Drag-free Spacecraft Research Articles

Minimum-Time Control for the Test Mass Release Phase of Drag-Free Spacecraft

The capture control of test mass by means of the electrostatic suspensions is crucial for drag-free spacecraft. The test mass must be released to the cage center of the inertial sensor accurately and quickly. This paper proposes a minimum-time capture control method for the test mass release phase of drag-free spacecraft. An analytical solution of optimal control is derived based on Pontryagin’s minimum principle and the linearized dynamics model of the test mass during the release phase. The parameters of the analytical solution are initially guessed with an approximate linear solution of the test mass dynamics model and are slightly modified by using differential correction. Compared with the exact numerical solution by the hp -adaptive pseudospectral method, the analytical solution is proved to be minimum-time. Numerical simulation shows that the proposed control method quickly captures the test mass to the cage center of the inertial sensor. The capture time to stabilization is only half that of the traditional controller.

Design of Finite Frequency Domain Disturbance Rejection Controller for the Drag-free Spacecraft in Space-borne Gravitational Wave Detection

Design of Finite Frequency Domain Disturbance Rejection Controller for the Drag-free Spacecraft in Space-borne Gravitational Wave Detection

NN-based reinforcement-learning optimal sliding mode control for drag-free and attitude of spacecraft with state constraints

This paper investigates a tracking control issue for a class of drag-free spacecraft with state constraints caused by the optical assembly. Firstly, a nonlinear kinematics and dynamics relative equation of coupling system of position and attitude is devised by a 6-degree of freedom (DOF) model of rigid body. Secondly, an optimal control method with a terminal functional is designed to meet state constraints. To solve the Hamilton-Jacobi-Bellman (HJB) equation generated by the optimal control of the nonlinear model, a policy iteration ideal is presented and the final numerical solution of the iteration is obtained by a critic neural network (NN). Thirdly, to enhance the robustness of the closed-loop system, an optimal sliding mode control is proposed, which can ensure the optimal and robustness performance simultaneously. At last, the simulation results demonstrate the performance of the proposed methods and the contrast of precision and robustness of two methods are showcased.

A multi-dimensional nonlinear optimisation method for the TianQin constellation

TianQin is a geocentric space-based gravitational wave detecting mission that relies on three drag-free spacecraft with a mean inter-spacecraft distance of approximately 1.7 × 105 km. Considering the efficiency requirement of orbit optimisation, we apply a gradient descent method based on variational gradient calculation and the damped Newton iterative method to find the most stable solution of the constellation near the given initial position and velocity of the spacecraft. The efficiency was improved and the number of orbital integrals required for gradient calculation was significantly reduced by over 83%. Based on this optimisation method, we analysed the influence of perturbation on the stability of the TianQin constellation, and Moon’s three-body perturbation was the main factor. In addition, the influence of the orbit elements on the optimisation results was studied. The influence of the initial mean anomaly can be ignored, and the stability of the optimised constellation decreases with an increase in the semi-major axis. Working in the ‘3 months on +3 months off’ observation scheme for 2 years, the optimisation result is the ideal direction when the normal direction of the orbital plane of the TianQin constellation points to RXJ0806.3 + 1527.

Test mass 6-DOF control allocation based on the null space for space gravitational wave mission

This paper proposes a novel 6-DOF control allocation based on the null space for the capture control of the drag-free spacecraft's test mass. Considering the unconstrained case firstly, an unconstrained time-varying weighted least square control allocation method is presented to eliminate the error of the test mass along every DOF synchronously to reach stable state quickly. Subsequently, an improved null-space-based method is proposed to modify the unconstrained solution of the weighted least square control allocation to meet the physical constraints of actuators. Numerical simulations illustrate the efficiency of the proposed control allocation scheme, which realizes coordinated control allocation of 6-DOF generalized forces, reduces allocation errors and computational complexity, and improves the efficiency of capture control of the test mass.

A Controller Design Method for Drag-Free Spacecraft Multiple Loops With Frequency Domain Constraints

Space-based gravitational wave detection requires a strict level of residual acceleration ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\sim$</tex-math></inline-formula> <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$10^{-15} \mathrm{~m/s}^{2} / \sqrt{\text{Hz}}$</tex-math></inline-formula> in the frequency band of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$0.1\text{mHz}\sim 1\text{Hz}$</tex-math></inline-formula> ) on the test masses along the sensitive axes. Because of the configuration of the detection spacecraft with two test masses, there are complex couplings between the spacecraft attitude, drag-free and suspension control loops in the drag-free and attitude control system. Moreover, the space environment disturbances and the limited noise levels of the actuators and sensors make it difficult for multiple control degrees of freedom to meet the index requirements at the same time. Currently, PID and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> methods are mainly used for its controller design, where the system is decoupled and divided into relatively independent control loops, and the controllers are designed to meet the requirements separately. However, parameter tuning usually requires empirical trial and error, leading to the low design efficiency. And the coupling relationships between loops cannot be well described and treated mathematically. Therefore, a controller design method for drag-free spacecraft multi loops is proposed in this paper, where the index requirements are transformed into frequency domain constraints and the optimization objectives are designed for better performances according to the control characteristics of different loops. Then the controllers are tuned by multi-population genetic algorithm improving the design efficiency. As mentioned, under the premise that the index requirements are all met, the couplings between loops are considered and some of the performances of the system can be optimized, such as the residual acceleration acting on the test masses. Numerical simulation and comparison verify the effectiveness of this method.

