N-impulse orbit transfer using genetic algorithms

A new formulation to the orbit transfer problem using genetic algorithm (GA) is presented. This formulation is general for noncoplanar elliptical orbits and can also implement any number of thrust impulses. The solution obtained by this formulation is guaranteed to insert the satellite in the final orbit exactly, even if the GAs did not converge to the global optimal solution. The formulation requires solving Lambert's problem to find the parameters of the transfer orbit for a given set of three design variables. The optimal solution is to perform a small inclination change along with the orbit raising at the first impulse and then perform most of the orbit inclination along with the circularization in the second impulse. The solution of the Lambert's problem yields the exact orbit transfer from the member's initial position to its final position during its assigned time of flight.