Kinematic control based on dual quaternion algebra and its application to robot manipulators

Abstract

The Lie group of unit quaternions and unit dual quaternions are denoted by Spin(3) and Spin(3) R 3 . Additional symbols and notationsMatrices corresponding to task Jacobians are represented by J . Particularly, the task Jacobian that maps the joint velocity vector to an R 8 -representation of the end-effector pose is denoted by J vec whereas the task Jacobian that maps the joint velocity vector to the unit dual quaternion twist is denoted by J ω .The variable γ is reserved to denote the upper bound of the H ∞ induced norm. Particularly, γ O and γ T are used to denote the noise-to-error upper bound in the H ∞ sense for the rotation and translational errors, respectively.