J2-Modified GVE-Based MPC for Formation Flying Spacecraft

Formation flying is an enabling technology for many future space missions. This paper presents an MPC controller that uses dynamics based on a modified version of Gauss’ Variational Equations which incorporates osculating J2 effects. A linear parameter-varying version of existing dynamics is developed, creating a highly accurate model that can easily be embedded in the MPC controller design. The linearization assumptions are shown to be consistent with typical formation flying scenarios. The controller is demonstrated on an MMS-like formation flying mission in a highly elliptical orbit using a commercial orbit propagator with realistic disturbances (including J2). These simulations show that formation flying using MPC with J2-modified GVEs requires fuel expenditures comparable to using unmodified GVEs in simulations with no J2 effects.