Spacecraft Angular Velocity Research Articles

Use of thermal data to estimate satellite rotation rate in the UPMSat-2

Attitude determination is a fundamental task of the Attitude Determination and Control Subsystem (ADCS). It involves determining the spacecraft’s orientation with respect to a reference system and calculating its angular velocity, which is essential for understanding where the payload is pointing and the spacecraft’s stability. The determination of the attitude is obtained using sensors such as Sun sensors, Nadir sensors, or Star trackers. Regarding the spacecraft angular velocity, gyroscopes or MEMs can be used to measure the angular velocity of the satellite, but in their absence the velocity can be derived from the attitude data of the other sensors. However, this method requires a sampling rate to be twice the frequency of the movement, otherwise the angular velocity cannot be calculated with traditional methods. To address this issue, this study proposes a thermal analysis of the external temperatures of a rotating satellite to obtain its rotation rate. This method is especially useful for satellites with low or limited data sample rates. The proposed methodology is used in the UPMSat-2 case to demonstrate the functionality of its experimental ADCS.

Spacecraft attitude control based on generalised dynamic inversion with adaptive neural network

AbstractThis paper proposes a robust generalised dynamic inversion (GDI) control system design with adaptive neural network (NN) estimation for spacecraft attitude tracking under the absence of knowledge of the spacecraft inertia parameters. The robust GDI control system works to enforce attitude tracking, and the adaptive NN augmentation compensates for the lack of knowledge of the spacecraft inertia parameters. The baseline GDI control law consists of a particular part and an auxiliary part. The particular part of the GDI control law works to realise a desired attitude dynamics of the spacecraft, and the auxiliary part works for finite-time stabilisation of the spacecraft angular velocity. Robustness against modeling uncertainties and external disturbances is provided by augmenting a siding mode control element within the particular part of the GDI control law. The singularity that accompanies GDI control is avoided by modifying the Moore-Penrose generalised inverse by means of a dynamic scaling factor. The NN weighting matrices are updated adaptively through a control Lyapunov function. A detailed stability analysis shows that the closed loop system is semi-global practically stable. For performance assessment, a spacecraft model is developed, and GDI-NN control is investigated for its attitude control problem through numerical simulations. Simulation results reveal the efficacy, robustness and adaptive attributes of proposed GDI-NN control for its application to spacecraft attitude control.

Wave-based attitude control of in-orbit spacecraft with large-amplitude slosh

This paper aims to reach high-quality attitude control and large-amplitude slosh suppression when a typical liquid-filled spacecraft executes three-axial large-angle maneuvers, by applying a wave-based attitude controller (WBAC). First, the sloshing dynamics is modeled by using a spherical pendulum, whose motion is expressed by splitting its coordinates. Thus, the large-amplitude lateral sloshing and the rotary sloshing as well as the over-all rigid motion of a liquid with respect to the tank in spacecraft can be approximately described. Second, the dynamics equations of system in terms of hybrid coordinate for the liquid-filled spacecraft are derived via the Lagrangian formulation. Third, an improved WBAC for three-axial large-angle maneuvers of in-orbit liquid-filled spacecraft is designed by adding a derivative control law and a gravity-gradient-torque compensation law to a wave-based control law. Simulations of three-axial large-angle maneuver demonstrate good performance of the WBAC in shortening completion time of attitude maneuvering, suppressing the jitter in the angular velocity of spacecraft, and accelerating the large-amplitude slosh suppression, simultaneously. The results indicate the potential applications of the proposed WBAC in the large-angle attitude maneuvering of liquid-filled spacecraft when there exists large-amplitude liquid slosh.

