Optimal fault-tolerant configurations of control moment gyros

an optimization method for fault-tolerant control moment gyros (CMG) configurations, which maximizes the angular momentum envelope of the CMGs even after a portion of CMGs has failed. To incorporate weighting according to the number of available CMGs, the optimization problem is formulated as a min?max problem and reduced to Thomson's problem under appropriate constraints. Using different weights enables the determination of optimal CMG configurations that take into account a maximization of the angular momentum that admits the possibility of CMG failure. Therefore, the resulting configuration is both optimal and fault tolerant, and maintains satellite attitude controllability in underactuated conditions. Furthermore, reliability-based weighting is shown as one possible criterion for determining the appropriate weights. By adding constraints to the azimuth angles of the gimbal axes, it is shown that the zero-momentum condition of CMG configurations can be satisfied using the proposed optimization method. The proposed method enables calculating various types of optimal CMG configurations without providing initial estimations.