Input shaping reference commands for trajectory following Cartesian machines

This work shows research into how input shaping, a real-time filtering method that is reviewed, affects spatial trajectory following ability for machines that can be modelled as two-orthogonal flexible modes. We prove that input shaping improves the tracking ability of two-dimensional circular and square trajectories for nearly all values of command speed (feedrate) as it is used in numerical controlled machine tools, and high speed coordinate measuring machines. An approximate high feedrate boundary for zero tracking error using input shaping might have been found. Even in the presence of large modelling errors, robust shapers have demonstrated important contour error reduction. This paper also develops a coherent input shaping scheme for the command generator velocity profile that is preferable to shape the single axis position signals.