Optimal transfer orbit design of spacecraft with finite thrust based on Legendre pseudospectral method

This article explores the application of the Legendre pseudospectral method to spacecraft orbital transfer with finite thrust optimization problem. Firstly, the model of the orbital transfer optimization control problem was established, while equations of motion were simplified based on some hypotheses. The performance was optimized to minimize the cumulative fuel consumption. The control variable was the thrust attack angle, and terminal state variable constraints included path angle, altitude, and velocity constraints. Then, the optimal control problem was transformed into a nonlinear programming problem (NLP) using the Legendre pseudospectral method. The dynamic optimization problem was transformed into a static parameter optimization problem. The state variables and control variables were selected as the optimal parameters at all collocation nodes. Lastly, the parameter optimization problem was solved using the SNOPT (Sparse Nonlinear Optimizer) software package. The SNOPT software package shows high convergence for a nonlinear programming problem. During the simulation, it was noted that the Legendre pseudospectral method is not sensitive to orbital transfer initial conditions. It was also observed that the optimal solutions of the orbital transfer optimization problem are fairly good in robustness. Therefore, the Legendre pseudospectral method is a viable approach to the spacecraft 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.