Traversal-flyby planning of walker-delta mega constellation using Hohmann maneuvers and phase sequencing

Abstract

The planning of the traversal flyby of constellation satellites (TFCS) belongs to the time dependent travelling salesman problems (TDTSPs), and the solving methods only simply based on optimization methods are inefficient and unstable for mega constellations. A planning method based on the Hohmann maneuvers and phase sequencing (HMPS) is proposed for the TFCS, visiting all constellation satellites twice at close range by only one observation satellite (OS). The initial inclination and the right ascension of the ascending node (RAAN) of the OS are taken as variables and are searched by the differential evolution (DE) algorithm. The total cumulative adjusted phase of the Hohmann-maneuver phasing is used to represent the objective function of the total velocity increment. For the two-body problem, the sorting of the desired OS’s initial phases is used to determine the flyby sequence, and then the flyby times and impulses are calculated based on the Hohmann maneuvers. For the J₂ perturbed problem, the multi-round phase sequencing is used. The proposed method is applied to solving the traversal flyby planning problems of small, medium and mega Walker-delta constellations. The results show that the HMPS method is efficient. Compared with the mixed-integer optimization using the DE algorithm, the proposed method can obviously improve the computational efficiency and reduce the fuel cost. For the mega constellation with 1584 satellites, the average velocity increment and mission duration per flyby are only 2.2 m/s and 1.3 h. Due to the regular distribution of the constellation satellites, the optimal flyby sequences for different Walker-delta constellations under the two-body dynamics show the obvious symmetry. The relation between the constellation configuration parameters and the situation that several flybys are completed by only one Hohmann transfer is revealed.