Symmetries in the Optimal Control of Solar Sail Spacecraft

The theory of optimal control is applied to obtain minimum-time trajectories for solar sail spacecraft for interplanetary missions. We consider the gravitational and solar radiation forces due to the Sun. The spacecraft is modelled as a flat sail of mass m and surface area A and is treated dynamically as a point mass. Coplanar circular orbits are assumed for the planets. We obtain optimal trajectories for several interrelated problem families and develop symmetry properties that can be used to simplify the solution-finding process. For the minimum-time planet rendezvous problem we identify different solution branches resulting in multiple solutions to the associated boundary value problem. We solve the optimal control problem via an indirect method using an efficient cascaded computational scheme. The global optimizer uses a technique called Adaptive Simulated Annealing. Newton and Quasi-Newton Methods perform the terminal fine tuning of the optimization parameters.     

Solar Sail Halo Orbits at the Sun–Earth Artificial L 1 Point

Halo orbits for solar sails at artificial Sun–Earth L₁ points are investigated by a third order approximate solution. Two families of halo orbits are explored as defined by the sail attitude. Case I: the sail normal is directed along the Sun-sail line. Case II: the sail normal is directed along the Sun–Earth line. In both cases the minimum amplitude of a halo orbit increases as the lightness number of the solar sail increases. The effect of the z-direction amplitude on x- or y-direction amplitude is also investigated and the results show that the effect is relatively small. In case I, the orbit period increases as the sail lightness number increases, while in case II, as the lightness number increases, the orbit period increases first and then decreases after the lightness number exceeds ~0.01.