Handeye calibration

[Goksan Isil (Alumni)]

Hi,
I'm trying to solve the hand-eye calibration problem (which is solving the sensor extrinsics transform from the robot base frame), through the equation A*X = X*B, where A is the delta motion of the robot base in robot base frame, X is the sensor extrinsics transform from robot base to sensor and B is the delta motion of the sensor in sensor frame.

In my cost function, at some point I do:

A = X*B*X^-1 where X is represented as 4-by-4 transformation matrix ( I generate this using 6 optimization parameters: 3 for translation, 3 for axis angle rotation, which is converted to rotation matrix via ceres::AngleAxisToRotationMatrix)

Even though the optimization is converging, I'm getting very noisy values for X (the extrinsics). So I was wondering if X*B*X^-1 could constitute a numerical issue.

Thanks in advance

[Sameer Agarwal]

Hard to say what the cause of the noise is based on the information you have provided. It also matters how you are computing XBX^{-1}.

Sameer

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[Dmitriy Korchemkin]

Are you computing X^{-1} using matrix inverse explicitly, or using SE3 group inverse:

X= [[R | t]; [0,0,0,1]] => X^{-1} = [[R^T | -R^T t]; [0,0,0,1]]?

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[Goksan Isil (Alumni)]

I've been using the matrix inverse explicitly.