Dual quaternion control: a review of recent results within motion control

Abstract

This paper presents a review of recent results in the field of dual quaternion based motion control. In addition, we derive two control laws for trajectory tracking control of a fully actuated rigid-body based on the resemblance of dual quaternion kinematics and dynamics to the quaternion based rotational kinematics and dynamics. A velocity error sliding surface and an integrator backstepping controller is derived and uniform asymptotic stability is shown, and the former is subsequently extended to the problem of trajectory tracking of the underactuated quadrotor platform using the hand-position technique. Numerical simulations demonstrate the theoretical results.