Stability of mechanical impedence controlled manipulators in workspace coordinates

The design of a controller for the implementation of impedance control for small interaction forces is considered. Impedance control refers to the specification of the mechanical impedance of the manipulator seen from the environment. The stability of the complete system with coordinate transformations is analyzed and a method for reducing the effect of Jacobian matrices with large condition numbers on stability test conservativeness is derived. An actual implementation of a stiffness controller (zero mass and damping) on the Rhino XR-1 robot is described.