Efficient Modelling of Small Bodies Gravitational Potential for Autonomous Proximity Operations

Abstract

Maintaining missions in proximity of small bodies requires extensive orbit determination and ground station time due to a ground-in-the-loop approach. Recent developments in on-board navigation paved the way for autonomous proximity operations. The missing elements for achieving this goal are a gravity model, simple enough to be easily used by the spacecraft to steer itself around the asteroid, and guidance laws that rely on a such an inherently simple model. In this research we identified a class of models that can represent well some characteristics of the dynamical environment around small bodies. In particular we chose to fit the positions and Jacobi energies of the equilibrium points generated by the balance of gravity and centrifugal acceleration in the body fixed frame. In this way these gravity models give also a good estimate of the condition of stability against impact for orbital trajectories. Making use of these approximate models we show autonomous guidance laws for achieving body fixed hovering in proximity of the asteroid while ensuring that no impact with the small body will occur during the approach.