Surely a robotic arm with 3 joints would suffice?
I can imagine it becoming a viable business to dig up a whole street and to install sockets for every space on both sides of the road, for electricity to be sold and parking charged for. We have seen this with the roads being dug up for fibre broadband.
What I don't ever imagine is the street outside my house ever having snake style robot arms every few yards, sockets I could imagine and I could imagine some gold rush where the streets get dug up to cash in on some electric car boom, even before electric cars are ubiquitous. With cable we had the streets dug up for relatively few takers, but in time, with broadband, everyone became dependent on that service.
The arm just has cable guides and the wiring for the plug. There's probably a $10 cell phone camera and a light source near the end, for zeroing in on the power socket. That eliminates the need for high precision positioning. There are no exposed joints, so the whole thing can be encased in a flexible covering for weather protection. If you put springs in the cables, the tentacle will deflect if bumped without damage.
Flexible robots like that have been used industrially, but the low precision and problems with cable wear have been a problem. For the power plug application, neither is a problem - final positioning is camera controlled, and the mechanism operates maybe once an hour in busy locations.
Tesla should have deployed this by now. Something about that thing seems to upset people, though.
Robotic gas station pumps have been built using more common robot technologies.[1][2] They're big, complicated, expensive, and commercial flops.
[1] https://www.youtube.com/watch?v=1YV79YcSvYQ [2] https://www.youtube.com/watch?v=qALPymP1f6Y