Dual Quaternions as a Tool for Modeling, Control, and Estimation for Spacecraft Robotic Servicing Missions

In recent years there has been an increasing interest in spacecraft robotic operations in orbit. In fact, several agencies and organizations around the world are investigating satellite proximity operations as an enabling technology for future space missions such as on-orbit satellite inspection, health monitoring, surveillance, servicing, refueling, and optical interferometry, to name a few. Contrary to more traditional satellite applications, robotic servicing requires addressing both the translational and the rotational motion of the satellite at the same time. One of the biggest challenges for these applications is the need to simultaneously and accurately estimate – and track – both relative position and attitude reference trajectories in order to avoid collisions between the satellites and achieve stringent mission objectives. Motivated by our desire to control spacecraft motion during proximity operations for robotic in-orbit servicing missions which do not depend on the artificial separation of translational and rotational motion, we have recently developed a complete theory to describe the 6-DOF motion of the spacecraft using dual quaternions. Dual quaternions emerge as a powerful tool to model the pose (that is, both attitude and position) of the spacecraft during all phases of the mission under a unified framework. In this paper, we revisit the basic theory behind dual quaternions, the associated Clifford algebras, and compare quaternion-based attitude rigid-body control laws and estimation algorithms, to their dual quaternion-based pose counterparts. We also show that the resulting mathematical structure lends itself to the straightforward incorporation of an adaptive estimation scheme known as concurrent learning, which allows us to also estimate on-the-fly the mass properties of the spacecraft.