Orbital Reference Frame Research Articles

Fuelless On-Orbit Assembly of a Large Space Truss Structure Using Repulsion of the Service Spacecraft by Robotic Manipulators

A servicing spacecraft motion control approach for the problem of on-orbit truss structure assembly is developed in this paper. It is considered that a cargo container with a rod set and servicing spacecraft are in orbit initially. The assembly procedure is based on spacecraft free-flight motion between the structure’s specified points. The spacecraft is equipped with two robotic manipulators capable of attaching to the structure and holding rods. In addition, the spacecraft can repulse from the structure with a given relative velocity using a manipulator, so the spacecraft and the structure receive impulses. The repulsion velocity vector is calculated in order to reach the structure target point to deliver and install the rod into the truss structure, or to reach the cargo container and take a rod. The problem of searching the repulsion velocity is formulated as an optimization problem with constraints, taking into account the limited value of the repulsion velocity, collision avoidance with structure, restrictions on the angular velocity and translational motion of the structure in the orbital reference frame. This problem is solved numerically with an initial guess vector obtained analytically for simplified motion cases. The application of the proposed control scheme to the assembly of a truss-based antenna is demonstrated. It is shown that the servicing spacecraft is successfully transferred between the structure points by means of manipulator repulsion. Main features and limitations of the assembly problem using a spacecraft with two manipulators are discussed.

Cavsiopy: a Python package to calculate and visualize spacecraft instrument orientation

Spacecraft attitude plays an important role in the observations of various atmospheric, planetary, and terrestrial parameters and phenomena that are of interest to the scientific community. Precise measurements from imagers, particle sensors, and antennas require accurate knowledge of instrument orientation. cavsiopy is an easy-to-install and use, light-weight open-source Python package for researchers who need to consider instrument pointing direction and observation geometry. cavsiopy contains the coordinate transformation routines and the corresponding rotation matrices from the spacecraft orbital reference frame (ORF) to any of the geocentric equatorial inertial for epoch J2000 (GEI J2K)/International Celestial Reference Frame (ICRF), Earth-centered, Earth-fixed (ECEF), International Terrestrial Reference Frame (ITRF), geodetic north-east-down, and geocentric north-east-center coordinate systems. Additionally, cavsiopy includes routines for importing Swarm-E ephemeris and generic two-line-element (TLE) data files; for the calculation of spacecraft azimuth, elevation, and orbital parameters; as well as for the 2D/3D visualization of the geometry between the instrument and the target. Functionality and utilization of cavsiopy for research problems are demonstrated with examples and visualizations for the Radio Receiver Instrument (RRI) and the Fast Auroral Imager (FAI) of e-POP/Swarm-E.

Application of Dynamic Neural Network Model for Magneto- Coulombic Attitude Control of Earth-Pointing Satellite

An active control of the satellite attitude using magneto-Coulombic actuators is proposed along the circular orbit. Equation for the required charges on the Coulomb shells is derived, which is used to find the available control torque along the three body axes. It is proved that the eigenvalues of the averaged control matrix of the magneto-Coulombic system in the body reference frame for different orientations and angular velocities components will converge to the same values as in the case of the eigenvalues of the averaged control matrix in the orbital reference frame. A dynamic neural network based control law is adapted and trained for the proposed system. The neural network based dynamic neural network controller has the advantages of handling the non-linearity, adaptation and on-board training, and robust to large changes in the parameters in the plant, such as the moments of inertia. It is shown that the stabilization accuracy of the dynamic neural controller is higher as compared to the proportional-derivative based controller.

A Study of the Motion of Four Linked Satellites Controlled Using Lorentz Forces

This paper considers four satellites connected to each other by electrodynamic tethers, which are assumed to be rigid in the mathematical model of the system’s motion. In the Earth’s magnetic field, current-carrying conductors are affected by Lorentz forces, which are used to control the motion of the system’s center of mass and the angular motion. The paper presents an algorithm for calculating the magnitude of the current to stop the drift of the center of mass of a tetrahedral formation relative to the desired orbital reference frame in low Earth orbit and spin the system up to a constant angular velocity relative to the center of mass. A numerical study of the convergence time to achieve the required motion is carried out depending on the maximum possible current and initial conditions.

