A Review on the Applications of Dual Quaternions

Abstract

This work explores dual quaternions and their applications. First, a theoretical construction begins at dual numbers, extends to dual vectors, and culminates in dual quaternions. The physical foundations behind the developed theory lie in two important fundamentals: Chasles’ Theorem and the Transference Principle. The former addresses how to represent rigid-body motion whereas the latter provides a method for operating on it. This combination presents dual quaternions as a framework for modeling rigid mechanical systems, both kinematically and kinetically, in a compact, elegant and performant way. Next, a review on the applications of dual quaternions is carried out, providing a general overview of all applications. Important subjects are further detailed, these being the kinematics and dynamics of rigid bodies and mechanisms (both serial and parallel), control and motion interpolation. Discussions regarding dual quaternions and their applications are undertaken, highlighting open questions and research gaps. The advantages and disadvantages of using dual quaternions are summarized. Lastly, conclusions and future directions of research are presented.