Optimization of Solar-Sail Control When a Vehicle Moves along Cyclic Heliocentric Trajectories

Abstract

This paper considers the problem of constructing time-optimal trajectories for a spacecraft (SC) with a solar sail. The trajectories under consideration consist of repeated cycles of spacecraft movement to the target heliocentric orbit and back to the initial one. A model of a perfectly reflecting sail is used, which allows using the programs for optimal control of the sail angle, obtained on the basis of the Pontryagin maximum principle. The heliocentric motion is modeled in a flat polar coordinate system, and the spacecraft itself makes cyclic flights between two terrestrial planets along a closed trajectory. A boundary-value problem is formulated, in the solution of which the approach of the spacecraft to the target planet with the equalization of velocities is ensured (the encounter problem). Simulations of four cycles of Earth–Mercury–Earth and Earth–Mars–Earth motion with a characteristic acceleration of the solar sail of 0.25 mm/s² have been carried out, for which the duration of one cycle is on average 2000 and 2341 days, respectively. Optimal sail-orientation control programs are obtained for a wide range of launch dates, and methods of searching for and choosing the initial values of conjugate variables are shown. The obtained results demonstrate the ability of a spacecraft with a solar sail to implement controlled motion along closed trajectories with a minimum duration of individual Earth–destination planet–Earth flights.