Feedrate optimization and trajectory control for micro/nanopositioning systems with confined contouring accuracy

Abstract

This article focuses on identifying and fully utilizing the dynamic capabilities of a nanopositioning system to optimally trace a given trajectory. This work develops a framework for abstracting the capabilities of the piezo-actuated nanopositioning systems and a methodology for using these capabilities to generate an optimal trajectory for a particular tool path on a given nanopositioning system while satisfying all the process-related requirements. Several dynamic capabilities of a typical nanopositioning system are identified and modeled as the constraints to drive the optimization problem. First, the velocity and acceleration capabilities of each individual axes are constrained by developing a simplified dynamic model of the performance envelope, which couple velocity and acceleration capabilities of each axis, as a function of displacement. Second, input command bandwidth constraints are introduced to mitigate frequency-related tracking difficulties encountered when traversing sharp geometric features at high velocity. Finally, the accuracy requirement is satisfied by developing a dynamic model of the instantaneous following error to estimate the contour error as a function of the velocity and acceleration at each moment. The above constraints are incorporated into a computationally efficient two-pass algorithm to generate a minimum time feedrate profile for a particular positioning system for any given trajectory. Linear zigzag and cubic spline airfoil trajectories are used to demonstrate the significant improvements in time and contouring accuracy realized through such an approach.