Optimal uses of reaction wheels in the pyramid configuration using a new minimum infinity-norm solution

Maximum Reaction-Wheel Array Torque/Momentum Envelopes for General Configurations

“…For the geometry of the torque envelope of a general RW configuration without colinear RWs, all discussions about the vertices and edges in Refs. [8][9][10][11] are valid, but those for the facets are not. The vertices are points where all wheels are saturated, and the edges have all but one wheel saturated (interested readers are directed to Ref.…”

“…They developed a method to calculate the maximum torque and momentum envelopes with three or more wheels. Yoon et al proposed a computationally efficient method using a null vector for a four-wheel RWA [10], and then extended their approach to more general RW configurations [11]. Karpenko and King presented an intuitive method to develop a polyhedron [4].…”

Maximizing the Onboard Capability of the Spacecraft Attitude Control System Based on Optimal Use of Reaction Wheels

“…Since the magnitudes of the available T/M may vary in different directions, and SC is not inertially symmetric in general, the magnitudes of the available body rate and acceleration also vary along the rotational directions. The optimality of agility performance is defined as the ability to achieve largest magnitudes of body rate and acceleration vectors along the worst direction (along which the vectors have minimum magnitude) [15].…”

“…The results are widely applicable to the general configuration (number of wheels, sizes, and axis directions) of an array of RWs. Hyungjoo [15] represents a simple method which defines the momentum/torque envelopes and a scheme to optimize the pyramid configuration based on the inertia properties. Jeffery [16,17] uses the ratio of the envelope volume to the inscribed sphere volume to predict the increase in SC slew performance that can be achieved using optimal control to solve minimumtime maneuvers about fixed axis without solving the optimal control problem.…”

“…wheel pyramid configuration relative to the corresponding inertia ellipsoid Another choice of configuration angles can be made with consideration of the SC inertia[15]. It is based on calculating the optimal value of the angle by equating the body accelerations in 3-axes as follows…”