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.

中文翻译：

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双重四元数作为航天器机器人服务任务的建模，控制和估算工具

近年来，人们对在轨航天器的机器人操作越来越感兴趣。实际上，世界各地的一些机构和组织正在研究卫星邻近操作，将其作为未来太空任务的一种启用技术，例如在轨卫星检查，健康监测，监视，维修，加油和光学干涉等。与更传统的卫星应用相反，机器人维修需要同时解决卫星的平移和旋转运动。这些应用的最大挑战之一是需要同时准确地估计和跟踪相对位置和姿态参考轨迹，以避免卫星之间发生碰撞并实现严格的任务目标。由于我们希望在不依赖于平移和旋转运动的人工分离的机器人在轨维修任务的近距离操作中控制航天器运动，最近我们开发了一种完整的理论来描述航天器的6自由度运动双四元数。双四元数是一种强大的工具，可以在统一框架下的任务的所有阶段中，对航天器的姿态（即姿态和位置）进行建模。在本文中，我们将回顾双四元数背后的基本理论，相关的Clifford代数，并将基于四元数的姿态刚体控制律和估计算法与基于双四元数的姿势对等体进行比较。