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Low-thrust trajectory design in the context of the three-body problem, particularly in the vicinity of liberation points, is addressed in this paper with a focus on efficiency and accuracy. The Fourier series, previously successful in approximating near-coplanar low-thrust trajectories within two-body dynamics, is applied to the challenging landscape of the three-body problem, marked by instability and nonlinearity. This paper introduces a novel approach for constructing an initial guess trajectory, that combines coast arcs from periodic orbits and intermediate trajectory arcs from other natural dynamical structures. The resulting initial guess trajectory is instrumental in generating efficient initial estimates for the coefficients of the Fourier series. The study encompasses the analysis of homoclinic and heteroclinic transfers in both two-dimensional and three-dimensional scenarios. The approximated trajectories derived from this methodology serve as invaluable starting points for high-fidelity optimization solvers, offering promise for enhancing the precision and efficiency of low-thrust transfers in cislunar space. • The shape method based on Fourier series is applied to the initial design of the transfer trajectories between periodic orbits in cislunar space. • An innovative approach to construct a continuous initial guess trajectory is introduced to derive initial guess values for the coefficients of Fourier terms. • An accurate approximation of the optimal transfer trajectory can be rapidly obtained. [ABSTRACT FROM AUTHOR]

This paper considers the problem of optimizing minimum-time and minimum-propellant many-revolution low-thrust geocentric orbit-raising maneuvers to an arbitrary target. The proposed direct single-shooting technique utilizes the regularized h , e element set as well as analytical models for ephemeris, shadow geometry, and thrust magnitude for ease of the optimization procedure. Third body and J 2 effects are included for higher fidelity of the computed solution. The gradient information supplied through adjoint sensitivities facilitates the convergence of the numerical optimization scheme. We also propose a new automated, fast and robust initial guess generation methodology by solving a sequence of unconstrained optimization orbit-raising sub-problems. The performance of the developed algorithm is demonstrated for orbit-raising to a variety of targets: the geosynchronous equatorial orbit, the Molniya orbit, and a near-rectilinear halo orbit. • A new low-thrust trajectory algorithm is developed using adjoint sensitivities. • The sequentially generated initial guesses are fast and robust to calculate. • An end-to-end optimization formulation computes minimum-time and minimum-fuel transfers. [ABSTRACT FROM AUTHOR]

Liquid crystal diffractive sails can generate controllable tangential radiation pressures, which have advantages in the Solar Polar Imager mission (SPI). This paper proposes a composite diffractive sail design consisting of an ideal passive diffraction grating sail and liquid crystal polarization gratings (LCPGs). The main diffractive grating sail generates thrust for orbital transfer with a sun-facing attitude. An optimal 3.8-year transfer trajectory is obtained by an improved direct method. Small-area LCPGs distributed around the edge are used for three-axis attitude control. The LCPGs can continuously modulate the force and torque by controlling the applied voltage based on the electro-optical characteristic of liquid crystal materials. A control strategy, including an adaptive attitude-tracking PD controller and a control allocation method, is designed to track the attitude profile generated by the transfer trajectory. Finally, the attitude-orbit coupling dynamics are used to simulate the whole process, and the results show that orbital insertion errors are minor. • A combined diffractive solar sail model using liquid crystal polarization gratings. • Independent and controllable three-axis attitude control of diffractive solar sails. • Optimizing transfer trajectory for solar polar mission based on the proposed sail. • An adaptive attitude-tracking PD controller and a control allocation method. [ABSTRACT FROM AUTHOR]

In this paper, Particle Swarm Optimization with energy-to-fuel continuation is proposed for initializing the co-state variables for low-thrust minimum-fuel trajectory optimization problems in the circular restricted three-body problem. Particle Swarm Optimization performs a search of the solution space by minimizing the weighted sum of squares of the two-point boundary-value problem final boundary condition residuals for the minimum-energy problem. Next, an energy-to-fuel homotopy is employed to transition the minimum-energy trajectory to a minimum-fuel trajectory, starting from the generated guess. The proposed methodology is applied to two low-thrust transfer problems in the Earth–Moon system: a transfer from a geostationary transfer orbit to an L1 halo orbit, and a transfer from an L2 halo orbit to an L1 halo orbit. The resulting minimum-fuel trajectories are validated with the literature. It is demonstrated that the methodology can successfully generate guesses for the initial co-state variables which converge to a solution for both scenarios. A strategically chosen particle swarm size is shown to improve the efficiency of the methodology. The proposed approach is of simple implementation, can be easily extended to other trajectory optimization problems, facilitates the discovery of multiple candidate trajectories, and does not require a user-provided guess, all of which are advantageous features for the preliminary phase of mission design. • Particle Swarm Optimization is proposed to guess the Lagrange co-states variables. • PSO initialization is paired with homotopy continuation for trajectory optimization. • The proposed algorithm facilitates discovery of multiple unique optimal trajectories. • Two minimum-fuel trajectory optimization problems are solved. • The effect of the particle swarm size on successful convergence is analyzed. [ABSTRACT FROM AUTHOR]

