Optimal design of orbital transfer with finite thrust based on legendre pseudospectral method

In this paper, the application of Legendre pseudospectral method to space vehicle orbital transfer with finite thrust optimization problem was studied. Firstly, the model of orbital transfer optimization control problem was established, while equations of motion were simplified based on some reasonable hypotheses. Performance was selected to minimize the total fuel consumption. The control variable was thrust attack angle. Terminal state variable constraints were path angle, altitude and velocity constraints. Then, the optimal control problem was transformed into nonlinear programming problem (NLP) using Legendre pseudospectral method. And dynamic optimization problem was transformed into static parameter optimization problem. The state variables and control variables were selected as optimal parameters at all collocation nodes. At last, parameter optimization problem was solved using the SNOPT software package. The SNOPT software package has high convergence to nonlinear programming problem. The simulation results demonstrate that Legendre pseudospectral method is not sensitive to orbital transfer initial conditions; they also show that the optimal solutions of orbital transfer optimization problem are fairly good in robustness. Therefore, Legendre pseudospectral method is a viable approach to the space vehicle orbital transfer with finite thrust optimization problem.