Controlled Change in the Dimensions of an Axisymmetric Spacecraft Descending in the Atmosphere of Mars

In the presented work, a controlled change by dimensions of a spacecraft descending in the atmosphere of Mars is considered. The aim of the work is to obtain a method for calculating the mass and mass-geometric characteristics of a spacecraft when changing its dimensions, which provides angular velocity passive control during the descent of this spacecraft in a low-density atmosphere. In the process of solving this problem, the geometric and mass-geometric characteristics of the descent spacecraft (volume, cross-sectional area, moments of inertia) were calculated. It is assumed that the outer shape of the spacecraft posterior to the incoming flow is a one-sheet rotational hyperboloid, which changes its dimensions during the spacecraft descent in the low-density atmosphere of Mars. As a result of solving the nonlinear programming problem, the minimum and maximum values of the main axial moments of inertia are obtained, which able to spin the spacecraft relative to the longitudinal axis of symmetry. The initial data for solving the nonlinear programming problem are the minimum volume and the maximum cross-sectional area of the hyperboloid, calculated according to the specified intervals of the variable controlling the dimensions of this surface. The method for calculating the mass and mass-geometric characteristics of a spacecraft when changing its dimensions ispresented, which makes it possible to control the magnitude of the angular velocity of a symmetric spacecraft in the low-density atmosphere of Mars without the use of onboard jet engines. In particular, it is shown in the work that as the height of the hyperboloid increases, the moment of inertia about the spacecraft longitudinal axis of symmetry decreases, accompanied by an increase in the moments of inertia about the transverse axes of symmetry. It can be shown that in this case there is an increase in the angular velocity of the spacecraft about the longitudinal axis, which makes it possible to achieve a stable orientation of the spacecraft upon entering the atmosphere. However, a more detailed study of the dynamics ofthe spacecraft relative motionwith a changeable shape in the atmosphere is beyond the scope of this work, but it can be presented in further publications.

Design of control moment gyro electric drive with strict requirements on ensuring desired rotational velocities

The paper discusses the issues of designing a control moment gyroscope electric drive with strict requirements in terms of the accuracy of ensuring a given rotation rate of the gyro motor suspension. A brief description of the control moment gyroscope electric drive applied currently is presented and the issues of improving the electric drive characteristics are discussed. As a solution, an electric drive is proposed which operates in the mode of feedback loop using angle sensors located on the axes of the gyroscope suspension and the engine rotor. The paper describes the arrangement of the control moment gyroscopes on advanced spacecraft for Earth remote sensing and presents the analytic expressions needed to calculate the control moments that affect the spacecraft. The moments are in the projection to the coordinate system brought into coincidence with the spacecraft. The paper compares spacecraft angular velocity stabilization errors for the cases of using the conventional scheme of control moment gyroscope electric drive and the newly developed one. The presented results can be used for developing control moment gyroscope electric drives to be mounted on spacecraft of different purpose with strict requirements on ensuring operation at specified rotational velocities.

A geometrical approach for the angular velocity determination using a star sensor

In this paper, a geometrical investigation of the star sensor image is performed under dynamic conditions where the angular velocity effects are non-negligible. It is shown that, when the spacecraft is rotating, the streaks left by the stars’ signal onto the star sensor detector belong to portions of conic sections which features depend on the angles between the instantaneous rotation axis, the sensor line of sight and the stars’ direction. The geometrical properties discussed in the first part of the paper can be used to develop new numerical methods for the evaluation of the angular velocity. Hence, the chord method is proposed and discussed. This approach needs at least two stars in two successive images and, despite its simplicity, is quite effective to get a preliminary estimation of the spacecraft angular velocity in terms of direction and magnitude. Using the stars’ centroids from two successive images, the chord method evaluates the angular velocity direction as the intersection of the normals to the streaks. The proposed method is firstly presented by means of simple examples using some reference geometries, and then it is applied to real scenarios by using a high fidelity star sensor simulator. The pre-processing and processing of simulated images are discussed, presenting the geometrical techniques used to cluster the streaks and compute the centroids. Results are presented and discussed, validating the reported theoretical speculations.

