Passivity-Based Control of Manipulator-Stage Systems on Vertical Flexible Beam

Abstract

We develop a novel passivity-based control framework of a manipulator-stage system sitting on a vertical flexible beam. We first model the vertical flexible beam by using Euler-Bernoulli theory and modal approximation while utilizing certain boundary conditions to take into account the effect of the gravity and interaction wrench between the manipulator-stage system and the beam. To separately achieve two control objectives, i.e. the joint tracking and the vibration suppression, we utilize the passive decomposition to split the dynamics into: 1) the stage and beam dynamics; and 2) its orthogonal complement, which converges to the robotic manipulator dynamics as the vibration is subdued. We further show that the linearized stage-beam dynamics is controllable and design an LQR control to stabilize the beam vibration only by using the stage motion. We also design control for the orthogonal complement dynamics in such a way that it can attain the manipulator joint tracking asymptotically as the vibration is suppressed. Experiments are also performed to verify the manipulator joint tracking while the vibration is suppressed internally via the stage motion.