Low cost implementation of mathematical functions using piecewise interpolation

Abstract

This paper presents a technique for implementing non-trivial n-dimensional mathematical functions in low-cost real time control systems. The proposed technique uses recursive piecewise multilinear interpolation to approximate the original mathematical function. The paper presents the theoretical basis of the proposed method and the software tool developed for implementation. The main implementation issues are explained in detail. The developed tool includes an automatic C-code generator that implements the best software solution in terms of computational time and cost. Finally, the paper describes the application of the technique to a torque control function for a scara robot.