Effects of the rotation of a spacecraft in an atmospheric close approach with the Earth

A maneuver called “Aerogravity Assisted” is known in the literature to increase the energy gains given by a close approach between a spacecraft and a planet using the atmosphere of the planet. Several previous papers showed the importance of this topic in different aspects. The present paper has the goal of studying the effects of the spacecraft rotation in this maneuver. This rotation implies in a variable ballistic coefficient and this fact can change the results of the maneuver. Several masses, sizes and angular velocities will be tested and the effects of these parameters will be measured. The dynamical model considers the atmosphere of the Earth, in terms of drag, the gravitational fields of the Earth and the Sun, assumed to be points of mass, and the rotating spacecraft. The Earth and the Sun are assumed to be in circular coplanar orbits around their common center of mass. The equations of motion are the ones given by the circular planar restricted three-body problem with the addition of the forces generated by the atmospheric drag. The primary objective is to map the energy variations of the spacecraft orbits due to this close approach as a function of the spacecraft angular velocity. This rotation can be used as control of the maneuver to try to reach different goals.

A generalized control law for uniform, global and exponential magnetic detumbling of rigid spacecraft

The problem of magnetic detumbling, also known as magnetic momentum unloading, is considered. The objective is to stabilize a rigid spacecraft angular velocity to zero only through magnetic actuation, i.e. magneto-torquers. We propose a generalized control law that is uniformly, globally exponentially stabilizing (UGES) and show that the celebrated b-dot law is one particular case of this law. Furthermore, we provide an explicit (time-varying) strict Lyapunov function to establish the stability claim.

Nutational oscillations suppression in attitude dynamics of spacecraft by relative motion of its movable module

Attitude dynamics of a spacecraft with a movable module on retractable beams are considered. The movable module is attached to the main body of the spacecraft by retractable beams of variable length. The spacecraft main body contains a simple jet-engine with constant thrust. The retractable beams can tilt the movable module relatively the main part of the spacecraft, which shifts the position of the mass center. The control scheme of the nutation oscillations suppressing is constructed. This control scheme uses the impulses of the jet-engine on intervals of positive values of the equatorial component of the spacecraft angular velocity at the constant angular displacement of the movable unit. The main aim of this work is to develop the simplest control algorithm, which can be applied in cases of simple constructional forms of the small spacecraft with primitive equipment, including nano-satellites, that is economically profitable and can be used in more space missions.

Gravitational Orientation of Progress MS-07 and Progress MS-08 Transport Cargo Spacecraft

The uncontrolled rotational motion of Progress MS-07 and Progress MS-08 transport cargo spacecraft in the mode of gravitational orientation of a rotating satellite was reconstructed. Modes were implemented in April and August 2018. The reconstruction was conducted using an integral statistical method according to measurements of spacecraft angular velocity. Measurement data obtained at a certain time interval were processed together with the least squares method by integrating the equations of spacecraft motion relative to the center of mass. As a result of processing, the initial conditions of motion and parameters of the used mathematical model were estimated. The correctness of the reconstruction was checked by measuring the current taken from the solar panels. In the mode of gravitational orientation, the spacecraft rotated around its longitudinal axis with an angular velocity of 0.1–0.2 deg/s oscillating relative to the local vertical.

Application of PIV and Delaunay Triangulation Method for Satellite Angular Velocity Estimation Using Star Tracker

The main objective of this paper is to apply a particle image velocimetry technique accompanied by Delaunay triangulation and spatial angles to consecutive images of star tracker in order to estimate the angular velocity of spacecraft. This method is independent of star identification or attitude matrix and can be performed parallel to conventional star tracker algorithms. It is computationally light and consumes a reasonable time to perform. An interrogation window containing two or more stars in the first image is selected and based on the peak of normalized cross correlation matrix, the same window in the second image is matched. In order to make sure that the matched windows are indeed the same, local recognition features, such as spatial angles for windows with two stars and Delaunay triangle planar angles for three or more stars, are compared. When matched, window center angular displacement is calculated in a fixed imaging time interval, and eventually, an angular rate is estimated. In order to evaluate the performance of the proposed method, Monte Carlo simulation of random night sky images is used. It is shown that for angular rates, about 1°/s accuracies better than 7e−5°/s are achieved. Accuracy decreases to 1e−3°/s for the rates of about 12°/s in 0.1-s time interval.

