Improved Trajectory Planning using Arbitrary Power Polynomials

Abstract

Increasing demands for higher operational speeds, the need for flexible machinery and recent developments in microchip technology have made programmable machine systems an attractive alternative to conventional systems. However, some difficulties still remain for proper control of programmable systems, especially at higher speeds. These can be categorized into two groups: trajectory planning and trajectory tracking. Conventional trajectory planning methods are ineffective for general application, especially when velocity and acceleration conditions are included. There are many mathematical functions but polynomials are shown to be the most versatile for trajectory planning; however, these can give curves with unexpected oscillations, commonly called meandering. Tracking of a motion in this situation could engender severe practical problems. In this study, a new interpolation method using polynomials with arbitrary powers is proposed to overcome this disadvantage.