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Journal:Applied Mathematical Modelling

Key Words:Inverse kinematics; Vector polynomial system; Elimination method; Dixon resultant; General decoupling manipulator

Abstract:Variable elimination of high dimensional polynomials is an essential problem for robot inverse kinematics, but it is hard to approach both high efficiency and precision simultaneously. This study proposes a unique elimination method for vector polynomial systems established for kinematic modelling of six-revolute serial manipulators, and then applies it to derive analytical inverse kinematic solutions in real time with high absolute precision. To begin, the kinematic modelling equations are parameterized into a non-redundant vector polynomial system, so as to make full use of vector properties in elimination processing. After that, an improved elimination method based on the Dixon resultant is proposed as a solution to the polynomial computation issue. Since there exist some duplicate terms in the Dixon polynomial, a linear constrained Dixon matrix is created by extracting linear terms from variable sequences. Furthermore, the inverse kinematic problem for six-revolute manipulators is addressed based on the elimination method, wherein the configurations of general decoupling manipulators are designed considering both precise machining and fast solutions. The proposed formulations are ported into the core algorithm of professional software, demonstrating that they are highly accurate and real-time required for precise manipulators of automatic use.

Indexed by:Journal paper

ISSN No.:0307-904X

Translation or Not:no

Date of Publication:2022-07-02