Solar Sail Orbit Raising with Electro-Optically Controlled Diffractive Film

The aim of this paper is to analyze the transfer performance of a spacecraft whose primary propulsion system is a diffractive solar sail with active, switchable panels. The spacecraft uses a propellantless thruster that converts the solar radiation pressure into propulsive acceleration by taking advantage of the diffractive property of an electro-optically controlled (binary) metamaterial. The proposed analysis considers a heliocentric mission scenario where the spacecraft is required to perform a two-dimensional transfer between two concentric and coplanar circular orbits. The sail attitude is assumed to be Sun-facing, that is, with its sail nominal plane perpendicular to the incoming sunlight. This is possible since, unlike a more conventional solar sail concept that uses metalized highly reflective thin films to reflect the photons, a diffractive sail is theoretically able to generate a component of the thrust vector along the sail nominal plane also in a Sun-facing configuration. The electro-optically controlled sail film is used to change the in-plane component of the thrust vector to accomplish the transfer by minimizing the total flight time without changing the sail attitude with respect to an orbital reference frame. This work extends the mathematical model recently proposed by the authors by including the potential offered by an active control of the diffractive sail film. The paper also thoroughly analyzes the diffractive sail-based spacecraft performance in a set of classical circle-to-circle heliocentric trajectories that model transfers from Earth to Mars, Venus and Jupiter.

On a Sailed Spacecraft Motion along a Handrail Fixed to Two Heliocentric Space Stations

Motion of a particle modeling a spacecraft with a solar sail along a handrail joining two heliocentric space stations is considered under the assumption that the sail is a perfect reflecting plane that can be located at any angle with respect to the direction of solar rays, the particle does not leave the plane of the orbit of the stations, the handrail is a tether that realizes an ideal unilateral constraint whose boundary is some ellipse, and the particle motion is sufficiently fast with respect to the orbital motion of the stations to neglect noninertiality of the orbital frame of reference. The equations of particle motion are written in dimensionless form without parameters, and the existence of an energy integral for the case of the sail orientation depending only on the spacecraft location is established. This integral is used for complete integration of the equations of motion for the particle relocations along the constraint boundary. The optimal length of the tether for the fastest relocation of a particle between the most remote points of the constraint boundary is computed for the case of the sail being orthogonal to the solar rays throughout the motion. Such a relocation time is computed in dimensionless form and for some real and hypothetical situations. A set of pairs of points in the constraint boundary between which relocation along the constraint boundary with zero initial and final velocities and with the invariably oriented sail is possible is constructed depending on the eccentricity of the ellipse. The result is presented as several plots that illustrate the evolution of the pairs’ regions as the eccentricity of the ellipse changes.

Averaging technique in the problem of satellite attitude stabilization in indirect position in the orbital reference frame with the use of Lorentz torque

A dynamically symmetric satellite in a circular orbit of small inclination is considered. The problem of the Lorentzian stabilization of the satellite in the orbital coordinate system in the indirect equilibrium position is solved under the conditions of the perturbing effect of the gravitational torque. To solve this problem, which is characterized by incomplete control, a method of averaging differential equations is developed. Using the original construction of the unsteady Lyapunov function, we obtain sufficient conditions for the asymptotic stability of the programmed satellite motion mode in the form of constructive inequalities with respect to the control parameters.

ATTITUDE RESTITUTION FOR MULTISPECTRAL EARTH OBSERVATION SATELLITE USING SPACE TRIANGULATION TECHNIQUE

Abstract. Earth observation satellites are equipped with navigation components (star trackers, gyroscopes) which estimates the attitude of the satellite, corresponding to its orientation in the orbital reference frame. This equipment is essential for the localisation of the images which is done a posteriori and for the registration of the different images for a pushbroom sensor. This concerns both the registration of the spectral bands and the registration of multi-temporal series. However, the required accuracy is not always compatible with the performance of the attitude restitution. Moreover, some specific applications need more stringent geometric control even if requirements are met. With a multi-spectral pushbroom instrument, the same object on ground is seen as many times as number of spectral bands at different time instants: the attitude profile of the platform can be completely reconstructed from the results of the mapping of the different spectral bands. An attitude reconstruction method is proposed based on space triangulation inversion technique. The framework of this study is low-frequencies noise perturbations applied to Venμs satellite. Cubic splines are used for the attitude error profile, with 60 free parameters. Provided the physical model is representative, we show on two test cases that the convergence is very good. The band registration quality is used as a proxy to assess the performances. Residuals errors are less than 0.05 pixel for all tested band couples.

Averaging technique in the problem of Lorentz attitude stabilization of an Earth-pointing satellite

An Earth-pointing satellite with Lorentz attitude control system is under consideration. The problem of the satellite attitude stabilization in the orbital reference frame in the presence of disturbances and complicated by underactuation is studied. The averaging technique is developed and applied in the problem. A rigorous mathematical justification is proposed, which makes it possible to consider a satellite with unequal moments of inertia and to obtain specific estimates for the control parameters that provide a solution to the problem of satellite attitude stabilization with the use of the Lorentz control torque. The octupole approximation of the Earth's magnetic field is used; the periodic functions of time arise in geomagnetic field induction. With the aid of nonlinear approach to the problem it is proved that Lorentz attitude control system ensures asymptotic stability of the satellite equilibrium under the perturbing action of disturbing torques provided dissipative torque is operating alongside with the restoring one. The proof is based on the Lyapunov direct method and the averaging technique. In the paper, original constructions of nonstationary Lyapunov functions are proposed. These constructions take into account the structure of perturbations acting on the considered system. With the aid of the proposed Lyapunov functions, sufficient conditions for the asymptotic stability of the satellite equilibrium position are derived. These conditions are formulated in terms of explicit inequalities on the control parameters. Thus, a constructive approach to the design of stabilizing controls is formulated.

