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The orbits of interest for potential missions are stable or nearly stable to maintain long term presence for conducting scientific studies and to reduce the possibility of rapid departure. Near Rectilinear Halo Orbits (NRHOs) offer such stable or nearly stable orbits that are defined as part of the L1 and L2 halo orbit families in the circular restricted three-body problem. Within the Earth-Moon regime, the L1 and L2 NRHOs are proposed as long-horizon trajectories for cislunar exploration missions, including NASA's upcoming Gateway mission. These stable or nearly stable orbits do not possess well-distinguished unstable and stable manifold structures. As a consequence, existing tools for stationkeeping and transfer trajectory design that exploit such underlying manifold structures are not reliable for orbits that are linearly stable. The current investigation focuses on leveraging stretching direction as an alternative for visualizing the flow of perturbations in the neighborhood of a reference trajectory. The information supplemented by the stretching directions are utilized to investigate the impact of maneuvers for two contrasting applications; the stationkeeping problem, where the goal is to maintain a spacecraft near a reference trajectory for a long period of time, and the transfer trajectory design application, where rapid departure and/or insertion is of concern. 

Particularly, for the stationkeeping problem, a spacecraft incurs continuous deviations due to unmodeled forces and orbit determination errors in the complex multi-body dynamical regime. The flow dynamics in the region, using stretching directions, are utilized to identify appropriate maneuver and target locations to support a long-lasting presence for the spacecraft near the desired path. The investigation reflects the impact of various factors on maneuver cost and boundedness. For orbits that are particularly sensitive to epoch time and possess distinct characteristics in the higher-fidelity ephemeris model compared to their CR3BP counterpart, an additional feedback control is applied for appropriate phasing. The effect of constraining maneuvers in a particular direction is also investigated for the 9:2 synodic resonant southern L2 NRHO, the current baseline for the Gateway mission. The stationkeeping strategy is applied to a range of L1 and L2 NRHOs, and validated in the higher-fidelity ephemeris model. 

For missions with potential human presence, a rapid transfer between orbits of interest is a priority. The magnitude of the state variations along the maximum stretching direction is expected to grow rapidly and, therefore, offers information to depart from the orbit. Similarly, the maximum stretching in reverse time, enables arrival with a minimal maneuver magnitude. The impact of maneuvers in such sensitive directions is investigated. Further, enabling transfer design options to connect between two stable orbits. The transfer design strategy developed in this investigation is not restricted to a particular orbit but applicable to a broad range of stable and nearly stable orbits in the cislunar space, including the Distant Retrograde Orbit (DROs) and the Low Lunar Orbits (LLO) that are considered for potential missions. Examples for transfers linking a southern and a northern NRHO, a southern NRHO to a planar DRO, and a southern NRHO to a planar LLO are demonstrated.


The libration point orbits in the Sun-Earth/Moon system are formed by concurrent gravitational influences by various celestial bodies, originating in a nonlinear dynamical regime. Coupled with the unstable nature of the orbit, the impact of any perturbations are expected to increase rapidly. The feasibility of a flow-based, Cauchy-Green tensor control strategy for station-keeping is examined. An orbit consistent with the mission objectives is selected for examination. The station-keeping process is stochastic, thus Gaussian random errors are introduced for simulation. The evolution of a velocity perturbation over time is monitored, beyond which the attainable state in the accessible region nearest to the target state is employed as a feedback to compute the necessary full, three-component corrective maneuver. The application and appropriateness of single axis control maneuvers for orbit maintenance are also evaluated. The selection procedure for certain parameters such as tolerances and weighting values are developed to incorporate the available dynamical information, yielding a versatile and straightforward strategy. Weighting matrices within the target point approach are effective in influencing the station-keeping costs as well as size and direction of maneuvers. Moreover, selection of appropriate tolerance values in the application of the Cauchy-Green tensor exploits the dominant stretching direction of the perturbation magnitude to inform the maneuver construction process. The work is demonstrated in the context of the upcoming Aditya-1 mission to a Sun-Earth/Moon L1 halo orbit for solar observations and the James Webb Telescope to a Sun-Earth/Moon L2 halo orbit for astronomy.

Non-Scientific Articles