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Stephen, J., Wine, S. and Le Bihan, N. (2006) Quaternion Singular Value Decomposition Based on Bidiagonalization to a Real or Complex Matrix Using Quaternion Householder Transformations. Applied Mathematics and Computation, 128, 727-738.

has been cited by the following article:

• TITLE: 6R Robot Inverse Solution Algorithm Based on Quaternion Matrix and Groebner Base

  AUTHORS: Zhensong Ni, Ruikun Wu

  KEYWORDS: 6R Robot, Quaternion Matrix, Groebner Base, Inverse Kinematics Analysis

  JOURNAL NAME: Advances in Linear Algebra & Matrix Theory, Vol.8 No.1, March 7, 2018

  ABSTRACT: This article proposes a new algorithm of quaternion and dual quaternion in matrix form. It applies quaternion in special cases of rotated plane, transforming the sine and cosine of the rotation angle into matrix form, then exporting flat quaternions base in two matrix form. It establishes serial 6R manipulator kinematic equations in the form of quaternion matrix. Then five variables are eliminated through linear elimination and application of lexicographic Groebner base. Thus, upper bound of the degree of the equation is determined, which is 16. In this way, a 16-degree equation with single variable is obtained without any extraneous root. This is the first time that quaternion matrix modeling has been used in 6R robot inverse kinematics analysis.