Product of the day - iRobot i755020, i7 Plus Robotic Vacuum Cleaner
Having seen how good the mid range roomba my parents have was at cleaning their carpets I took the plunge and went for this almost top of the range self-emptying model. It has not disappointed. There are reviews it there saying to wait until it's fixed. Well, I've had mine for about 4 months now and it's given me no trouble at all so maybe I'm lucky, or maybe they've dealt with the issues others had.
I use it in a completely dumb mode and trigger it from the button on it's back every time so I can't review it's Alexa integration but the killer win for me is how hands-off it is with the self-emptying bin. It takes itself back to base and empties itself, then rolls out and carries on. For a lazy person like me, it's great. You just leave it to it and get on with your life.
Another good point is this model has rubbery rollers so doesn't get hair caught up in it so much. It does occasionally need the rollers to be lifted out (very easy) and cleaned (also very easy) but as we have two cats and a long haired lady in the house it's better than I'd hoped in this respect. 

Yes, it's a lot of cash, but a job I didn't like doing has gone away.

Click Here for iRobot i755020
IrobotIrobot i755020Vacuum cleaner