Project

Eclipse Conscious, Ephemeris Driven Low-thrust Trajectory Design using a Hybrid Optimal Control Method

Goal: The aim of this project is to design a methodology and supporting algorithms to design fuel-optimal low-thrust interplanetary eclipse-conscious transfers in a full ephemeris dynamical model. In particular, the methodology is to be applied to re-supply/Earth-return mission to the Lunar Gateway in the 9:2 Earth-Moon L2 Southern NRHO. The hybrid methodology relies on pre-computing stable/unstable pseudo-invariant manifolds of differentially corrected quasi-periodic orbits and using them as long terminal coast arcs, while formulating and solving the rest of the problem using indirect optimization methods.

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Project log

Sandeep Singh
added a research item
A novel indirect-based trajectory optimization framework is proposed that leverages ephemeris-driven, "invariant manifold analogues" as long-duration asymptotic terminal coast arcs while incorporating eclipses and perturbations during the optimization process in an ephemeris model; a feature lacking in state of the art software like MYSTIC and Copernicus. The end-to-end trajectories are generated by patching Earth-escape spirals to a judiciously chosen set of states on pre-computed manifolds. The results elucidate the efficacy of the proposed trajectory optimization framework using advanced indirect methods and by leveraging a Composite Smooth Control (CSC) construct. Multiple representative cargo re-supply trajectories are generated for the Lunar Orbital Platform-Gateway (LOP-G). The results quantify accurate ∆V costs required for achieving efficient eclipse-conscious transfers for several launch opportunities in 2025 and are anticipated to be used for analogous un-crewed lunar missions.
Sandeep Singh
added a research item
A novel methodology is proposed for designing low-thrust trajectories to quasi-periodic, near rectilinear Halo orbits that leverages ephemeris-driven, "invariant manifold analogues" as long-duration asymptotic terminal coast arcs. The proposed methodology generates end-to-end, eclipse-conscious, fuel-optimal transfers in an ephemeris model using an indirect formulation of optimal control theory. The end-to-end trajectories are achieved by patching Earth-escape spirals to a judiciously chosen set of states on pre-computed manifolds. The results elucidate the efficacy of employing such a hybrid optimization algorithm for solving end-to-end analogous fuel-optimal problems using indirect methods and leveraging a composite smooth control construct. Multiple representative cargo re-supply trajectories are generated for the Lunar Orbital Platform-Gateway (LOP-G). A novel process is introduced to incorporate eclipse-induced coast arcs and their impact within optimization. The results quantify accurate Δ costs required for achieving efficient eclipse-conscious transfers for several launch opportunities in 2025 and are anticipated to find applications for analogous uncrewed missions.
Sandeep Singh
added 2 research items
In this work, end-to-end low-thrust transfers from a GTO orbit to a low-altitude lunar orbit by exploiting the manifolds of a chosen Earth-Moon L1 halo orbit was studied. The practicality of piece-wise, minimum-time transfers that exploit halo orbit manifolds is demonstrated, which offers more flexibility to meet mission objectives. It is known that the structure of the manifolds varies substantially due to the presence of the Sun and its contribution has to be considered to obtain more realistic trajectories. To incorporate Sun’s perturbation, we study (1) manifolds’ behavior within a Bi-Circular Problem (BCP) dynamics and (2) Sun’s impact on the previously converged trajectories obtained using the standard Circular Restricted Three-Body Problem (CR3BP). Comparisons of the resulting trajectories using the CR3BP and BCP are presented.
Sandeep Singh
added 2 research items
Near-Rectilinear Halo Orbits (NRHOs) are deemed to be favorable candidates for establishing a near-future crewed space station in the cis-lunar space. Although the 9:2 resonant southern $L_2$ NRHO has been earmarked as the working orbit for the Lunar Gateway Mission, a plethora of other neighboring resonant NRHOs are also viable options. The invariant manifolds of these periodic orbits provide natural pathways to a state in the vicinity of fixed points on the NRHOs. These manifolds can be leveraged while designing optimal low-thrust trajectories for both `NRHO-bound' and `Earth-bound' missions. In this work, the effects of the ephemeris model (JPLs DE436) on three NRHO manifolds derived based on the Circular Restricted Three Body (CR3BP) assumptions are characterized and presented. The three neighboring NRHOs are then investigated in the domain of the aforementioned mission categories for piece-wise minimum-time and minimum-fuel, low-thrust transfers facilitated by invariant manifolds of the NRHOs. The minimum-time and minimum-fuel trajectory optimization problems are formulated using the indirect formalism of optimal control and solved using a single-shooting solution scheme. The relative merits of the stable manifolds are studied with regard to minimizing either mission time of flight or minimization of fuel consumption, for a set of representative low-thrust family of transfers.
A renewed interest in revisiting the Moon has blown wide open the previously ajar door to research avenues in the field of Earth-Moon transfer trajectories. While the advent of low-thrust propulsion systems has opened up possibilities to undertake more complicated missions, designing optimal transfer trajectories in this domain is no easy feat. Historically, the Circular Restricted Three Body Problem (CR3BP) assumptions have been extensively used for trajectory design in the cis-lunar space. The existence of natural pathways, also known as invariant manifolds, which wind on and off a close vicinity of periodic orbits existing near the libration points, can be leveraged to design more efficient transfer trajectories. In this paper, we study the transfer of a small spacecraft to a low-altitude moon orbit by making use of the manifolds of a chosen L1 Halo orbit. We demonstrate the practicality for a piece-wise, minimum-time transfer that riding the manifold in either direction from the Halo orbit provides, which directly enables more mission objective complexity.
Sandeep Singh
added a project goal
The aim of this project is to design a methodology and supporting algorithms to design fuel-optimal low-thrust interplanetary eclipse-conscious transfers in a full ephemeris dynamical model. In particular, the methodology is to be applied to re-supply/Earth-return mission to the Lunar Gateway in the 9:2 Earth-Moon L2 Southern NRHO. The hybrid methodology relies on pre-computing stable/unstable pseudo-invariant manifolds of differentially corrected quasi-periodic orbits and using them as long terminal coast arcs, while formulating and solving the rest of the problem using indirect optimization methods.