Point-to-Point Reference Trajectories Generation using Frequency-Aware B-Splines/NURBS

Implementing Non-Uniform Rational B-Splines in motion controllers involves challenges like computational complexity, parameterization issues, high-fidelity interpolation needs, real-time processing requirements, hardware limitations, system integration, error management, and the demand for user-friendly design tools, all of which necessitate advanced algorithms, robust hardware, and effective interfaces for successful implementation. Expanding the standard sine profile allows for the creation of a generalized, symmetric, frequency-sensitive basis function for generating point-to-point motion trajectories, while other functions like polynomials, sigmoids, and harmonic models can also be utilized. This study employs the basis function at the jerk level to meet the motion system’s constraints, and time shifts create B-spline-like and NURBS-like profiles for CAD and motion control, eliminating the need for interpolation and curve fitting. Utilizing vector notation and algorithms reduces computational demands on both the CAD and the motion controller sides, enabling real-time implementation. Frequency-sensitive B-spline profiles enhance both repetitive and random walk motions, facilitate data collection, and help segment the workspace into regions with unique frequency characteristics. A model-free approach addresses position-dependent errors, and experimental results validate the effectiveness of these techniques. Robust statistical models based on Multivariate Analysis of Variance are developed to both characterize and assess the performance of a precision motion system under the proposed framework. For example, the mean positioning error of the motion system improved from 2.29 μm to 0.717 μm at the maximum operating frequency of 90 rads under the model-free approach.