Method for in-orbit redesign for TianQin orbit configuration

The space-based gravitational wave observatory mission consists of three drag-free controlled spacecraft, which form an equilateral triangle configuration. Due to the injection error, the configuration will deviate from the originally designed one, and the injection configuration cannot keep stability for a long term, which will affect the performance of the gravitational wave detection. In this study, we propose a method for reconfiguration using multiple-revolution Lambert solutions. In addition, assuming that the real-time data of spacecraft’s motion states can be obtained with high accuracy and the propulsion system can ensure the magnitude and accuracy of maneuvers, and taking the cost of reconfiguration and configuration stability requirements into account, a novel method of redesigning configuration based on differential evolution algorithm is proposed. Finally, the numerical simulations show that the redesigned configuration not only can reduce the maneuver cost significantly, but also can meet the requirements of long-term stability requirements.

Mixed-Sensitivity Control for Drag-Free Spacecraft Based on State Space

This paper investigates a mixed-sensitivity control method for a class of drag-free spacecraft-needed frequency-separation control, which overcomes the coupled problem of a multiple-in multiple-out (MIMO) system with multiple sensitive-axes and disturbances of actuators. Firstly, the relative dynamics equation is established based on the character of displacement error, which is separated by that test-mass (TMs) tracking ideal orbit with high-frequency displacement and cavity of spacecraft tracking TMs with low-frequency displacement. Secondly, the feedback gain matrix is obtained by the LMI/SDP, which is devised by a general system containing a weight function. Finally, the simulation results demonstrate the performance of the proposed method.

Event‐triggered prescribed performance robust collision‐free capturing control for drag‐free spacecraft system

This paper addresses the capturing control problem of a plug-and-play modularized drag-free spacecraft system, including two spherical proof masses, where the performance constraints, collision risk, uncertain model parameters, unknown external disturbances, and limited communication are considered simultaneously. First, a nonlinear relative dynamics of spherical proof masses with respect to spacecraft is formulated for the capture process. Second, two different prescribed performance event-triggered robust collision-free capturing control strategies are developed to capture the free-floating proof masses successfully. Suppose only the performance metrics on the relative position are considered, and an event-triggered adaptive terminal sliding mode capturing controller is implemented to achieve the capture process within a finite time. Suppose more performance constraints, such as the user predefined capture duration and the performance bounds on both the relative position and the relative velocity, are taken into account, and an event-triggered appointed-time prescribed performance capturing controller is proposed to solve the above issues. In particular, an artificial potential function is utilized to avoid the collision, and a relative threshold event-triggered rule is employed to save the communication source between the controller and the actuator without any Zeno behaviour. The simulation results demonstrate the efficacy and superiority of the proposed method.

Event-triggered adaptive terminal sliding mode tracking control for drag-free spacecraft inner-formation with full state constraints

This paper investigates the reconstruction and maintenance of the inner-formation system for an innovative drag-free spacecraft with double spherical test masses in consideration of unknown model uncertainties, external disturbances, and actuator saturation. First, spherical test mass 1 is prescribed as the ‘leader’ of the inner-formation system, which is freely floating in the nearly pure gravitational orbit without any control. The nonlinear relative orbit dynamics of the outer spacecraft and spherical test mass 2 with respect to spherical test mass 1 is deduced and the micro configuration of the inner-formation system is introduced. For the outer spacecraft, the aim is to track the spherical test mass 1 in real-time, such that both the center of masses coincided with each other. For the spherical test mass 2, the goal is tracking the reference trajectory, which is designed as a space circular fly-around spherical test mass 1 based on the Clohessy-Wiltshire equation. The state constraints caused by the limit cavity size are analyzed. Second, to achieve these goals with satisfied performance, an event-triggered adaptive terminal sliding mode tracking control strategy is developed for the inner-formation. The adaptive terminal sliding mode technique is implemented to overcome the model uncertainties and external disturbances and to accomplish the reconstruction process in a finite time. Two kinds of barrier functions are utilized to tackle the state constraints. The relative threshold event-triggered mechanism is embedded to save the computation source onboard, evidently. The simulation results demonstrate the efficacy and superiority of the proposed method.

