Minimum-time low-thrust many-revolution geocentric trajectories with analytical costates initialization

Traditionally, indirect methods for trajectory optimization start with the non-intuitive guesses of the initial costates, but it is difficult to generate the initial guesses for the low-thrust many-revolution problems. In this paper, a new indirect method with analytical initialization of the costates has been developed for obtaining the minimum-time low-thrust geocentric rendezvous trajectories. The initial guesses of the rendezvous state and costates are initialized by starting with an analytical solution and taking some reduced optimal control problems as transitions. The reduced problems are considered with different independent variables and final conditions, in which the solutions are all equivalent, and one of these problems is easier to solve. In addition, the paper embeds the reduced problem into a switched system, which allows analytical costates evaluation, such that it can be solved efficiently in combination with the orbital averaging technique. The application of the proposed method to the geocentric rendezvous mission from the geostationary transfer orbit to the geostationary orbit is presented. Numerical simulations have shown that the favorable estimations provided by the proposed reduced problem enable a rapid convergence for the many-revolution rendezvous problem.