Spacecraft Orbital Motion Research Articles

Research on Auxiliary Effect of Lorentz Force for On-orbit Servicing of Spacecraft

Background: On-orbit servicing of spacecraft is mainly aimed at repairing failed spacecraft, maintaining and upgrading normally operating spacecraft to extend their life in order to reduce the increase of space debris and maintain the space environment. Objective: In performing on-orbit servicing, the spacecraft typically requires continuous control force to hover for a long period of time in order to maintain a relatively stationary state towards the target. Methods: Considering the limited amount of fuel carried, the Lorentz force is introduced into onorbit servicing to assist spacecraft in hovering. In order to demonstrate the feasibility of using Lorentz force as spacecraft thrust, many related patents have been provided. Results: Firstly, the velocity of the spacecraft's orbital motion and the variation of the geomagnetic field were given, and the specific expression of the Lorentz force in the relative dynamics model of the spacecraft was deduced. When studying the auxiliary effect of Lorentz force, a critical angle was defined. The relation between the critical angle and the Lorentz force on the auxiliary effect of spacecraft hovering was analyzed through numerical examples. Conclusion: Furthermore, based on the influence of the charge-to-mass ratio on the critical angle, the variation law of the Lorentz force-assisted spacecraft hovering area with different charge-tomass ratios was derived.

KIAM Astrodynamics Toolbox for spacecraft orbital motion design

The KIAM Astrodynamics Toolbox, a new software library for designing spacecraft orbital motion, is introduced. The toolbox is developed at the Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences using Fortran and Python languages, thus combining the computational speed and the flexibility of program design. The library can be useful for space flight mechanics specialists, as well as for students in relevant educational programs.

On control of spacecraft orientation to the ground data acquisition station

The article dwells on the spacecraft attitude control to point the onboard antenna to the ground data acquisition station during the communication session. Antenna is fixed relative to the spacecraft body. Pur-pose of the antenna is to receive the flight task aboard the spacecraft and to downlink the telemetry infor-mation. When orbiting, the spacecraft position relative to the ground data acquisition station changes contin-uously. It is due to the diurnal rotation of the Earth, spacecraft orbital motion and angular motion of the spacecraft relative to the center of mass under the impact of the disturbing and control moments. To tilt the spacecraft uses reaction wheels, installed in axes of coordinate system coupled with spacecraft center of mass. Electromagnets are used to unload the reaction wheels. The reaction wheels control law is suggested, which tilts the spacecraft to point the antenna to the ground data acquisition station. Mathematical model of the spacecraft dynamics relative to center of mass is given, using the suggested reaction wheels control law. The following external disturbing moments, acting on the spacecraft in flight, are taken into consideration: gravitational, magnetic, aerodynamic moments and solar radiation moment of forces. Dipole model of the magnetic field of the Earth is used to calculate the magnetic moments. Software was developed and space-craft dynamics was simulated on the personal computer with the specified initial data. Simulation initial con-ditions correspond to the attitude control mode of the spacecraft relative to the orbital coordinate system with the specified accuracy. Simulation results verify the applicability of the suggested reaction wheel control law. Key words: electrical axis of the antenna, mathematical model, coordinate system, transformation matrix, vector.

Forecast and Correction of the Orbital Motion of the Space Vehicle Using Regular Quaternion Equations and Their Solutions in the Kustaanheimo–Stiefels Variables and Isochronic Derivatives

