Why do we not have autonomous helicopters? We see a lot of fixed wing autonomous UAVs. What is preventing this in the case of helicopters? 
I know the helicopter flight dynamics are complicated. But what exactly is the complication in this case?
Don't we? Most consumer and commercial UAV are helicopters.

If you mean military-only models, consider what jobs military-only helos do. It's troop transport or close combat - both necessarily manned functions. Commercial drones suffice for non-military-specific jobs.

If you wonder why they have 4 rotors rather than 1-2, it's lower complexity - quads can use simple fixed rotors and blades, and only vary power on each rotor. Larger drones with turbine power may well go to 1-2 rotors.