## Multi-objective Optimization of Orbit Transfer Trajectory Using Imperialist Competitive Algorithm

##### Abstract

This paper proposes a systematic direct approach to carry out effective multi-objective optimization of space orbit transfer with high-level thrust acceleration. The objective is to provide a transfer trajectory with acceptable accuracy in all orbital parameters while minimizing spacecraft fuel consumption.
With direct control parameterization, in which the steering angles of thrust vector are interpolated through a finite number of nodes, the optimal control problem is converted into the parameter optimization problem to be solved by nonlinear programming. Besides the thrust vector direction angles, the thrust magnitude is also considered as variable and unknown along with initial conditions. Since the deviation of thrust vector in spacecraft is limited in reality, mathematical modeling of thrust vector direction is carried out in order to satisfy constraints in maximum deviation of thrust vector direction angles. In this modeling, the polynomial function of each steering angle is defined by interpolation of a curve based on finite number of points in a specific range with a nominal center point with uniform distribution. This kind of definition involves additional parameters to the optimization problem which results the capability of search method in satisfying constraint on the variation of thrust direction angles.
Thrust profile is also modeled based on polynomial functions of time with respect to solid and liquid propellant rockets. Imperialist competitive algorithm is used in order to find optimal coefficients of polynomial for thrust vector and the optimal initial states within the transfer. Results are mainly affected by the degree of polynomials involved in mathematical modeling of steering angles and thrust profile which results different optimal initial states where the transfer begins. It is shown that the proposed method is fairly beneficial in the viewpoint of optimality and convergence. The optimality of the technique is shown by comparing the finite thrust optimization with the impulsive analysis.
Comparison shows that the accuracy is acceptable with respect to fair precision in orbital elements and minimum fuel mass. Also, the convergence of the optimization algorithm is investigated by comparing the solution of the problem with other optimization techniques such as Genetic Algorithm. Results confirms the practicality of Imperialist Competitive Algorithm in finding optimum variation of thrust vector which results best transfer accuracy along with minimizing fuel consumption.