Explicit Analytic Solution to the Satellite Formation-Keeping Problem

This paper presents explicit and exact formation-keeping guidance schemes that use a new method to determine control inputs and state trajectories. With this approach rooted in some recent advances in analytical dynamics, explicit control inputs to exactly maintain a given formation configuration are easily determined using continuous thrust propulsion systems. The complete nonlinear problem is addressed, and no linearizations and/or approximations are made. The approach provides a marked improvement over existing results in that the control forces, which cause geometric formation-keeping constraints to be exactly satisfied for Keplerian reference orbits, are found in closed form. Extensive computational simulations are performed to demonstrate the ease of implementation and the numerical accuracy attained.