Integrated optimization of staging and trajectory of launch vehicles using B-spline curves

In this paper, in order to simultaneously optimize the staging and trajectory of launch vehicles, changes are made in the structure of the trajectory optimization problem. In this approach, the flight times of all stages are considered freely and as optimization variables. During the solution and in each iteration, by using the values of the flight times in that iteration and the fuel consumption rate of each stage, the masses of the fuel and structure of the stages and the initial and instantaneous masses of the vehicle are calculated. By minimizing the initial mass as the objective function of the integrated optimization problem, the optimal flight trajectory is obtained in the form of the optimal state and control values, and the optimal budget of the fuel and structure masses between different stages is calculated. In this paper, to implement the dynamic equations, the direct collocation method is used, and to approximate the variables, the B-spline curves are used. By using the B-spline curves, despite the discreteness of the relevant parameters as optimization variables, a continuous concept for the optimal solution can be created. The presented approach in this paper for integrated optimization of staging and trajectory and the use of B-spline curves in the approximation of the multiphase problem with free final times can lead to reduce the initial weight of the Europa 2 launch vehicle by 30% to perform a specific mission.