Anythings possible…I personally think it would be hysterical.
One guy even built robotic rubiks cube solver with his mindstorms set!
There are big-boy versions of RSX by the name of “motion control.”
Once upon a time I designed some stuff for Allen-Bradley–they make everything you’re likely to need: Allen-Bradley Products | Allen-Bradley
Even some tiny ~$100 ones: Allen-Bradley Products | Allen-Bradley
The drag-and-drop software is even similar to the Lego variety:
Good luck!