Application of a modified genetic algorithm to the trajectory optimization of a launch vehicle second stage

The demand for increased payload or reduced propellant requirements requires the trajectories of spacecrafts and launch vehicles to be optimized. In order to achieve the optimum trajectory, a recently proposed modified Genetic Algorithm is combined with non-linear programming techniques are presented here. It is then applied to a launch vehicle ascent trajectory optimization. As opposite to the conventional genetic algorithm, here for selection criteria, penalty function along with fitness function is used with comparatively large penalty parameter value, which makes it powerful enough to achieve optimization for desired objective function value. The algorithm is implemented in MATLAB and validated by applying it to the constrained brachistochrone problem. It is then applied to the second stage trajectory of a nanosat launch vehicle. The vehicle was designed assuming a gravity turn trajectory, which is accomplished by trial and error. With the proposed automatic approach, the mass of payload achieved is 9.0 kg at a final altitude of 250.21 km and at a velocity of 7.86 km/s. This value is within the constraints imposed here and results show that it is essentially the same as that of the gravity trajectory under the exact same final states, thus demonstrating the ability of the optimizer to automatically narrow down the area of search. The performance then can be further improved by conventional optimizers.