Earth Gravity In-Orbit Sensing: MPC Formation Control Based on a Novel Constellation Model

Missions finalized at measuring the space-time variations of the Earth gravity field have become of high relevance in recent years. These missions are indeed of interest for scientific purposes and applications in several fields. Precise observations of the Earth gravity field can be accomplished by measuring the distance between two satellites flying in suitable orbits. Several mission concepts foresee an active formation control to maintain the distance variations between the two satellites within given bounds. In this paper, we first present an original constellation model, called the Triangle Dynamics (TD) model, which is particularly suitable to describe the orbital dynamics of satellite pairs. Open-loop simulations are performed, where the TD model is compared with a standard model, derived from the well-known Hill–Clohessy–Wiltshire (HCW) equations. The simulation results show that the TD model provides more accurate predictions than the HCW model. Then, we propose a formation control approach based on a new Model Predictive Control (MPC) algorithm. The core of this algorithm is the TD model, which is used in real-time to predict the behavior of the satellite pair, allowing the computation of an optimal formation control command. A case study concerned with the Next Generation Gravity Mission (NGGM) is presented to demonstrate the effectiveness of the proposed MPC-TD algorithm.