Pose tracking without linearand angular-velocity feedback using dual quaternions

Abstract

Since vision-based sensors typically cannot directly measure the relative linear and angular velocities between two spacecraft, it is useful to develop attitude- and position-tracking controllers- namely, pose-tracking controllers-that do not require such measurements. Using dual quaternions and based on an existing attitude-only tracking controller, a pose-tracking controller that does not require relative linear- or angular-velocity measurements is developed in this paper. Compared to the existing literature, this velocity-free pose-tracking controller guarantees that the pose of the chaser spacecraft will converge to the desired pose independent of the initial state, even if the reference motion is not sufficiently exciting. In addition, the convergence region does not depend on the gains chosen by the user. The velocity-free controller is verified and compared with a velocity-feedback controller through two simulations. In particular, the proposed velocity-free controller is compared qualitatively and quantitatively with a velocity-feedback controller and an extended Kalman filter using a relatively realistic satellite proximity-operation scenario.