Abstract: At present, most of the research on low thrust escape trajectory optimization were limited to planar escape or unconstrained engine model. Using the indirect method, the unknown parameters of the two-point-boundary-value-problem were bounded in a hyper unit sphere by multiplying a positive unknown parameter to the fuel optimal performance index. Firstly, the two-dimensional short-time fuel-optimal escape trajectory without control constraint was solved by the homotopy method and curve fits technology. Finally, the three-dimensional long-time fuel-optimal escape trajectory with control constraint was solved. This method is validated to be high-accuracy, good-convergence and efficient for low thrust escape trajectory optimization.

Key words: Low thrust, Escape trajectory, Fuel optimization, Interplanetary exploration