Rigid body motion stability of translation and rotation without linear and angular velocity measurements via dual quaternion

In this paper, we propose dual quaternion based dynamic output feedbacks for the translational and rotational stability problem of a rigid body without linear velocity and angular velocity measurements. Dual quaternion is a new kind of tools to express the motion of rigid bodies in 3D space, including translation and rotation. Our approach consists of an output feedback controller and introducing an auxiliary system whose input is the relative error between the states of the rigid body and the states of the auxiliary system. The resulting linear and angular velocity free control algorithm guarantees the asymptotical stability of the rigid body. Next, a stability algorithm based on unit dual quaternion is also proposed for the rigid body under its general dynamics. One simulation is provided to show the effectiveness of the proposed control algorithm.