Hi there! If you'd like to get up to speed on impact measures, I would recommend these papers and the Reframing Impact sequence.
I think there are proposals that (are hoped? with more research?) might lead to changeable utility functions, i.e. an agents won't try to stop you from changing their utility function.
'Don't self modify' utility functions, I don't think are around yet - the tricky part might be in getting the agent recognize itself, the goal, or something.
Most of what I've seen has revolved around thought experiments (with math).
In AI Alignment: Why It's Hard and Where To Start, at 21:21, Yudkowsky says:
I get the impression that there are some pointers to this in Attainable Utility Preservation (but saying "maximise attainable utility over this set of random utility functions" seems like it would just fire up instrumentally convergent drives), but I could be wrong.
So, 3½ years later, what is the state on "do nothing" utility functions?