Fuel-optimal precise rendezvous guidance law in elliptical reference orbit with J₂ perturbation

For rendezvous near an elliptical reference orbit, a numerical gradient algorithm and a genetic algorithm for optimization were adopted to determine the optimal transfer time and impulses. The solutions for half-revolution and complete-revolution rendezvous were also given to eliminate the singularities. Based on the optimization algorithms, a two-impulse iteration method with linear gradient was proposed for rendezvous guidance to eliminate the impact of J₂ perturbation on relative motion. The simulation results of rendezvous near reference orbit with different eccentricities show that the guidance algorithm is simple, feasible and can be used in remote rendezvous near circle and arbitrary elliptical reference orbit.