  Impedance control is a well-established technique to control interaction
forces in robotics. However, real implementations of impedance control with an
inner loop may suffer from several limitations. Although common practice in
designing nested control systems is to maximize the bandwidth of the inner loop
to improve tracking performance, it may not be the most suitable approach when
a certain range of impedance parameters has to be rendered. In particular, it
turns out that the viable range of stable stiffness and damping values can be
strongly affected by the bandwidth of the inner control loops (e.g. a torque
loop) as well as by the filtering and sampling frequency. This paper provides
an extensive analysis on how these aspects influence the stability region of
impedance parameters as well as the passivity of the system. This will be
supported by both simulations and experimental data. Moreover, a methodology
for designing joint impedance controllers based on an inner torque loop and a
positive velocity feedback loop will be presented. The goal of the velocity
feedback is to increase (given the constraints to preserve stability) the
bandwidth of the torque loop without the need of a complex controller.
