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A supervised stochastic learning method called the Gaussian Process Regression (GPR) is used to design an autonomous guidance law for low-thrust spacecraft. The problems considered are both of the time- and fuel-optimal regimes and a methodology based on "perturbed back-propagation" approach is presented to generate optimal control along neighboring optimal trajectories which form the extremal bundle constituting the training data-set. The use of this methodology coupled with a GPR approximation of the spacecraft control via prediction of the costate n-tuple or the primer vector respectively for time- and fuel-optimal trajectories at discrete time-steps is demonstrated to be effective in designing an autonomous guidance law using the open-loop bundle of trajectories to-go. The methodology is applied to the Earth-3671 Dionysus time-optimal interplanetary transfer of a low-thrust spacecraft with off-nominal thruster performance and the resulting guidance law is evaluated under different design parameters using case-studies. The results highlight the utility and applicability of the proposed framework with scope for further improvements. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the manifolds of three Near-Rectilinear Halo Orbits (NRHOs) and optimal low-thrust transfer trajectories using a high-fidelity dynamical model. Time- and fuel-optimal low-thrust transfers to (and from) these NRHOs are generated leveraging their 'invariant' manifolds, which serve as long terminal coast arcs. Analyses are performed to identify suitable manifold entry/exit conditions based on inclination and minimum distance from the Earth. The relative merits of the stable/unstable manifolds are studied with regard to time- and fuel-optimality criteria, for a set of representative low-thrust family of transfers. [ABSTRACT FROM AUTHOR]

Inspired by the original developments of recursive power series by means of Lagrange invariants for the classical two-body problem, a new analytic continuation algorithm is presented and studied. The method utilizes kinematic transformation scalar variables differentiated to arbitrary order to generate the required power series coefficients. The present formulation is extended to accommodate the spherical harmonics gravity potential model. The scalar variable transformation essentially eliminates any divisions in the analytic continuation and introduces a set of variables that are closed with respect to differentiation, allowing for arbitrary-order time derivatives to be computed recursively. Leibniz product rule is used to produce the needed arbitrary-order expansion variables. With arbitrary-order time derivatives available, Taylor series-based analytic continuation is applied to propagate the position and velocity vectors for the nonlinear two-body problem. This foundational method has been extended to also demonstrate an effective variable step size control for the Taylor series expansion. The analytic power series approach is demonstrated using trajectory calculations for the main problem in satellite orbit mechanics including high-order spherical harmonics gravity perturbation terms. Numerical results are presented to demonstrate the high accuracy and computational efficiency of the produced solutions. It is shown that the present method is highly accurate for all types of studied orbits achieving 12–16 digits of accuracy (the extent of double precision). While this double-precision accuracy exceeds typical engineering accuracy, the results address the precision versus computational cost issue and also implicitly demonstrate the process to optimize efficiency for any desired accuracy. We comment on the shortcomings of existing power series-based general numerical solver to highlight the benefits of the present algorithm, directly tailored for solving astrodynamics problems. Such efficient low-cost algorithms are highly needed in long-term propagation of cataloged RSOs for space situational awareness applications. The present analytic continuation algorithm is very simple to implement and efficiently provides highly accurate results for orbit propagation problems. The methodology is also extendable to consider a wide variety of perturbations, such as third body, atmospheric drag and solar radiation pressure. [ABSTRACT FROM AUTHOR]