Optimal Two-Impulse Rendezvous on Perturbed Orbit via Genetic Algorithm

Two-impulse fuel-optimal rendezvous under J₂ perturbation with constrained transfer time is studied in this paper. First, the mathematic model of two-body Lambert transfer of spacecraft is established. Then, J₂ perturbed Lambert´s problem is solved Based on analytical orbit theory via error iteration method. Furthermore, the procedure of the improved genetic algorithm for this problem is proposed, reducing the possibility of being attracted to a local minimum, thus, more likely to find the global minimum in the given search space. Finally, two optimal rendezvous problems are used as test cases: spacecraft rendezvous on coplanar circular orbits under two-body assumption and noncoplanar elliptic orbits under J₂ perturbations, with the result of the former case proved to be consistent with Hohmann transfer´s result. The simulation result verifies the accuracy and validity of this method.