Lagrange Point Orbits Research Articles

Micro-spacecraft in Sun-Venus Lagrange point orbit for the Venera-D mission

The baseline Venera-D mission, proposed to be launched after 2026, consists of an orbiter and a landing module, which includes a lander and a small long-lived station. In this work, we present the possibility of augmenting the mission with one or two micro-spacecraft in Lagrange point orbits to significantly enhance the science return. Both L1 and L2 collinear points, situated at about 1 million km from Venus, are considered for scientific objectives. The paper focuses on trajectory design for the micro-spacecraft to be deployed by the Venera-D mission. The transfer scenario we propose performs the insertion of micro-spacecraft into Lagrange point orbit by making use of the main orbiter’s propulsion, while the propulsion on board micro-spacecraft is used only for trajectory correction and station-keeping manoeuvres. This scenario allows the Venera-D mission to add one or two micro-spacecraft of mass about 50 kg with only a total ΔV budget 30 m/s over 3 years on orbit.

Enhancing Station-Keeping Control With the Use of Extended State Observers

Recently there has been a resurgence of interest in missions to the moon and a major challenge of such missions is to provide a continuous communication between the Earth and the Moon's far side. Orbits around the $L_2$ Earth-Moon Lagrange point have been a topic of interest in this field due to their potential for constant communication with both the Earth and the Moon, however the Lagrange point orbits are innately unstable and so station-keeping control is required to maintain them. Station-keeping problems are highly nonlinear and a traditional approach to control design is first to linearize the nonlinear system. However, this first-order approximation introduces errors if there are large injection errors. This paper demonstrates how a simple Extended State Observer (ESO) can be used to improve the convergence time of spacecraft to the reference orbit given with large injection errors. Additionally, solar radiation pressure (SRP) a dominant disturbance in deep-space, can lead to inefficient station-keeping if it is not taken into account in the reference orbit design. New reference orbits can be designed that exploit the SRP perturbation but this assumes that it is known apriori. Here we show how an ESO could provide an in-orbit measurement of the SRP which could be used to modify the reference trajectory to a more fuel efficient one. Finally, it is shown how an ESO can be used to estimate, not only the disturbance, but simultaneously the velocity of the spacecraft meaning that only the position of the spacecraft is required.

The Sun–Earth saddle point: characterization and opportunities to test general relativity

The saddle points are locations where the net gravitational accelerations balance. These regions are gathering more attention within the astrophysics community. Regions about the saddle points present clean, close-to-zero background acceleration environments where possible deviations from General Relativity can be tested and quantified. Their location suggests that flying through a saddle point can be accomplished by leveraging highly nonlinear orbits. In this paper, the geometrical and dynamical properties of the Sun–Earth saddle point are characterized. A systematic approach is devised to find ballistic orbits that experience one or multiple passages through this point. A parametric analysis is performed to consider spacecraft initially on $$L_{1,2}$$ Lagrange point orbits. Sun–Earth saddle point ballistic fly-through trajectories are evaluated and classified for potential use. Results indicate an abundance of short-duration, regular solutions with a variety of characteristics.

Distributed adaptive synchronization for multiple spacecraft formation flying around Lagrange point orbits

This paper presents a distributed adaptive control framework for multiple spacecraft formation flying around Lagrange point orbits, which account for unmeasurable velocities and (spacecraft) mass uncertainties. The nominal trajectory for the formation system is a halo orbit parameterized by Fourier series expansions. Such an explicit, albeit approximate, description of the nominal trajectory facilitates each spacecraft in formation to include the relative state information into a cooperative feedback control system design, so that the relative motion can be driven towards a desired trajectory while maintaining a group synchronization during the maneuver. The developed distributed control strategies rely on the protocols formulated on an undirected topology with mutual information interactions, utilizing every available neighbor-to-neighbor communication data couplings, in order to improve the reliability of the formation. Numerical simulations show that the proposed adaptive control laws guarantee global asymptotic convergence and system robustness.

