robot-calibration

Attempt at calibrating the ur10e robot + mocap system for exposed demo.

Model

The system assumes that the xyz world coordinates of the pen tip can be given by

[x, y, z, 1]' = Tb * Te * Tr * Tp * [0, 0, 0, 1]'

Where:

• Tb is the transform from the world frame to the robot base (as given by the mocap system)
• Te is the transform that corrects for the error we made when eyeballing the robot base in the mocap system
• Tr is the transform from the robot base to the robot end-effector (as given by the robot's forward kinematics)
• Tp is the transform from the end-effector to the pen tip (simple translation along z is assumed)

This code estimates Te (a: rotation around z-axis, xyz: xyz translation) and Tp (p: translation along z) by minimizing the squared euclidean distance between the predicted position of the pen (see equation above) and the observed position (e.g. given by mocap tracking).

Usage

python -m robot_calibration <ipt-file> --verbose --out <out-file> --fmt transforms

Notes:

• ipt-file should be a numpy matrix with 35 columns (16 for Tb, 16 for Tr, 3 for the xyz of the pen)
• If ipt-file is omitted, it will try to read from standard in
• If out-file is omitted, it will write to standard out
• Valid formats are transforms (2 x 16 numpy array) or params (json dict with x,y,z,a,p)
• Customize initial guesses by e.g. --x0 0.001 (to guess a 1mm +x error for the robot base transform).
• Optimizer step size and number of iterations can be changed with --lr and --iters