Prism constant question
I can only speak to Trimble or Leica. Leica has a very accurate 360 prism if you take care to orient the yellow triangle back towards the instrument (it's looking at you, but used to align like a sight). The larger circular prisms are better for all robotics as long as they're good quality prisms & pointed correctly. Some even have aiming sights (like on some traverse sets). The Trimble 360 prism is the least accurate of the bunch, but is till capable of tight work if you take effort to point on entire peice of glass back at the robot. The passive 360 has an odd number of prisms, the active has an even number - so you can use a divider between the prisms as a "sight" on the passive one, and on of the prisms themselves as a "sight" on the active one. The new MT1000 prism (disco ball thing) is supposed to be more accurate by default. If you're dealing with a lot of slope none of the 360's are all that great. If pointing accuracy becomes a major concern, say for tight control or layout, invest in a nodal prism. They usually have a weird constant, but there is no error intruduced by pointing.
I haven't used a brand new Leica much, I know they actually don't turn to center - only apply a calculated offset. I think prism pointing would still affect performance, though.