Optimization of Many-Revolution Minimum-Time Low-Thrust Trajectories Using Sundman Transformation

Minimum-time planet-centric transfer maneuvers are investigated for spacecraft equipped with solar-powered, low-thrust electric thrusters. Many orbital revolutions in the presence of perturbations make the task of trajectory design quite challenging. To enhance the numerical convergence properties of the standard single-shooting solution methods, the Sundman transformation is integrated within the indirect formulation. Another contribution of the paper is that we incorporate higher-fidelity gravity spherical harmonics (up to any desired degree and order) into the derivation of the optimal control law using a complex-step based numerical method. Many-revolution GTO-to-GEO orbit transfer maneuvers are considered with various levels of thrust magnitude and with perturbations due to the Earth's second zonal harmonic, higher degree and order gravity spherical harmonics, Moon's gravity, and Earth-induced eclipses. The results demonstrate that trajectories with up to 450 revolutions can be generated.