Abstract:

A method for optimizing of low thrust transfer trajectory from Sun Earth halo orbit to Sun Mars halo orbit based on invariant manifolds and gauss pseudospectral method (GPM) is proposed. Frist, the optimization model of low\|thrust trajectory is established in heliocentric inertial coordinate system, and the principle for choosing the entrance and the exit in transfer trajectory based on the theory of invariant manifolds is given, by the use of this principle, the entrance of Sun Earth invariant manifolds and the exit of Sun Mars invariant manifolds is chosen for both initial state and final state of the transfer trajectory. Then, the optimal control problem is discretized into a nonlinear programming (NLP) problem based on the GPM, and the initial value of the NLP problem is given by using the inverse polynomial shape based approach. The numerical simulation is proposed at last and is used to demonstrate that the GPM for optimizing of low thrust transfer trajectory is valid, in addition, the initial error obtained from the inverse polynomial shape based algorithm is small and make the NLP has fast convergence characteristics.

Key words: Gauss pseudospectral method, Invariant manifolds, Halo orbit, Low thrust