We present a new approach to solving a class of problems arising in the architecting of satellite swarms. A key problem addressed in this paper is the "concurrent" design and control of orbits to achieve a swarm configuration. Although any design criterion may be used, we demonstrate our approach for fuel consumption since the premium for fuel is extraordinarily high for spacecraft. We show how certain elements of optimal periodic control theory provide a very natural setting for this problem. Using the general-purpose dynamic optimization software, DIDO, we show how satellite formations can easily be designed without the use of any analytical results. If a natural zero-propellant solution does not exist, the by-product of our approach automatically determines the minimum fuel and the associated controls required to maintain the formation configuration.
Spacecraft agility is limited by the maximum torque that reaction wheels can provide. Therefore, a reaction wheel array is typically configured to maximize the inscribed sphere of the reaction wheel torque envelope. Agility is then determined by dividing the spherical torque by the maximum principal inertia. This industry standard approach can severely underestimate the true capability of an attitude control system. An agility envelope considers the reaction wheel torque envelope along with the spacecraft inertia tensor. The agility envelope can therefore be used as a means to quantify the conservatism associated with the standard approach in order to improve slew performance of a conventional attitude control system without the need for larger, more costly hardware or new control algorithms. This paper, presents a simple approach for constructing the agility envelope of a reaction wheel attitude control system. The agility envelope is applied to determine design curves for limits on angular acceleration and rate for maneuver design and for finding the reaction wheel skew angles that maximize agility for a given spacecraft configuration. A surprising result is the observation that maximizing the inscribed sphere of the reaction wheel torque envelope does not, in general, optimize agility.
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