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 non-integrable and, therefore, nonholonomic constraints induced by the angular momentum conservation. Some of the previous literatures 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. This paper discusses the path-tracking problem of an arbitrary trajectory of 9-dimension, which consists of 6-dimension for the manipulator joints and 3-dimension for the satellite orientation. The main scenario is that since 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 is followed by computer simulation that illustrates the e ectiveness of the scheme. The relationship of singular points with computational convergency is also discussed.