A Solution of the Inverse Kinematics Problem for a 7-Degrees-of-Freedom Serial Redundant Manipulator Using Grobner Bases Theory

被引：5

作者：

Xavier da Silva, Sergio Ricardo ^{[1
]}

Schnitman, Leizer ^{[1
]}

Cesca Filho, Vitalino ^{[2
]}

机构：

[1] Fed Univ Bahia UFBA, Dept Comp Sci, Mechatron Grad Program, 02 Prof Aristides Novis St, BR-40210630 Salvador, BA, Brazil

[2] Fed Univ Pampa UNIPAMPA, 111 Pedro Anunciacao Ave, BR-96570000 Bage, RS, Brazil

来源：

MATHEMATICAL PROBLEMS IN ENGINEERING | 2021年 / 2021卷

关键词：

ALGORITHM;

D O I：

10.1155/2021/6680687

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

This article presents a solution of the inverse kinematics problem of 7-degrees-of-freedom serial redundant manipulators. A 7-degrees-of-freedom (7-DoF) redundant manipulator can avoid obstacles and thus improve operational performance. However, its inverse kinematics is difficult to solve since it has one more DoF than that necessary for reaching the whole workspace, which causes infinite solutions. In this article, Grobner bases theory is proposed to solve the inverse kinematics. First, the Denavit-Hartenberg model for the manipulator is established. Second, different joint configurations are obtained using Grobner bases theory. All solutions are confirmed with the aid of algebraic computing software, confirming that this method is accurate and easy to be implemented.

引用

页数：14

共 17 条

[1] Bruno Buchberger's PhD thesis 1965: An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal [J].

Buchberger, B .

JOURNAL OF SYMBOLIC COMPUTATION, 2006, 41 (3-4) :475-511

[2]

Cox David, 2013, Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, DOI [DOI 10.1007/978-3-319-16721-3, 10.1007/978-3-319-16721-3, DOI 10.1007/978-0-387-35651-8]

[3]

Craig J.J., 2017, Introduction to robotics: mechanics and control, V4th

[4]

Denavit J., 1955, DESCRIPTION DISPLACE

[5] A new efficient algorithm for computing Grobner bases (F4) [J].

Faugére, JC .

JOURNAL OF PURE AND APPLIED ALGEBRA, 1999, 139 (1-3) :61-88

[6]

Ghosal A., 2006, Robotics: Fundamental Concepts and Analysis

[7]

Hartenberg R., 1965, Kinematic synthesis of linkages

[8]

Kuhlemann I, 2016, PROCEEDINGS OF 2016 THE 2ND INTERNATIONAL CONFERENCE ON CONTROL, AUTOMATION AND ROBOTICS, P49, DOI 10.1109/ICCAR.2016.7486697

[9]

LEE CSG, 1982, COMPUTER, V15, P62, DOI 10.1109/MC.1982.1653917

[10]

Paul R.P., 1981, Robot manipulators: mathematics, programming, and control: the computer control of robot manipulators

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