Trajectory optimization of continuous-thrust spacecraft roundtrip flights via Pseudospectral method

The problem of optimal roundtrip trajectory for the continuous-thrust spacecraft is studied by using the Pseudospectral method. The movement of the spacecraft is described by the Gauss equation using the modified equinoctial elements in the Gauss orbital coordinates. Given the staying orbit, the roundtrip flight mission is divided into transfer, stay and return phases. Considering the minimum-fuel-consumption performance, the optimal roundtrip flight problem is established. Furthermore, because the multi-phase trajectories optimization problem is hard to be resolved by the indirect method, the Pseudospectral method is applied to do with the three phase orbital maneuver problem. The simulations demonstrate that the minimum fuel-consumption roundtrip flight mission is well accomplished, and the simulation results also show that the trajectories of the transfer phase and the return phase are near symmetrical.