Electric sail phasing maneuvers for constellation deployment

The aim of this work is to investigate heliocentric phasing maneuvers performed by a spacecraft propelled by an Electric Solar Wind Sail, that is, an innovative propellantless propulsion system that consists of a spinning grid of charged tethers that uses solar wind momentum to produce thrust. It is assumed that the Electric Solar Wind Sail may be controlled by varying its attitude with respect to a classical orbital reference frame, and by switching the tether grid off to obtain Keplerian arcs along its phasing trajectory. The analysis is conducted within an optimal framework, the aim of which is to find both the optimal control law and the minimum-time phasing trajectory for a given angular drift along the (assigned) working orbit. A typical phasing scenario is analyzed, by considering either a drift ahead or a drift behind maneuver on a circular, heliocentric orbit of given radius. The paper also investigates the possibility of using an Electric Solar Wind Sail-based deployer to place a constellation of satellites on the same working orbit. In that case, the optimal flight time is obtained in a compact, semianalytical form as a function of both the propulsion system performance and the number of the sail-deployed satellites.

Comparison between direct and indirect approach to solar sail circle-to-circle orbit raising optimization

This paper deals with the optimization of the transfer trajectory of a solar sail-based spacecraft between circular and coplanar heliocentric orbits. The problem is addressed using both a direct and an indirect approach, while an ideal and an optical force model are used to describe the propulsive acceleration of a flat solar sail. In the direct approach, the total flight time is partitioned into arcs of equal duration, within which the sail attitude is assumed to be constant with respect to an orbital reference frame, and a nonlinear programming solver is used to optimize the transfer trajectory. The aim of the paper is to compare the performance of the two (direct and indirect) approaches in term of optimal (minimum) flight time. In this context, the simulation results show that a direct transcription method using a small number of arcs is sufficient to obtain a good estimate of the global minimum flight time obtained through the classical calculus of variation.

Digital and Pulse-width Control of the Satellites and Space Robots Orientation in Initial Modes

Abstract Problems of nonlinear digital and pulse-width control for the spacecraft orientation in initial modes are considered – during their separation from a launcher rocket up to regular attitude stabilization in orbital reference frame. Developed methods, algorithms and the computer simulation results on the initial orientation modes of the small satellites and space robots in sun-synchronous orbit are presented.

Thrust and torque vector characteristics of axially-symmetric E-sail

The Electric Solar Wind Sail is an innovative propulsion system concept that gains propulsive acceleration from the interaction with charged particles released by the Sun. The aim of this paper is to obtain analytical expressions for the thrust and torque vectors of a spinning sail of given shape. Under the only assumption that each tether belongs to a plane containing the spacecraft spin axis, a general analytical relation is found for the thrust and torque vectors as a function of the spacecraft attitude relative to an orbital reference frame. The results are then applied to the noteworthy situation of a Sun-facing sail, that is, when the spacecraft spin axis is aligned with the Sun-spacecraft line, which approximatively coincides with the solar wind direction. In that case, the paper discusses the equilibrium shape of the generic conducting tether as a function of the sail geometry and the spin rate, using both a numerical and an analytical (approximate) approach. As a result, the structural characteristics of the conducting tether are related to the spacecraft geometric parameters.

Logarithmic spiral trajectories generated by Solar sails

Analytic solutions to continuous thrust-propelled trajectories are available in a few cases only. An interesting case is offered by the logarithmic spiral, that is, a trajectory characterized by a constant flight path angle and a fixed thrust vector direction in an orbital reference frame. The logarithmic spiral is important from a practical point of view, because it may be passively maintained by a Solar sail-based spacecraft. The aim of this paper is to provide a systematic study concerning the possibility of inserting a Solar sail-based spacecraft into a heliocentric logarithmic spiral trajectory without using any impulsive maneuver. The required conditions to be met by the sail in terms of attitude angle, propulsive performance, parking orbit characteristics, and initial position are thoroughly investigated. The closed-form variations of the osculating orbital parameters are analyzed, and the obtained analytical results are used for investigating the phasing maneuver of a Solar sail along an elliptic heliocentric orbit. In this mission scenario, the phasing orbit is composed of two symmetric logarithmic spiral trajectories connected with a coasting arc.

