Indirect Optimization of Underactuated Spacecraft Formation Reconfiguration in Elliptic Orbits

Abstract

This paper proposes analytical solutions to optimal underactuated spacecraft formation reconfiguration in elliptic orbits, without either the radial or in-track thrust. For either underactuated case, the dynamical model of underactuated formation reconfiguration was developed, based on which the system controllability and reconfiguration feasibility then were analyzed. By using the indirect optimization method, a detailed optimization procedure was designed, and the optimal trajectory of formation reconfiguration was derived analytically for the underactuated cases. A fully actuated optimal reconfiguration scheme was introduced to make comparisons. Numerical simulations indicated that the proposed optimal underactuated reconfiguration schemes can manage formation reconfiguration with a control cost similar to that of the fully actuated scheme, even in the absence of radial or in-track thrust. Numerical comparisons with existing nonoptimal reconfiguration schemes further verified that the proposed optimal schemes can perform underactuated formation reconfiguration in an energy-optimal way.