Motion Of Spacecraft Research Articles

Zodiacal exoplanets in time (ZEIT) – II. A ‘super-Earth’ orbiting a young K dwarf in the Pleiades Neighbourhood

We describe a "super-Earth"-size ($2.30\pm0.15R_{\oplus}$) planet transiting an early K-type dwarf star in the Campaign 4 field observed by the K2 mission. The host star, EPIC 210363145, was identified as a member of the approximately 120-Myr-old Pleiades cluster based on its kinematics and photometric distance. It is rotationally variable and exhibits near-ultraviolet emission consistent with a Pleiades age, but its rotational period is ~20 d and its spectrum contains no H$\alpha$ emission nor the Li I absorption expected of Pleiades K dwarfs. Instead, the star is probably an interloper that is unaffiliated with the cluster, but younger (< 1 Gyr) than the typical field dwarf. We ruled out a false positive transit signal produced by confusion with a background eclipsing binary by adaptive optics imaging and a statistical calculation. Doppler radial velocity measurements limit the companion mass to <2 times that of Jupiter. Screening of the lightcurves of 1014 potential Pleiades candidate stars uncovered no additional planets. An injection-and-recovery experiment using the K2 Pleiades lightcurves with simulated planets, assuming a planet population like that in the Kepler prime field, predicts only 0.8-1.8 detections (vs. ~20 in an equivalent Kepler sample). The absence of Pleiades planet detections can be attributed to the much shorter monitoring time of K2 (80 days vs. 4 years), increased measurement noise due to spacecraft motion, and the intrinsic noisiness of the stars.

Constrained Autonomous Precision Landing via Dual Quaternions and Model Predictive Control

The problem of powered descent guidance and control for autonomous precision landing for next-generation planetary missions is addressed. The precision landing algorithm aims to trace a fuel-optimal trajectory while keeping geometrical constraints such as the line of sight to the target site. The design of an autonomous control algorithm managing such mission scenarios is challenging due to fact that critical geometrical constraints are coupled with the translational and rotational motions of the lander spacecraft, leading to a complex motion-planning problem. This problem is approached within the model predictive control framework by representing the dynamics of the rigid body in a uniform gravity field via a piecewise affine system taking advantage of the unit dual-quaternion parameterization. Such a parameterization in turn enables a six-degree-of-freedom motion planning in a unified framework while also admitting a quadratic cost on the required control commands to minimize propellant consumption. A novel feature of the proposed approach is the development of convex representable subsets in the configuration space in terms of unit dual quaternions. The stability and reachability issues of the corresponding piecewise affine model predictive control approach are then discussed. Numerical simulations are presented to demonstrate the effectiveness of the proposed methodology for autonomous precision landing.

Phase tracking for pulsar navigation with Doppler frequency

Doppler frequency in pulsar navigation is an effect caused by spacecraft and pulsar motion, which would worsen the pulsar navigation accuracy. To describe this influence, we establish the Doppler frequency measurement model based on pulsar timing. With this model, we describe the relationship between the phase estimation performance and the observation time when Doppler frequency exists. To reduce the pulsar navigation error due to the Doppler frequency, we designed the phase tracking loop for the pulsar navigation. The pulsar frequency can be modified before the phase estimation. As a result, the impact of the Doppler frequency could be lessened, and the observation interval lengths can be lengthened to improve the phase estimation performance.

Fast, Safe, Propellant-Efficient Spacecraft Motion Planning Under Clohessy–Wiltshire–Hill Dynamics

This paper presents a sampling-based motion planning algorithm for real-time and propellant-optimized autonomous spacecraft trajectory generation in near-circular orbits. Specifically, this paper leverages recent algorithmic advances in the field of robot motion planning to the problem of impulsively actuated, propellant-optimized rendezvous and proximity operations under the Clohessy–Wiltshire–Hill dynamics model. The approach calls upon a modified version of the FMT* algorithm to grow a set of feasible trajectories over a deterministic, low-dispersion set of sample points covering the free state space. To enforce safety, the tree is only grown over the subset of actively safe samples, from which there exists a feasible one-burn collision-avoidance maneuver that can safely circularize the spacecraft orbit along its coasting arc under a given set of potential thruster failures. Key features of the proposed algorithm include 1) theoretical guarantees in terms of trajectory safety and performance, 2) amenability to real-time implementation, and 3) generality, in the sense that a large class of constraints can be handled directly. As a result, the proposed algorithm offers the potential for widespread application, ranging from on-orbit satellite servicing to orbital debris removal and autonomous inspection missions.

