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An analysis of the momentum conservation equations of a redundant free-flying spacecraft/manipulator system acting in a zero-gravity environment is presented. In order to follow a predefined end-effector path, the inverse kinematics at velocity level is considered. The redundancy is solved alternatively in terms of pseudoinverses and null-space components of the manipulator inertia matrix, the manipulator Jacobian matrix, and the generalized Jacobian matrix. A general manipulation task is defined as end-effector continuous path tracking with simultaneous attitude control of the spacecraft. Three subtasks of the general task are considered. The case of manipulator motions that yield no spacecraft attitude disturbance is analyzed in more detail and a special 'fixed-attitude-restricted' (FAR) Jacobian is defined. Through singular-value decomposition of this Jacobian, corresponding FAR dexterity measures (FAR manipulability and FAR condition number) are derived.>
Nenchev et al. (1992) studied this question.