I suggest to go with the solution mentioned in post #3.
There is nothing wrong with predefined actions. They exactly describe how an animation should be performed. They can include limits, non-linear animation and any “hick-up” you want. You can even see the graphs in an graphical editor. You can create endless actions (see extend mode in graph editor). Predefined actions are much easier to design then trying to develop formulas to create the necessary transformations via code.
An action is like a function: y = fct(x)
you control the current output with the keyframe: pose = action( keyframe )
Another benefit of this view is, you can include as many transformations as you like. You are not restricted to a single bone/channel. E.g. you can manipulate a complete walkcycle with just one action (try that with Python ).
User controlled playback
Now you might argument: It always plays the same.
It plays the same only, if you use the (most commonly use-case) play mode. You can determine what keyframe to be played by using the property mode at the ActionActuator. (Do not forget to activate the actuator after modifying the property).
This way you can change the property with any method you like (PropertyActuators, Python). This is a pretty simple but very powerful method.
You still think you need a more dynamic animation?
Indeed a single action is pretty “one dimensional” as you have one input (the keyframe) only. But you can combine actions to add another input. This way you get a two (and more-) dimensional action:
pose = fct( actionA(keyframeA, actionB(keyframeB) )
There are several methods to achieve this effect:
A) have a separate Armature for each action (pretty heavy and hard to manage)
B) have separate bones for each action (actions should not share any channels/bones)
C) use action layers to blend actions together.
If you look at a real robot you will find the same method: Each actuator is an engine that follows exactly one path (turning or translating) within some limits. The complex motion is a result of combining the “atomic” animations.