Optimal Control for a Cooperative Rendezvous Between Two Spacecraft from Determined Orbits

The mathematical model of a far-distance cooperative rendezvous between two spacecraft in a non-Keplerian orbit was established. Approximate global optimization was performed by a type of hybrid algorithm consisting of particle swarm optimization and differential evolution. In this process, the double-fitness function was established according to the objective function and the constraints; the double-fitness function was used to enable a better choice between the solutions obtained by the two algorithms at every iteration. In addition, the costate variables obtained were set as the initial values of the sequential quadratic programming to greatly increase the possibility of finding the approximate global optimal solution. After performing the calculations and simulations, it was concluded that the fuel required for orbiting was not influenced by the initial positions of the two spacecraft if the initial orbits of the two spacecraft were determined. However, the time consumption is strongly influenced in this situation.