Motion Of Spacecraft Research Articles

Acquisition of Moon Measurements by Earth Orbiting Sensors for Lunar Calibration

The reflected light from the Moon can be utilized as a reference for radiometric calibration by employing a model to generate reference values corresponding to the Moon observations made by instruments. Using a calibration target that is outside the atmosphere provides a distinct advantage for space-based instruments; however, the lunar irradiance sensed by satellite instruments naturally changes as the host spacecraft traverses its orbit. This article presents a study of the potential impact on lunar radiometric measurements due to their acquisition from an orbiting platform. A simulation of a Sun-synchronous orbit was coupled to the U.S. Geological Survey (USGS) lunar model to generate predicted irradiances for points along orbit passes through several lunations. These irradiance values exhibit variations tied to the spacecraft motion, arising primarily from changes in the Moon-sensor distance and the phase angle. The two effects are similar in overall magnitude, but their respective contributions depend on the time of month and the orbit. Relative changes in irradiance mostly fall within an envelope of ±0.006% per second, except at the smallest phase angles. These studies enable planning space-based Moon observations to minimize the change in the target irradiance, an important consideration for measurements acquired for radiometric characterization of the Moon.

Control and maintenance of fully-constrained and underconstrained rigid body motion on Lie groups and their tangent bundles

<p style='text-indent:20px;'>Presented herein are a class of methodologies for conducting constrained motion analysis of rigid bodies within the Udwadia-Kalaba (U-K) formulation. The U-K formulation, primarily devised for systems of particles, is advanced to rigid body dynamics in the geometric mechanics framework and a novel development of U-K formulation for use on nonlinear manifolds, namely the special Euclidean group <inline-formula><tex-math id="M1">\begin{document}$ {\mathsf{SE}(3)}$\end{document}</tex-math></inline-formula> and its second order tangent bundle <inline-formula><tex-math id="M2">\begin{document}${\mathsf{T}^2\mathsf{SE}(3)} $\end{document}</tex-math></inline-formula>, is proposed in addition to the formulation development on Euclidean spaces. Then, a Morse-Lyapunov based tracking controller using backstepping is applied to capture disturbed initial conditions that the U-K formulation cannot account for. This theoretical development is then applied to fully-constrained and underconstrained scenarios of rigid-body spacecraft motion in a lunar orbit, and the translational and rotational motions of the spacecraft and the control inputs obtained using the proposed methodologies to achieve and maintain those constrained motions are studied.</p>

Использование регулярных переменных в задаче оптимизации траектории КА с малой тягой

The regularization of spacecraft motion equations by the Kustaanheimo-Stiefel transformation for coordinates and Sundman’s transformation for time in the case of interplanetary low-thrust optimal transfer is considered. From Pontryagin’s maximum principle, the thrust vector optimal control is derived under the limited power condition. The Earth-Mars transfer problem is solved in the regular variables. The comparison of calculated trajectories with the ones obtained by the parameter continuation method is performed, and the stability properties of the two-point boundary value problem in the Cartesian and regular variables are studied.

Maximizing the Accuracy of Double Probe Electric Field Measurements Near Perigee: The Case of the Van Allen Probes Instruments

AbstractThe Van Allen Probes spacecraft flew through the inner radiation belt and the plasmasphere, probing the extremely dynamic coupling between the thermosphere, the ionosphere and the subauroral magnetosphere. Examining the electrodynamics of this region using Van Allen Probes data required that the ∼1 mV/m electric field (E‐field) of interest be measured in a region where the E‐field due to spacecraft motion was ∼100 mV/m. This means that the E‐field, the magnetic field, and the spacecraft velocity had to be measured to better than 1%. The instruments on board the Van Allen Probes have achieved this accuracy, delivering reliable near equatorial E‐field measurements even below three Earth radii. The objective of this commentary is to summarize the methodology developed over the years to maximize the accuracy and scientific return of these double probe E‐field measurements below L = 3.

