Abstract
This paper proposes an optimal,robust,and efficient guidance scheme for the perturbed minimum-time low-thrust transfer toward the geostationary orbit.The Earth's oblateness perturba-tion and shadow are taken into account.It is difficult for a Lyapunov-based or trajectory-tracking guidance method to possess multiple characteristics at the same time,including high guidance opti-mality,robustness,and onboard computational efficiency.In this work,a concise relationship between the minimum-time transfer problem with orbital averaging and its optimal solution is iden-tified,which reveals that the five averaged initial costates that dominate the optimal thrust direction can be approximately determined by only four initial modified equinoctial orbit elements after a coordinate transformation.Based on this relationship,the optimal averaged trajectories constitut-ing the training dataset are randomly generated around a nominal averaged trajectory.Five poly-nomial regression models are trained on the training dataset and are regarded as the costate estimators.In the transfer,the spacecraft can obtain the real-time approximate optimal thrust direc-tion by combining the costate estimations provided by the estimators with the current state at any time.Moreover,all these computations onboard are analytical.The simulation results show that the proposed guidance scheme possesses extremely high guidance optimality,robustness,and onboard computational efficiency.
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