An impulsive model predictive static programming based station-keeping guidance for quasi-halo orbits

Abstract

In this paper, a control effort minimizing optimal station-keeping guidance is designed and implemented to regulate a spacecraft around an L1 quasi-halo orbit in the Sun–Earth–Moon elliptic four-body problem. The station-keeping guidance is formulated as a finite time, non-linear optimal control problem with hard terminal output constraints and Impulsive Model Predictive Static Programming (I-MPSP) is used to obtain station-keeping maneuvers. The algorithm is iterative, where the guessed station-keeping maneuvers are optimally updated by a simple closed-form equation until an output terminal constraint is satisfied and an optimal cost function is obtained. The technique involves the calculation of sensitivity matrices that is done in a computationally efficient manner owing to their recursive nature. Through extensive simulations, in the presence of disturbance forces and uncertainties, a closed-loop application of I-MPSP guidance results in a trajectory that remains tightly bound to the reference orbit over a long-duration mission.