Control of Oriented Mechanical systems: A Method Based on Dual Quaternion

Simultaneous position and attitude control without linear and angular velocity feedback using dual quaternions

“…The classical definition of quaternion is q = q 1 i + q 2 j + q 3 k + q 4 , where q 1 , q 2 , q 3 , q 4 ∈ R and i, j, and k satisfy the following properties [5]:…”

“…It has been argued that dual quaternions are the most compact and efficient way to simultaneously express the translation and rotation of robotic kinematic chains [13], [14]. Moreover, it has been shown that combined position and attitude control laws based on dual quaternions automatically take into account the natural coupling between the rotational and translational motion [5], [6]. Additionally, dual quaternions allow combined position and attitude control laws to be written compactly as a single control law.…”

“…They provide a compact way to represent not only the attitude but also the position of a rigid body. They have been successfully applied to inertial navigation [1], rigid body control [2], [3], [4], [5], [6], [7], spacecraft formation flying [8], inverse kinematic analysis [9], computer vision [10], [11] and animation [12]. It has been argued that dual quaternions are the most compact and efficient way to simultaneously express the translation and rotation of robotic kinematic chains [13], [14].…”

Fast adaptive pose tracking control for satellites via dual quaternion upon non-certainty equivalence principle

“…It is shown that the unit dual quaternion is the most compact and computationally efficient tool among others [1,5,6]. Due to such efficiency of the unit dual quaternion in 6-DOF rigid body dynamics, it is recently adopted to the controller design problems in [3,4,7,9,12,14,15] to name a few.…”

Dual quaternion-based bimodal global control for robust rigid body pose kinematic stabilization

“…There are few works on unwinding avoidance in the context of pose stabilization using unit dual quaternions [12], [20], [21], [22]. All of them are based on a discontinuous feedback approach and are prone to chattering for initial conditions arbitrarily close to the discontinuity.…”