Rapid generation of low-thrust many-revolution earth-center trajectories based on analytical state-based control

Traditional direct and indirect methods suffer the drawbacks of poor computational efficiency and low convergence property for the low-thrust many-revolution trajectory optimization. For this reason, an analytical state-based control scheme is presented to achieve the rapid generation of low-thrust Earth-center trajectories. Based on dynamical simplifications and a Sundman transformation, an analytical state-based control law is derived according to the Pontryagin's maximum principle (PMP). Then, two types of nominal trajectories are elaborately determined, and consequently, the dynamical integration for the state-based control calculations is avoided. Furthermore, two constraint management techniques for thrust ratio and terminal time are proposed to enforce the satisfaction of control and boundary constraints, respectively. Finally, a rapid generation scheme for the low-thrust, many-revolution, Earth-center trajectories is developed based on the proposed techniques. Simulations of orbital transfer and rendezvous to GEO missions are conducted with comparison to the shape-based method, and the results verify the advantages of the proposed approach on the feasibility and computational efficiency.