B-Spline-Decomposition-Based Approach to Multiaxis Trajectory Tracking: Nanomanipulation Example

Abstract

In this brief, a B-spline-decomposition (BSD)-based approach to output tracking with preview is explored to achieve high-speed, large-range nanomanipulation in experiments. The BSD approach is developed to address challenges in preview-based output tracking of nonminimum-phase systems to achieve precision tracking with good robustness to dynamics variations and no demanding online computation. In the BSD approach, a library of output elements and their corresponding input elements is constructed a priori ; then the previewed future desired trajectory is decomposed into a finite number of output elements, and the control input is synthesized using the corresponding input elements with chosen pre- and post-actuation times. The BSD technique uses the uniform B-splines to construct the output elements, the iterative learning control techniques to obtain the input elements, and the stable-inversion theory to quantify the pre- and post-actuation times. In this brief, we demonstrate and evaluate the BSD technique for preview-based precision tracking in experiments, by implementing it to a nanomanipulation application using a scanning probe microscope. The experiments showed that the tracking speed can be substantially improved using the BSD technique over using feedback control alone.