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Key research themes
1. How can invariant manifolds and periodic orbits around Earth-Moon libration points be exploited to design efficient orbit transfer trajectories?
This research theme focuses on leveraging the dynamics of periodic orbits and their invariant manifolds around Earth-Moon libration points (such as L1 and L2) to devise low-fuel, feasible transfer trajectories between Earth orbits, lunar orbits, and beyond, extending even to Near-Earth Asteroids (NEAs). These dynamical structures provide natural pathways and energy-efficient corridors that can be exploited to design transfers including lunar swing-bys, stable halo or Lissajous orbits, and escape trajectories with reduced ∆V requirements. The understanding and computational construction of these invariant manifolds and periodic/quasi-periodic orbits underpin mission planning strategies that minimize fuel consumption and optimize trajectory timing in the Earth-Moon system.
Key finding: This study identified a family (G) of retrograde periodic orbits about the Earth-Moon L1 point within the Circular Restricted Three-Body Problem (CR3BP) that naturally connect low Earth orbits (LEO) to low lunar orbits (LLO)... Read more
Key finding: By modeling the Earth-Moon system under solar perturbations through the Bicircular Problem (BCP), this work revealed that the stable manifolds of quasi-periodic halo orbits around the Earth-Moon L2 point bend closer to Earth... Read more
Key finding: Using the CR3BP framework and dynamical systems theory, this paper computed transfers from low Earth orbit to quasi-periodic Lissajous orbits around Earth-Moon collinear points L1 or L2 using just two maneuvers—one for... Read more
Key finding: Extending the CR3BP to include low-thrust propulsion, this work analyzed how low-thrust affects dynamical structures such as zero velocity curves and periodic orbits near the Moon, demonstrating the existence of novel... Read more
2. How can optimal control and feedback strategies be applied to achieve fuel-efficient low-thrust orbit transfers and trajectory maintenance?
This theme emphasizes the use of advanced control theory, including nonlinear feedback control, optimal feedback laws, and the Theory of Functional Connections (TFC), to design fuel-efficient low-thrust spacecraft trajectories and to maintain or generate periodic orbits under perturbations. These approaches overcome limitations of classical open-loop optimal control by providing closed-loop solutions that respond robustly to perturbations and uncertainties. They also introduce methodologies to embed orbit and mission constraints analytically, yielding computationally tractable algorithms for practical trajectory optimization and station-keeping in multi-body dynamical environments.
Key finding: Using a globally diffeomorphic linearizing transformation and generating function techniques, this paper derived closed-form analytical feedback optimal control laws for nonlinear low-thrust interplanetary trajectories,... Read more
Key finding: This study applied the Theory of Functional Connections (TFC) to design a sub-optimal linear control law for continuous thrust components, enabling satellites to maintain periodic orbits (e.g., Earth resonant or... Read more
Key finding: This paper introduced a coordinate transformation leveraging problem symmetries to linearize otherwise nonlinear and coupled mission constraints in orbit transfers, enabling the application of the Theory of Functional... Read more
Key finding: This study proposed a saturated nonlinear feedback control law for low-thrust orbit injection into elliptic quasi-synchronous Martian orbits from a highly elliptical capture orbit. The feedback guidance relies only on... Read more
Key finding: Employing the Gauss form of the Lagrange Planetary Equations, the authors modeled low-thrust orbit raising from elliptical to circular orbits using three control laws, including burn arc and inertial steering thrusting modes.... Read more
3. What are the effects and mitigation strategies of thrust misalignments and perturbations in orbit transfer maneuvers and maintenance?
This theme explores the theoretical and practical consequences of thrust misalignments—angular and magnitude deviations—from nominal thrust directions, which introduce unintended translational forces and torques affecting spacecraft attitude, trajectory, and mission success during orbit transfers or station-keeping. Research within this theme examines covariance propagation of errors, nonlinear effects including vehicle mass property changes and center of mass shifts, dynamic coupling between attitude and orbital motion, and proposes control or maneuver strategies—such as spin stabilization and split burns—to compensate for these disturbances, critical to ensuring accuracy, fuel efficiency, and mission longevity.
Key finding: This comprehensive review highlighted how small thrust misalignments (angular deviations as low as milliradians) produce undesired forces and torques causing attitude deviations and orbit insertion errors, potentially... Read more