Using dual quaternions in robotics

We advocate for the use of dual quaternions to represent poses and twists for robotics. We show how to represent torques and forces using dual quaternions. We introduce the notion of the Lie derivative, and explain how it can be used to calculate the behavior of actuators. We show how to combine dual quaternions with the Newton-Raphson method to compute forward kinematics for parallel robots. We derive the equations of motion in dual quaternion form. This paper contains results we have not seen before, which are listed in the conclusion.