Periodic motion about asteroids via low-thrust feedback control

In recent years, asteroid exploration has gained increasing interest from the scientific community and several space agencies, with mission objectives ranging from investigation on the origin of the solar system to resource exploitation. The irregular geometry and mass distribution of minor celestial bodies yields a highly perturbed gravitational environment, and orbital motion in their proximity is unpredictable over a wide time horizon as a result. This research considers 433 Eros, a large near-Earth asteroid with highly irregular geometry. In the scientific literature, periodic motion was proven to exist about Eros, if harmonics (2,0) and (2,2) of the gravitational potential are modeled, and is particularly interesting for science missions, due to predictability and repetitiveness with respect to the body frame attached to the asteroid. This research employs high-fidelity orbit propagation, with the use of modified equinoctial elements and the combined inclusion of two representations for the gravitational field, i.e. spherical harmonics and constant-density polyhedral model. The latter is fundamental, to avoid singularities while the spacecraft approaches the asteroid surface. In this dynamical framework, periodic orbits are shown to become unstable in the presence of a high-fidelity gravitational model, and the probe turns out to escape or impact the asteroid after relatively short time. To avoid this, low-thrust feedback control is proposed as an effec- tive and convenient option for extended mission durations. Specifically, two different nonlinear feedback laws are proposed and tested: (i) Lyapunov-based orbit control and (ii) nonlinear hybrid predictive control, which combines gain adaptation and feedback linearization. The latter approach employs an extended formulation of the Battin-Giorgi description of translational motion relative to a non-Keplerian path, with the final goal of tracking the desired motion about Eros. To assess the performance of the low-thrust feedback control at hand, a Monte Carlo campaign is run, in the presence of several nonnominal conditions, such as orbit determination errors and uncertainties related to the asteroid gravity field, accompa- nied by temporary thrust unavailability and misalignment. After orbit acquisition, the relative position error turns out to be modest. The same low-thrust control technique is also successfully tested if the spacecraft must pursue Keplerian motion. The numerical results unequivocally point out the effectiveness of low-thrust feedback control in achieving high-accuracy orbit tracking in the proximity of highly irregular celestial bodies such as asteroid Eros, even in nonnominal flight conditions.