Improving Design of Aerospace Vehicle Orbital Transfer Optimization with Finite Thrust Based on Legendre Pseudospectral Method

Abstract

This article explores the application of the Legendre pseudospectral method to aerospace vehicle orbital transfer with a problem of finite thrust optimization. Firstly, the model of the orbital transfer optimization control problem was originated, while the equations of motion are derived from some simplifying assumptions. For maximum control of accumulated fuel consumption, the performance was optimized. The variable of control was the attack angle of thrust, and the variable of terminal condition constraints included path angle, altitude, and velocity constraints. Next, the Legendre pseudospectral method which was used to transform the optimal control problem into NLP (Nonlinear Programming) problem. The transformation of the problem was realized from dynamic optimization to quiescent parameter majorization. The variables of state and control were used as the optimal parameters for all collocation nodes. Lastly, SNOPT software package was selected as the solution to the parameter optimization problem. The SNOPT software package shows high convergence for a nonlinear programming problem. During the simulation, it was noted that the Legendre pseudospectral method is insensitive to orbital transfer initial prerequisites. It was also observed that the optimal solutions to the orbital transfer optimization problem are relatively excellent in robustness. Therefore, Legendre pseudospectral method is a feasible approach to the aerospace vehicle orbital transfer with a finite thrust optimization problem. The orbit optimization method proposed in this paper can also provide reference and guidance for solving other interplanetary orbital transfer optimization problems.