The problem here is that you are using two completely different "mechanisms" to drive the two rigs.
IK and FK, just calculate Rotations of Joints... NOTHING Else. In FK the rotation IS the driver, but in IK the Goal position defines the rotations.
Your Robot, uses NO rotational information whatsoever.
The only way I see you have parity between the two systems, is either try and replicate the Model inside Cinema 4D using some sort of Dynamics, Connectors e.t.c., OR find a correlation between parts of the Cinema 4D Rig (Joint rotations) and your controller motors.
So for example:
Make a pose inside C4D. Then try to manually replicate that pose using your controllers. When you're satisfied with the result, compare all the rotations on the Joints, and the Parameters of your Motors (how much did they rotate, and which ones).
By doing this, you may be able to find a correlation between the two systems that's close enough for your Project.
I would start by posing the tip of the nose, as it involves fewer moving parts.
Nice Project. Good luck!