Simultaneous attitude and position tracking using dual quaternion parameterized dynamics

This paper presents the simultaneous attitude and position control of rigid bodies using the unit dual quaternion. A dual quaternion is a compound of a unit quaternion and a translational vector, using the dual number formalization, such that the real part represents the rotation and the dual part, the translation transformation. Since the unit dual quaternion can be used to represent the rigid body dynamics in the 3D space, then the error dual quaternion can be used to design feedback control laws for both set-point stabilization, and attitude and position tracking. Simulation results using a rigid-body model are presented to show the performance of the dual quaternion formalism for simultaneous attitude and position control.