This disclosure relates to the fields of motion determination and motion control for large, flexible space structures. Flexible structures are those whose stiffness is low along one or more axes such that the structure exhibits broad, slow differential displacements along that axis when exposed to external forces and torques. The disclosure resolves challenges of measuring and controlling this motion. The disclosure includes a sensor suite for measuring displacements, a means of integrating these measurements and estimating displacements in real time, and control implementation.
U.S. Pat. No. 9,973,266 and U.S. Publ. No. 2019/0238216 show a system for assembling a large number of small satellite antenna assemblies in space to form a large array. The entire content of the '266 patent is incorporated herein by reference. As disclosed in the '266 Patent,
A large array in space is formed by joining several smaller elements by connectors, such as joints, hinges, tape-springs. Each element can be considered as rigid, flexure being largely in the connectors that connect the elements to each other. The connectors have a storage configuration in which they are bent so that the antenna elements 300 are folded upon each other to be compact for transport into space. And the connectors have default bias to a deployed configuration in which they expand so that the antenna elements are unfolded and expand into a large planar configuration in space. In addition, the control satellite 200 need not be distinct from the small satellites 302, but rather the control satellite 200 can be connected to the small satellites 302, such as directly embedded within the array 100.
However, the low mass-per-unit aperture arrays can physically bend or deviate from their nominal positions due to external forces in deployed orbit around the Earth (e.g., low earth orbit (LEO), medium earth orbit {MEC}), etc.). For example, there can be both displacement and rotation in the connectors. Analysis has revealed that there could be as much as 70 cm displacement in an 8 m diameter array, which can be corrected, for example, to displacement of 10 cm or less by appropriate mechanical or structural compensations. This can be achieved by use of, e.g., torque rods that apply a magnetic moment against the Earth's magnetic field which moves the connectors toward their fully deployed configuration and moves the array of antenna elements toward the full planar configuration. Residual displacement (after the mechanical compensation) is compensated by beamforming corrections, for example by applying a phase correction to the beam. Thus, the structural compensation applies a coarse correction, whereas the phase adjustment applies a fine correction. The maximum displacement that beamforming compensation can correct for is limited to a fraction of the wavelength of the frequency used (the wavelength at 900 MHz is 33.33 cm).
Accordingly, a system and method are provided with various mechanical modes of deviations, their effect on beamforming and the methods for compensating structural deflections.
In describing the illustrative, non-limiting embodiments of the disclosure illustrated in the drawings, specific terminology will be resorted to for the sake of clarity. However the disclosure is not intended to be limited to the specific terms so selected, and it is to be understood that each specific term includes all technical equivalents that operate in similar manner to accomplish a similar purpose. Several embodiments of the disclosure are described for illustrative purposes, it being understood that the disclosure may be embodied in other forms not specifically shown in the drawings.
Referring to
The structure 10 is flat and rectangular or square, with the communication components (e.g., antenna elements 19) at one side surface 7 (
The antenna element 10 also has one or more connectors 14, such as a hinge, joint, spring or tape-spring connector, that connect the antenna element 10 to one or more neighboring antenna elements 10. As shown, the antenna element 10 can be rectangular or square and encompass multiple antenna elements 300, and one or more connectors can be positioned at or along one or more of the edges or sides of the antenna element 10. Accordingly, the antenna elements 10 can have a storage configuration in which the antenna elements 10 are folded upon each other for storage, and an operating configuration in which the antenna elements 10 are substantially planar and unfolded for use in space. In this manner, large numbers of antenna elements 10 can be transported to space in the storage configuration and deployed into the operating configuration in space. It will be recognized that the system can utilize any suitable connection system, for example such as the one shown and described in U.S. Patent Pub. Nos. 2020/0361635, 2020/0366237, and 2020/0365966, the entire contents of which are hereby incorporated by reference.
The connectors can be subject to bending or flexing in the operating configuration. For example, the maximum flex at the connector 14 might be several degrees. Any flex results in a deviation of the antenna elements from the planar configuration in which the communication side (and/or the solar side) of the plurality of antenna elements are planar. That deviation, which is undesirable since it can affect beam formation. The maximum flex angle is limited to a couple of degrees (less than about 2° in each connector) at the connector 14, as a function of the drivers of the mechanical design.
