Angular-momentum-based sizing of control moment gyro cluster for an agile spacecraft

The sizing of a control moment gyro (CMG) cluster is covered sparsely in literature, but it is of considerable interest 2 to a practicing engineer. In this paper, the sizing of a cluster of four control moment gyros is investigated based on the mission angular momentum requirement of a typical agile spacecraft. The CMG skew angle β and individual CMG angular momentum h are determined as part of the sizing. The work focuses on the sizing of a minimally redundant cluster of four CMGs in a pyramid and roof-type arrangement considering their external angular momentum surfaces. Two approaches are discussed: the first considers maximum angular momentum about individual axis separately, and the second considers the momentum requirement about two axes simultaneously. The internal momentum surfaces of the CMG clusters are analyzed. Gimbal angle desaturation and the fuel consumed for it by the roof-type and pyramid configurations are also examined. Both the four CMG clusters are able to meet the maximum nonspherical angular momentum demanded by a typical mission about each axes. However, using method 1, the cluster is able to generate only 88% of the two-axis mission demand. The clusters meet the mission demand completely with method 2 using 20% more angular momentum per CMG and an increase in skew angle by 8–11° compared to method 1. The 20% increase in momentum increases power consumption by 11%. For a typical gimbal angle desaturation, the roof-type cluster uses 8.5% more fuel than the pyramid arrangement. However, the former has only one major internal singular surface in contrast with seven for the latter. This makes the roof-type arrangement very desirable to keep the singularity avoidance algorithm simple and amenable with the CMGs 3 operating within the momentum capability, and achieve the required spacecraft agility

Autonomous Formation Keeping of Geostationary Satellites with Regional Navigation Satellites and Dynamics

In this paper, the reduced dynamic autonomous formation control of geostationary-Earth-orbit satellites using Indian Regional Navigation Satellite System observables is presented. Generally, the navigation signal is used to determine the position, velocity, and time kinematically. The kinematic formulation, however, is geometric and vulnerable to data outage and cycle slip. Weak geometry of navigation satellites causes high dilution of precision. In this situation, dynamics can provide the estimates with little degradation in accuracy. This requires combining Indian Regional Navigation Satellite System observables with orbital dynamics of the geostationary-Earth-orbit satellites in an extended Kalman filter setup, resulting in improved position and velocity estimates. Moreover, solar radiation pressure coefficient, ephemeris error, and any other unaccounted minute forces are estimated through an empirical acceleration model, along with receiver clock bias and drift, in a reduced dynamics formulation. Furthermore, it is demonstrated that these position and velocity estimates permit autonomous station and formation keeping of geostationary-Earth-orbit satellites. The classical technique using the sun and moon and solar radiation perturbing accelerations to advantage is used to control eccentricity and inclination vectors of each satellite in the formation. The formation-keeping control maneuvers are performed autonomously, whenever an individual satellite's eccentricity or inclination limit is exceeded

A Comparative Study of Liapunov Stability Analyses of Flexible Damped Satellites

A literal Liapunov stability analysis of a spacecraft with flexible appendages often requires a division of the associated dynamic potential into as many dependent parts as the number of appendages. First part of this paper exposes the stringency in the stability criteria introduced by such a division and shows it to be removable by a “reunion policy.” The policy enjoins the analyst to piece together the sets of criteria for each part. Employing reunion the paper then compares four methods of the Liapunov stability analysis of hybrid dynamical systems illustrated by an inertially coupled, damped, gravity stabilized, elastic spacecraft with four gravity booms having tip masses and a damper rod, all skewed to the orbital plane. The four methods are the method of test density function, assumed modes, and two and one-integral coordinates. Superiority of one-integral coordinate approach is established here. The design plots demonstrate how elastic effects delimit the satellite boom length