I’ve searched for evidence that this already exists, but found none. Today’s invention is a part of gun control logic for military tanks.
When a tank commander selects a target, probably on a touch screen, the system calculates the fastest route to bringing the main gun around to a firing position.
There are three main components to be considered.
1) What is the current rotation rate and direction of the body of the tank?
2) What are these values for the turret relative to the main body?
3) what are the linear speed and direction of the tank body?
Using these values, the system may choose to send power to the sprocket wheels and/or to the turret drive motion. The system works out whether it’s faster to go anti-clockwise or clockwise and selects the various motor settings accordingly.
Since it also understands inertia, the computer dedicated to this modelling task will take account of the need to slow the barrel’s rotational and translational speed, at the end of its movement, so that its time-to-target is minimised.
The crew would probably need racing seats with extra padding, to cope with the sudden changes in speed and direction.