The regular quaternion equations of the orbital motion of a spacecraft (SC) proposed by us earlier in four-dimensional Kustaanheimo–Stiefel variables (KS-variables) are considered. These equations use as a new independent variable a variable related to real time by a differential relation (Sundman time transformation) containing the distance to the center of gravity. Various new regular quaternion equations in these variables and equations in regular quaternion osculating elements (slowly varying variables) are also constructed, in which the half generalized eccentric anomaly, widely used in celestial mechanics and space flight mechanics, is used as a new independent variable. Keplerian energy and time are used as additional variables in these equations. These equations are used to construct quaternion equations and relations in variations of KS-variables and their first derivatives and in variations of Keplerian energy and real time; the isochronous derivatives of the KS-variables and of their first derivatives and the matrix of isochronous derivatives for the elliptical Keplerian motion of the spacecraft are found, which are necessary for solving the problems of predicting and correcting its orbital motion. The results of a comparative study of the accuracy of the numerical integration of the Newtonian equations of the spatial restricted three-body problem (Earth, Moon, and spacecraft) in Cartesian coordinates and the regular quaternion equations of this problem in KS-variables are presented, which show that the accuracy of the numerical integration of regular quaternion equations is much higher (by several orders) of the accuracy of numerical integration of equations in Cartesian coordinates. This substantiates the expediency of using regular quaternion equations of the spacecraft orbital motion and the quaternion equations and relations in variations constructed in the article on their basis for the prediction and correction of the orbital motion of a spacecraft.

Modelling of Spacecraft Orbit via Neural Networks

In order to have a spacecraft orbital motion model, the developer usually tends to use traditional spacecraft orbital motion models. In order to have a good model, the developer resorts to modelling techniques that are more complex. Increasing model complexity increases algorithm execution time and prevents its usage on-board a spacecraft. This is due to real time constraints and limited computational resources usually imposed by the spacecraft on-board computer. This article develops a new method based on neural networks. The developed method allows the developer of spacecraft orbital motion model to alleviate the problem of increasing execution time with increasing model complexity. The positioning error percent of the proposed algorithm should not be more than 5%. The new method effectiveness evaluation is confirmed by the calculations using three test cases. The first test case has been the exact solution of the two-body problem. The second test case has been the Gamma Ray Observatory (GRO) spacecraft verified simulator. The third test case is a spacecraft simulated on the General Mission Analysis Tool (GMAT), which is developed by NASA and private industries. The maximum obtained error percent of the new method in all the test cases is 0.6%, which is considered a very good performance compared to the predefined 5% bound. The average execution time of traditional spacecraft motion models increases approximately 700% as the disturbance model complexity increases. On the contrary, the developed neural networks algorithm has approximately a constant average execution time regardless of the complexity of the disturbance models utilized. This enables using of the newly developed neural networks algorithm with very complex disturbance models without any increase of the computational load.

Spacecraft orbital stability zones around asteroid 99942 Apophis

In this work, we study spacecraft orbital motion around potentially “dangerous” near-Earth asteroid (99942) Apophis under the combined effects of perturbations from the third-body gravity, asteroid's non-spherical gravitational field, and the direct solar radiation pressure, incorporating possible asteroid's shadow crossings. To identify possibly stable orbital zones around Apophis, we vary initial conditions of the semimajor axis, inclination, and the longitude of ascending node. The stability is defined in terms of spacecraft lifetime in orbits without collisions or escapes. We have found two regions of stable orbits (initially circular) with a lifetime of up to 3 years: the one with small initial radii (about 400 m), lying close to the modified Laplace plane, the other with initial radii of 1.5–2.5 km, lying near the terminator plane. We also compared the cases accounting for full factors to those without shadows to see the influence of eclipse on the stable orbits. Results demonstrate the importance of considering the asteroid's shadow effect in the long-term orbital evolution - the eclipse may significantly change spacecraft lifetime (in years) at low orbits.

Analysis of a distant retrograde orbit in the Hill three-body problem

In this study, spacecraft orbital motion in the Hill three-body problem is considered. When the secondary body moves in a circular orbit whose center is the primary body, a distant retrograde orbit (DRO) exists on the plane of revolution of the secondary body. In this study, a three-dimensional DRO including an out-of-plane motion is investigated. First, the motion in each direction is assumed as a simple trigonometric motion, and relations between the ratios of the amplitudes and the ratios of the angular velocities are derived. Then, a stability criterion of the three-dimensional DRO is obtained from the maximum eigenvalues of the monodromy matrix. A comparative study is executed between the present analytical results and the numerical simulations, and it validates the analytical results.