Thus, it is important that the structure 10 and the array 5 (
The opening in the array (here shown as the center, though the opening can be positioned at any suitable position) enables placement of a central processor to control all the small satellites via high-speed serial links and a set of antennas for communication with the ground station. The antenna elements 19 are positioned at the communication side surface 7 of the array and the solar cells are positioned at the solar side 9 of the array 5. The arrow 11 shows the boresight, which for a planar phased array refers to a normal to the array's plane. Any beam off-boresight is called an edge beam (e.g.,
The small satellites 10 communicate with end user devices (such as cell phones) on Earth, and with the central processor 200, which in turn communicates with a gateway at the ground station. The signals communicated to/by the small satellites are aggregated together, such that the small satellites collectively transmit and receive signals to the end user devices. However, any bending or flexing of the array can cause the signals from the individual small satellites to deviate or be out of phase from the desired phase.
As the mass per unit aperture is reduced, the stiffness of the array is reduced and the array encounters greater flexure. The arrows in
The example of
However, other bends are possible, for example bends that only partially extend along the array, bends that are offset from the center diameter, bends that extend at other positions and locations that do not pass through the center of the array, and multiple bends. And, while the bend 20 is shown having a sharp angle between the left and right halves 22, 24, the bend can be more curved. And, the left and right halves 22, 24 need not be planar, but can be curved due to slight deviations or bends at connectors between antenna modules 10.
Referring to
While
General displacements such as those in
The embodiment in
Thus,
The effect of modal array deformation and caused by coupled flexure on beamforming can be minimized by considering the instantaneous position of each antenna element while computing the corresponding phases used for beamforming. This is accomplished by placing position sensors 20 (
As shown in
The sensor 50 in this embodiment is a standard Global Positioning System (GPS) sensor device that automatically estimates position in a global co-ordinate system and provides carrier phase and pseudorange output data for individual received GPS signals. As shown in
As noted, any bending, flexing, deformation or perturbations in the array result in a change in distance between the various small satellites 10, which in turn can cause signals transmitted or received by one or more of the small satellites to deviate or be out of phase from the desired phases, that can degrade the aggregate signals from all the small satellites. Thus, the system of the present disclosure conducts a position correction for each of the antenna elements 19 in small satellites 10 so that their phases align when aggregated towards/from the intended beam direction. The phase is determined by frequency, the azimuth and elevation scan angles towards the direction of the beam and the relative position of the antenna elements across the small satellites and the array.
The beamforming phase (in radians) of each antenna element is given by:
ϕe=2π(fc/c)·[XeYeZe]·[sin(El)cos(El)·sin(Az)cos(El)·cos(Az)]′
where, fc is carrier frequency (in Hz); c is the speed of light (in m/s), Xe, Ye and Ze are positions of each antenna element 10 (in meters) relative to the geometrical center of the nominal array plane in master co-ordinate system (nadir defined in Z-direction); and Az and El are Azimuth and Elevation scan angles of a target beam (in radians) relative to the nominal array reference plane. The sensors 20 can be a standard Global Positioning System (GPS) sensor device that automatically estimates position in a global co-ordinate system. The GPS sensors 20 sense the position (typically to about 1 meter), for instance the X, Y, Z, then the position relative to the geometric center are determined by the processor 12 based on those GPS coordinates. The beamforming phase is used to determine the phase compensation in degrees (360×displacement/wavelength, where wavelength is calculated at the carrier frequency of communication. The phase of each antenna element 10 is different from its neighbor based on the direction where the beam is pointed; when the elements 10 are displaced away from that plane, the phase is adjusted based on the displacement of the element from the plane.
From this consistent set of array element positions, the central processor (at the Control satellite 200) computes the amplitude table's elevation/azimuth 86 and phase calculator's elevation/azimuth indices 94 for each beam that is to be illuminated by the micron array at certain (coarse) timing instants. The amplitude 88 and phases 96 to be applied varies according to the location of the satellite element 10 in the array, as well as its displacement from its nominal array position. These are computed at the central processor and distributed to the satellite elements 10. To obtain amplitude and phases at intermediate instants, the micron array, may if required, interpolate that data. The small satellites 10 together may then create both transmit and receive beams, at the appropriate carrier frequencies, for the beams.
