Planning spiral motions of nonholonomic free-flying space robots

The orientation of a space satellite may change due to the actuation of an attached manipulator. Such a motion is subject to the nonintegrable and, therefore, nonholonomic constraints induced by the angular momentum conservation. Some of the previous literature proposed methods to produce a desired change of the satellite orientation by controlling the attached manipulator. These methods treated the point-to-point control problem mainly and, thus, one cannot apply them to the path-tracking problem. The path-tracking problem of an arbitrary trajectory of nine dimensions, which consists of six dimensions for the manipulator joints and three dimensions for the satellite orientation, is discussed. The main scenario is that because such a trajectory is generally infeasible, we search for a feasible motion that approximates the desired trajectory within a designated margin. We name the motion the "spiral motion." A computational scheme for planning the spiral motion is presented, and this is followed by computer simulation that illustrates the effectiveness of the scheme. The relationship of singular points with computational convergency is also discussed.