Deployable Reflector Research Articles

Rigid-Foldable Doubly Curved Deployable Reflectors Based on Miura–Ori Pattern

This paper introduces a novel deployable reflector concept which achieves single degree-of-freedom folding of solid doubly curved surfaces. A set of folding kinematics is constructed using the Miura–Ori pattern and the Hoberman linkage to allow compact collision-free stowage of a fully rigid truss-supported solid-surface reflector structure. In this paper, the baseline kinematic architecture is introduced, and a design methodology using Bayesian optimization to systematically obtain optimally stowed geometries is detailed. An example design is carried out to demonstrate the methodology. Optimal parameters are produced, the design space is explored, and a detailed design based on the optimal parameters is made, along with its derivative variants. Finally, a prototype model and quantification of surface errors confirm the validity of resulting designs.

Numerical Investigation on the Thermal Characteristics of Lightweight Metal Mesh-Based Reflector Antenna with Various Knitting Conditions

Proper prediction of the temperature variation in a metallic wire mesh for spaceborne large deployable reflector antennas is essential for evaluating the dimensional stability of the antenna under extreme on-orbit thermal environments. However, predicting the temperature of a mesh is difficult because of its complex yarn configuration. To analyze the thermal behavior of the spaceborne mesh antenna reflector, the thermal optical characteristics with various knitting methods of the metallic mesh were obtained experimentally in this study. Subsequently, to analyze the thermal sensitivity of the reflector based on its optical properties, an on-orbit thermal analysis of the mesh reflector was performed based on measurements of the mesh specimen. We also investigated the influence of deployable solar panels on the thermal gradient of the reflector.

Electrostatically Actuated X-Band Mesh Reflector with Bend-Formed Support Structure

Increasing the size of radio frequency (RF) reflectors in space can enhance gain and spatial resolution in applications such as space-based communication and remote sensing. The size of current passive deployable reflectors is limited by a tradeoff between diameter and surface precision, which causes RF performance to degrade as size increases. A promising approach to overcome this tradeoff is to combine in-space manufacturing, which enables large structures, with distributed embedded actuation, which enables precise control over the reflector surface. Here we demonstrate a reflector antenna system that integrates these two technologies, using a candidate in-space manufacturing process, termed “Bend-Forming,” with embedded electrostatic actuators. We design and fabricate a 1-m-diam prototype of an electrostatically actuated X-band reflector with a knitted gold-molybdenum mesh as the reflector surface, carbon-fiber-reinforced plastic booms as electrodes, and a truss support structure fabricated with Bend-Forming. We characterize the RF performance of this reflector, successfully demonstrating i) control over a wide range of focal lengths by suppressing a pull-in instability and ii) beam steering over an angular range of 4.2° via asymmetric electrostatic actuation. This work lays the foundation for future space communication and remote sensing technologies, offering a scalable solution to enhance RF performance through in-space manufacturing and precision control.

Development of Deployable Reflector Antenna for the SAR-Satellite: Part 1. Design and Analysis of the Main Reflector Using Honeycomb Sandwich Composite Structure

The deployable reflector antenna based on the synthetic aperture radar is a satellite component that consists of a unit structure in the form of a folded reflector. During the launch process, this satellite antenna is in the stowed condition to improve storage efficiency. It is then deployed to perform the space mission in the on-orbit condition. Due to these structural characteristics of the deployable reflector antenna, the reflector is possible to be loaded in the limited volume of the launch vehicle with the reduced size. Additionally, because the deployable reflector antenna is made by the lightweight material of the carbon fiber reinforced polymer and honeycomb core, it can reduce the launching cost and improve the revisit interval. In this paper, the conceptual design of the main reflector of the deployable reflector antenna was conducted. The main reflector was designed as the honeycomb sandwich composite structure. To design the main reflector, the stacking sequence of the composite material and honeycomb core was investigated to maximize the structural stiffness and minimize the antenna’s mass. Subsequently, finite element analyses including modal, quasi-static, structural–thermal coupling, and transient response were performed to numerically evaluate the structural performance of the lightweight composite reflector antenna.

