Control problems for a multibody spacecraft via shape changes: constant nonzero angular momentum

In this paper, a three dimensional reorientation problem for an underactuated multibody spacecraft in the case of constant nonzero angular momentum is studied. The spacecraft is underactuated because it is in a free floating mode where no external forces or torques are applied. The only means of actuation are provided by the joint actuators. The control construction is based on a formula for approximating the orientation changes induced by small amplitude periodic shape changes and nonzero angular momentum. On the basis of the formula, an explicit algorithm is provided for synthesizing periodic open loop shape changes for reorientation of the spacecraft from a given initial orientation to a desired final orientation within a specified finite time interval while the initial and final shapes of the spacecraft are the same. In particular, the algorithm can be applied to transfer the spacecraft to one of its relative equilibria. An example of reorientation of a four link multibody spacecraft illustrates the general results.