Spacecraft long-duration phasing maneuver optimization using hybrid approach

Abstract Before a manned orbital rendezvous mission, the target spacecraft usually performs several maneuvers to adjust the initial phase angle of the orbital rendezvous and to coordinate the injection of the chaser. This maneuvering process is referred to as the “target phasing mission”. This target phasing presents an orbital long-duration two-point boundary value problem. Further, when the maneuver revolution numbers are used as design variables, the target phasing maneuver's optimization becomes a mixed integer nonlinear programming problem. This paper presents a new optimization method for this phasing maneuver mission, employing a hybrid approach. First, we provide an approximate phasing optimization problem that considers the phase angle influences of node drift and orbital altitude decay. This problem is then optimized using a hybrid approach that integrates branch-and-bound and sequential quadratic programming. Second, a shooting iteration method is adopted to improve the solution to the approximate problem in order to satisfy the terminal constraints of high-precision numerical integration. The proposed method is then applied to an operational target phasing maneuver problem. The results lead to four major conclusions: (1) The proposed approximate phasing optimization model presents a good approximation of the operational mission. (2) The hybrid optimization approach can solve the approximate problem effectively, and the shooting iteration used to arrive at a high-precision solution converges steadily and rapidly. (3) Compared with mixed-code genetic algorithm, the proposed method can obtain a similar result with a lower computation cost and, compared with the approximate model that does not consider node drift and orbital altitude decay, the proposed method has better convergence efficiency. (4) The terminal time of target phasing remains almost constant when the initial semi-major axis increases in a limited interval, and the transition appears only when there is a change in the terminal revolution number.