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This work is focused on impedance control of robot manipulators performing six-degree-of-freedom interaction tasks. An energy-based formulation leads to formally deriving the dynamic equation characterizing a mechanical impedance at the end effector. An inverse dynamics strategy with contact force and moment measurement is adopted to obtain a configuration-independent desired impedance. For given contact force and moment, an impedance control scheme is proposed acting on both translational displacement and rotational displacement where end-effector orientation is described using a singularity-free representation in terms of a unitary quaternion. Experimental results on an industrial robot with open control architecture are presented.
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Siciliano et al. (2002) studied this question.