Formation flying control for the MMS mission using GVE-based MPC

Formation flying is an enabling technology for many future space missions. This paper presents an MPC (model predictive control) controller that uses dynamics based on a modified version of Gauss' variational equations which incorporates osculating J
₂
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 mission using a commercial orbit propagator with realistic disturbances (including J
₂
). These simulations show that (formation flying using MPC with J
₂
-modified GVEs requires fuel use comparable to using unmodified GVEs in simulations with no J
₂
effects