DOA estimation for attitude determination on communication satellites

In order to determine an appropriate attitude of three-axis stabilized communication satellites, this paper describes a novel attitude determination method using direction of arrival （DOA） estimation of a ground signal source. It differs from optical measurement, magnetic field measurement, inertial measurement, and global positioning system （GPS） attitude determination. The proposed method is characterized by taking the ground signal source as the attitude reference and acquiring attitude information from DOA estimation. Firstly, an attitude measurement equation with DOA estimation is derived in detail. Then, the error of the measurement equation is analyzed. Finally, an attitude determination algorithm is presented using a dynamic model, the attitude measurement equation, and measurement errors. A developing low Earth orbit （LEO） satellite which tests mobile communication technology with smart antennas can be stabilized in three axes by corporately using a magnetometer, reaction wheels, and three-axis magnetorquer rods. Based on the communication satellite, simulation results demonstrate the effectiveness of the method. The method could be a backup of attitude determination to prevent a system failure on the satellite. Its precision depends on the number of snapshots and the input signal-to-noise ratio （SNR） with DOA estimation.     

Near minimum-time feedback attitude control with multiple saturation constraints for agile satellites

Agile satellites are of importance in modern aerospace applications,but high mobility of the satellites may cause them vulnerable to saturation during attitude maneuvers due to limited rating of actuators.This paper proposes a near minimum-time feedback control law for the agile satellite attitude control system.The feedback controller is formed by specially designed cascaded sub-units.The rapid dynamic response of the modified Bang–Bang control logic achieves the near optimal property and ensures the non-saturation properties on three-axis.To improve the dynamic performance,a model reference control strategy is proposed,in which the on-line near optimal attitude maneuver path is generated by the cascade controller and is then tracked by a nonlinear back-stepping controller.Furthermore,the accuracy and the robustness of the control system are achieved by momentum-based on-line inertial identification.The rapid attitude maneuvering can be applied for tasks including the move to move case.Numerical simulations are conducted to verify the effectiveness of the proposed control strategy in terms of the saturation-free property and rapidness.     

An improved quaternion Gauss–Newton algorithm for attitude determination using magnetometer and accelerometer

For the vector attitude determination, the traditional optimal algorithms which are based on quaternion estimator(QUEST) measurement noise model are complicated for just two observations. In our application, the magnetometer and accelerometer are not two comparable kinds of sensors and both are not small field-of-view sensors as well. So in this paper a new unit measurement model is derived. According to the Wahba problem, the optimal weights for each measurement are obtained by the error variance researches. Then an improved quaternion Gauss–Newton method is presented and adopted to acquire attitude. Eventually, simulation results and experimental validation employed to test the proposed method demonstrate the usefulness of the improved algorithm.     

Adaptive dynamic surface control of NSVs with input saturation using a disturbance observer

An adaptive dynamic surface control(DSC)scheme is proposed for the multi-input and multi-output(MIMO)attitude motion of near-space vehicles(NSVs)in the presence of external disturbance,system uncertainty and input saturation.The external disturbance and the system uncertainty are efficiently tackled using a Nussbaum disturbance observer(NDO),and the adaptive controller is constructed by combining the dynamic surface control technique to handle the problem of‘‘explosion of complexity’’inherent in the conventional backstepping method.For handling the input saturation,an auxiliary system is designed with the same order as that of the studied MIMO attitude system.Using the error between the saturation input and the desired control input as the input of the designed auxiliary system,a series of signals are generated to compensate for the effect of the saturation in the dynamic surface control design.It is proved that the developed control scheme can guarantee that all signals of the closed-loop control system are semi-globally uniformly bounded.Finally,simulation results illustrate that the proposed control scheme can achieve satisfactory tracking performance under the composite effects of the input saturation and the external disturbance.     

