Efficient formulation of hexapod kinematics enabling real time adaptive feedforward control

The tracking performance of manipulators can be improved considerably by adaptive feedforward control (AFFC). However, complex kinematics hinder the application to parallel kinematic manipulators (PKMs). This paper proposes a compact and efficient formulation of the full PKM kinematics enabling real-time application of AFFC to complex PKMs. The efficient kinematic formulation is the basis for the inverse dynamics used to compute the feedforward signal. A Kalman filter is used for online estimation of the parameters in the equations of motion. A parallel multi-rate implementation is used, which, together with the efficient kinematic formulation, allows for a feedforward sampling time as low as 0.5 ms. The parameters are updated every 30ms, which suffices to track the slow parameter variations. The application to a highly repeatable flexure-based manipulator is considered. Experimental results for the manipulator show that the tracking error can be reduced by 97.5% compared to using feedback control only.