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C. Ott, A. Albu-Schäffer, A. Kugi, G. Hirzinger:
"On the Passivity-Based Impedance Control of Flexible Joint Robots";
IEEE Transactions on Robotics, 24 (2008), 2; 416 - 429.

In this paper, a novel type of impedance controllers for
flexible joint robots is proposed. As a target impedance, a desired
stiffness and damping are considered without inertia shaping. For
this problem, two controllers of different complexity are proposed.
Both have a cascaded structure with an inner torque feedback loop
and an outer impedance controller.For the torque feedback, a physical
interpretation as a scaling of the motor inertia is given, which
allows to incorporate the torque feedback into a passivity-based
analysis. The outer impedance control law is then designed differently
for the two controllers. In the first approach, the stiffness and
damping terms and the gravity compensation term are designed
separately. This outer control loop uses only the motor position
and velocity, but no noncollocated feedback of the joint torques or
link side positions. In combination with the physical interpretation
of torque feedback, this allows us to give a proof of the asymptotic
stability of the closed-loop system based on the passivity properties
of the system. The second control law is a refinement of this
approach, in which the gravity compensation and the stiffness implementation
are designed in a combined way. Thereby, a desired
static stiffness relationship is obtained exactly. Additionally, some
extensions of the controller to viscoelastic joints and to Cartesian
impedance control are given. Finally, some experiments with the
German Aerospace Center (DLR) lightweight robots verify the developed
controllers and show the efficiency of the proposed control
approach.

http://dx.doi.org/10.1109/TRO.2008.915438