a third field of view of the first lidar device when the vehicle is located at the third position and a second bounding box representative of a fourth field of view of the second lidar device when the vehicle is at the fourth position; and

responsive to determining that the first bounding box and the second bounding box overlap above a predetermined threshold, adding the pair including the third position of the vehicle and the fourth position of the vehicle to the subset of pairs of the positions of the vehicle.

20. The computing device of claim 15 , wherein the operations further comprise:

determining an intrinsic calibration transformation that allows to produce lidar returns for the second and the first lidar devices with similar intensity values.

21. The computing device of claim 20 , wherein the determining the intrinsic calibration transformation includes:

transforming based on the extrinsic calibration transformation a third subset of the lidar returns recorded by the second lidar device to obtain a calibrated third subset of the lidar returns;

aggregating the calibrated third subset of the lidar returns with a fourth subset of the lidar returns recorded by the first lidar device into a three-dimensional grid of cells that is representative of the environment; and

determining the intrinsic calibration transformation based on lidar returns from the third subset and the fourth subset that hit a same cell in the three-dimensional grid of cells.