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Very nice. When it is said that it is ignoring the orientation, is this simply that the vision systems returns only X and Y coordinate to the robot?
If you look at the following
discussion, it looks like if you are teaching a round/symmetrical object, if your pick position is not perfectly in the middle, there seems to be a match angle that still affects the repeatability of the picking position. What I understand from that discussion is that the angle found between the pattern that you taught and the pattern that you found still has an impact on position result. Here is a picture to try to illustrate my point. Can you try to explain in more details how this object orientation feature works.


Your thinking is correct. If you have taught a part that is symmetrical like the circle in your example, the precision and repeatability of the system will depend on your waypoint. The lack of feature on the part will make it difficult to predict in what orientation the vision system will detect the part. The distance between your waypoint and the actual part's center will induce what seems like a decrease the system's repeatability. This is detailed in the
discussion you are referring to.  

When you select the Ignore object orientation checkbox, the robot will move to that X and Y position without rotating its wrist. If you have an offset between the waypoint taught and the actual part's center using a symmetrical part, this offset will be applied even with the Ignore object orientation checkbox. Considering your example, the robot would move to the cross icons in the figure shown.