Classic Matrix Decompositions in Clifford Algebra with Applications to Kinematic Analysis

One of the advantages of dual algebra is the capability to express in elegant and compact notation operations and transformations on geometric algebra objects. This capability proved to be useful in different areas of engineering such as kinematics, dynamics, robot vision and computer graphics. This paper addresses the problem of extending the QR, SVD and LU matrix decompositions to the field of dual numbers. The availability of these new computational tools should give the possibility of a wider use of Clifford algebra in engineering. The results herein presented are based on the solution of Sylvester type of linear matrix equations. The need of new variable types or overload operators is avoided. Only standard linear algebra library routines are required. Although they have a general validity, the algorithms herein presented are applied to screw motion estimation from body points coordinates and to kinematic synthesis of the function generator RCCC spatial linkage. For a ready use of the matrix algorithms herein proposed, MATLAB source code is listed in the Appendix.