Hierarchical shape optimization for large deployable membrane reflector with spatial skirt cable

In the shape optimization analysis of electrostatically controlled deployable membrane reflector (ECDMR), the poor balance of the membrane with spatial skirt cable is the main reason for the degradation of the reflector surface precision. At the same time, while in the optimization of the pre-stress of large deployable reflectors, the membrane structure has strong geometric nonlinearity, and the lack of necessary gradient information leads to low efficiency of the calculation. Therefore, according to the structural characteristics of the cable-membrane reflector, the two optimization objectives of the highest surface precision and the most uniform stress distribution is considered, and a hierarchical shape optimization method is proposed based on membrane theory and unbalance force analysis, which realizes the solution of the multi-objective optimization problem when the three optimization objectives have different priorities. The interior effective membrane reflective surface is analyzed using membrane theory, and the external membrane with spatial skirt cable is analyzed using nonlinear finite element method. The gradient information required for optimization is also obtained by unbalance force analysis, which ensures better optimization efficiency and can solve large-scale optimization problems. Therefore, the node positions and element equilibrium stresses of the structure can be optimized simultaneously, which further expands the search space of the equilibrium state and reduces the possibility of falling into local optimal solutions. Finally, a numerical example of a 30 m aperture ECDMR is calculated and analyzed, and the results show that the proposed method can obtain a high surface precision with a fast solution speed.

Implementation of “digital twin” technology within the thermo-elastic distortion testing of a precision carbon fiber reflector for the spacecraft antenna subsystem

Mirror antenna subsystems (AS) with the deployable reflectors are important integral parts of the telecommunication spacecraft payloads and provide reception and transmission of the information in a given service area [14]. The reflector design shall provide strength and stiffness, specified radiofrequency (RF) characteristics and antenna pattern boresight error of the AS. Performance compliance shall be approved in the frame of ground experimental testing, and thermo-elastic distortion (TED) testing to assess their effect on the antenna pattern boresight error is the part of the ground testing. This testing is hard to carry out because of the following aspects resulting in lack of the guaranteed achieved criteria to assess the test results: considerable difference of thermal and physics behavior between carbon-fiber-reinforced polymer (CFRP) filler and epoxide component and the steep CFRP anisotropy result in increased variation of the layer strain-stress state and internal stresses which make the design behavior undefined under thermal environment; it is almost impossible in the frame of the testing to implement and maintain the real map of the thermal fields of specified accuracy on the large-sized object due to the fact that the temperature in a giant thermal chamber is extremely varying; in the frame of testing it is possible to carry out few optical measurements for the deformed reflector surface points which are not enough to provide the required level of confidence for geometric parameters variation; the test lasts 50 days and requires cost-intensive chamber exploitation, huge power consumption operating fluid rate (liquid nitrogen), expensive equipment providing thermal modes. Development and implementation of the cutting-edge digital twin technology is the effective method to address TED testing issue. The main idea of the technology is to substitute real object to be tested with digital model verified based their parameter compliance using convergence criteria. The paper presents technology block diagram, convergence criteria and correlation technique of the predicted and measured TED cases. Evaluation data of the deformed reflector effects on AS RF performances are given and demonstrate that performances comply with the specified requirements and qualify successfully the digital twin technology under real testing. The digital twin was successfully implemented in 2019 year in JSC RESHETNEV in the frame of reflector TED testing for RF antenna subsystem with shaped antenna pattern for Express-AMU7 spacecraft, which was launched and accepted for the flight operation in 2021. This is the first time in the Russian space industry tests using the digital twin technology of a domestic reflector for RF space AS with parameters at the imported analogues level have been successfully qualified. The qualification of this technology will ensure the competition of domestic high-tech developments and will solve the problems of import substitution and increase the share of the Russian component in the global space telecommunications market.