Deploying process modeling and attitude control of a satellite with a large deployable antenna

Modeling and attitude control methods for a satellite with a large deployable antenna are studied in the present paper. Firstly, for reducing the model dimension, three dynamic models for the deploying process are developed, which are built with the methods of multi-rigid-body dynam- ics, hybrid coordinate and substructure. Then an attitude control method suitable for the deploying process is proposed, which can keep stability under any dynamical parameter variation. Subse- quently, this attitude control is optimized to minimize attitude disturbance during the deploying process. The simulation results show that this attitude control method can keep stability and main- tain proper attitude variation during the deploying process, which indicates that this attitude con- trol method is suitable for practical applications.     

Local controllability and stabilization of spacecraft attitude by two single-gimbal control moment gyros

The attitude control problem of a spacecraft underactuated by two single-gimbal control moment gyros （SGCMGs） is investigated. Small-time local controllability （STLC） of the attitude dynamics of the spacecraft-SGCMGs system is analyzed via nonlinear controllability theory. The conditions that guarantee STLC of the spacecraft attitude by two non-coaxial SGCMGs are obtained with the momentum of the SGCMGs as inputs, implying that the spacecraft attitude is STLC when the total angular momentum of the whole system is zero. Moreover, our results indi- cate that under the zero-momentum restriction, full attitude stabilization is possible for a spacecraft using two non-coaxial SGCMGs. For the case of two coaxial SGCMGs, the STLC property of the spacecraft cannot be determined. In this case, an improvement to the previous full attitude stabilizing control law, which requires zero-momentum presumption, is proposed to account for the singu- larity of SGCMGs and enhance the steady state performance. Numerical simulation results demonstrate the effectiveness and advantages of the new control law.     

Low-frequency Periodic Error Identification and Compensation for Star Tracker Attitude Measurement

The low-frequency periodic error of star tracker is one of the most critical problems for high-accuracy satellite attitude determination.In this paper an approach is proposed to identify and compensate the low-frequency periodic error for star tracker in attitude measurement.The analytical expression between the estimated gyro drift and the low-frequency periodic error of star tracker is derived firstly.And then the low-frequency periodic error,which can be expressed by Fourier series,is identified by the frequency spectrum of the estimated gyro drift according to the solution of the first step.Furthermore,the compensated model of the low-frequency periodic error is established based on the identified parameters to improve the attitude determination accuracy.Finally,promising simulated experimental results demonstrate the validity and effectiveness of the proposed method.The periodic error for attitude determination is eliminated basically and the estimation precision is improved greatly.     

Image Smearing Modeling and Verification for Strapdown Star Sensor

To further extend study on celestial attitude determination with strapdown star sensor from static into dynamic field, one prerequisite is to generate precise dynamic simulating star maps. First a neat analytical solution of the smearing trajectory caused by spacecraft attitude maneuver is deduced successfully, whose parameters cover the geometric size of optics, three-axis angular velocities and CCD integral time. Then for the first time the mathematical law and method are discovered about how to synthesize the two formulae of smearing trajectory and the static Gaussian distribution function (GDF) model, the key of which is a line integral with regard to the static GDF attenuated by a factor 1/ L s (L s is the arc length of the smearing trajectory) along the smearing trajectory. The dynamic smearing model is then obtained, also in an analytical form. After that, three sets of typical simulating maps and data are simulated from this dynamic model manifesting the expected smearing effects, also compatible with the linear model as its special case of no boresight rotation. Finally, model validity tests on a rate turntable are carried out, which results in a mean correlation coefficient 0.920 0 between the camera images and the corresponding model simulated ones with the same parameters. The sufficient similarity verifies the validity of the dynamic smearing model. This model, after parameter calibration, can serve as a front-end loop of the ground semi-physical simulation system for celestial attitude determination with strapdown star sensor.     