Over the past few decades, a considerable increase in the number of space debris has become a serious threat to the safety of the operating satellites. So, collision avoidance maneuvers have become indispensable in providing immediate and cost-effective solutions. The unavoidable presence of uncertainty associated with any physical system adds to the challenge. In this paper, a method is presented to determine the fuel-optimal collision avoidance trajectory using a convex optimization technique while incorporating the evolution of uncertainty associated with the space objects. The safety of the satellite is ensured by the collision avoidance constraints which involve calculating the instantaneous collision probability and using the Mahalanobis distance. An avoidance region is also demarcated around a space object with uncertain states to prevent any collision. Posing the problem as a convex optimization problem helps to eliminate the problem caused by dependency of the optimization variables on the initial guesses used. However, convexification of this problem with evolving uncertainty and collision probability calculation presents a set of challenges. The evolution of the positional error covariance ellipsoid leads to a feasible non-convex space surrounding the avoidance region. Moreover, implementation of a convex optimization formulation here requires convexification of the expression for collision probability, which is originally not purely convex in nature when a Gaussian probability density function is involved. This paper presents an approach to tackle the above-mentioned challenges. The satellite is returned to its nominal orbit in a timely manner, as time spent off the nominal trajectory can often lead to disruption of the space mission. The effects of various parameters on the required Δv are also explored. • Collision avoidance maneuver is formulated as a convex optimization problem. • Collision probability calculation and nonconvex feasible region are convexified. • The optimization includes evolution of uncertainty in the states of space objects. • An approximated Mahalanobis distance leads to a more conservative approach. • The effects of orbital, control and uncertainty parameters are explored. [ABSTRACT FROM AUTHOR]

Hydroterra was selected in September 2018 as one of the three candidates for the ESA's Earth Explorer-10 mission. Hydroterra aims at observing and improving the understanding of fundamental processes of daily water cycle, enhancing prediction capability of extreme rainfall and related flooding. To achieve this goal, the mission concept envisages placing a satellite embarking a synthetic aperture radar instrument in geosynchronous orbit. The satellite is designed to be launched with VEGA-C into low Earth orbit and to be transferred to the operational orbit by means of electric propulsion. In this paper, the multidisciplinary optimization process carried out to obtain the baseline electric orbit raising transfer for Hydroterra will be presented. The computed trajectory will meet the mission requirements, including targeting to the operational orbit, the launcher performance model, and the target on-station mass. Additionally, system-level constraints related to the satellite design that have an influence on the ideally optimized trajectory will be derived and considered in the optimization. In particular, the impact of the solar cell degradation on the thrust and specific impulse levels of the thruster due to the passage through the Van-Allen belts, the need to re-charge the batteries before entering the next eclipse, and the agility requirements will be accounted for. The obtained results show that a feasible electric orbit raising trajectory can be successfully obtained for the Hydroterra mission. • The Hydroterra electric orbit raising and satellite are concurrently optimized. • Solar cells damage, power, agility, launcher and on-station mass requirements apply. • Four thruster operational points switching criteria are defined to streamline the optimization problem. • A feasible baseline transfer minimizing the time in the Van-Allen belts is found. [ABSTRACT FROM AUTHOR]

The aim of this work is to investigate the performance of a solar sail-based spacecraft in an optimal apse line rotation maneuver. Considering a heliocentric two-body motion and a low-performance solar sail with an ideal force model, this study derives the optimal steering law that maximizes the final rotation angle of the osculating orbit apse line. Starting from an approximated (Gaussian) form of the Lagrange's planetary equations, the achievable argument of periapsis and the required flight times are obtained in a parametric way, for given values of parking orbit eccentricity and sail (reference) propulsive acceleration, as the solutions of an optimal control problem. The numerical simulations show that, for sufficiently large values of the orbit eccentricity, the maximum argument of periapsis is roughly proportional to the sail (reference) propulsive acceleration. An approximate locally-optimal steering law is also derived, and the results of the optimization problem are applied to Earth- and Venus-following orbits, where the planets trajectories are assumed to be circular and coplanar with the spacecraft parking orbit. • The work analyzes the apse line rotation maneuver of a solar sail-based spacecraft. • A heliocentric mission scenario is considered in the mathematical model. • The problem is solved in an optimal framework using an indirect approach. • The paper presents a set of graphs and approximate expressions to solve the problem. • A mission application involving a planet-following mission scenario is discussed. [ABSTRACT FROM AUTHOR]

