# 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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