Revised single‐spacecraft method for determining wave vector k and resolving space‐time ambiguity

AbstractA practical method is proposed for determining the wave vector of waves from single‐spacecraft measurements. This wave vector knowledge can then be used to remove the space‐time ambiguity produced by frequency Doppler shift associated with spacecraft motion. The method involves applying the Wiener‐Khinchin theorem to cross correlations of the current and magnetic field oscillations and to autocorrelations of the magnetic field oscillations. The method requires that each wave frequency component map to a unique wave vector, a condition presumed true in many spacecraft measurement situations. Examples validating the method are presented.

Terminal control of aerospace system subhypersonic first stage

The problem of forming command control of the subhypersonic first stage of an aerospace system in climb is considered. Passive motion of spacecraft in conditions of maximum atmospheric density disturbance is analyzed. Achieving the prescribed value of the angle of climb is the terminal motion condition. Terminal height is a controlled value. An algorithm of terminal control for the formation of command value of aerodynamic lift coefficient is proposed. The Newton method with one or more iterations at the correction step is used in determining command control. The serviceability and efficiency of the algorithm compensating the influence of variations of atmospheric density on the preset terminal altitude condition of spacecraft motion are analyzed. The results of simulating spacecraft motion with terminal control for maximally rarefied and maximally dense atmosphere are discussed. Possible improvement of the terminal control algorithm is suggested.

Particle filter-based relative rolling estimation algorithm for non-cooperative infrared spacecraft

The issue of feature point mismatching among infrared image sequence would bring big challenge to estimating the relative motion of non-cooperative spacecraft for it couldn’t provide the prior knowledge about its geometric structure and motion pattern. The paper introduces particle filter to precisely match the feature points within a desired region predicted by a kinetic equation, and presents a least square estimation-based algorithm to measure the relative rolling motion of non-cooperative spacecraft. The state transition equation and the measurement update equation of non-cooperative spacecraft are represented by establishing its kinetic equations, and then the relative pose measurement is converted to the maximum posterioriprobability estimation via assuming the uncertainties about geometric structure and motion pattern as random and time-varying variables. These uncertainties would be interpreted and even solved through continuously measuring the image feature points of the rotating non-cooperative infrared spacecraft. Subsequently, the feature point is matched within a predicted region among sequence infrared image using particle filter algorithm to overcome the position estimation noise caused by the uncertainties of geometric structure and motion pattern. Finally, the position parameters including rotation motion are estimated by means of solving the minimum error of feature point mismatching using least square estimate theory. Both simulated and real infrared image sequences are induced in the experiment to evaluate the performance of the relative rolling estimation, and the experimental data show that the rolling motion estimated by the proposed algorithm is more robust to the feature extraction noise and various rotation speed. Meanwhile, the relative rolling estimation error would increase dramatically with distance and rotation speed increasing.

Применение методов имитационного моделирования в задачах изучения движения околоземных космических аппаратов

Применение методов имитационного моделирования в задачах изучения движения околоземных космических аппаратов

Maneuvering Spacecraft Tracking via State-Dependent Adaptive Estimation

In this study, an adaptive estimation algorithm is developed to estimate the state of a spacecraft that performs impulsive maneuvers. The accurate tracking of a maneuvering spacecraft with impulsive burns is a challenging problem since the magnitude and the time of occurrence of impulsive maneuvers are usually unknown a priori. To deal with this problem, an adaptive state estimation algorithm is developed in this study using a bank of extended Kalman filters along with interacting multiple models that account for spacecraft motion with and without impulsive maneuvers. Motivated by the fact that impulsive maneuvers usually occur when certain conditions on the spacecraft state are satisfied, the multiple extended Kalman filters are systematically blended using a state-dependent transition probability. Since the information about the conditions based on which impulsive maneuvers occur is explicitly used in the state-dependent transition probability, the proposed algorithm can predict the impulsive maneuvers more accurately and thus produce more accurate state estimates. The proposed algorithm is demonstrated with two illustrative examples: 1) tracking of a geostationary satellite performing station-keeping maneuvers and 2) tracking of a spacecraft performing orbital transfers.

On the coupled dynamics of small spacecraft and elastic deployable appendages

A thorough investigation of the dynamics of finite-mass satellites with a deployable elastic arm is presented. This work is focused on the interaction between spacecraft rigid body motion and its flexible arm dynamics during the deployment process. The classical Newton–Euler formulation and the Lagrangian approach are applied to the study of the dynamics of spacecraft and its deploying arm. Utilizing a non-Newtonian floating frame to define the arm elastic deformation field, the interactions between the spacecraft and its moving arm have been simulated. Complete equations of motion show that the spacecraft motion induces dynamical stiffness on the arm; in addition, axial and lateral motions of the deploying elastic arm change the spacecraft mass-characteristics and thus influence the spacecraft’s rigid body motions. The overall dynamic behavior is highly dependent on spacecraft mass characteristics in addition to the “arm deployment time (ADT)”. The results of case studies clearly indicate that some assumptions previously applied in appendage dynamic analysis are not conservative and produce erroneous results. This study realistically investigates the dynamics of elastic deploying appendages by considering finite-mass characteristics for small and massy spacecraft. The results reveal that for massive spacecraft the arm’s flexible dynamics is mainly excited through deployment, while for small spacecraft the energy transfers to the arm base and the spacecraft rigid body motion is considerably stimulated. Moreover, this work has further highlighted the effects of ADT in the overall system response. The findings of this work show that the energy distribution between arm’s elastic dynamics and spacecraft rigid body motions is an important factor in the design of any control system to limit unwanted arm-tip motions.

