Optimal Low-Thrust Interplanetary Trajectories by Direct Method Techniques

Abstract

A direct optimization method has been developed and utilized to compute a wide range of optimal low-thrust interplanetary trajectories. This method replaces the optimal control problem with a nonlinear programming problem which in turn is solved by using sequential quadratic programming. The direct approach is capable of modeling multiple powered and coast arcs, planetary gravity assists, and constant-thrust and variable-thrust electric propulsion systems. The advantages of the direct approach include reduction in the design space, ease of establishing good initial guesses for the design parameters, and improved flexibility for handling “mixed” optimal control problems with continuous control functions and discrete control parameters. Numerical results are presented for three interplanetary mission examples and the results from the direct method show an excellent match with published optimal trajectories. In addition, optimal trajectories are obtained for a new low-thrust interstellar transfer problem.