Singularity problem of control moment gyro cluster with vibration isolators

As powerful torque amplification actuators, control moment gyros (CMGs) are often used in the attitude control of many state-of-the-art high resolution satellites. However, the distur-bance generated by the CMGs can not only reduce the attitude stability of a satellite but also dete-riorate the performance of optic payloads. Currently, CMG vibration isolators are widely used to target this problem. The isolators can affect the singularity of the CMG system as they are placed between the CMGs and the satellite bus and provide additional freedoms to the CMG system due to their flexibility. The formulation of the output torque of a CMG is studied first considering the dynamic imbalance of its spin rotor and then the deformation angle as a result of the isolator’s flex-ibility is calculated. With the additional freedoms, the influence of isolator on the singularity problem is studied and a new steering logic to escape from the singular states is proposed.     

Research on vacuum plume and its effects

In vacuum environment, the exhaust flow of attitude control thrusters would expand freely and produce the plume, which possibly causes undesirable contamination, aerodynamic force and heating effects to the spacecraft. Plume work station (PWS) is developed by Beihang University (BUAA) for numerically simulating the vacuum plume and its effects. An approach which combines the direct simulation Monte Carlo (DSMC) method and difference solution of Navier-Stokes (N-S) equations is applied. The internal flows in nozzles are simulated by solving the NS equations. The flow parameters at nozzle exit are used as the inlet boundary condition for the DSMC calculation. Experimental studies are carried out in a supersonic low density wind tunnel which could simulate the 60-80 km altitude environment to investigate the plume and its effects. To demonstrate the capability of PWS, numerical simulations are performed for the vacuum plume of several typical attitude control thrusters. The research results are of great help for the engineering design.     

A new vibration mechanism of balancing machine for satellite-borne spinning rotors

The centrifugal force and overturning moment generated by satellite-borne rotating payload have a significant impact on the stability of on-orbit satellite attitude, which must be controlled to the qualified range. For the satellite-borne rotors＇ low working revs and large centroidal deviation and height, and that the horizontal vibration produced by centrifugal force is not of the same magnitude as the torsional vibration by overturning moment, the balancing machine＇s measurement accuracy is low. Analysis shows that the mixture of horizontal vibration and torsional vibration of the vibrational mechanism contribute mainly to the machine＇s performance, as well as the instability of vibration center position. A vibrational mechanism was put forward, in which the horizontal and torsional vibration get separated effectively by way of fixing the vibration center. From experimental results, the separation between the weak centrifugal force signal and the strong moment signal was realized, errors caused by unstable vibration center are avoided, and the balancing machine based on this vibration structure is able to meet the requirements of dynamic balancing for the satellite＇s rotating payloads in terms of accuracy and stability.     

Simultaneous state and actuator fault estimation for satellite attitude control systems

In this paper, a new nonlinear augmented observer is proposed and applied to satellite attitude control systems. The observer can estimate system state and actuator fault simultaneously. It can enhance the performances of rapidly-varying faults estimation. Only original system matrices are adopted in the parameter design. The considered faults can be unbounded, and the proposed augmented observer can estimate a large class of faults. Systems without disturbances and the fault whose finite times derivatives are zero piecewise are initially considered, followed by a discussion of a general situation where the system is subject to disturbances and the finite times derivatives of the faults are not null but bounded. For the considered nonlinear system, convergence conditions of the observer are provided and the stability analysis is performed using Lyapunov direct method. Then a feasible algorithm is explored to compute the observer parameters using linear matrix inequalities (LMIs). Finally, the effectiveness of the proposed approach is illustrated by considering an example of a closed-loop satellite attitude control system. The simulation results show satisfactory perfor-mance in estimating states and actuator faults. It also shows that multiple faults can be estimated successfully.     

Adaptive Integral-type Sliding Mode Control for Spacecraft Attitude Maneuvering Under Actuator Stuck Failures

A fault tolerant control (FTC) design technique against actuator stuck faults is investigated using integral-type sliding mode control (ISMC) with application to spacecraft attitude maneuvering control system. The principle of the proposed FTC scheme is to design an integral-type sliding mode attitude controller using on-line parameter adaptive updating law to compensate for the effects of stuck actuators. This adaptive law also provides both the estimates of the system parameters and external disturbances such that a prior knowledge of the spacecraft inertia or boundedness of disturbances is not required. Moreover, by including the integral feedback term, the designed controller can not only tolerate actuator stuck faults, but also compensate the disturbances with constant components. For the synthesis of controller, the fault time, patterns and values are unknown in advance, as motivated from a practical spacecraft control application. Complete stability and performance analysis are presented and illustrative simulation results of application to a spacecraft show that high precise attitude control with zero steady-error is successfully achieved using various scenarios of stuck failures in actuators.     

