A Geometric Framework for Stiffness Mappings of Compliant Robotic Systems on the Special Euclidean Group

In this article, the stiffness mapping of compliant robotic systems is generalized to the special Euclidean group SE(3). A geometric framework is proposed to unify the existing stiffness models. We analyze the symmetry and exactness relationship between joint and Cartesian stiffness matrices in this framework. To verify the theoretical results, motions of different types of manipulators, including serial and parallel ones, are tested in simulations. Based on the conservative property of the stiffness matrix, an impedance control strategy to achieve variable stiffness is proposed. In addition, a feasible stiffness identification method is developed using the skew-symmetric structure of the stiffness matrix.