Dynamic modeling and control of spacecraft robotic systems using dual quaternions
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As of 2014, the space servicing market has a potential revenue of $3-$5B per year due to the ever-present interest to upkeep existing orbiting infrastructure. In space servicing, there is a delicate balance between system complexity and servicer capability. Basic module-exchange servicers decrease the complexity of the servicing spacecraft, but is likely to require a more complex architecture of the serviced satellite (the host) in terms of electrical and mechanical connections. With increasing dexterity of the servicing satellite, host satellites can remain closer to flight-proven heritage architectures, which is a practice commonly adopted to increase reliability of space missions. This increased dexterity is provided through the on-orbit exchange of end-effector tools appended to a robotic arm. The dynamic coupling between such an arm and the satellite base has been the subject of intense academic scrutiny and its understanding is essential to the success of robotic servicing missions. In this work, we address different phases of a servicing mission using the dual quaternion formalism. First, we propose a dual quaternion pose-tracking controller that adaptively estimates the mass properties of a spacecraft using either a continuous-time implementation of the concurrent learning framework, or a discretized implementation. The advantage of incorporating concurrent learning lies in enhancing the parameter convergence characteristics of the adaptation scheme. Next, we provide the derivation of the dynamic equations of motion for a spacecraft with a serial robotic manipulator. This derivation uses a Newton-Euler approach formulated in dual quaternion algebra. This model is subsequently adapted to perform end-effector pose stabilization and end-effector pose tracking using the Differential Dynamic Programming control framework. A generalization of the dual quaternion-based framework for modeling of spacecraft with a rooted tree topology and five different types of joints is provided. The formulation is validated on a two-arm robotic spacecraft. This model is then used to implement a generalizable modification to the concurrent learning algorithm that allows “aggressively” estimating the 77 parameters that compose the mass properties of the rigid bodies in the two-arm multibody system.