Approximate solution of spacecraft motion with an inward constant radial acceleration

This Short Communication analyzes the motion of a spacecraft whose primary propulsion system generates an inward, radial propulsive acceleration of constant magnitude. Starting from the classical literature results regarding the more common outward radial-thrust case, the proposed mathematical model uses a set of modified non-singular orbital elements to describe the spacecraft motion around a generic primary body. Assuming a circular parking orbit and a small propulsive acceleration magnitude, a perturbation method, based on an asymptotic series expansion truncated at second order, is used to obtain analytical expressions of the spacecraft propelled trajectory. The obtained results are applied to an orbital targeting problem and, in this context, the resulting spacecraft trajectory is accurately approximated through analytical functions. The proposed procedure is also able to well estimate the thrust level and the swept angle required to reach the target state.

An application of symplectic integration for general relativistic planetary orbitography subject to non-gravitational forces

Spacecraft propagation tools describe the motion of near-Earth objects and interplanetary probes using Newton’s theory of gravity supplemented with the approximate general relativistic n-body Einstein–Infeld–Hoffmann equations of motion. With respect to the general theory of relativity and the long-standing recommendations of the International Astronomical Union for astrometry, celestial mechanics and metrology, we believe modern orbitography software is now reaching its limits in terms of complexity. In this paper, we present the first results of a prototype software titled General Relativistic Accelerometer-based Propagation Environment (GRAPE). We describe the motion of interplanetary probes and spacecraft using extended general relativistic equations of motion which account for non-gravitational forces using end-user supplied accelerometer data or approximate dynamical models. We exploit the unique general relativistic quadratic invariant associated with the orthogonality between four-velocity and acceleration and simulate the perturbed orbits for Molniya, Parker Solar Probe and Mercury Planetary Orbiter-like test particles subject to a radiation-like four-force. The accuracy of the numerical procedure is maintained using a 5-stage, 10^mathrm{th}-order structure-preserving Gauss collocation symplectic integration scheme. GRAPE preserves the norm of the tangent vector to the test particle worldline at the order of 10^{-32}.

Investigation of Stable Regions of Spacecraft Motion in Binary Asteroid Systems by Terminal Condition Maps

Investigation of Stable Regions of Spacecraft Motion in Binary Asteroid Systems by Terminal Condition Maps

Online collision avoidance trajectory planning for spacecraft proximity operations with uncertain obstacle

The spacecraft relative motion trajectory planning is one of the enabling techniques for autonomous proximity operations, especially in the increasingly complicated mission environments. Most traditional trajectory planning methods focus on improving the performance criteria in the deterministic conditions, whereas various uncertain elements in practice would significantly degrade the trajectory performance. Considering the uncertainties underlying the collision avoidance constraints, this paper suggests a model predictive control based online trajectory planning framework in which the obstacle information in higher-precision would be consistently updated by the onboard sensor. To improve the computational efficiency of the online planning framework, the rotating hyperplane (RH) technique is utilized to transform the nonlinear ellipsoidal keep-out zone constraints into convex formulations. And the concept of rotation window is introduced to eliminate the unexpected mismatch between the spacecraft motion and hyperplane rotation in the conventional RH method, which in sequence improves the RH method’s capability for multiple obstacle avoidance problem. Moreover, a three-dimensional (3-D) extension strategy is proposed to simplify the computation procedure when applying the RH method for a 3-D collision avoidance problem. Numerical simulations are carried out to validate the performance of the proposed online trajectory planning framework in addressing the uncertain collision avoidance constraints.

Fault-Tolerant Model-Free Predictive Control of Spacecraft Coupled Rotational–Translational Relative Motion

AbstractThe problem of controlling coupled six-degrees-of-freedom (6-DOF) relative motion of an integrated-actuation spacecraft in the presence of actuator faults, and especially failures, is inves...

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.

A robust end-to-end deep learning framework for detecting Martian landforms with arbitrary orientations

With increasingly massive amounts of high-resolution images of Mars, automated detection of geological landforms on Mars has received widespread interest. It is significant for acquiring knowledge of distant planetary surfaces and processes, or manifold onboard applications such as spacecraft motion estimation and obstacle avoidance. This is a challenging task, not only because of the multiple sizes of targets and complex image backgrounds, but also the various orientations of some bar-shaped landforms in satellite images captured from the top view. The existing methods for directed landform detection require several pre or post-processing operations to extract possible regions of interest and final detection results with orientation, which are very time consuming. In this paper, a new end-to-end deep learning framework is developed for detecting arbitrarily-directed landforms. This framework, named Rotated-SSD (Single Shot MultiBox Detector, SSD), can locate and identify different landforms on Mars in one pass, by using rotatable anchor-box based mechanism. To enhance its robustness against angle variation of the targets and complex backgrounds, a new efficient match strategy is proposed for anchoring default boxes to ground truth boxes in the model training process and an autoencoder-based unsupervised pre-training operation is introduced to improve both the model training and inference performance. The proposed framework is tested for detection of bar-shaped buttes and dark slope streaks on satellite images. The detection results show that our framework can significantly contribute to onboard motion estimation systems. The comparative results demonstrate that the proposed match strategy outperforms other state-of-the-art match strategies with regard to model training efficiency and prediction accuracy. The pre-training strategy can facilitate the training of deep architectures in case of limited available training data.