The following equation shows the corrections in phase because of displacement of elements from their nominal positions:
DirCosineVec=[r·sin(ElPH);r·cos(ElPH)·sin(AzPH);r·cos(ElPH)·cos(AzPH)]
Beamforming phase (in radians), ϕ=2·π·fc·RelDelay
where, fc is frequency of operation (in Hz) and c is speed of light (in m/s); x is the direction cosine vector in North (x-axis) direction; y is the direction cosine vector in the East (y-axis) direction; and z is the direction cosine vector in the Down (z-axis) direction.
Thus, the system compensates for flexing by measuring displacements in each antenna element in X, Y and Z axes and then correcting the phase of each antenna element accordingly. If there was no flexure, then X, Y, Z could be set as a constant. The system operates dynamically and in real-time providing the required phases without manual interaction, while the sensors continually sense the X, Y, Z position. The placements of the sensors 49 and 50 in the example realization are chosen to coincide with the maximum displacements due to the primary oscillation modes of the aperture structure. Because the beamforming phase is used to determine the phase compensation based on the displacement of the structure elements 10 from a planar configuration, the system must compensate for any additional flexing by mechanically correcting the relative positioning of the spacecraft elements 302 where possible. Where each small satellite 10 has its own sensor 20, the deviation/phase correction can be determined based on the position of that sensor. However, where a single sensor is provided for multiple small satellites, the deviation and phase correction for each small satellite 10 can be extrapolated based on the positions of that surrounding small satellites with respect to the sensor. The displacements and phase correction can be determined locally by the processor 12 at that small satellite 10, or at a centrally located processor such as at the central satellite 200 (
The placement of the sensors 20 is chosen (based on the oscillation modes of the aperture structure) so that the locations of all antenna elements 10 can be computed by spatial interpolation, which are communicated to a central processor that computes the beamforming phase vectors of all the antenna elements in the array according to the equation shown above.
The GPS sensors 20 provide the estimated X, Y and Z positions, which are used to compute the Xe, Ye, and Ze parameters in the formula instead of assuming them to be at a known position in nominal plane, based on the geometry.
The example considering a 10.3 m array with 8.7 degrees flexing is already mentioned above with respect to
Thus,
The motion is determined initially using a set of sensors 20 that provide location- or position-based measurements, which in one embodiment can be GPS receivers performing carrier-phase differential (CD-GPS) measurements. This can be conducted in accordance with any suitable manner for determining the position and velocity difference between any pair of GPS units 20, precise to ≈2 cm relative displacement. On a large, flexible structure though, multiple such CD-GPS solutions can be combined to improve the estimate of displacements with respect to one another. If the GPS units 20 are located near highly mobile regions of the structure 10 when experiencing a modal displacement, the CD-GPS solutions allow an estimate of the coefficients associated with a mathematical model of that displacement.
Because of the limitations of CD-GPS computation rates, these estimates are computed in real-time between available CD-GPS solutions by inertial measurement unit (IMU) data provided at a much higher rate. Timing misalignments between CD-GPS and IMU solutions are resolved via propagation of the existing solution.
The coefficients estimated using these integrated solutions are made available at a high rate for a specific digital beamforming application. However, such modal estimation can be made available for a variety of purposes.
As shown, the estimator 54 includes a structure displacement complementary filter 56, and a correction and control module 58. The filter 56 receives position data from the GPS sensors in an array format and receives acceleration data from the IMU sensors 21 in an array format. The filter 56 fuses or combines the position data and the acceleration data. The position data alone only provides accuracy to about 1 meter; however, fusing the position data with the acceleration data provides accuracy to a few millimeters (perhaps 3-8 mm or better). That data fusion can be accomplished in any suitable manner, such as by a Weiner filter and checking for outliers.
The displacement filter 56 utilizes the position and acceleration data to determine the current displacement of the antenna element 10. For example, the displacement filter may determine that the specific antenna element 10 is displaced by 5 mm, meaning that it is 5 mm from where it should be.