Area-oriented coordinated trajectory planning of dual-arm space robot for capturing a tumbling target

The growing amount of space debris poses a threat to operational spacecraft and the long-term sustainability of activities in outer space. According to the orbital mechanics, an uncontrolled space object will be tumbling, bringing great challenge to capture and remove it. In this paper, a dual-arm coordinated ‘‘Area-Oriented Capture"(AOC) method is proposed to capture a non-cooperative tumbling target. Firstly, the motion equation of the tumbling target is established, based on which, the dynamic properties are analyzed. Then, the ‘‘Area-Oriented Capture"concept is presented to deal with the problem of large pose(position and attitude) deviation and tumbling motion. An area rather than fixed points/devices is taken as the object to be tracked and captured. As long as the manipulators' end-effectors move to a specified range of the objective areas(not fixed points on the target, but areas), the target satellite will be hugged by the two arms.At last, the proposed method and the traditional method(i.e. fixed-point oriented capture method)are compared and analyzed through simulation. The results show that the proposed method has larger pose tolerance and takes shorter time for capturing a tumbling target.     

ACTIVE CONTROL OF DYNAMIC RESPONSE OF LARGE DEFLECTION PLATES WITH PIEZOELECTRIC ACTUATORS USING FINITE ELEMENT METHOD

The transient behavior of isotropic and homogeneous plates has been a subject of interest. The present investigation is concerned with the large deflection transient analysis and control of plates with piezoelectric sensors and actuators under applied transverse loads. In this paper, the incremental finite element equations considering the geometric nonlinearity of piezoelectric smart structures are developed based on Total Lagrange approach by using the virtual velocity incremental variational principles. A four-node Mindlin plate element with reduced and selective integration is adopted. The resulting increment equations are solved by using Newmark's direct integration approach. Transient response of plates with piezoelectric sensors and actuators subjected to transverse dynamic loading is investigated. The active damping is introduced on the plates by coupling a negative velocity feedback algorithm in a closed control loop. The numerical results show that piezoelectric actuators can produce significant damping and suppress transient vibration effectively. Finally, the effects of the number and locations of the piezoelectric actuators on the control system are also investigated.     

Spaceborne GPS receiver antenna phase center offset and variation estimation for the Shiyan 3 satellite

In determining the orbits of low Earth orbit (LEO) satellites using spaceborne GPS, the errors caused by receiver antenna phase center offset (PCO) and phase center variations (PCVs) are gradually becoming a major limiting factor for continued improvements to accuracy. Shiyan 3, a small satellite mission for space technology experimentation and climate exploration, was developed by China and launched on November 5, 2008. The dual-frequency GPS receiver payload delivers 1 Hz data and provides the basis for precise orbit determination within the range of a few centime-ters. The antenna PCO and PCV error characteristics and the principles influencing orbit determi-nation are analyzed. The feasibility of PCO and PCV estimation and compensation in different directions is demonstrated through simulation and in-flight tests. The values of receiver antenna PCO and PCVs for Gravity Recovery and Climate Experiment (GRACE) and Shiyan 3 satellites are estimated from one month of data. A large and stable antenna PCO error, reaching up to 10.34 cm in the z-direction, is found with the Shiyan 3 satellite. The PCVs on the Shiyan 3 satellite are estimated and reach up to 3.0 cm, which is slightly larger than that of GRACE satellites. Orbit validation clearly improved with independent k-band ranging (KBR) and satellite laser ranging (SLR) measurements. For GRACE satellites, the average root mean square (RMS) of KBR resid-uals improved from 1.01 cm to 0.88 cm. For the Shiyan 3 satellite, the average RMS of SLR resid-uals improved from 4.95 cm to 4.06 cm.     

