Time/Space-Separation-Based Gaussian Process Modeling for the Cross-Coupling Effect of a 2-DOF Nanopositioning Stage

Multiple-axis nanopositioning stages are widely used in nanotechnology, which suffer not only from hysteresis nonlinearity but also from cross-coupling effect. A vast body of literature has been proposed to model the hysteresis nonlinearity. However, few efforts have been made to describe the cross-coupling effect due to its complexity, and most of the presented works considered only the effect of the motion of the other axis from the aspect of lumped system. Actually, the cross-coupling effect has a spatiotemporal behavior, which means that it depends not only on the motion of the other axis but also on the contacting position of the axes. In this article, a time/space-separation-based Gaussian process modeling method is developed to describe the spatiotemporal cross-coupling effect. The spatiotemporal output of the system is first separated into a few spatial basis functions and the corresponding temporal coefficients by using the principle component analysis. Then, the frequency-separation-based Gaussian process is introduced to model the system dynamics in a low-dimensional temporal domain. Finally, by using the time/space synthesis, the spatiotemporal cross-coupling model can be constructed. Experiments are presented to demonstrate the effectiveness of this modeling method.