But most of robotics is about AI. The electric and hydraulic aspects are old technologies.

I think the battery problem still remains unsolved, other than that yes it's old technology.

I am not sure batteries would be a problem for a household robot. There are power sockets everywhere. And the robot can take a break from most tasks to charge itself (and like a dog it would spend most of the day sleeping anyway!).

An advanced household robot would not even have to take charging breaks because it would be well up to the task of plugging itself in wherever it would work (except for the dog walking part, obviously)

In a similar line of thinking, I am actually kind of surprised that there are no wired quadrocopter swarms yet, that would form a bucket line of short cables to trade range for the power and infinite endurance of a grid connection. I am quite sure that there must be applications where this deal would be worthwhile.

The idea of Thethered UAVs isn't new. Problem is probably the danger of high voltage tethers that they use.

Why do they need a high voltage tether? They don't need a high voltage battery.

To transmit power, its better to use high voltage and low current. Reduces transmission losses; uses much lighter cables. Then where the power is needed its stepped down with transformers or 'buck converters'.

Thanks, those were the trigger words to conjure up an interesting Google results page.

If you need to connect them with a wire, you might as well sustain them in the air with a long stick and spare the energy.

Might still be cheaper (storage, transport, setup, investment) than a crane or scaffolding when you don't need to support heavy loads. And scaling would only be limited by how much power you can push through the chain, whereas sticks need to be quite massive just to support themselves once you go beyond a few meters of length.

It's not a swarm, but I think the one drone from 3D Robotics can be tethered for essentially unlimited flight time. So that's some progress towards what you have in mind.

True, but you also need the interface for AI, which was BD developing. Human facing AI has a serious limitation if it lives 100% in the box.