Paper Title
On The Dynamic Analysis of Free-Flying And Free-Floating Behaviors of A Flexible Space Robot

Abstract
The dynamic behavior of a space robot, considering free-flying and free-floating modes of operation for the shuttle/spacecraft motion, is studied in this paper. For the free-flying space manipulator, the governing equations of motion are derived by means of Lagrange’s approach. For the free-floating mode, Kane’s method is used to facilitate deriving the equations governing the nonholonomic behavior of the robot manipulator. Assumed mode method, incorporating quasi-comparison functions, is employed to express elastic displacements of the flexible arms. For both space robots, the resulting nonlinear problem is separated into two sets of equations by a perturbation approach; one for rigid-body maneuvering of the robot and the other for elastic vibrations and rigid-body perturbations. The kinematic redundancy of the free-flying space robot is removed, assuming that attitude of the spacecraft is controlled during the maneuvering and conservation of linear momentum is governed on the rigid robot. Accordingly, path planning of the free-flying space robot can be accomplished analytically. In the free-floating mode, the kinematic redundancy is removed by imposing both conservation of linear and angular momentums on the manipulator system. Since the conservation of angular momentum is nonintegrable, the free-floating robot manipulator behaves as a nonholonomicsystem; hereby the trajectory tracking in the free-floating mode is done numerically. A numerical example is presented to establish a comparison between the dynamic behaviors of the two robotic systems. Index Terms—Space robot, Kane’s dynamics,Lagrange’s dynamics,free-flying, free-floating.