Optimal Trajectory Planning of Formation Flying Spacecraft

This paper introduces a closed-loop Guidance and Control optimal algorithm that balances the propellant consumption and the need for collision avoidance among formation flying spacecraft. This model-based algorithm is purely algebraic and computes the spacecraft trajectories from the knowledge of the formation linearized relative dynamics equations and the formation full state. Using Pontryagin’s maximum principle, Guidance generates the control inputs required to obtain the optimal trajectory from the current state until the target state, and does so for each of a set of regularly spaced time instants. After each recomputation, Control applies the optimal inputs until the next regularly spaced time instant, when Guidance updates the optimal trajectory again. Simulation results for the algorithm applied to a 3-spacecraft formation in GTO are presented.