Years ago, I had the opportunity to board a Bell 407 for a long distance flight and put every question related to helicopters that crossed my mind to the pilot when we were forced to land due to visibility issue and also while we refueled.
I realize now that I've missed something important: do rotorcraft including helicopters have autopilots like fixed wing aircraft do, or is that ruled out due to their peculiar flight mechanics?
Yes, helicopters can be fitted with autopilots. Some are very simple, others are quite advanced. The more advanced ones can, for instance, follow a pre-programmed route, climb/descent to a pre-selected altitude, fly an ILS approach, perform a go-around automatically.
They are not ordinarily found in small helicopters due to cost and lack of necessity. All modern offshore helicopters that I've encountered have them and they are used extensively. Usually they are engaged shortly after take-off and disengaged shortly before landing.
This Article about HeliSAS seems to elude to the fact they can and certified systems exist. The specs of this helicopter list it as having
...Airbus Helicopters’ advanced Helionix® avionics suite with a 4-axis digital autopilot