Control of a service satellite during its mission on space debris removal from orbits with high inclination by implementation of an ion beam method

The largest population of space debris is observed in the low-Earth-orbit region with altitudes of 600–1000 km and inclinations of 80–100°. As follows from the predictive calculations, space debris removal from this region exactly is of the first priority. For this reason, our article discusses the problems of controlling the motion of service spacecraft – space debris object cluster when the space debris object is removed from a low orbit with high inclination. In the conceptual design of the spacecraft presented hereinafter, the electric propulsion system contains two electric propulsion thrusters of stationary plasma thruster type, each of which is mounted with the possibility of independent rotation respect to two mutually perpendicular directions. An ion beam injector forms an ion beam with 65 mN of thrust. Spacecraft motion control, including the thrust vector control, is provided by coordinated rotation of thrusters. For such concept, a strategy and an algorithm for controlling the motion of the spacecraft center of mass are proposed, which are based on the control of the spacecraft lateral and longitudinal motion that is understood as the control of the relative distance between the spacecraft and the space debris object. The strategy of spacecraft lateral motion control assumes that due to the thrusters' rotation the spacecraft should be displaced in such a way that the vector of the relative range between the spacecraft and the space debris object coincides with the direction of the transversal of the orbital coordinate system. For the practical implementation of the control, an algorithm has been developed for controlling the thrusters' rotation to create the required values of the spacecraft acceleration projections. The mathematical model includes the equations of motion of the spacecraft center of mass taking into account the aerodynamic deceleration. The solar panels' orientation to the Sun is provided by the spacecraft roll rotation relative to its longitudinal axis and turning the solar panels relative to their axis of rotation. The change in the ion beam momentum transfer is considered using a simple simulation model. Mathematical modeling was performed for the following parameters of the initial orbit: altitude: 800 km; eccentricity: 0.0005; and inclination: 900. For the proposed control algorithm, a range of possible thrust of a single thruster was 51–60 mN. The simulation results show that the proposed control can be used to remove space debris object from low orbits with high inclination, taking into account the roll spacecraft rotation to keep the solar panels’ orientation to the Sun.

Frozen Orbits Under Radiation Pressure and Zonal Gravity Perturbations

The orbital motion of spacecraft around asteroids is strongly disturbed primarily because of solar radiation pressure (SRP) and higher-order gravitational forces. To achieve stable orbits in such an environment, the implementation of frozen orbits is a promising approach. This research derives semi-analytical solutions of frozen orbits subject to SRP and zonal gravity up to the fourth order based on singly averaged Lagrange planetary equations. Moreover, the stability of frozen orbits is characterized analytically by introducing linearized variational equations, revealing the complex eigenstructures of the proposed frozen orbits. These analytical theories identify several different types of stable frozen orbits, which are further validated via high-fidelity numerical simulations. Consequently, this paper demonstrates the feasibility and intriguing dynamic characteristics of frozen orbits around asteroids.

Optimization problem of attitude control of a spacecraft with bounded rotary energy using quaternions

