Models for Rhumb-Line Attitude Maneuvers and Error Propagation Effects

Abstract

The attitude control of a spin-stabilized spacecraft is usually performed by a forced precession of the spin axis produced by a series of pulsed thrust actuations. A sun sensor is used for the proper timing of the thrust pulses so that the spin axis describes a rhumb-line path on the unit-sphere. The rhumb-line equations are derived from first principles and are interpreted and visualized in geometrical terms. Thruster performance parameters (i.e., the magnitude and centroid time of the thrust pulses) constitute the principal error sources governing the accuracy of the maneuver. These errors affect the total maneuver path length and its inertial heading direction, that is, the rhumb angle. An analytical model is constructed for describing the propagation of path-length and rhumb-angle errors into the resulting attitude at the conclusion of the maneuver. Detailed simulations with relevance to actual spacecraft applications have been performed to arrive at an understanding of the expected error magnification for different maneuver input parameters and initial conditions. Finally, a model is also presented for the propagation of the statistical characteristics of the input errors into the resulting error covariances of the final attitude parameters.