RE: Infinitely Variable Driven Platform
I have no sources for this but have sen it done and used the end
result on a large lathe.
My dad used to convert older belt driven lathes using an infinitely
variable hydraulic transmission that originally was used on the
landing gear of bombers from WWII.  I would expect this to be a much
more expensive solution and the electronic/electrical solutions
suggested by others but really worked very well.