X-Ray Pulsar-Based Navigation Considering Spacecraft Orbital Motion and Systematic Biases

The accuracy of X-ray pulsar-based navigation is greatly affected by the Doppler effect caused by the spacecraft orbital motion and the systematic biases introduced by the pulsar directional error, spacecraft-borne clock error, etc. In this paper, an innovative navigation method simultaneously employing the pulse phase (PP), the difference of two neighbor PPs (DPP) and the Doppler frequency (DF) of X-ray pulsars as measurements is proposed to solve this problem. With the aid of the spacecraft orbital dynamics, a single pair of PP and DF relative to the spacecraft’s state estimation error can be estimated by using the joint probability density function of the arrival photon timestamps as the likelihood function. The systematic biases involved to the PP is proved to be nearly invariant over two adjacent navigation periods and the major part of it is eliminated in the DPP; therefore, the DPP is also exploited as additional navigation measurement to weaken the impact of systematic biases on navigation accuracy. Results of photon-level simulations show that the navigation accuracy of the proposed method is remarkably better than that of the method only using PP, the method using both PP and DF and the method using both PP and DPP for Earth orbit.

Анализ космических траекторий для экспедиции Земля-Апофис-Земля и движения космического аппарата вокруг астероида Апофис

Анализ космических траекторий для экспедиции Земля-Апофис-Земля и движения космического аппарата вокруг астероида Апофис

Effectiveness Analyses of an Electrospray Sustainer Engine Installed on a Spacecraft Maneuvering in Vicinity of an Asteroid

Motion in vicinity of complex bodies is unstable due to the dynamic changing of the irregular gravitational field. Standard spacecraft power plants designed for interplanetary flights do not provide a stable orbital motion near irregular bodies. In this paper the effectiveness analysis of an electrospray engine power plant used as a sustainer engine in an asteroid exploration mission is considered. Authors describe mathematical models of the spacecraft's motion in an unstable gravitational field as the classical n-body problem. Using simple control schemes for the spacecraft's orbital motion allows basic requirements for the spacecraft's power plant to be defined: thrust level and exhaust velocity. Ion Electrospray Systems are designed to be installed on small satellites, however, effectiveness analyses shows that the characteristics of the calculated engine system is close enough to the characteristics of an electrospray system. Authors demonstrate that ion Electrospray System modules are effective enough to be installed on spacecraft in asteroid exploration missions.

Analysis of spacecraft orbital motion around the asteroid Apophis

Analysis has shown that it is possible to choose a main spacecraft orbit (~0.5 km radius) and a minisatellite orbit (~1.5 km radius), so that passive motion of the spacecraft around the asteroid remains stable within the context of a given model for a sufficiently long duration of time, i.e., approximately a month for the main spacecraft and several years for the minisatellite, until Apophis approaches the Earth in 2029.

Model Predictive Control for Spacecraft Rendezvous and Docking: Strategies for Handling Constraints and Case Studies

This paper presents a strategy and case studies of spacecraft relative motion guidance and control based on the application of linear quadratic model predictive control (MPC) with dynamically reconfigurable constraints. The controller is designed to transition between the MPC guidance during a spacecraft rendezvous phase and MPC guidance during a spacecraft docking phase, with each phase having distinct requirements, constraints, and sampling rates. Obstacle avoidance is considered in the rendezvous phase, while a line-of-sight cone constraint, bandwidth constraints on the spacecraft attitude control system, and exhaust plume direction constraints are addressed during the docking phase. The MPC controller is demonstrated in simulation studies using a nonlinear model of spacecraft orbital motion. The implementation uses estimates of spacecraft states derived from relative angle and range measurements, and is robust to estimator dynamics and measurement noise.

Averaging analyses for spacecraft orbital motions around asteroids

This paper summarizes a few cases of spacecraft orbital motion around asteroid for which averaging method can be applied, i.e., when central body rotates slowly, fast, and when a spacecraft is near to the resonant orbits between the spacecraft mean motion and the central body’s rotation. Averaging conditions for these cases are given. As a major extension, a few classes of near resonant orbits are analyzed by the averaging method. Then some resulted conclusions of these averaging analyses are applied to understand the stability regions in a numerical experiment. Some stability conclusions are obtained. As a typical example, it is shown in detail that near circular 1:2 resonant orbit is always unstable.

