Hyper Dual Quaternions representation of rigid bodies kinematics

Hyper-Dual Quaternions, HDQ, are first introduced in this paper. Utilizing the Hyper-Dual Numbers, HDN, Dual Quaternions, DQ, and hyper-dual angle, the general expression of HDQ is obtained. Rigid single- and multi-body kinematics such as in a serial robot kinematics, are then expressed in HDQ form. Taking advantage of the dual numbers' automatic differentiation feature, HDQ encompasses both body pose (translational and rotational) and body velocities in a compact form with no need for further pose differentiation. (C) 2020 Elsevier Ltd. All rights reserved.