I did some lab testing with SICK OD Mini Prime laser distance sensor, and eSeries UR3.
Minimum distance that you can program is 0.1mm. Tool doesn’t move when programmed to smaller distances.
Below you can see graph of data captured by robot when moving between 2 waypoints 0.1mm apart from each other on tool X axis.
Distance sensor is connected to analog input with sensitivity set to 1mA/0.1mm. Actual and target poses are scaled in meters.
This was captured in lab conditions with no load attached to the tool flange. I’d still advice getting demo with real life scenario.