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In my opinion, using a robot to calibrate is a good approach as you should get:
As you should be able to generate only a translational motion along the rail, you will have in my opinion to generate multiple translation / orientations (rotations) for the pattern. Or move the rail in translation and in rotation. The ideal case I think would be to cover the space in an hemisphere above the calibration pattern.
The best would be to use a 6 dof robot to move the calibration pattern like in this video.
Almost the same topic: Industrial Calibration Library Update and Presentation.
