Modeling and impedance control of a two-manipulator system handling a flexible beam

In this paper, a hybrid impedance control algorithm is proposed to stabilize a flexible beam handled by two manipulators to a desired position/orientation while suppressing its vibration, and simultaneously control the internal forces between the manipulators and beam. The algorithm combines impedance control and an I-type force feedback by designing a proper response of the interaction force including external and internal forces. No information about the vibration is used in the controller. The asymptotic stability is analyzed based on the vibration dynamics of the beam approximated by m assumed modes, where the number m can be as large as necessary. Three particular cases of using different mode functions are discussed under free-free, clamped-free and pinned-pinned boundary conditions. The validity of the proposed scheme is demonstrated by simulations