Optimization of multiple-impulse, multiple-revolution, rendezvous-phasing maneuvers

A new hybrid optimization approach is proposed for the design of a rendezvous-phasing strategy with combined maneuvers, which is normally considered as a complex multiple-impulse, multiple-revolution, nonlinear rendezvous problem. In this approach, a feasible iteration optimization model is first formulated using a multiple-revolution Lambert algorithm, and a parallel simulated annealing algorithm is employed to locate the unperturbed solution. Subsequently, an infeasible iteration optimization model accounting for trajectory perturbations is formulated, and a sequential quadratic programming algorithm is used to obtain the perturbed solution, with the unperturbed solution as an initial reference solution. The global convergence ability of the proposed approach is verified by solving a classical same-circle rendezvous problem. Two different solutions satisfying Lawden's necessary optimality conditions are located and one solution outperforms an optimal solution previously reported. The proposed approach is further evaluated in a practical two-day rendezvous-phasing mission with different initial conditions. It is shown that this approach is effective and efficient and the combined maneuvers can save propellant at a range of 4-35% when compared with the special-point maneuvers.