Rigid body motion tracking without linear and angular velocity feedback using dual quaternions

Abstract

This paper takes advantage of a new, recently proposed representation of the combined translational and rotational dynamic equations of motion of a rigid body in terms of dual quaternions. We show that combined position and attitude tracking controllers based on dual quaternions can be developed with relatively low effort from existing attitude-only tracking controllers based on quaternions. We show this by developing an almost globally asymptotically stable nonlinear controller capable of simultaneously following time-varying position and attitude profiles without linear and angular velocity feedback based on an existing attitude-only tracking controller without angular velocity feedback.

Extended Kalman Filter for Spacecraft Pose Estimation Using Dual Quaternions

“…Note that the rotational and translational kinematic equations written in terms of dual quaternions [7].…”

“…As a consequence, the associated computational complexity for implementation is reduced. Moreover, the state estimate of the DQ-MEKF can be directly used by the pose controllers given in [7,8] without additional conversions.…”

“…Recently, Filipe and Tsiotras [7,8] have proposed a new method to develop pose controllers starting from existing attitude-only controllers by using the transfer principle between quaternion and dual quaternion descriptions [9]. In particular, unit dual quaternions offer a compact representation of the position and attitude of a frame with respect to another frame.…”

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

“…For the spacecraft pose control systems, several algorithms with dual quaternion representation are appeared in [3,4,12]. All of them take the advantage of the dual quaternion algebra and succeed in stabilizing the system for both rotational and translational motions simultaneously.…”

“…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.…”