Dynamics and attitude control of space-based synthetic aperture radar

Abstract This work tackles the problem of attitude control of a space-based synthetic aperture radar with a deployable reflector antenna, representing a lightly damped uncertain vibratory system with highly nonlinear dynamics. A control strategy based on two identifiable in-orbit vector parameters is proposed to make the robust controller less conservative. The first parameter is used in the feedforward loop to achieve a trade-off between the energy efficiency of maneuvers and the amplitudes of the oscillatory response. The feedback loop utilizes the second parameter to accurately handle the controller-structure interactions by adaptive notch filters. The notch filters are included in the augmented plant at the design stage to guarantee closed-loop robustness against disturbances, unmodeled dynamics, and parametric uncertainty. The system’s robustness and specified requirements are confirmed by formal criteria and numerical simulations using a realistic model of the flexible spacecraft.

Analysis of Cross-Polarized Field by Panel Misalignment Errors in a Deployable Reflector Antenna

This paper analyzes the generation mechanism of a cross-polarized field resulting from panel misalignment errors in a solid-surface deployable antenna. Misalignment of the panel in a deployable antenna results in path length error and rotation of the unit normal vector on the reflector surface. However, in terms of the analysis of cross-polarization (cross-pol) generation, rotational error is a more significant factor. In the aperture field, the distributions of cross-pol components are calculated to identify the polarization characteristics of the radiated field. For uniform misalignment, the peak-to-cross polarization (XPOL) is found to be smaller than -50 dB for misalignment angles less than 3°. Furthermore, when the panels are non-uniformly misaligned with a sinusoidal distribution, the cross-pol level depends on the angular position of the maximum misalignment.

ИССЛЕДОВАНИЕ ХАРАКТЕРИСТИК РАЗВЕРТЫВАЕМОЙ КОСМИЧЕСКОЙ ЗЕРКАЛЬНОЙ АНТЕННЫ С РАЗРЕЖЕННОЙ ОТРАЖАЮЩЕЙ ПОВЕРХНОСТЬЮ

The article presents the results of a study of the characteristics of a space parabolic mirror with a deployable reflector. A model of the reflector truss structure formed by two asymmetric parabolic networks with tension cables is presented. Three variants of the sparse structure of the reflecting film of the reflector are presented, differing in periodically repeating hexagonal holes with different sizes. A complex electrodynamic modeling of the radiation characteristics of a parabolic mirror antenna with a developed model of a truss-bearing structure and the proposed structures of reflective films, allowing to reduce the mass of the reflector and increase the reliability of the antenna system, are carried out. The estimation of the frequency dependences of the characteristics of the variants of the parabolic mirror antenna model is given. Recommendations on the use of sparse reflective films for small, medium and large apertures of deployable reflectors are proposed.

Rigid-Foldable Parabolic Deployable Reflector Concept Based on the Origami Flasher Pattern

This paper presents a novel deployable reflector concept based on the origami flasher pattern. The proposed folding architecture achieves rigid foldability for flasher patterns applied to doubly curved surfaces, allowing parabolic reflectors to be divided into a number of rigid panels for efficient stowage. Such an architecture provides an intermediate solution between current rigid-surface and flexible-surface reflectors, offering both surface precision and stowage compactness. The proposed patterns have a positive-finite degree of mobility, and so reliable and deterministic deployment is realized through suitable actuation. A Bayesian optimization approach is used in conjunction with kinematics and collision models in order to find optimal stowage patterns that accommodate finite thickness panels and supporting structures. For the generated optimal patterns, panel split line geometries are designed analytically to eliminate gaps while avoiding collision at panel edges during folding.

