Stiffness control on redundant manipulators: a unique and kinematically consistent solution

When applying stiffness control to redundant manipulators, three kinematic factors are considered due to the redundancy: (i) how to use the inverse kinematics to obtain the redundant joint displacement dθ from Cartesian displacement dx, (ii) how to use the inverse kinematics to obtain Cartesian force f from redundant joint torque τ, and (iii) how to obtain Cartesian stiffness matrix K_p from joint stiffness matrix K_θ. This paper applies the conservative congruence transformation (CCT) to redundant manipulators, and proposes a unique and kinematically correct solution of the stiffness control for redundant manipulators. The concept of generalized instantaneous potential energy (GIPE) is introduced. Results of numerical simulation using both Cartesian-based and joint-based control schemes are presented and discussed.