Robot impedance control with nondiagonal stiffness

Impedance control is a widely adopted strategy to execute tasks involving i nteraction of a robot manipulator with the environment. The goal: is to imp ose an end-effector dynamic behavior described by a mechanical impedance. A crucial point is the definition of the elastic contribution in the impedan ce equation according to the task requirements; this is achieved by a prope r choice of the equivalent stiffness matrix. In this paper an energy-based argument is used to derive the dynamic equation of a mechanical impedance c haracterized by a translational part and a rotational part. The adoption of unit quaternions to describe orientation displacements leads to a geometri cally consistent definition of the stiffness in the impedance equation. Rem arkably, off-diagonal elements in the equivalent stiffness matrix are consi dered; namely, coupling forces with orientation displacements and coupling moments with position displacements. The equilibrium and the stability of t he impedance equation are discussed as well as the geometric properties of the stiffness matrix.