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Lidar IMU Extrinsic Calibration Overview

1. Overall Structure

2. Hand-Eye Caliration Method

masterly based on hand-eye calibration method

The extrinsic matrix is from IMU axis to Lidar axis.

Lidar_pose = Extrinsic * IMU_pose * Extrinsic.inverse()

3. Solve AX = XB

The function performs the Hand-Eye calibration using various methods.

  • One approach consists in estimating the rotation then the translation (separable solutions).

  • Separable solutions solving separately damages the integrity of the kinematics problem and leads to coupling errors in the calculation of rotation and translation.

R. Tsai, R. Lenz A New Technique for Fully Autonomous and Efficient 3D Robotics Hand/EyeCalibration

F. Park, B. Martin Robot Sensor Calibration: Solving AX = XB on the Euclidean Group

R. Horaud, F. Dornaika Hand-Eye Calibration

  • Another approach consists in estimating simultaneously the rotation and the translation (simultaneous solutions).

  • Simultaneous solutions handle rotation and translation simultaneously and describes pose transformation in a unified manner, reducing complexity and improving calibration accuracy.

N. Andreff, R. Horaud, B. Espiau On-line Hand-Eye Calibration

K. Daniilidis Hand-Eye Calibration Using Dual Quaternions

In this program, we use K. Daniilidis’s Dual Quaternions method to solve AX=XB problem.

4. Dual Quaternion

  • dual number:

  • dual quaternion:

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point b to point a :

use quaternion:  pa = q * pb * q̄

A line in space with direction la through a point pa to a line in space with direction lb through a point pb: 

la = q * lb * q̄

Hand-Eye Transformation with Unit Dual Quaternions:

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ǎ denote the screw of a camera motion, and b̌  denote the screw of the hand motion.

Multiplying on the right with q.

Let a = (0, a) and a’ = (0, a’), as well as b = (0, b), b’ = (0, b’).

SVD:

results:

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v7, v8 is the last two right-singular vectors
  • compare to two-steps method(Tsai method) and nonlinear method:

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   Behavior of the dual quaternion (DUAL), the nonlinear (NLIN), and the two-step (SEPA) algorithms with variation in noise. The RMS rotation error is shown on the left; the RMS relative translation error is on the right.

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The RMS error in rotation (left) and the RMS relative error in translation (right) as a function of the number of hand and camera motions.

5. Related Page

module design https://docs.opencv.org/4.x/d9/d0c/group__calib3d.html#gaebfc1c9f7434196a374c382abf43439b

past calibration result

https://printeger.github.io/2022/08/14/Lidar-IMU-Extrinsic-Calibration-Experiment.html

This post is licensed under CC BY 4.0 by the author.