Iterative learning of impedance control

This paper proposes an iterative learning control scheme for impedance control of robotic tasks when the tool endpoint covered by soft and deformable material presses a rigid object or environment at a prescribed periodic force pattern. To this end, an iterative learning control scheme for a class of linear dynamical systems with a negative feedback structure is analyzed and convergence of the proposed learning update law after a sufficient number of repetitions is proved. It is shown that this convergence realizes impedance matching in a sense of electric circuit theory of the feedback system can be expressed as a lumped-parameter electric circuit. The iterative learning control scheme is then applied for a case of impedance control of robotic tasks when the characteristics of reproducing force of the deformable material is nonlinear in its displacement and unknown and the tool mass is uncertain. Simulation results are also presented, which show effectiveness of the proposed learning control scheme.