Statistical Characterization of Position-Dependent Behavior Using Frequency-Aware B-Spline

Abstract

Stretching the definition of the standard Sine profile allows building a generalized symmetric frequency-aware basis function that can be used to generate reference motion trajectories. Other profiles such as polynomials, sigmoid, and harmonic-based models can be equally used under the proposed technique. Despite being suitable at the level of any higher-order time derivative, in this study, the generic basis function is realized at the jerk level such that the generated signals adhere to the limitations of the driven motion system. Introducing suitable time shifts, replicas of basis functions can be obtained giving rise to B-spline like frequency-aware profiles that can be used to realize the actual motion under any desired kinematical constraints, which are neatly written to reduces the computation burden at the motion controller side. Utilizing mainly the frequency-aware B-spline profiles, frequency-dependent random walk motion is presented and used to collect information about the driven motion system to help in characterizing any position-dependent errors through the statistical means, i.e. Analysis of Variance, and Design of Experiments. This allows dividing the working space in which motion takes place into several spatial regions with preferred frequency contents. The effectiveness of these proposed profiles is shown through hardware experiments using a precision motion system.