Axis Kinematics Algorithm for Satellite Manipulator System in Orbital Motion

The paper presents a PoE (product of exponential)–based algorithm to compute the kinematics of general floating-base manipulators, e.g., satellite manipulators. This algorithm is referred to as axis kinematics in this paper which provides up to second-order kinematics including the Jacobian and its time-derivative in terms of spatial screws which are equivalent to the exponential coordinates in the Lie algebra $\mathfrak{s}\mathfrak{e}$(3). As input to the algorithm, an orbital motion of the satellite is derived through Keplerian orbit elements. The base body motion corresponding to the satellite is modeled as a new type of spatial screw that enables elliptic motion. Ultimately, the kinematics of the satellite manipulator system in an elliptical orbit motion is represented in terms of the PoE composed of a set of spatial screws. The proposed method is validated through a numerical example of a satellite manipulator system.