Application of Hyper-Dual Numbers to Multibody Kinematics

Abstract

Hyper-dual numbers (HDNs) are applied in this paper to multibody kinematics. First, the hyper-dual angle that encompasses a body's position, orientation, as well as its velocity, is defined as an element of the hyper-dual transformation matrix. Then, the “automatic differentiation” feature of the dual numbers is used to obtain the second derivative of a body pose. The body's velocity and acceleration are obtained from the elements of the hyper-dual transformation matrix by algebraic manipulations only, with no need for further time derivatives of the body pose. A robot manipulator is presented as an exemplary application of HDNs to multibody kinematics.