Spline Input-type Final-state Control for Long-span Motion

Abstract

In high-speed and high-precision positioning control, a method has been proposed to calculate the feedforward input for each time step using a time polynomial through final state control. Furthermore, to avoid numerical issues, a method has also been proposed to divide the positioning time into multiple segments and to obtain the feedforward input using a piecewise polynomial. However, even with this method, numerical issues arise for a long-span motion by higher-order polynomials. In this study, we propose a method that uses a spline function to generate feedforward input. A spline function is a function that continuously connects polynomials in each interval, including derivatives. Since it is numerically more stable than the piecewise polynomial, it is possible to obtain appropriate feedforward inputs even when numerical issues occur even for the piecewise polynomial. The effectiveness of the proposed method is verified through simulations.