Algorithm of the Time-Optimal Reorientation of an Axially Symmetric Spacecraft in the Class of Conical Motions

The problem of the time-optimal turn of a spacecraft as a rigid body with one axis of symmetry and bounded control function in absolute value is considered in the quaternion statement. For simplifying problem (concerning dynamic Euler equations), we change the variables reducing the original optimal turn problem of axially symmetric spacecraft to the problem of optimal turn of the rigid body with spherical mass distribution including one new scalar equation. Using the Pontryagin maximum principle, a new analytical solution of this problem in the class of conical motions is obtained. Algorithm of the optimal turn of a spacecraft is given. An explicit expression for the constant in magnitude optimal angular velocity vector of a spacecraft is found. The motion trajectory of a spacecraft is a regular precession. The conditions for the initial and terminal values of a spacecraft angular velocity vector are formulated. These conditions make it possible to solve the problem analytically in the class of conical motions. The initial and the terminal vectors of spacecraft angular velocity must be on the conical surface generated by arbitrary given constant conditions of the problem. The numerical example is presented. The example contain optimal reorientation of the Space Shuttle in the class of conical motions.

Spacecraft angular velocity estimation algorithm for star tracker based on optical flow techniques

An integrated navigation system often uses the traditional gyro and star tracker for high precision navigation with the shortcomings of large volume, heavy weight and high-cost. With the development of autonomous navigation for deep space and small spacecraft, star tracker has been gradually used for attitude calculation and angular velocity measurement directly. At the same time, with the dynamic imaging requirements of remote sensing satellites and other imaging satellites, how to measure the angular velocity in the dynamic situation to improve the accuracy of the star tracker is the hotspot of future research. We propose the approach to measure angular rate with a nongyro and improve the dynamic performance of the star tracker. First, the star extraction algorithm based on morphology is used to extract the star region, and the stars in the two images are matched according to the method of angular distance voting. The calculation of the displacement of the star image is measured by the improved optical flow method. Finally, the triaxial angular velocity of the star tracker is calculated by the star vector using the least squares method. The method has the advantages of fast matching speed, strong antinoise ability, and good dynamic performance. The triaxial angular velocity of star tracker can be obtained accurately with these methods. So, the star tracker can achieve better tracking performance and dynamic attitude positioning accuracy to lay a good foundation for the wide application of various satellites and complex space missions.

Relative State and Inertia Estimation of Unknown Tumbling Spacecraft by Stereo Vision

A novel algorithm is proposed to estimate the relative state, including position, attitude, linear velocity, angular velocity, and inertia parameters of an unknown tumbling spacecraft, by stereo vision. Feature points of the target are selected in situ , and their positions and velocities are estimated by the measurements of perspective projection and optical flow. Then, the relative attitude and angular velocity of the spacecraft are estimated by a unit quaternion method and least square method, respectively. After that, the relative position and translational velocity of the spacecraft, together with the relative positions of the detected feature points, are estimated simultaneously based on the relative translational motion model of the target by successive images. Finally, inertia parameters of the spacecraft are estimated by a quadratic optimization method based on angular momentum conservation subject to physical constraints. The performance of the newly proposed algorithm is verified by comparing with an existing case in the literature. Moreover, the performance is validated by Monte-Carlo simulations in different cases.

On the recovery of the reference trajectory of rotation

The boundary value problem of determining the time dependence of the spacecraft angular velocity vector from measurements performed by uniaxial transducers rigidly fixed in the body-fixed frame is stated and solved. The proposed algorithm ensures that the mean and variance of the variations in the estimates of the angular velocity vector are smaller than the corresponding accuracy characteristics of uniaxial transducers. The implementation of the proposed technique permits increasing the accuracy of inertial measurement devices.