Orbit period modulation for relative motion using continuous low thrust in the two-body and restricted three-body problems

This paper presents rich new families of relative orbits for spacecraft formation flight generated through the application of continuous thrust with only minimal intervention into the dynamics of the problem. Such simplicity facilitates implementation for small, low-cost spacecraft with only position state feedback, and yet permits interesting and novel relative orbits in both two- and three-body systems with potential future applications in space-based interferometry, hyperspectral sensing, and on-orbit inspection. Position feedback is used to modify the natural frequencies of the linearised relative dynamics through direct manipulation of the system eigenvalues, producing new families of stable relative orbits. Specifically, in the Hill–Clohessy–Wiltshire frame, simple adaptations of the linearised dynamics are used to produce a circular relative orbit, frequency-modulated out-of-plane motion, and a novel doubly periodic cylindrical relative trajectory for the purposes of on-orbit inspection. Within the circular restricted three-body problem, a similar minimal approach with position feedback is used to generate new families of stable, frequency-modulated relative orbits in the vicinity of a Lagrange point, culminating in the derivation of the gain requirements for synchronisation of the in-plane and out-of-plane frequencies to yield a singly periodic tilted elliptical relative orbit with potential use as a Lunar far-side communications relay. The Delta v requirements for the cylindrical relative orbit and singly periodic Lagrange point orbit are analysed, and it is shown that these requirements are modest and feasible for existing low-thrust propulsion technology.

Trajectory refinement of three-body orbits in the real solar system model

In this paper, an automatic algorithm for the correction of orbits in the real solar system model is described. The differential equations governing the dynamics of a massless particle in the n-body problem are written as perturbation of the circular restricted three-body problem in a non-uniformly rotating, pulsating frame by using a Lagrangian formalism. The refinement is carried out by means of a modified multiple shooting technique, and the problem is solved for a finite number of trajectory states at several time instants. The analysis involves computing the dynamical substitutes of the collinear points, as well as several Lagrange point orbits, for the Sun–Earth, Sun–Jupiter, and Earth–Moon gravitational systems.

Early Mission Design of Transfers to Halo Orbits via Particle Swarm Optimization

Particle Swarm Optimization (PSO) is used to prune the search space of a low-thrust trajectory transfer from a high-altitude, Earth orbit to a Lagrange point orbit in the Earth-Moon system. Unlike a gradient based approach, this evolutionary PSO algorithm is capable of avoiding undesirable local minima. The PSO method is extended to a “local” version and uses a two dimensional search space that is capable of reducing the computation run-time by an order of magnitude when compared with published work. A technique for choosing appropriate PSO parameters is demonstrated and an example of an optimized trajectory is discussed.

Orbit control strategy for Lagrange point orbits based on an analytical method

The periodic or quasi-periodic orbits around collinear Lagrange points present many properties that are advantageous for space missions. These Lagrange point orbits are exponentially unstable. On the basis of an analytical method, an orbit control strategy that is designed to eliminate the dominant unstable components of Lagrange point orbits is developed. The proposed strategy enables the derivation of the analytical expression of nonlinear control force. The control parameter of this strategy can be arbitrarily selected provided that the parameter is considerably lower than the negative eigenvalue of motion equations, and that the energy required keeps the same order of magnitude. The periodic or quasi-periodic orbit of controlled equations remains near the periodic or quasi-periodic orbit of uncontrolled equations.

Low-energy, low-thrust transfers to the Moon

The low-thrust version of the low energy transfers to the Moon exploiting the structure of the invariant manifolds associated to the Lagrange point orbits is presented in this paper. A method to systematically produce low-energy, low-thrust transfers executing ballistic lunar capture is discussed. The coupled restricted three-body problems approximation is used to deliver appropriate first guess for the subsequent optimization of the transfer trajectory within a complete four-body model using direct transcription and multiple shooting strategy. It is shown that less propellant than standard low energy transfers to the Moon is required. This paper follows previous works by the same authors aimed at integrating together knowledge coming from dynamical system theory and optimal control problems for the design of efficient low-energy, low-thrust transfers.