Studies on global analytical mode for a three-axis attitude stabilized spacecraft by using the Rayleigh–Ritz method

With extending the Rayleigh–Ritz procedure to study the hub-plate system, the characteristics of global analytical modes are addressed for a typical rigid–flexible coupling dynamic system, i.e., a three-axis attitude stabilized spacecraft installed with a pair of solar arrays. The displacement field of the solar arrays is expressed as a series of admissible functions which is a set of characteristic orthogonal polynomials generated directly by employing Gram–Schmidt process. The rigid body motion of spacecraft is represented by the product of constant and generalized coordinate. Then, through Rayleigh–Ritz procedure, the eigenvalue equation of the three-axis attitude stabilized spacecraft installed with a pair of solar arrays is derived. Solving this eigenvalue equation, the frequencies and analytical expressions of global modes for the flexible spacecraft are obtained. To validate the present analysis, comparisons between the results of the present method and ANSYS software are performed and very good agreement is achieved. The convergence studies demonstrate the high accuracy, excellent convergence and high efficiency of the present approach. Finally, the method is applied to study the characteristics of global modes of the flexible spacecraft.

Terminal control of the trajectory and rotational motion of an active spacecraft during a rendezvous with a passive spacecraft

In this work, the problem of a spacecraft's rendezvous is considered in the radial coordinate system, taking into consideration the effect of the difference gravitational acceleration, using a control algorithm with the prediction model based on the minimization of the generalized work functional. The analytical formulas have been derived to compute the control actions when the motion of the center of mass and the motion about the center of mass, when solving the parametric optimization problem, are considered in a unified terminal formulation. The analytical solution is based on a special prediction model that has an analytical solution in the advanced modeling of the rendezvous process. The results of modeling a spacecraft's rendezvous are presented.

Analysis of the effect of various disturbing factors on high-precision forecasts of spacecraft orbits

The necessity of taking many force components disturbing spacecraft (SC) orbits into account is demonstrated for the example of forecasts of GLONASS ephemerides. The disturbances of SCs in high-earth orbits (HEO) and low-earth orbits (LEO) are systematized, and the degree of their effect on SC motion is estimated. Disturbance models are developed that provide essential increases of the accuracy of one-day forecasts of GLONASS and GPS ephemerides. Modeling results are presented that allow, depending on the required accuracy of SC orbit forecasts, the determination of the necessary list of disturbances included in the model.

Dynamics modeling and attitude control of a flexible space system with active stabilizers

Attitude control of rigid-flexible multi-body systems by active stabilizers is studied in this paper. During slewing maneuvers, flexible members like solar panels may be excited to vibrate. These vibrations, in turn, produce oscillatory disturbing forces on other subsystems and consequently produce error in the spacecraft motion. Also, to develop a proper model-based controller for such complicated system, the system dynamic model is derived. However, due to practical limitations and real-time control implementation, the system dynamic model should be structured such that low computations burden will be imposed on the model-based controller. In this paper, in contrast to many accumulating dynamic modeling approach, a precise compact dynamic model for an active stabilized spacecraft (ASS) system with flexible members is derived. Toward this goal, the total system is virtually partitioned into two rigid and flexible portions. Moreover, the obtained model of these complicated systems is vigorously verified using ANSYS and ADAMS programs. Finally, based on the derived dynamics and a proper virtual damping parameter, an attitude control algorithm is then developed. The suggested controller structure takes the advantage of utilizing the piezoelectric smart materials to dissipate the vibration of solar panels. The obtained results reveal the merits and effectiveness of the proposed suggested modeling and control methods for reliable attitude maneuvering of the system. In addition, it will be shown that the undesired vibrations of the flexible solar panels result in disturbing forces on the ASS system which can be significantly eliminated by the proposed attitude control algorithm.

