Are there full scale helicopters capable of sustaining inverted flight? Background

I'm a model aviation enthusiast and really enjoy seeing how far people can push the limits of aerobatics. Model aircraft are able to push the limits well beyond full scale due to their small size. I understand that this is only possible because models are small* so they can withstand forces that would kill any occupants in a manned craft. Also, model aircraft are typically overpowered when compared to full scale aircraft

For example, I don't have a model plane that isn't capable of a 30 degree climb, and it's quite common for aerobatic model airplanes to have thrust to weight ratios exceeding 1.5:1 or even 2:1. 

Question

When I first saw some of what model helicopters were capable of I was blown away. Having also seen some full scale helicopter aerobatics (Red Bull Demonstration) I've been wondering just what full scale helicopters are capable of. 

In the Red Bull Demonstration it looked like the helicopter might use some negative (or at least neutral) collective while rolling, however it did not appear that it would have enough to sustain an inverted hover or inverted flight. This got me wondering: has there been a full scale helicopter capable of sustaining inverted flight or an inverted hover (which takes even more power)? If there hasn't, would it be possible to purpose build a helicopter that would be capable of doing so? 

Note

I'm just wondering about technical possibility of creating a machine capable of this maneuver. For the scope of this question, please ignore the regulatory, legal, and economical obstacles that would need to be overcome to attempt such a feat (not to mention finding a pilot willing to try).

Also, I'm only asking about full scale inverted flight. I understand physics get in the way very fast if someone were to try to design a full scale helicopter capable of all the aerobatics models do.

*some model airplanes and helicopters can be greater than 35% full scale, but that is still small when compared to full scale aircraft.
There is no real helicopter capable of sustained inverted flight and certainly not of hovering inverted.  

The simple reason is that there is no operational need to do so.

Is it theoretically possible?  Yes, but you have a lot of engineering problems to overcome.  In addition to inverted fuel and oil systems, the rotor head will be much more complex than it needs to be.

When flying normally, the fuselage effectively hangs like a pendulum underneath the rotor with a large nut (OK, it's more complex than that) holding the rotor onto the rotor shaft hub.  The rotor pulls the fuselage up.

To fly inverted, the rotor must be able to push the fuselage up so the hub would have to be engineered to apply and withstand the appropriate forces in both directions.

Then, the rotating blade cuffs, and associated hinges, must be designed so that the blades can have negative pitch (as seen from the normal attitude) across the full range.  In turn, this means that the collective mechanism must be designed so that it is possible to set positive and negative pitch as required.  

The blades would also need to be more rigid, so that they do not cone excessively and contact the fuselage.  This would add more forces to the head joints which would need to be strengthened.

Finally, you must "reverse" the cyclic controls so that the expected collective pressure, cyclic back; nose up; reduce speed; works in the opposite sense.

I've probably not considered other factors.

All of this would add significant complexity and weight which, given that there is no requirement for inverted flight, will not happen.

By the way, the power required to fly or hover inverted would be the same as for normal flight.  There is no intrinsic reason why inverted flight would need more power - blades rotating at a certain speed, with a particular angle of attack will generate the same amount of lift no matter which way they are pointing.

The reason model helicopters can do this is that the ratio of the weight of the rotor to the weight of the fuselage is much lower than for a real helicopter, and therefore requires a lot less power to produce the required lift, and models have a much higher power to weight ratio.

The reason real helicopters can go inverted for a short time in aerobatic manoeuvres is because the momentum on the fuselage is pulling away from the rotor so that the lift vector pointing up, toward the fuselage, is countered. Consider an outside loop, which would be impossible, since the momentum of the fuselage and the lift vector would combine.

You should be able to demonstrate this in a model with a normally designed rigid head.  Add some (secure) ballast in the fuselage until you must accelerate in ground effect to gain translational lift in order to be able to climb out.  Now try to fly inverted!