Abstract The aim of this paper is to propose a semi-analytical method for the analysis of a two-impulse transfer between two coplanar elliptic orbits, assuming each maneuver to change the magnitude of the spacecraft velocity only, without affecting its direction. Using a recent mathematical model that describes the spacecraft dynamics in a compact analytical form within a two-dimensional multiple-impulse scenario, this work proposes an algorithm to calculate the global minimum velocity variation required to complete the transfer. The characteristics of the optimal transfer trajectory, which is tangent to both the parking and the target orbit, are obtained as a function of a single variable, which defines the angular position of the first maneuver. This feature allows the designer to analyze the cotangential transfer in a parametric form, thus obtaining a trade-off solution between the total velocity variation and the desired characteristics of the transfer orbit. Highlights • This paper analyzes a two-impulse cotangential transfer between el-lipses. • The optimal transfer trajectory is obtained as a function of a single angular variable. • A simple algorithm is proposed for finding the total Δ V of a two-impulse transfer. • The method gives a trade-off solution between Δ V and the transfer orbit characteristics. [ABSTRACT FROM AUTHOR]

Abstract This paper investigates the concept of capturing near-Earth asteroids into bound orbits around the Earth by using aerobraking. To guarantee that the candidate asteroids cannot present an impact risk during aerobraking, an initial aerobraking hazard analysis is undertaken and accordingly only asteroids with a diameter less than 30 m are considered as candidates in this paper. Then, two asteroid capture strategies utilizing aerobraking are defined. These are termed single-impulse capture and bi-impulse capture, corresponding to two approaches to raising the perigee height of the captured asteroid's orbit after the aerobraking manoeuvre. A Lambert arc in the Sun-asteroid two-body problem is used as an initial estimate for the transfer trajectory to the Earth and then a global optimisation is undertaken, using the total transfer energy cost and the retrieved asteroid mass ratio (due to ablation) as objective functions. It is shown that the aerobraking can in principle enable candidate asteroids to be captured around the Earth with, in some cases, extremely low energy requirements. Highlights • An aerobraking hazard analysis is undertaken to select candidate asteroids. • Two asteroid capture strategies using aerobraking are proposed. • Maximum mass ratio of captured asteroid and spacecraft is obtained. • Best candidate asteroids which can be captured using aerobraking are found. [ABSTRACT FROM AUTHOR]

This paper solves the problem of the on-line joint optimization of the target orbit and flight trajectory of a launch vehicle experiencing a thrust drop failure, and proposes state-triggered indices to improve the solving efficiency. The 'highest-height index' is triggered first to find the maximum-height circular orbit (MCO) in the orbital plane formed at the time of failure. If the orbital altitude is less than the perigee height of the prescribed target orbit, the MCO will be regarded as the optimal circular orbit to ensure safety. If not, the 'minimal orbital plane deviations index' is triggered to subsequently find the optimal elliptical orbit (OEO), where the orbital inclination and longitude of the ascending node are preferentially adjusted on the basis of the MCO. Furthermore, if the OEO is coplanar with the target orbit, a 'minimal orbital shape deviations index' is triggered to find the optimal rescue orbit, which eliminates the deviations of the perigee altitude, semi-major axis and perigee argument on the basis of the OEO. Estimation of the geocentric angle of the injection point, construction of the approximated sub-problem, and convexification processing are adopted to provide initial guesses to boost the computing. Monte Carlo simulations show that the method not only converges to the optimal or sub-optimal solution for different failure states, which avoids suspended calculations, non-convergence, and constraint violations that are common when directly solving this type of rescue problem, but also meets the basic requirements of on-line applications. • State triggered index is proposed to get optimal rescue orbit if thrust drop occurs. • Orbital altitude, plane, and shape are adjusted sequentially to ensure solvability. • Convexification and range estimation are used to get initial value and boost solving. • Simulations show the adaptability to various fault scenarios and on-line application. [ABSTRACT FROM AUTHOR]

In this paper, a suborbit to orbit mission profile is analysed for spaceplanes. The proposed mission profile for spaceplanes is currently being considered for multiple earth observation missions and is considered as an extension of the skip re-entry problem which is a highly coupled and nonlinear problem. To solve the problem, we utilise both the Fuzzy Satisfactory Goal Programming (FSGP) method and the Radau Pseudospectral Method (RPM) as the problem includes more than two objective functions conflicting with each other, and needs to be optimised with pre-emptive priorities. A realistic spaceplane model is used with equality and inequality constraints, to demonstrate the feasibility of suborbit-orbit-suborbit manoeuvres through numerical simulations. The simulation results generated by the proposed methodology show that significant propellant savings can be made using multi-objective trajectory optimisation for spaceplanes for future theatre observation missions. • An optimisation problem formulation for a suborbit/orbit manoeuvring. • Reduction of the computational time of the problem by changing an objective function. • Trajectory analysis for efficient flight. [ABSTRACT FROM AUTHOR]