The original control problem of optimal reorientation from a state of rest to a state of rest is considered and solved. The control function is torque vector. Problem of optimal control is investigated in detail for statement when control is restricted and the used functional of optimality includes kinematical rotary energy and time of maneuver. For solving and synthesis of the optimal control program, the quaternion method and the Pontryagin’s maximum principle are applied. Analytic solution of the proposed problem is presented basing on the differential equation connecting the angular velocity vector and quaternion of spacecraft attitude. It is shown that a chosen criterion of optimality provides a turn of a spacecraft with rotation energy which does not exceed the required value. This property of proposed control increases safety of flight. The time-optimal problem was solved also. The control law is formulated in the form of an explicit dependence of the control variables on the phase coordinates. All key expressions and equations are written in quaternion form which is convenient for onboard realization and implementation. The analysis of the special control regime of the spacecraft was made. Analytical formulas were written for duration of acceleration and braking. For specific cases of spacecraft configurations (dynamically symmetric spacecraft and spheric-symmetrical spacecraft as particular cases), complete solution of optimal control problem in closed form is given. Numerical example and the results of mathematical simulation for spacecraft motion under optimal control are demonstrated. This data supplements the made theoretical descriptions, and illustrates the practical feasibility of the designed algorithm for controlling the spatial orientation of the spacecraft showing reorientation process in visual form.

Determination of the Spatial Resolution of Radar Images in Remote Sensing of the Earth

Introduction. The analysis of the current state and prospects of space-based radar surveillance tools is important for determining their functions in global aerospace information systems, which aim to monitor air and space, as well as the Earth's surface. Radar surveillance information is used for the purposes of economic analysis, environmental monitoring, mineral search, emergency monitoring, detection and recognition of specified object s at sea and on land, as well as for ensuring national security. In this regard, it is of relevance to develop methods for preliminary assessment of the resolution capacity of novel high-precision onboard radar systems installed on a spacecraft, considering their main technical characteristics, the parameters of the spacecraft movement and the influence of the atmosphere. A priori estimation of spatial resolution values requires a method for calculating the corresponding indicators meeting the required quality of the synthesized radio holograms.Aim. To derive mathematical dependencies and logical rules allowing a priori estimation of the spatial resolution of radar images obtained by the onboard equipment of a radar complex.Materials and methods. Analytical methods were used to determine the resolution error of onboard radar systems with a synthesized aperture in the lateral (azimuthal) direction and range, as well as the theory of radar signal processing.Results. A comparison of the experimental and analytical data on the resolution capacity of an actual radar system confirmed the validity on the proposed method. The developed methodology was used to determine the procedure of calculating the error when estimating the resolution capacity in terms of azimuth and range. Conclusion. The proposed method can be used for both designing novel radar systems and comparing existing radar complexes, depending on the resolution requirements.

Dynamic Problem of Optimal Control of Spacecraft Attitude under Restriction on Phase Variables

An analytical solution to the optimal control problem of spacecraft reorientation from an arbitrary initial angular position into a required final angular position under the restrictions on control functions and phase variables is presented (the controlling moment and angular velocity are restricted). Time of slew maneuver is minimized. The specific case was considered when maximum admissible kinetic energy of rotation is significant restriction. Constructing the optimal control of reorientation is based on Pontryagin’s maximum principle and the quaternionic variables and models. It is shown that optimal mode is piecewise-continuous control when a direction of spacecraft’s angular momentum is constant relative to the inertial coordinate system during rotation of a spacecraft; for a per forming an optimal turn, the moment of forces is parallel to a straight line fixed in inertial space. Two types of optimal control are possible depending on the given initial and final positions and spacecraft’s moments of inertia — relay control with one switching point when the controlling moment is maximal over the entire time interval of control (segments of acceleration and braking), and relay control with two switching point consisting of intensive acceleration, motion by inertia with the absented moment and an exit onto restriction of rotation energy, and then final braking with the maximum controlling moment. The analytical equations and relations for a finding the optimal control program are written down. The calculation formulas for determining the time characteristics of maneuver and computing a duration of acceleration and braking are given. The proposed algorithm of control provides maximally fast implementation of spacecraft reorientation under the limited kinetic energy of rotation. For an axially symmetric solid body (spacecraft), the optimal control problem, in dynamical statement, was solved completely — we obtained the dependences as explicit functions of time for the control variables, and relations for calculating the key parameters of the law of control are derived. The numerical example and results of mathematical simulation of spacecraft motion under the optimal control are presented, demonstrating the practical feasibility of the developed method for control of spacecraft attitude.