Effects of petal misalignment errors on radiation pattern of deployable reflectors

ABSTRACT As one source type of random surface errors, misalignment errors usually lead to petal rigid body rotation or translation for petal-type deployable reflectors, which deteriorate petal-type surface from its ideal parabolic shape. To evaluate the effects of misalignment errors on antenna performance, a novel method is proposed to reveal the degradation of petal misalignment errors on average radiation pattern for petal-type deployable reflectors. Based on coordinate transformations, the surface deviation from ideal parabolic shape caused by petal misalignment errors is introduced into an explicit far-field formula, which promotes the far-field formula as explicit functions of petal misalignment displacements in this novel method. By assuming Gaussian distribution of misalignment errors, the average radiation patterns with varying standard deviations of petal misalignment errors are obtained. Compared with the existing methods of random error characterisation, the effectiveness of the proposed method is verified. Simulations show that among the petal misalignment errors, both the petal rigid body rotation around hinge link axis and translation along boresight direction provide deterioration effects on antenna radiation pattern, and the proposed method can provide design guidelines for hinge structural design.

Optimization of the efficiency of large deployable reflectors by measuring the error around the feed

Large Deployable Reflector (LDR) systems are commonly used as mesh reflectors for large aperture space antennas in aerospace applications since they provide affordability while guaranteeing at the same time a high gain and a high directivity. To improve the surface accuracy several methods have been studied, most of which measure the distance between the cable-net system that forms the reflector surface and the desired paraboloid. In this paper we want to improve the reflector’s ability to convey a greater concentration of reflected rays in the direction of the feed. To deal with this issue, a numerical optimization algorithm has been proposed, both in the case of prime-focus reflector and with offset. During the explanation of the algorithm, numerical examples will be reported, thus demonstrating the goodness of the algorithm, and its effectiveness will also be demonstrated using the Monte Carlo method.

A model predictive control for attitude stabilization and spin control of a spacecraft with a flexible rotating payload

Many Earth Observation missions, implementing space-based microwave sensing techniques for collecting surface information, employ spinning sensors to cover large swaths of terrestrial areas, thus improving the rate at which global maps of those measured data are generated. These spacecraft (as Soil Moisture Active Passive (SMAP) developed by NASA or Copernicus Imaging Microwave Radiometer (CIMR) currently under development by Thales Alenia Space) consist of a main non-spun platform and a rotating part composed of an antenna boom, a deployable reflector and a rotation mechanism. As the reflector is designated to rotate about the nadir axis producing conically scanned antenna beams with precise surface incidence angle, the payload pointing accuracy needs to be addressed at both spin subsystem and platform level. In this work, a representative model of the dynamic behaviour of SMAP satellite is developed as a study case to design the proposed control strategies; in particular, a SMAP-like payload structural model is built using FEM commercial codes. The spacecraft is equipped with a Reaction Wheels Assembly (RWA) to accomplish both momentum compensation for the spun element and three-axis attitude control and a motor for the spin mechanism. The objective of the study is to develop the spacecraft control architecture in the frame of Model Predictive Control (MPC) theory. MPC refers to a class of algorithms in which the control action is obtained by computing an open-loop optimal sequence of control moves over a predefined time horizon; moreover, the ability to set constraints on process inputs and outputs directly in the problem formulation allows to account for actuators’ limits. In the study two operative phases of the satellite are addressed: the Spin-up, in which the 6-meter diameter antenna is spun-up to the operative condition of 14.6 RPM, and the Science Phase, in which precise nadir pointing and stability of the flexible system must be kept for acquiring high-resolution measurements. To this purpose, control–structure interaction between attitude/spin control system and flexible dynamics, as well as system’s imbalances, are carefully addressed by the proposed control architecture. The nonlinear in-orbit dynamics of the flexible spacecraft is then used to evaluate the performance of the MPC controller in terms of pointing accuracy and robustness to uncertainties.

