Robot Kinematics, using Dual Quaternions

Abstract

From the point of view of classical mechanics, deriving the equations of motion for systems of coupled rigid bodies is regarded as a straightforward procedure: once a suitable set of generalized coordinates and reference frames have been chosen, what remains is to either apply Lagrange’s equations or Newton and Euler’s equations to obtain the differential equations of motion. As the complexity of multibody system increases, the need for more elegant formulation of the equation of motion becomes an issue of paramount importance. Our primary focus is on the kinematic analysis of rigid bodies and serial manipulators (robotic systems)  using simultaneously, both homogeneous transformations (4x4) matrices and Dual Quaternions, for the sake of results comparisons (cost,complexity,storage capacity etc.) . This paper has been done mainly for educational and peadagogical purposes, hoping that the scientific community will finally adopt and use Dual Quaternions at least when dealing with multibody systems and specially robotics.DOI: http://dx.doi.org/10.11591/ijra.v1i1.275