Efficient Optimization for Time-Constrained Encounter of Spacecraft with Multirevolution Phasing

“Spacecraft encounter” refers to a close flyby or fast proximity between two or more spacecraft in space. It involves the approach of one spacecraft to another, whether for observation, communication, capture, or interception purposes. This paper presents a novel approach to planning orbital encounter missions for spacecraft within a specified time constraint. The proposed method takes advantage of a unique encounter process where the vehicle performs only two in-plane impulses and matches the target location at the encounter position using multirevolution phasing. To ensure the minimum maneuvering fuel consumption from the selection of the encounter position and analyze the optimality of the proposed encounter maneuver, the determination method of the minimal orbital intersection distance is first given by constructing constraint equations in polynomial form. Then, the algorithm framework for determining the optimal encounter maneuvers is established. This scheme allows us to derive the optimal maneuver position, direction, and impulse magnitude, thereby creating a detailed two-layer solution framework for an arbitrary target. Concurrently, the strategy accommodates orbital phase deviations by proffering a rapid correction method that factors in the perturbation environment. To expand this optimal encounter maneuver planning method to multitarget missions, we develop a reduced-order allocation procedure for optimal pairing between vehicles and targets. Through the use of numerical simulations exemplified by one single-target and two multitarget missions, it is evident that the proposed method is both highly efficient and effective for encountering any given target.