Review and evaluation of warp-knitted patterns for metal-based large deployable reflector surfaces

A large deployable reflector antenna (LDA) is comprised of numerous components. One of the key components of this reflector antenna is the reflector surface. Several types of reflector surfaces have been developed and used, namely, metal mesh-based reflector surfaces, membrane-based reflector surfaces, etc. The benefits presented by warp-knitted metal mesh-based reflector surfaces are their foldability and light weight structural characteristics. Typical metal mesh-based reflector surfaces are produced using a warp knitting textile manufacturing process. A warp-knitted metal mesh reflecting surface is an elastic, open structured knit with a low bending stiffness produced on a high gauge knitting machine (E26 or higher gauge) consisting of a compatible metal yarn (typically tungsten or molybdenum). This paper gives an overview about the requirements for mesh reflector surfaces stated in the literature. Afterwards, an overview of different patterns currently investigated by the LDA community is given. The names given to the various types of patterns in the literature often differ. The construction of the various patterns is therefore first optical analysed and compared. Subsequently, the different patterns are evaluated on the basis of the requirements. Based on the requirements and the possibilities of the warp knitting machine, new possible patterns are identified and evaluated. For the development of a new reflector surface, the identified patterns are developed as a warp-knitted spacer fabric. This decision increases the stiffness of the knitted fabric. This new concept for an advanced reflector surfaces is introduced by Large Space Structures GmbH (LSS) (concept) and ITA (production technology).

Angular Displacement Control for Timoshenko Beam by Optimized Traveling Wave Method

The vibration of flexible structures in spacecraft, such as large space deployable reflectors, solar panels and large antenna structure, has a great impact on the normal operation of spacecraft. Accurate vibration control is necessary, and the control of angular displacement is a difficulty of accurate control. In the traditional control method, the mode space control has a good effect on suppressing low-order modes, but there is control overflow. The effect of traveling wave control on low-order modes is worse than the former, but it has the characteristics of broadband control. It can better control high-order modes and reduce control overflow. In view of the advantages and disadvantages of the two control methods, based on Timoshenko beam theory, this paper uses vector mode function to analyze the modal of spacecraft cantilever beam structure, establishes the system dynamic equation, and puts forward an optimized traveling wave control method. As a numerical example, three strategies of independent mode space control, traditional traveling wave control and optimized traveling wave control are used to control the active vibration of beam angle. By comparing the numerical results of the three methods, it can be seen that the optimal control method proposed in this paper not only effectively suppresses the vibration, but also improves the robustness of the system, reflecting good control performance. An innovation of this paper is that the Timoshenko beam model is adopted, which considers the influence of transverse shear deformation and moment of inertia on displacement and improves the accuracy of calculation, which is important for spacecraft accessory structures with high requirements for angle control. Another innovation is that the optimized traveling wave control method is exquisite in mathematical processing and has good results in global and local vibration control, which is not available in other methods.

Parametric design optimization approach to petal-type solid surface deployable reflectors

A parametric design approach to the petal-type solid surface deployable reflector is presented, in which the generic parametric model of the reflector is established and its division parameters are optimized to simplify the structure, increase deployment reliability and improve electrical performance. For this goal, the estimated expression of the division number of petals is first derived as the initial value of subsequent optimization algorithm. Then the estimation-trial algorithm is developed, its corresponding three-level nested optimization model is established, and the reference circle model for improving the efficiency in solving the aforementioned model is proposed. Furthermore, the deployment scheme of this kind of reflectors is implemented by Euler’s rotation theorem combined with rigid-body registration. In addition, the parameter analysis is made to determine which parameters dominate the division number of petals. Finally, the effectiveness of this method in configuration, deployment and optimality together with the improvement in deployment reliability and electrical performance are verified. It is revealed that reflectors designed with this method need fewer petals compared with the existing reflectors of this class, deploy smoothly, have lower deployment failure probability, as well as have higher antenna gains and lower relative sidelobe levels. The results indicate the petal-type solid surface deployable reflector characterized by compact structure, high reliability and good electrical performance can be obtained with the approach proposed in this paper.

