Application of Hyper Dual Numbers to Multibody Kinematics

Abstract

Hyperdual numbers (HDNs) are applied in this paper to multibody kinematics. First, the hyperdual angle that encompasses a body's position, orientation, as well as its velocity, is defined as an element of the hyperdual transformation matrix. Then, the “automatic differentiationâ€‌ 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 hyperdual 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.