output velocity equation of compliance control

Robotics Asked by rrrruo on October 3, 2021

I am trying to implement a compliance controller for a robot arm and stumbled upon an existing code snippet where the compliance velocity of the endeffector is calculated by:

$v_{out} = v_{in} + frac{F}{K} – frac{dot{F}}{B} $

where $F$ is a 6D wrench vector, $K$ is a given stiffness with the units $frac{N}{m/s}$ & $frac{Nm}{rad/s}$ and $B$ is a given damping with the units $frac{N}{m}$ & $frac{Nm}{rad}$.

I don’t understand where this equation comes from, in particular the second part. In (cartesian space) admittance control, there is e.g. the equation $dot{x}=C cdot F$, where C is the compliance, thus the inverse of stiffness $K$. But how to explain the second part $frac{dot F}{B}$? Is there any reference literature which are recommended?

Many thanks in advance!

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