Vibration Control for Manipulators on a Translationally Flexible Base

In this contribution the problem of vibration control is studied on the basis of a fundamental oscillatory system consisting of a mass spring system and an additional mass. The proposed control strategy couples the orbits of the two masses such that both masses stop, while simultaneously stabilizing the second mass to a desired equilibrium. Using a coordinate and input transformation, the control strategy is directly transferred to an n-link manipulator mounted on a base with linear translational stiffness. Using semidefinite Lyapunov functions and a conditional stability argument, it is shown that the proposed control strategy damps out base vibrations, while additionally achieving a desired configuration in the task-space. Finally, the proposed method is compared to a state-of-the-art approach using numerical simulations.