Robot "damping"

There are a few demostrations on the internet of damped robotic arms or cheetahs.

The damping is probably a combination of actions, with inputs from various sensors,, however ONE action appears to be that the servos provide feedback which the robot uses to send a particular brand of positional information to the servo which results in more stability and reduced oscillation or "springiness".

Is it possible to use those cheap hobby servos and a fairly humble program to achieve some similar (if lower quality) effect??

I think that it will be possible, somehow. I’d guess that force sensors will provide the most useful feedback for smooth movements. Instead of direct force measurement it may be possible to measure the motor current, which increases with the required force. As long as the servos are not overloaded, they reach and keep the given position, so that no extra position feedback is required.