The displacement filter 56 outputs the displacement data to the correction and control module 58, which applies a physical displacement to the antenna element 10 to correct for the displacement. The correction and control module 58 uses current and extrapolated deformation constant estimates and determines displacement position and rate estimates. It then applies the correction to a drive device such as a torque actuator or torque mechanism by a damping torque model 62, which sends a torque command 64, 66 to the torque rod. The torque rod then applies a torque to the antenna element 10 to move the antenna element 10 back to the desired position. Thus, the processing device (either at the array of antenna elements or at the central controller 200) operates the drive device to move one or more of the plurality of antenna element structures 10 to correct for structural displacement of the antenna element structures.
The correction and control module 58 also outputs the displacement data (e.g., the 5 mm displacement) to the digital beamformer 68. The digital beamformer 68 computes and applies a phase correction to the beam. It can compute for individual sensor points, or take into account other sensor points.
In addition, the displacement filter 56 outputs the displacement data (e.g., 5 mm displacement) to provide an IMU bias estimate table 60 that feeds back to the IMU array 52. Thus, the displacement filter 56, IMU bias estimates 60, and IMU filter 52 provide a feedback loop that resets the conditions in displacement and velocity so that the next IMU reading is more accurate. It will be recognized that the feedback loop can proceed from the correction and control module 58, instead of the displacement filter 56. The control loop can include both digital and mechanical components, forming an Altitude and Orbit Control System (AOCS).
Each CD-GPS 51 solution is specific to a single time. As a result, given N GPS inputs, the time at which the estimation occurs can vary quite a bit. As shown in
During a high-rate IMU-only phase, the IMU biases estimated during the low-rate CD-GPS updates are subtracted from the IMU solutions to obtain a precise measure of the motion of the many structure elements. This motion maps to a specific structure constant set that is close to but not necessarily exactly described by the low-rate solution. The IMU-only phase also updates structure constants using a Kalman filter, this time by propagating the structure constant dynamics model and taking only the IMU output as expected measurements. Bias estimates are held constant until the next CD-GPS update. Central spacecraft motion effects are removed from the measured IMU data. Note that the measured motion of the central spacecraft may also include motion associated with the structural modes, so a mean motion estimate using all IMU information can be made if no central spacecraft motion update is available.
The combined low-rate CD-GPS and high-rate IMU estimation technique is shown in
S This system also establishes a structural mode control for a large, flexible spacecraft that is symmetric across the center of mass. The control law associated with the estimated CD-GPS/IMU mode dynamics can take any basic nonlinear form, or a linear form if the structure is sufficiently rigid. Because mode motion is oscillatory as a function of the estimated mode shape constants, and because digital compensation for some motion is possible, the selected control law need only force the system to remain within an allowable equilibrium motion.
For systems with a significant first bending mode (see
Thus, as described above, the present system determines the amount of local movement of the structural array 30, and then corrects that. It is further noted that co-pending application no., which is based on provisional application No. 62/976,143, determines the amount of flexing or bending of the structural array 5, and then corrects that by performing torque-rod control that compensate for the bending, such as performed by the control module 58, torque model 62, and torque commands 64,66 (
In one example embodiment, structure 10 is an antenna assembly with a solar panel that receives solar energy from the Sun and generates solar power for use by the structure. The overall structure is flat and rectangular or square, such as a tile, with the communication components (e.g., antenna elements) at one side surface facing the Earth (nadir) to communicate with user devices (e.g., cell phones) and an opposite side surface facing in the opposition direction (zenith) with solar cells that generate solar power for use by the electronic components, e.g., a processing device, antennas, antenna front end modules. Here the control satellite 200 is fixedly connected to the small satellites 302, shown at the center of the array 100 and visible in the array 5.
It is important that the structure 10 and the array 5 remain as flat (i.e., planar) as possible to maximize solar power generation by the solar side and communication with the Earth on the communication side. Thus, it is desirable for the array 5 to be substantially flat, i.e., that the structures 10 are flat and that they are planar with one another. However, the structure 10 and/or array 5 is subject to forces in space that can cause the structure 10 or array 5 to flex or bend. To correct for any bending or flexing, the structure 10 has symmetrically-placed GPS units 50, inertial measurement units 49, and actuators 23 on each small spacecraft.
