# What is the achievable stiffness of a impedance/admittance controlled robot (incl. haptic devices), given its structural and control stiffnesses?

EDIT: I realised I missed the point of the paper completely (thanks to very-skim reading ;) ). So, this part of it I'm relating to is about how much damping - not how much stiffness - should we display to obtain stability, given a structural stiffness. I changed the question accordingly - what is achievable stiffness of a impedance/admittance controlled robot, given its structural and control stiffnesses? (Stiffness/compliance is, of course, mathematically just one of the terms in total impedance/admittance)

Let us consider a haptic device with mechanical and control parts, and mechanical part is not infinitely rigid (compliant). Basically, it would be a robot with impedance or admittance control. I thought perceivable stiffness can be just as simple as serial connection of two stiffnesses - and so the stiffer mechanical structure is, the better it can display control stiffness:

$k = \frac{k_e k_c}{k_e + k_c}$

where $k_c$ is stiffness control. Still, I cannot find any confirmation to this, although something very similar is stated in Samur's "Performance Metrics for Haptic Interfaces". I would be very grateful if you could refer me to some sources or just plain prove it wrong or right (:

In a paper (here, p. 728) I only found stability condition for virtual damping value in relation to virtual stiffness, given structural stiffness.