Optimal design of minimum fuel in orbital transfer with finite thrust

The application of Legendre pseudospectral method to the optimization space vehicle orbital transfer with finite thrust is studied. Firstly, the model of orbital transfer optimal control is established. Then, the optimal control problem is transformed into a nonlinear programming problem (NLP) using Legendre pseudospectral method, and the dynamic optimization problem is transformed into a static parameter optimization problem. The state variables and control variables are selected as optimal parameters at all collocation nodes. Finally, the parameter optimization problem is solved using the SNOPT software package. The simulation results demonstrate that Legendre pseudospectral method is not sensitive to orbital transfer initial conditions; they also show that the optimal solutions of the orbital transfer optimization problem are fairly good in robustness. Therefore, Legendre pseudospectral method is a viable approach to the optimization of space vehicle orbital transfer with finite thrust.