On the stiffness control and congruence transformation using the conservative congruence transformation (CCT)

The conservative congruence transformation (CCT), K_θ-K_g=J_θ^TK_pJ_θ, was proposed by Chen and Kao (2000) as the correct congruence transformation to replace the conventional mapping, K_θ=J_θ^TK_pJ_θ, proposed by Salisbury (1980). The conventional mapping was shown, to lead to physically inconsistent results when external force is present in stiffness control. Theoretical proofs are also provided to show the conservative nature of the CCT, and the non-conservative property of the conventional mapping. The CCT is established as the general and valid mapping of the stiffness matrices between the joint and Cartesian spaces of robotic manipulators. In this paper, the work of CCT is extended to a redundant planar manipulator. Numerical simulations are presented to illustrate issues related to the application of generalized inverse in the analysis of redundant manipulators.