Distributed attitude synchronization control for a group of flexible spacecraft using only attitude measurements

This paper considers the problem of attitude synchronization control of a group of flexible spacecraft under an undirected communication graph and in the absence of measurements of both modal variables and spacecraft angular velocities. To solve this problem, a nonlinear observer is introduced to estimate the unmeasurable modal variables and spacecraft angular velocities. Then, the backstepping technique is used to design the control law. The stability of the overall closed-loop system is guaranteed by the Lyapunov approach together with Barbalat’s Lemma. The performance of the control scheme derived here is illustrated through numerical simulations.

Deterministic Algorithms to Estimate Spacecraft Angular Velocity from Single Vector Measurements

This paper presents two fast convergence deterministic algorithms for spacecraft angular velocity estimation from single vector measurement. When the spacecraft is in high velocity state, the successive measurements of a single vector are taken as two different observation vectors and connected by the angular dynamic equations. Based on the pseudoinverse of the full column rank coefficient matrix, the optimal approximation solution of angular velocities is obtained. Simulation results show that the proposed algorithm can converge within a short time and the combined use of the algorithm and a simple α filter can improve the accuracy.

On the attitude stabilization of a rigid spacecraft using two skew control moment gyros

The attitude control of a rigid spacecraft with two skew single-gimbal control moment gyros (CMGs), which is subject to an underactuated nonholonomic constraint, is investigated. Nonlinear control theory is used to show that the combined dynamics of the spacecraft-CMG system are small-time locally controllable (STLC) from and feedback stabilizable to any equilibrium where two CMGs never encounter certain special configurations. Specially, the attitude stabilization issue is approached under the restriction that the total angular momentum of the spacecraft-CMG system is zero, which not only guarantees that the feasible equilibrium attitude can be any orientation but also renders STLC for these attitudes. In order to overcome the troublesome singular problem of two skew CMGs, a nonlinear approximation of the full attitude equations is derived for control law design by assuming that the spacecraft angular velocity is small. A novel singular quaternion stabilization law is then proposed to stabilize the spacecraft attitude with bounded angular velocities, which in turn ensures the satisfaction of the small angular velocity assumption during the entire control process. Numerical examples and experimental results validate the effectiveness of the proposed control method in stabilizing the full spacecraft-CMG system.

A Spaceborne Gravity Gradiometer Concept Based on Cold Atom Interferometers for Measuring Earth’s Gravity Field

We propose a concept for future space gravity missions using cold atom interferometers for measuring the diagonal elements of the gravity gradient tensor and the spacecraft angular velocity. The aim is to achieve better performance than previous space gravity missions due to a very low white noise spectral behavior and a very high common mode rejection, with the ultimate goals of determining the fine structures of the gravity field with higher accuracy than GOCE and detecting time-variable signals in the gravity field better than GRACE.

Magnetometer-only attitude and angular velocity filtering estimation for attitude changing spacecraft

This paper presents an improved real-time sequential filter (IRTSF) for magnetometer-only attitude and angular velocity estimation of spacecraft during its attitude changing (including fast and large angular attitude maneuver, rapidly spinning or uncontrolled tumble). In this new magnetometer-only attitude determination technique, both attitude dynamics equation and first time derivative of measured magnetic field vector are directly leaded into filtering equations based on the traditional single vector attitude determination method of gyroless and real-time sequential filter (RTSF) of magnetometer-only attitude estimation. The process noise model of IRTSF includes attitude kinematics and dynamics equations, and its measurement model consists of magnetic field vector and its first time derivative. The observability of IRTSF for small or large angular velocity changing spacecraft is evaluated by an improved Lie-Differentiation, and the degrees of observability of IRTSF for different initial estimation errors are analyzed by the condition number and a solved covariance matrix. Numerical simulation results indicate that: (1) the attitude and angular velocity of spacecraft can be estimated with sufficient accuracy using IRTSF from magnetometer-only data; (2) compared with that of RTSF, the estimation accuracies and observability degrees of attitude and angular velocity using IRTSF from magnetometer-only data are both improved; and (3) universality: the IRTSF of magnetometer-only attitude and angular velocity estimation is observable for any different initial state estimation error vector.