Attitude coordination for spacecraft formation with multiple communication delays

Communication delays are inherently present in information exchange between spacecraft and have an effect on the control performance of spacecraft formation. In this work, attitude coordination control of spacecraft formation is addressed, which is in the presence of multiple communication delays between spacecraft. Virtual system-based approach is utilized in case that a constant reference attitude is available to only a part of the spacecraft. The feedback from the virtual systems to the spacecraft formation is introduced to maintain the formation. Using backstepping control method, input torque of each spacecraft is designed such that the attitude of each spacecraft converges asymptotically to the states of its corresponding virtual system. Furthermore, the backstepping technique and the Lyapunov–Krasovskii method contribute to the control law design when the reference attitude is time-varying and can be obtained by each spacecraft. Finally, effectiveness of the proposed methodology is illustrated by the numerical simulations of a spacecraft formation.     

A data transmission scheduling algorithm for rapid-response earth-observing operations

With the development of rapid-response Earth-observing techniques, the demand for reducing a requirements-tasking-effects cycle from 1 day to hours grows rapidly. For instance, a satellite user always wants to receive requested data in near real-time to support their urgent mis- sions, such as dealing with wildfires, volcanoes, flooding events, etc. In this paper, we try to reduce data transmission time for achieving this goal. The new feature of a responsive satellite is that users can receive signals from it directly. Therefore, the traditional satellite control and operational tech- niques need to be improved to accommodate these changes in user needs and technical upgrading. With that in mind, a data transmission topological model is constructed. Based on this model, we can deal with the satellite data transmission problem as a multi-constraint and multi-objective path- scheduling problem. However, there are many optional data transmission paths for each target based on this model, and the shortest path is preferred. In addition, satellites represent scarce resources that must be carefully scheduled in order to satisfy as many consumer requests as possible. To efficiently balance response time and resource utilization, a K-shortest path genetic algorithm is proposed for solving the data transmission problem. Simulations and analysis show the feasibility and the adaptability of the proposed approach.     

Basic performance of BeiDou-2 navigation satellite system used in LEO satellites precise orbit determination

The visibility for low earth orbit（LEO） satellites provided by the BeiDou-2 system is analyzed and compared with the global positioning system（GPS）. In addition, the spaceborne receivers＇ observations are simulated by the BeiDou satellites broadcast ephemeris and LEO satellites orbits. The precise orbit determination（POD） results show that the along-track component accuracy is much better over the service area than the non-service area, while the accuracy of the other two directions keeps at the same level over different areas. However, the 3-dimensional（3D） accuracy over the two areas shows almost no difference. Only taking into consideration the observation noise and navigation satellite ephemeris errors, the 3D accuracy of the POD is about30 cm. As for the precise relative orbit determination（PROD）, the 3D accuracy is much better over the eastern hemisphere than that of the western hemisphere. The baseline length accuracy is 3.4 mm over the service area, and it is still better than 1 cm over the non-service area. This paper demonstrates that the BeiDou regional constellation could provide global service to LEO satellites for the POD and the PROD. Finally, the benefit of geostationary earth orbit（GEO） satellites is illustrated for POD.     

Attitude tracking control for variable structure near space vehicles based on switched nonlinear systems

An adaptive robust attitude tracking control law based on switched nonlinear systems is presented for a variable structure near space vehicle (VSNSV) in the presence of uncertainties and disturbances. The adaptive fuzzy systems are employed for approximating unknown functions in the flight dynamic model and their parameters are updated online. To improve the flight robust performance, robust controllers with adaptive gains are designed to compensate for the approximation errors and thus they have less design conservation. Moreover, a systematic procedure is developed for the synthesis of adaptive fuzzy dynamic surface control (DSC) approach. According to the common Lyapunov function theory, it is proved that all signals of the closed-loop system are uniformly ultimately bounded by the continuous controller. The simulation results demonstrate the effectiveness and robustness of the proposed control scheme.