The spatial conservative congruence transformation for manipulator stiffness modeling with coordinate and noncoordinate bases

Abstract

This paper presents systematic methods to approach the spatial conservative congruence transformation (SCCT) and applies it to the stiffness transformation and matrices of robotic systems via the strategy of changing basis. Through geometrical analysis, the realization of the Cartesian stiffness of manipulators is shown to be basis dependent. We illustrate that the SCCT is conservative as well as directly represents the spatial stiffness mapping relationship for robotic stiffness control. Examples of the serial manipulators are given to help one to better understand the source of the asymmetric 6×6 Cartesian stiffness matrix in the presence of external loads using the SCCT algorithm. The SCCT suggests an explicit and generalized stiffness transformation relationship for robotic systems. © 2005 Wiley Periodicals, Inc.