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Two answer both your questions, yes there are solutions but you need to get your hands dirty and build some of then yourself. I'm assuming you're camera is fixed WRT the workspace and views the working volume of the robot.

  1. We have such a system and we place a fiducial marker taped in place on the table. We use ar_track_alvar but there are a few to choose from. We then have measure as accurately as possible where this maker is relative to the robot base, this we setup as a static transform. Then when you detect the location of the marker in the camera frame you can calculate the extrinsic calibration you want.

  2. Using the process described above our system automatically calibrates itself every time it's started. This avoids having to worry about the camera being knocked when the systems not in use.

Hope this helps.