A variant of visual correction in the problem of spacecraft navigation

Possibility of correction of parameters of spacecraft orbital motion using observations of not more than one ground landmark at short time intervals is considered.

Effect of Kinematic Rotation-Translation Coupling on Relative Spacecraft Translational Dynamics

A CCURATEmodeling of the differential translation and rotation between two spacecraft is essential for cooperative distributed space systems, spacecraft formation flying (SFF), rendezvous, and docking. High-fidelity relative motion modeling, as opposed to absolute motion modeling, is particularly important for autonomous missions [1]. Point-mass models for relative spacecraft translational motion have been extensively studied over the past 50 years, since Clohessy and Wiltshire (CW) presented a rendezvous model for a circular reference orbit and a spherical Earth [2]. Following the work of Clohessy and Wiltshire, variants on the point-mass model were developed, such as generalizations to elliptic reference orbits [3–5] and an oblate Earth [6,7]. The growing interest in SFF motivated the research of relative spacecraft motion modeling, yielding more accurate and complete equations and solutions for perturbed relative motion [8–10]. However, most of the works focused on point-mass, 3 degrees-offreedom (DOF) spacecraft. Obviously, performing a space mission that consists of several cooperative space vehicles requires modeling the relative rotational motion in addition to the relative translation, that is, 6-DOF models. Models for the relative motion of 6-DOF spacecraft have gained attention in the literature only in recent years. Among the first to suggest treating the spacecraft relative angular velocity in an SFF control problem were Pan and Kapila [11], who addressed the coupled translational and rotational dynamics of two spacecraft. By defining two body-fixed reference frames, one attached to the leader and the other attached to the follower, it was proposed [11] to use a two-part relative motion model: one that accounts for the relative translational dynamics of the body-fixed coordinate frame origins, and another that captures the relative attitude dynamics of the two body-fixed frames. A similar modeling approach was used for relative motion estimation [1]. In addition, tensorial equations of motion for a formation consisting ofN spacecraft, each modeled as a rigid body, were derived [12]. However, only the absolute equations of motion were developed [12]; a relative version of these equations was not given. Moreover, a clear mathematical relationship between the developed models and the traditional nonlinear point-mass relative motion and CW models was not provided. The coupling between the translational and rotational motion in the aforementioned models [1,11] was induced by gravity torques. The kinematic coupling, which is essentially a projection of the rotational motion about the center of mass (c.m.) onto the relative translational configuration space, was neglected. It is this kinematic coupling that the current paper is concerned with. In general, rigid-body dynamics can be represented as translation of the c.m. and rotation about the c.m. [13]. Thus, spacecraft relative motion must be composed by combining the relative translational and rotational dynamics of arbitrary points on the spacecraft. Whenever one of these points does not coincide with the spacecraft’s c.m., a kinematic coupling between the rotational and translational dynamics of these points is obtained. The purpose of this paper is to quantify the kinematic coupling effect and to show that this effect is key for high-precision modeling of tight SFF, rendezvous, and docking. This effect is also important in vision-based relative attitude and position control, where arbitrary feature points on a target vehicle are to be tracked. Given two rigidbody spacecraft, the model presented herein is formulated in a general manner that describes the motion between any two arbitrary points on the spacecraft. The relative translational motion is then generated by both the spacecraft orbitalmotion and the rotation about the c.m. In addition, this paper provides a CW-like approximation of the relative motion that includes the kinematic coupling. This new approximation is aimed at alleviating an apparent contradiction in linearized relative motion theories: to obtain linear equations of motion, the spacecraft are assumed to operate in close proximity. However, if the spacecraft are close to each other, then they can no longer be treated as point masses, because the spacecraft shape and size affects the relative translation between off-c.m. points. This effect is accentuated as the distances between spacecraft decrease. The remainder of this paper is organized as follows. First, a background on the relative position and attitude dynamics is given. Then, a new coupled relative spacecraft motion model is presented. The newly developed model is then examined in a simulation.