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Trajectory design in cislunar space under a High-Fidelity Ephemeris Model (HFEM) is pursued through a nonlinear optimization perspective anchored on the transition of solutions from lower fidelity models, namely the Circular Restricted…

Optimization and Control · Mathematics 2026-03-27 António Nunes , Sérgio Brás , Pedro Batista , João Xavier

A computational approach is developed for the design of continuous low thrust transfers in the planar circular restricted three-body problem. The transfer design method of invariant manifolds is extended with the addition of continuous low…

Optimization and Control · Mathematics 2015-10-12 Shankar Kulumani , Taeyoung Lee

The design of transfers to periodic orbits in the Earth-Moon system has regained prominence with NASA's Artemis and CNSA's Chang'e programs. This work addresses the problem of linking ballistic capture trajectories - exploiting multi-body…

Earth and Planetary Astrophysics · Physics 2026-01-09 Lorenzo Anoè , Roberto Armellin , Jack Yarndley , Thomas Caleb , Stéphanie Lizy-Destrez

Dynamical structures in the circular restricted three-body problem (CR3BP) are fundamental for designing low-energy transfers, as they aid in analyzing phase space transport and designing desirable trajectories. One of these dynamical…

Chaotic Dynamics · Physics 2026-05-14 Naoki Hiraiwa , Mai Bando , Yuzuru Sato , Shinji Hokamoto

The problem of minimizing the transfer time between periodic orbits in the Earth-Moon elliptic restricted three-body problem using a multi-mode propulsion system is considered. By employing the true anomaly on the primary orbit as the…

Optimization and Control · Mathematics 2025-09-10 George V. Haman , Anil V. Rao

Spacecraft trajectory design is a global search problem, where previous work has revealed specific solution structures that can be captured with data-driven methods. This paper explores two global search problems in the circular restricted…

Machine Learning · Computer Science 2024-12-31 Jannik Graebner , Anjian Li , Amlan Sinha , Ryne Beeson

The Circular Restricted Three-Body Problem (CR3BP) models the motion of a massless body under the gravitational influence of two primaries. We present a method for approximating a given family of periodic orbits by low-degree implicit…

Algebraic Geometry · Mathematics 2026-04-30 Ruiqi Huang , Anton Leykin

Near-Earth Objects (NEOs) are attractive exploration targets due to their accessibility, scientific value, and resources. Although trajectory design has revealed efficient pathways to these bodies, systematic strategies for Earth-NEO…

Earth and Planetary Astrophysics · Physics 2026-03-31 Alessandro Beolchi , Mauro Pontani , Kathleen Howell , Chiara Pozzi , Sean Swei , Elena Fantino

We demonstrate the remarkable effectiveness of boundary value formulations coupled to numerical continuation for the computation of stable and unstable manifolds in systems of ordinary differential equations. Specifically, we consider the…

Dynamical Systems · Mathematics 2017-06-01 Renato C. Calleja , Eusebius J. Doedel , Antony R. Humphries , Alexandra Lemus , Bart E. Oldeman

In recent years, stable and unstable manifolds of invariant objects (such as libration points and periodic orbits) have been increasingly recognized as an efficient tool for designing transfer trajectories in space missions. However, most…

Dynamical Systems · Mathematics 2021-10-01 Bhanu Kumar , Rodney L. Anderson , Rafael de la Llave

Mission designers must study many dynamical models to plan a low-cost spacecraft trajectory that satisfies mission constraints. They routinely use Poincar\'e maps to search for a suitable path through the interconnected web of periodic…

Chaotic Dynamics · Physics 2020-09-09 Xavier M. Tricoche , Wayne R. Schlei , Kathleen C. Howell

Optimization of low-thrust trajectories that involve a larger number of orbit revolutions is considered a challenging problem. This paper describes a high-precision symplectic method and optimization techniques to solve the minimum-energy…

Space Physics · Physics 2019-09-19 Zhibo E , Davide Guzzetti

In this work, we investigate trajectories that require thrust to maintain periodic structure in the circular restricted three-body problem (CR3BP). We produce bounds in position and velocity space for the energy-constrained reachable set of…

Dynamical Systems · Mathematics 2024-11-19 Colby C. Merrill , Jackson Kulik , Dmitry Savransky

This work presents a new method for generating impulsive trajectories in restricted two-body systems by leveraging Riemannian geometry. The proposed method transforms the standard trajectory optimization problem into a purely geometric one…

Systems and Control · Electrical Eng. & Systems 2025-08-18 Samuel G. Gessow , James Tseng , Eden Zafran , Brett T. Lopez

Multi-rendezvous spacecraft trajectory optimization problems are notoriously difficult to solve. For this reason, the design space is usually pruned by using heuristics and past experience. As an alternative, the current research explores…

Optimization and Control · Mathematics 2020-11-16 Aleksandar Petrov , Ron Noomen

The optimization of low-thrust, multi-revolution orbit transfer trajectories is often regarded as a difficult problem in modern astrodynamics. In this paper, a flexible and computationally efficient approach is presented for the…

Optimization and Control · Mathematics 2024-09-11 Mirko Leomanni , Gianni Bianchini , Andrea Garulli , Renato Quartullo

In this work, we develop a new method to design energy minimum low-thrust missions (L2-minimization). In the Circular Restricted Three Body Problem, the knowledge of invariant manifolds helps us initialize an indirect method solving a…

Optimization and Control · Mathematics 2016-07-04 Maxime Chupin , Thomas Haberkorn , Emmanuel Trélat

In this paper we study the problem of designing periodic orbits for a special class of hybrid systems, namely mechanical systems with underactuated continuous dynamics and impulse events. We approach the problem by means of optimal control.…

Optimization and Control · Mathematics 2017-02-16 Sara Spedicato , Giuseppe Notarstefano

In this paper, we seek optimal solutions for a transfer from a parking orbit around the Moon to a halo orbit around $L_2$ of the Earth-Moon system, by applying a single maneuver and exploiting the stable invariant manifold of the hyperbolic…

This study proposes a new automated strategy for designing and optimizing three-dimensional interplanetary low-thrust (LT) trajectories. The method formulates the design as a hybrid optimal control problem and solves it using a two-step…

Optimization and Control · Mathematics 2023-09-22 Burhani M. Burhani , Elena Fantino , Roberto Flores , Manuel Sanjurjo-Rivo
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