Low-Thrust Optimal Control of Spacecraft Hovering for Proximity Operations

Spacecraft relative hovering is an important phase for proximity operations around nearearth space. Future space missions have raised the demand for efficient and reliable control strategies for carrying out proximity operations, and the increasing application of small satellites such as Cubesats has imposed more constraints on control algorithms. This paper designs the low-thrust optimal control maneuvers to maintain the relative motion in a bounded region, and proposes control strategies to maximize the residency time of disturbed motion in a hovering region while minimizing the fuel consumption. A semi-analytical approach is introduced to handle the fuel-optimal problem with constant tangential thrust, based on an initial guess from the analytical solution of the energy-optimal problem. Finally, a strategy for long-term hovering is presented by assembling the fundamental steps into a cycle. Numerical simulations are carried out at each stage to verify the efficiency and robustness of proposed approaches.