Finite-element modelling, analysis and design of anisogrid composite lattice spoke of an umbrella-type deployable reflector of space antenna

Practical design procedure of a new configuration of anisogrid composite lattice spoke of an umbrella-type deployable reflector of space antenna is presented in the paper. The spoke has a form of long lattice shell with the cross-section made in the form of rounded rectangle. The loads applied to the spoke are generated by the radio-reflective stretched mesh of the deployed reflector. Mass of the spoke is taken as an objective function in the formulated design problem, with constraints imposed on the characteristics of deformability, strength, and stability of the structure. The solution of the problem is based on the results of parametric analyses performed using the finite-element method. The set of design parameters of lattice structure includes the angle orientation of helical ribs, number of helical ribs of one orientation, widths of the helical and hoop ribs, and height of the ribs. A specialised algorithm is developed and applied to the generation of finite-element model for the anisogrid lattice spoke with rectangular cross-section. Using this model, the effects of variations of the parameters of lattice structure on the maximum deflection, maximum stresses in the ribs, and buckling load factor are analysed. Based on the results of these analyses the optimum set of the parameters of lattice structure is identified. At the first stage, feasible values of the structural parameters satisfying the set of constraints are calculated. Then, the optimum combination delivering the minimum value of the spoke mass is determined.

The contact problem in FEM analysis of filiform structure for large deployable reflectors

Space reflectors need a continuous increase of size to improve the quality of the communication. Considering the small space available in launchers, the antenna must be assembled within the vector and deployed in the space environment. The antenna requires a thin metallic mesh sustained by an appropriate net structure. The best reflector efficiency is reached when all the metallic wires keep in stable contact, allowing the electrical field to be homogeneous. The number of wires involved is enormous, so that, the modelling requires a simple structural approach connected to a reliable contact tool. Single wires can be modelled by beams, but this opens a non-trivial contact managing. As a matter of fact, the wires describe a thin surface, but the contact is realized by 3D crossing. This point is the main objective of the present work which suggests a way to overcome the crossing while maintaining the structure modelling in a 2D field. The contact efficiency needs that the wires do not exceed the elastic strength, causing a lowering of loading contacts due to irreversible deformations. Taking advantage of the present approach, an investigation over the percentage of active contacts in a full mesh is performed, so that optimally applied tensile loads are identified.

Digital Beamforming for Spaceborne Reflector-Based Synthetic Aperture Radar, Part 1: Basic imaging modes

Deployable reflector antennas illuminated by a digital feed array enable spaceborne synthetic aperture radar (SAR) systems to image an ultrawide, continuous swath at a fine azimuth resolution. This is facilitated by the use of dedicated imaging modes and by multidimensional digital beamforming (DBF) techniques. This article is part 1 of a tutorial trilogy, where a focus is put on the required onboard functionality, operational techniques, and DBF aspects, for which a rigorous mathematical description is included. To maintain general validity, the functional implementation for the various modes is detailed, thus avoiding restricting the description to a specific realization. The reader is assumed to be familiar with the general concept of SAR and, otherwise, referred to the literature on the topic. The approach followed in the trilogy is to start with a basic imaging concept and then move to more advanced modes, thus successively increasing the complexity; the mathematical description follows the same approach.

Modified design of the deployable mesh reflector antenna for mini satellites

This paper is devoted to the development of a light-weight deployable mesh reflector antenna for mini satellites with synthetic aperture radar (SAR) payload. The analyses of the electromagnetic and mechanical properties of the multi-beam deployable reflector antenna are performed for the space-borne dual-band (X- and S-bands) synthetic aperture radar (SAR) system based on digital beam forming (DBF). The reflector antenna is of offset type with a diameter of 3.35 m and weight of 7.8 kg. The DBF-SAR system is designed for mini satellites of total mass < 150 kg.