Coupled orbit–attitude dynamics and relative state estimation of spacecraft near small Solar System bodies

Abstract

The effects of dynamical coupling between the rotational (attitude) and translational (orbital) motion of spacecraft near small Solar System bodies is investigated. This coupling arises due to the weak gravity of these bodies, as well as solar radiation pressure. The traditional approach assumes a point-mass spacecraft model to describe the translational motion of the spacecraft, while the attitude motion is considered to be completely decoupled from the translational motion. The model used here to describe the rigid-body spacecraft dynamics includes the non-uniform rotating gravity field of the small body up to second degree and order along with the attitude dependent terms, solar tide, and solar radiation pressure. This model shows that the second degree and order gravity terms due to the small body affect the dynamics of the spacecraft to the same extent as the orbit–attitude coupling due to the primary gravity (zeroth order) term. Variational integrators are used to simulate the dynamics of both the rigid spacecraft and the point mass. The small bodies considered here are modeled after Near-Earth Objects (NEO) 101955 Bennu, and 25143 Itokawa, and are assumed to be triaxial ellipsoids with uniform density. Differences in the numerically obtained trajectories of a rigid spacecraft and a point mass are then compared, to illustrate the impact of the orbit–attitude coupling on spacecraft dynamics in proximity of small bodies. Possible implications on the performance of model-based spacecraft control and on the station-keeping budget, if the orbit–attitude coupling is not accounted for in the model of the dynamics, are also discussed. An almost globally asymptotically stable motion estimation scheme based solely on visual/optical feedback that estimates the relative motion of the asteroid with respect to the spacecraft is also obtained. This estimation scheme does not require a model of the dynamics of the asteroid, which makes it perfectly suited for asteroids whose properties are not well known.