Dynamic Analysis of Maneuvering Flexible Spacecraft Appendage Using Higher Order Sandwich Panel Theory

THIS PAPER IS DEVOTED TO THE VIBRATION OF ROTATING FLEXIBLE SPACECRAFT. THE MANEUVER OF THE SPACECRAFT IS MODELED BY A CONSTANT TORQUE INPUT ACTING ON THE HUB. FOR THE FIRST TIME IN THIS PAPER THE EQUATIONS OF MOTION OF FLEXIBLE SPACECRAFT ARE DERIVED BASED ON HIGHER ORDER SANDWICH PANEL THEORY (HSAPT). HAMILTON€™S PRINCIPLE IS USED FOR DRIVING THE GOVERNING PARTIAL DIFFERENTIAL EQUATIONS OF MOTION. THE GENERALIZED DIFFERENTIAL QUADRATURE METHOD (GDQ) IS UTILIZED TO SOLVE THE PARTIAL DIFFERENTIAL EQUATIONS OF MOTION. THE EFFECT OF DIFFERENT PARAMETERS ON VIBRATION OF ROTATING FLEXIBLE SPACECRAFT APPENDAGE IS INVESTIGATED. IT IS ALSO INVESTIGATED THE EFFECT OF THESE PARAMETERS ON NATURAL FREQUENCIES. THE RESULT OF HSAPT AND EULER BERNOULLI THEORY IS COMPARED WITH EACH OTHER. TO SHOW THE ACCURACY THE NATURAL FREQUENCIES OF RECENT PAPER ARE COMPARED WITH THE LITERATURE.

Control of in-plane orbit parameters of a geostationary low-thrust satellite

The article focuses on the development of algorithms for controlling the parameters of the orbit of a geostationary satellite with the help of a low- thrust engine. We consider only the control of two-dimensional parameters that define the position of the satellite in the orbital plane, namely, the orbit time, the eccentricity and the point longitude of satellite observation. A two-dimensional problem of geostationary spacecraft terminal control is formulated. It is assumed that the correction maneuver is carried out by creating low transversal acceleration with the help of low-thrust electric propulsion, and the control vector consists of a sequence of durations of powered and unpowered portions. In this regard, the two-dimensional terminal control problem is solved in a discrete setting. For this purpose, a discrete model of the motion of a geostationary spacecraft in the orbital plane under the influence of low transversal acceleration is developed. It is quite difficult to solve the problem posed by using the traditional method of dynamic programming based on the use of the Bellman equation since the resulting discrete model of the satellite motion is a non-linear system of equations. Therefore, an approximate pattern of solving the problem on the basis of a three-step algorithm of the terminal control of the orbit time, eccentricity and point longitude of satellite observation is proposed in the paper. As a result, the plane terminal control problem is solved in an analytical form. Analytical expressions for estimating the costs of characteristic velocity correction maneuver using a three-step algorithm of terminal control are obtained. In modeling the motion of a geostationary satellite under the influence of low transversal acceleration the algorithm showed sufficiently high accuracy.

Optimization of spatial turns of «AIST-2» small spacecraft on the basis of the principle of minimum control

The efficiency of using the principle of minimum control in solving the task of synthesizing the system of controlling a spacecraft spatial turn by arbitrarily set angles up to 180 degrees is analyzed, with the Aist-2 small spacecraft taken as an example. The tensor of inertia has the form of a diagonal matrix. Flywheels the rotors of which are parallel to the principal central axes of the spacecraft inertia are used as actuating devices of the system that controls motion round the center of masses. The control moment developed by each flywheel, is proportional to the angular acceleration of its rotor. The energy spent on the control, proportional to the sum of modules of angular accelerations of flywheel rotors is accepted as an index of the optimality of the spacecraft spatial turn. Euler dynamic equations are reduced to finite-difference recurrent relations to model unperturbed spacecraft motion around the center of masses. An auxiliary dynamic system is introduced the parameters of which are chosen on the basis of the solution of the task posed to use the principle of minimum control that ensures minimum costs of control. The results of mathematical modeling confirmed the efficiency of the proposed principle. In comparison with the traditional method of control (acceleration, motion at a constant angular velocity, braking) two-fold economy of electrical power is achieved.

Changing the magnetic field intensity during the motion of spacecraft

In this paper the change of the intensity vector of geomagnetic field during the motion of the spacecraft in orbit in direct dipole model was investigated. The dependences of the intersection point coordinates of the vector intensity of the geomagnetic field with the unit radius Earth sphere were found, their graphs were built and their extremes were determined. The relations of the intersection point velocity of the vector intensity of the geomagnetic field to the unit radius Earth sphere were found, their graphs were built and their extremes determined. The graphs of each component of the geomagnetic field along the trajectory of the spacecraft and the combined graphs were built.

Using Vision Systems for Determining the Parameters of Relative Motion of Spacecrafts

Using Vision Systems for Determining the Parameters of Relative Motion of Spacecrafts

The Techniques to Control a Space Laboratory Orbital Motion During Conducting of Gravity-sensitive Processes on Its Board

The following article deals with three different techniques to control orbital motion of spacecraft with big flexible structures during conducting of gravity-sensitive processes on its board. These processes require low level of microaccelerations. There were given examples of application of the techniques, recommendations for application of these techniques in practice, discussed advantages and disadvantages of each technique.