To correct for any bending or flexing at the connectors which attach each of the antenna elements to its neighboring elements, the processing device 12 or a central processor determines the flex or bending of the array 5 or structure 10. The processing device of the structure 10 and/or array 5 dynamically monitors the structure 10 and/or array 5 in real time for small displacements due to structural modes of the structure 10 or array 5. That can be done, for example by monitoring the GPS sensors 20 positioned at one or more of the antenna assemblies 10, which provides position and velocity using carrier-phase differential GPS (CD-GPS) 51. And, by monitoring the IMU sensors 21, which are positioned as close as possible to the GPS sensors and provide acceleration data from which position data is further determined. The processing device determines a structural or physical correction and activates a mechanical device to apply a force to the antenna elements to physically move the antenna elements toward the planar configuration. The processing device also determines an adjustment to electronically correct for any residual displacement that is not corrected by the physical correction. In one embodiment, the processing device applies a phase correction to the beam to correct for any displacement that is not corrected by the physical correction.
When the structure 10 is configured as an antenna array 5, it (e.g., antenna 19 or antenna elements) communicates with processing devices on Earth, such as for example a user device (e.g., cell phone, tablet, computer) and/or a ground station. The present disclosure also includes the method of utilizing the structure 10 to communicate with processing devices on Earth (i.e., transmit and/or receive signals to and/or from). The present disclosure also includes the method of processing devices on Earth communicating with the structure 10 (i.e., transmit and/or receive signals to and/or from). In addition, while the structure 10 is used in Low Earth Orbit (LEO) in the examples disclosed, it can be utilized in other orbits or for other applications. Still further, while the system has been described as for an array of antenna assemblies, the system can be utilized for other applications, such as for example data centers, telescopes, reflectors, and other structures, both implemented in space or terrestrially. The system of the present disclosure can also be utilized in combination with a structural correction system, such as shown and described in U.S. application Ser. No. 17/175,262, filed Feb. 12,2021, entitled AOCS System To Maintain Planarity For Space Digital Beam Forming Using Carrier Phase Differential GPS, IMU And Magnet Torques On Large Space Structures, and claiming priority from U.S. Application No. 62/976,143, filed Feb. 13, 2020, the entire contents of which are hereby incorporated by reference.
In addition, it is noted that operation is described as occurring at the control satellite 200, which may or may not be fixedly embedded in the array. However, operation can also be at the common satellite 10 processing device 12 if GPS and IMU data from other structures 10 is distributed in such fashion. In another embodiment of the present disclosure, data (such as position and attitude) can be transmitted from the satellite 10 and/or 200 (e.g., by the common satellite processing device 12 and/or the control satellite processing device, if such are not coincident) to a ground station. The ground station processing device can then determine the necessary correction and/or other flight information and transmit a control signal to the satellite 10 and/or 200 (e.g., common satellite processing devices 12 and/or control satellite processing device) to control the correction via the torque rod 23, in addition to performing other ground-based tasks.
It is further noted that the drawings may illustrate and the description and claims may use several geometric or relational terms and directional or positioning terms, such as planar, linear, curved, circular, flat, left, and right. Those terms are merely for convenience to facilitate the description based on the embodiments shown in the figures, and are not intended to limit the disclosure. Thus, it should be recognized that the system can be described in other ways without those geometric, relational, directional or positioning terms. In addition, the geometric or relational terms may not be exact. For instance, walls or surfaces may not be exactly flat, or planar to one another but still be considered to be substantially planar because of, for example, roughness of surfaces, tolerances allowed in manufacturing, etc. And, other suitable geometries and relationships can be provided without departing from the spirit and scope of the disclosure.
The foregoing description and drawings should be considered as illustrative only of the principles of the disclosure. The system may be configured in a variety of shapes and sizes and is not intended to be limited by the embodiment. Numerous applications of the system will readily occur to those skilled in the art. Therefore, it is not desired to limit the disclosure to the specific examples disclosed or the exact construction and operation shown and described. Rather, all suitable modifications and equivalents may be resorted to, falling within the scope of the disclosure.
This application claims the benefit of priority of U.S. Provisional Application No. 62/976,107, filed on Feb. 13, 2020, the content of which is relied upon and incorporated herein by reference in its entirety.
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