Geometrical approach to the conservative congruence transformation (CCT) for robotic stiffness control

In this paper, the conservative congruence transformation (CCT) for robot stiffness control is investigated by using geometrical methods. With the strategy of changing basis, it indicates that the formulation of stiffness matrix depends on the choice of coordinates. Thus, we show that the CCT can directly represent the spatial mapping relationship in robotic stiffness control. The CCT theory suggests a generalized transformation relationship in stiffness control and establishes the complete formulation of the 6 × 6 Cartesian stiffness matrix in the presence of external loads.