Generalised Modelling, Simulation and Control Design for Manipulators with Flexible Links and Flexible/Rigid Joints

In this paper, a generalised Euler-Lagrange assumed modes for formulation for a manipulator with multiple flexible links and flexible joints is presented. The general modelling scheme is validated through computer simulations and analysis of the simplified single and two link manipulator models, with two different combinations of links and joints, namely first, flexible link (s) and rigid joint(s) and the second, flexible link(s) and flexible joint(s). To resolve the control complexity associated with the under-actuated flexible link and flexible joint manipulator, a singular perturbation model and control design for tracking are proposed with simultaneous suppression of the tip and joint vibrations.