A Perspective on Methods for Trajectory Optimization

Abstract

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.