Space Debris Removal using a Tether: A Model

Focused on the removal of space debris, this paper studies the modeling of a target satellite connected to a chaser satellite by a tether. All dynamic couplings between the flexible and rigid modes of the satellites are accounted for. The tether attached to both satellites is modeled as a massless spring when stretched and non-existent when compressed. The objective of this work is to model the behaviour of the three bodies: chaser, tether, and target in the orbital reference frame for arbitrary initial conditions of the target satellite. Simulations of the whole system including the chaser Attitude and Orbit Control System (AOCS) are performed to evaluate its ability to damp the debris tumbling motion and to tow the debris.

Numerical Model for the Orbit of the Earth

In this paper, we constructed a 3-D numerical model of the Earth-Sun geometry. Our model defines Earth's orbit as an inclined plane of spherically symmetric system. We calculated the degree of the tilt of the Earth orbit to the ecliptic plane by converting from ecliptic frame of reference to the orbital frame of reference and then we made all the measurement. Initial inputs of our model are aphelion and perihelion parameters. It is interesting to examine that our results obtained from Earth inclined orbit are same that observed value from Earth's circular orbit. In other words, values of the axial tilt of Earth and Sun, the time taken for the Sun to move from vernal equinox to autumnal equinox and then back to the vernal equinox does not change. Moreover, we were also able to derive mathematical relations for finding the length of the apparent solar days throughout the year. On introducing the new types of the length of the day, called Saurya day, the rate of precession of equinox is calculated.

Autonomous Control Program for Special Spacecraft Debris Collector Rendezvous Transfer with Fragment of Space Debris with Low-thrust

The problem of fragment of space debris located at geostationary orbit disposal is studied. For this purpose, a special spacecraft debris collector is used. The main part of disposal operation – rendezvous transfer with fragment of space debris - is studied. Relative motion of a spacecraft debris collector about the fragment of space debris is considered in an orbital cylindrical reference frame. Secular and periodic components of relative motion are determined in an implicit form. Spacecraft debris collector motion control is carried out by its transversal acceleration from thrust switching. Radial thrust component is equal to zero. Boundary conditions for rendezvous transfer are formulated in terms of secular and periodic components of motion. The Motion control program for secular components contained two active areas and passive areas between them. Active areas duration were determined as functions of boundary conditions and passive area duration (free parameter). An analytical solution for the determined control program is formulated in an implicit form. Satisfaction of boundary conditions for periodic components is carried out by passive area duration and rendezvous start moment determination. Equations to determine these parameters are formulated. Numerical simulation is carried out.

Advanced numerical study of the three-axis magnetic attitude control and determination with uncertainties

Attitude motion of a satellite equipped with magnetic control system is considered. System comprises of three magnetorquers and one three-axis magnetometer. Satellite is stabilized in orbital reference frame using PD controller and extended Kalman filter. Three-axis attitude is analyzed numerically with advanced assumptions: inertia tensor uncertainty, disturbances of unknown nature, magnetometer errors are taken into account. Stabilization and determination accuracy dependence on orbit inclination is studied.

Orbital reference frame estimation with power spectral density constraints for drag-free satellites

The drag-free satellites are widely used in the field of fundamental science as they enable the high-precision measurement in pure gravity fields. This paper investigates the estimation of local orbital reference frame (LORF) for drag-free satellites. An approach, taking account of the combination of the minimum estimation error and power spectral density (PSD) constraint in frequency domain, is proposed. Firstly, the relationship between eigenvalues of estimator and transfer function is built to analyze the suppression and amplification effect on input signals and obtain the eigenvalue range. Secondly, an optimization model for state estimator design with minimum estimation error in time domain and PSD constraint in frequency domain is established. It is solved by the sequential quadratic programming (SQP) algorithm. Finally, the orbital reference frame estimation of low-earth-orbit satellite is taken as an example, and the estimator of minimum variance with PSD constraint is designed and analyzed using the method proposed in this paper.

Nonlinear dynamics of flexible tethered satellite system subject to space environment

The paper studies the nonlinear dynamics of a flexible tethered satellite system subject to space environments, such as the J2 perturbation, the air drag force, the solar pressure, the heating effect, and the orbital eccentricity. The flexible tether is modeled as a series of lumped masses and viscoelastic dampers so that a finite multidegree-of-freedom nonlinear system is obtained. The stability of equilibrium positions of the nonlinear system is then analyzed via a simplified two-degree-freedom model in an orbital reference frame. In-plane motions of the tethered satellite system are studied numerically, taking the space environments into account. A large number of numerical simulations show that the flexible tethered satellite system displays nonlinear dynamic characteristics, such as bifurcations, quasi-periodic oscillations, and chaotic motions.