Optimal Reconfigurations of Two-Craft Coulomb Formation in Circular Orbits

Abstract

Optimal reconfigurations of a two-spacecraft Coulomb formation are determined by applying nonlinear optimal control techniques. The objective of these reconfigurations is to maneuver the two-craft formation between two charged equilibria configurations. The four optimality criteria considered are minimum time, minimum acceleration of the separation distance, minimum Coulomb and electric propulsion fuel usage, and minimum electrical power consumption. The reconfiguration between equilibra is first considered by varying the desired separation distance. In a radial relative equilibrium configuration, only the Coulomb force is required to control the in-plane motion and to steer the satellites from their initial to their final radial position. In this reconfiguration maneuver, the gravity gradient torque is exploited to stabilize the in-plane motion. For along-track and orbit normal equilibrium locations, the reconfiguration maneuver requires hybrid controls. Here the Coulomb force is varied to control the separation distance and inertial micro-thrusters are activated for control in the transverse directions. Second, a reconfiguration involving hybrid control is used to maneuver the crafts from any initial equilibrium position to a final one. The goal is to determine optimal maneuvers maximizing the use of Coulomb propulsion while minimizing the electric propulsion usage. The two-point boundary value problem optimization formulation is numerically solved via pseudo-spectral methods. Pontryagin’s Minimum Principle verifies the open loop solutions’ optimality.