Design and Control of Libration Point Spacecraft Formations

Abstract

We investigate the concurrent problem of orbit design and formation control around a libration point. The problem formulation is based on a framework of multi-agent, nonlinear optimal control. The optimality criterion is fuel consumption modeled as the L1-norm of the control acceleration. Fuel budgets are allocated by isoperimetric constraints. The nonsmooth optimal control problem is discredited using DIDO, a software package that implements the Legendre pseudospectral method. The discretized problem is solved using SNOPT, a sequential quadratic programming solver. Among many, one of the advantages of our approach is that we do not require linearization or analytical results; consequently, the inherent nonlinearities associated with the problem are automatically exploited. Sample results for formations about the Sun-Earth L2 point in the 3-body circular restricted dynamical framework are presented. Globally optimal solutions for relaxed and almost periodic formations are presented for both a large separation constraint (about a third to half of orbit size), and a small separation constraint (a few hundred km or about 5_10_6 of orbit size).