Local Form of Loss of Stability of Honeycomb Energy Absorber Plates

Landing devices perform the energy absorption function during the spacecraft motion. Precise analytical solution to the problem of stability of a lengthy plate with free edge exposed to the edge compressive load was obtained in order to analyze operation of the honeycomb materials used in structural elements absorbing the moving bodies energy. General solution analysis of the differential equation for a lengthy plate bending in the deflected position was carried out, and general solution is subjected to the boundary conditions corresponding to the loaded free edge. Critical load value and form of the loss of stability were determined. Critical load identified value was significantly lower than the critical load for a plate supported on the loaded edge. The loss of stability identified form was characterized by sharp deflection localization near the loaded edge and could create conditions for forming a local fold near the loaded edge. Obtained analytical solution was verified by comparing it with results of the similar numerical solution. Comparison performed revealed satisfactory agreement both in the critical load value and in the form of loss of stability for two solutions obtained by different methods. The results obtained could be used in designing energy absorbers made of honeycomb materials, as well as in other areas of technology

Research and optimization of the hydraulic performance of bench lines for testing of low thrust spacecraft engines

Low thrust engines perform important functional tasks in control systems of motion, orientation and stabilization of spacecraft on various paths and space orbits. They are subject to high-reliability and long operating time in pulsed modes with a large number of starts. Bench tests of the engines are a special part of the program development of low thrust engines with high reliability and efficiency. The article analyses wave processes in hydraulic lines of test benches, which prevent obtaining reliable parameters and performances of engines during tests. Authors show that the exclusion of oscillation processes in test bench systems is the main condition for the organization and planning of tests. Similarity conditions for bench hydraulic lines of spacecraft propulsion systems are developed. A methodology for estimating the frequency responses of the bench lines during pulsed test modes is presented. Mathematical functions of geometric parameters of the bench hydraulic lines on the pulse responses of low thrust engines are obtained, allowing optimization of the bench propellant feeding system to avoid resonance oscillation processes. Research results provide reliable estimates of the parameters and reliability of low thrust engines.

Multi-Instrument Characterization of Magnetospheric Cold Plasma Dynamics in the June 22, 2015 Geomagnetic Storm.

We present a comparison of magnetospheric plasma mass/electron density observations during an 11‐day interval which includes the geomagnetic storm of June 22, 2015. For this study we used: Equatorial plasma mass density derived from geomagnetic field line resonances (FLRs) detected by Van Allen Probes and at the ground‐based magnetometer networks EMMA and CARISMA; in situ electron density inferred by the Neural‐network‐based Upper hybrid Resonance Determination algorithm applied to plasma wave Van Allen Probes measurements. The combined observations at L ∼ 4, MLT ∼ 16 of the two longitudinally separated magnetometer networks show a temporal pattern very similar to that of the in situ observations: A density decrease by an order of magnitude about 1 day after the Dst minimum, a partial recovery a few hours later, and a new strong decrease soon after. The observations are consistent with the position of the measurement points with respect to the plasmasphere boundary as derived by a plasmapause test particle simulation. A comparison between plasma mass densities derived from ground and in situ FLR observations during favorable conjunctions shows a good agreement. We find however, for L < ∼3, the spacecraft measurements to be higher than the corresponding ground observations with increasing deviation with decreasing L, which might be related to the rapid outbound spacecraft motion in that region. A statistical analysis of the average ion mass using simultaneous spacecraft measurements of mass and electron density indicates values close to 1 amu in plasmasphere and higher values (∼2–3 amu) in plasmatrough.

Concurrent Learning Adaptive Finite-Time Control for Spacecraft With Inertia Parameter Identification Under External Disturbance

This article investigates the postcapture control problem for the combined spacecraft formed after a service spacecraft captures a noncooperative target by manipulators. Two concurrent learning adaptive finite-time controllers are developed to achieve trajectory tracking and inertia parameter identification simultaneously. As a very common uncertainty affecting the spacecraft motion, the external disturbance should be considered, but it is ignored in most studies identifying inertia parameters. In this article, the presented controllers are designed according to the specific knowledge of the external disturbance: one controller is designed based on the disturbance bound that is assumed to be known; the other identifies the disturbance parameters together with the inertia parameters, presupposing that the nonlinearities involved in the external disturbance are known. Both of the two controllers require no a priori knowledge of the mass and inertia matrix of the combined spacecraft and take the input saturation into account. Sufficient conditions to identify inertia parameters are also given with no need of persistent excitation. The convergence of the closed-loop system is proved within the Lyapunov framework. Numerical results show that the proposed controllers can track the desired position and attitude trajectories in finite time, and, at the same time, the inertia parameters converge to their real values.