B-spline-decomposition-based approach to multi-axis trajectory tracking: Nanomanipulation example

In this article, a B-spline-decomposition (BSD)-based approach to output tracking with preview is explored to achieve high-speed, large-range nanomanipulation in experiments. When a finite (in time) preview of the future desired trajectory is available, precision output tracking of nonminimum-phase (NMP) systems can be achieved by using the preview-based stable-inversion technique. The performance of the preview-based inversion approach, however, can be sensitive to uncertainties of system dynamics. Moreover, the computation involved in the implementation can be demanding. The BSD approach has been developed recently to address these challenges. In the BSD approach, a library of desired output elements and their corresponding input elements is constructed a priori, then the previewed future desired trajectory is decomposed into a summation of finite number of output elements, and the control input is synthesized by using the corresponding input elements with chosen pre- and post-actuation times. In this work, we demonstrate and evaluate the BSD technique for precision tracking with preview 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 by using the BSD technique over using feedback control alone.