Modelling and control of a redundant parallel robotic manipulator — Numerical simulation and experimental results

The aim of this contribution is a systematic approach of modelling, simulation and control of a parallel robotic manipulator. Regarding the framework of structured analysis of dynamical systems, the mathematical description yields a set of differential equations and some additional holonomic constraints which appear as algebraic relations between single state variables. By defining a number of ficticious additional input and output variables this descriptor representation can be interpreted as coupling or constraint control problem. A suitably constructed state feedback that keeps the closed loop system on an invariant manifold of consistent/allowed states yields a state-space model which functions as a basis for numerically stable simulation and exterior controller design. Using an extended Kalman filter as state observer the derived control law is applied to the robotic system in the lab and shows the general applicability of the proposed procedure.