If the body is a ball, the head would have to fly. You could make the head like a drone with a single fan with control surfaces under it to control its motion.
Here is an example:
https://www.youtube.com/watch?v=2RK_rl6oXfo . There are several other similar projects.
Very noisy and very short time it could stand.
A bouncing head does not contradict mechanical linkage between two hemispherical wheels.
If you have a large wheel, then you would also want some shock-absorbers - and those would allow the sphere to move up and down a little bit relative to the centre of mass.
I see a big issue with hemispherical wheels: the contact points with the ground are very close together.
While you could compensate with active electronics against falling forwards and backwards (like a Segway does), that wouldn't compensate for the ball rolling sideways.
Also, it would be difficult to turn by driving the wheels at different speeds (like a tank, Segway and R2 units).
With solid hemispheres you would be better to build them like a unicycle ... and I can see two ways to keep the balance and turn:
1. You do like a unicyclist and wave weighted arms around inside the sphere to keep the balance and turn the ball.
2. You make the machine a gyroscope, spin a large heavy wheel inside, and you turn by jumping or not at all.
Either would be very complex though and the droid could stand up only for as long as the battery lasts - but longer than if the head flew.
The easiest solution I can see, is to not have
hard hemispheres but to make them out of rubber. Inside the hemispheres would be a segway-like robot that uses wheels at a reasonable distance apart.
The rubber hemispheres would flatten where the wheels touch the ground through the rubber skin. You would also want some way to stretch the rubber back into a sphere everywhere else. If the wheels would have tires then you wouldn't need additional shock-absorbers.
