Already the most glaring example, and which we tend to forget a little, is that the Internet has made it possible (and still makes it possible) to avoid an incalculable amount of physical travel by people, hence saving fantastic fuel.
I don't know if we can put that to the benefit of something "tick", but we had ABC2019 crying over the electrical consumption of server farms (which probably consume less than vehicles having moved in parkings)

In the field of home automation, there are heating savings made by avoiding heating all the time, since you can turn on the heating a short time before returning home, and leave it the rest of the time at a minimum ... It is well known, but just to say that the domains in "tick" overlap, in different cases of their uses, so there is a combination of several effects (ordering by internet, travel avoided, and economy of central heating... To which we can add that transport can be tolerated "a little longer", by occupying minds in public transport thanks to mobile telephony/TV, which here also avoids the use of individual vehicles. Transport that can be carried out by automatic shuttles, optimizing consumption... Etc... Etc...
So yes I think, there are favorable impacts on the environment, not necessarily on the use of robotics / home automation directly as a tool, but with what we do with it / s in a way reasoned, even combined.