It's not usually that complex (fortunately). You'll often find there's a CMD switch for each of the autopilots ( e.g. three switches for the Left, Centre , and Right autopilot), hence allowing the pilots to select which one of the autopilots is doing the driving.
Some newer types (e.g. 777) have a CMD switch for each pilot, if either is pressed a random autopilot out of the three is engaged.
Are you talking redundancy here or an autopilot for each of the three axes?