On the Numerical Modelling and Error Compensation for General Gough-Stewart Platform

Abstract

Parallel robots are specially designed to perform high-precision tasks. Nevertheless, manufacturing, assembling and control issues can reduce their capacity to perform adequately. Observing the acquired measurement data with high-precision devices - such as laser-based instruments - it is not surprising that the error data follows patterns or have a structure because, in many cases, the greatest error comes from a mechanical bias introduced by manufacturing issues. Even though we cannot determine with certainty where the error comes from, a pattern in the measured data suggests that it is feasible that it can be modelled and corrected - in a significant proportion - by purely software applications, without the need of disassembling or re-manufacturing any component. This work deals with the problem of finding a mathematical model which adequately fits the error data from the legs of a general Gough-Stewart platform. Hence, we obtain an expression which can be subtracted from the control parameters in order to compensate the inherent mechanical error in the legs. The purpose of this article is two-fold: 1) to present numerical results of the beneficial effects of the error compensation in the legs as well as in the end-effector, and 2) to introduce a numerical methodology to find a model for error compensation and to numerically simulate its effects. Numerical, graphical and statistical evidence of the error improvements, according this methodology, is provided.