Calibration of LiDAR sensors

1. A method of calibrating a LiDAR sensor mounted on a vehicle, the method comprising:

positioning the vehicle at a distance from a target, wherein:

the target comprises a planar mirror and features surrounding the planar mirror, an optical axis of the planar mirror being substantially horizontal;

the vehicle is positioned and oriented relative to the planar mirror so that an optical axis of the LiDAR sensor is nominally parallel to the optical axis of the planar mirror, and the target is nominally centered at a field of view of the LiDAR sensor;

acquiring, using the LiDAR sensor, a three-dimensional image of the target, wherein the three-dimensional image of the target includes images of the features of the target and a mirror image of the vehicle formed by the planar mirror; and

determining a deviation from an expected alignment of the LiDAR sensor with respect to the vehicle by analyzing the images of the features and the mirror image of the vehicle in the three-dimensional image of the target;

determining a position and an orientation of the LiDAR sensor relative to the target based on the images of the features;

determining a position and an orientation of the LiDAR sensor relative to the mirror image of the vehicle based on the mirror image of the vehicle; and

determining a transformation from a LiDAR coordinate system into a vehicle coordinate system based on: (i) the position and the orientation of the LiDAR sensor relative to the target, and (ii) the position and the orientation of the LiDAR sensor relative to the mirror image of the vehicle.

2. The method of claim 1 further comprising:

re-calibrating the LiDAR sensor with respect to the vehicle based on the deviation from the expected alignment of the LiDAR sensor with respect to the vehicle.

3. The method of claim 1 further comprising:

determining that the deviation from the expected alignment of the LiDAR sensor exceeds a threshold; and

providing an alert in response to determining that the deviation from the expected alignment of the LiDAR sensor exceeds the threshold.

4. The method of claim 1 wherein the field of view of the LiDAR sensor is less than 180 degrees in a horizontal direction.

5. The method of claim 1 wherein the LiDAR coordinate system has three translational degrees of freedom and three rotational degrees of freedom, and the vehicle coordinate system has three translational degrees of freedom and three rotational degrees of freedom.

6. The method of claim 5 wherein:

the three translational degrees of freedom of the LiDAR coordinate system are along three orthogonal axes including an x-axis, a y-axis, and a z-axis, and the three rotational degrees of freedom of the LiDAR coordinate system include roll rotation around the x-axis, pitch rotation around the y-axis, and yaw rotation around the z-axis; and

the three translational degrees of freedom of the vehicle coordinate system are along three orthogonal axes including an X-axis, a Y-axis, and a Z-axis, and the three rotational degrees of freedom of the vehicle coordinate system include roll rotation around the X-axis, pitch rotation around the Y-axis, and yaw rotation around the Z-axis.

7. The method of claim 6 further comprising determining, using two or more distance sensors positioned adjacent to the vehicle, a yaw angle of the vehicle with respect to the optical axis of the planar mirror.

8. The method of claim 7 further comprising determining, using the two or more distance sensors, a lateral position of the vehicle along an axis that is orthogonal to the optical axis of the planar mirror and a vertical axis.

9. The method of claim 7 wherein each of the two or more distance sensors comprises an ultrasonic sensor or a laser sensor.

10. The method of claim 6 further comprising determining, using six distance sensors, a yaw angle, a roll angle, a pitch angle, and a translational position of the vehicle along three orthogonal axes in a coordinate system of the planar mirror.

11. The method of claim 10 wherein each of the six distance sensors comprises an ultrasonic sensor or a laser sensor.

12. The method of claim 1 wherein determining the deviation from the expected alignment of the LiDAR sensor with respect to the vehicle comprises:

storing a reference matrix relating to an expected relationship between the LiDAR sensor and the vehicle;

determining a matrix relating to a current relationship between the LiDAR sensor and the vehicle; and

determining the deviation from the expected alignment of the LiDAR sensor with respect to the vehicle by comparing the matrix to the reference matrix.

13. The method of claim 12 further comprising re-calibrating the LiDAR sensor with respect to the vehicle based on the matrix relating to the current relationship between the LiDAR sensor and the vehicle.