Precise Control of Small Satellites in Close Clusters using Simplified Nonlinear Model Predictive Control

Precise translational control is explored with a simplified nonlinear model predictive control (MPC) scheme for member satellites in a close cluster in an Earth-orbiting environment. Recognizing that the nonlinear dynamical effects in relative satellite dynamics are small but complicated to be directly incorporated into the dynamical model used in the MPC formulation, we present a successive-optimization-based MPC scheme in which the nonlinear effects are incorporated in the form of constant disturbances which are evaluated and updated between two successive optimizations through an intervening high-fidelity nonlinear propagation of the member satellite orbit. The convergence of the predicted disturbance sequence with successive optimizations allows us to make accurate predictions about the future trajectory of the satellite and thus to precisely control its state. The effectiveness of the proposed scheme is evaluated through extensive nonlinear simulations.