Higher- Order Cayley Maps for Minimal Parameterization of Rigid Body Motion

Abstract

The main goal of this research is the development of a new approach of minimal parameterization to the rigid body displacement and motion. Using the isomorphism between the Lie group of the rigid displacements and Lie group of the orthogonal dual tensors, a solution of the problem is given. Using the higher-order Rodrigues dual vector, dual Wiener-Milenkovic parameterization, dual orthographic projection, dual Lambert parameters and their shadows the minimal dimensional representations of this problem are obtained.