Pseudo-holonomic behavior of planar space robots

The angular momentum of a free-flying space robot is a conserved quantity. This conservation law acts as a nonholonomic constraint and manifests itself when cyclic motion of the joints of the space robot produces a change in the orientation of the whole system. Consequently closed trajectories in the joint space of the robot usually fail to produce closed trajectories in the workspace. In this paper the authors first show that there exist some closed paths that are “holonomic loops” in the sense that the nonholonomic space robot exhibits holonomic behavior globally on these trajectories. When the joints of the space robot move along these trajectories, the end-effector traces a closed curve in the workspace. In this paper, the authors present a simple method to plan such trajectories that produce repeatable motion of the space robot