Symbolic analysis of the base parameters for closed-chain robots based on the completion procedure

Abstract

This paper presents a symbolic analysis of the base parameters for closed-chain robots by means of the completion procedure in polynomial ideal theory. The regressor of the robot dynamics is represented as a matrix of multivariate polynomials and reduced to the "normal form" based on Buchbergers' algorithm by constructing reduced Grobner bases from kinematic constraint equations. The linear independence of column vectors of the reduced regressor is examined by the Gauss-Jordan elimination method. The original dynamic parameters are regrouped and some of them are eliminated based on the results. This method derives all the base parameters systematically in theory. Two examples are presented to illustrate the merits of the new method.