Influence of Three-Body Gravitational Perturbation for Drag-Free Spacecraft

This paper mainly studies the motion and control of the drag-free spacecraft system for a high-precision mission. In high-precision missions, the influence of three-body gravitational perturbation on a drag-free spacecraft system is still lack of relevant research. To this end, we first established a relative motion model of the test mass and the spacecraft based on multibody dynamics, and the equations of the relative motion of the test mass and the spacecraft cavity were obtained through coordinate transformation. The difference between the sun orbit and the Earth orbit is comparatively analyzed by a numerical solution. The influence of gravitational forces from the Earth, the moon, and the sun on the relative motion is studied in detail. Secondly, a sliding mode controller is designed for the high-precision mission. Finally, the performance of the controller is analyzed from the time domain and the frequency domain. Numerical simulation results show that the controller can meet the requirements of the time domain and the frequency domain.

TianQin Space-Based Gravitational Wave Detector: Key Technologies and Current State of Implementation

TianQin is a project of a space-based gravitational wave detector for detecting GW events in the millihertz frequency range. The space-based detector must be implemented on three identical drag-free spacecraft orbiting around the Earth. The key technologies that form the principles of operation of the space-based GW detector are, first, an ultrastable transponder laser interferometer and, second, a system for compensating nongravitational disturbances. This work discusses the basic principles of operation and the current state of the key technologies developed in the PRC. At the current level of technological readiness, it is expected that TianQin will be launched in the second half of the next decade and will serve as a space observatory for a wide class of astrophysical sources of gravitational waves.

Investigation of charge management using UV LED device with a torsion pendulum for TianQin

TianQin is a Chinese space-based observatory concept with three drag-free spacecraft orbiting the earth to observe gravitational-waves in the millihertz range. Electrical charge is inevitably accumulating on its isolated test masses which are used as the mirrors for interferometers to measure gravity variation. Charge management system based on ultraviolet (UV) light is developed to reduce the charge-induced noises acting on the test mass in space gravitational experiments such as GP-B, LISA, LISA Pathfinder and TianQin mission. The UV LED is a new UV light source with some advantages relative to mercury lamps, such as smaller size, lighter weight, lower power consumption and higher efficiency. For these reasons, ground-based tests for the combination of UV LED and inertial sensor are essential. This paper presents the development of a charge management system based on a UV LED, its application to a torsion pendulum system with a TianQin-like test mass, and assesses the charge-management performance of the system. The experimental results indicate that the isolated test mass can be charged positively or negatively through UV illumination. It demonstrates that the charging and discharging rates can both reach higher than 105 e s−1, as well as spectral measurement of the pendulum charge resulting in a white noise level equivalent to ∼5 × 105 e Hz−1/2, satisfying the TianQin requirement.

Astrodynamical middle-frequency interferometric gravitational wave observatory AMIGO: Mission concept and orbit design

AMIGO is a first-generation Astrodynamical Middle-frequency Interferometric Gravitational Wave (GW) Observatory. The scientific goals of AMIGO are to bridge the spectra gap between first-generation high-frequency and low-frequency GW sensitivities: to detect intermediate mass BH coalescence; to detect inspiral phase and predict time of binary black hole coalescences together with binary neutron star &amp; black hole-neutron star coalescences for ground interferometers; to detect compact binary inspirals for studying stellar evolution and galactic population. The mission concept is to use time delay interferometry (TDI) for a nearly triangular formation of three drag-free spacecraft with nominal arm length 10,000 km, emitting laser power 2–10 W and telescope diameter 300–500 mm. The design GW sensitivity in the middle frequency band is [Formula: see text] Hz[Formula: see text]. Both geocentric and heliocentric orbit formations are considered. All options have LISA-like formations, that is, the triangular formation is [Formula: see text] inclined to the orbit plane. For all solar orbit options of AMIGO, the first-generation TDI satisfies the laser frequency-noise suppression requirement. We also investigate for each option of orbits under study, whether constant equal-arm implementation is feasible. For the solar-orbit options, the acceleration to maintain the formation can be designed to be less than 15 nm/s2with the thruster requirement in the 15 [Formula: see text]N range. AMIGO would be a good place to test the feasibility of the constant equal-arm option. Fuel requirement, thruster noise requirement and test mass acceleration actuation requirement are briefly considered. From the orbit study, the solar orbit option is the mission orbit preference. We study the deployment for this orbit option. After a last-stage launch from 300 km Low Earth Orbit (LEO), each S/C’s maneuver to an appropriate 2-degree-behind-the-Earth AMIGO formation in 95 days requires only a [Formula: see text]v of about 80 m/s.

A HERO for General Relativity

HERO (Highly Eccentric Relativity Orbiter) is a space-based mission concept aimed to perform several tests of post-Newtonian gravity around the Earth with a preferably drag-free spacecraft moving along a highly elliptical path fixed in its plane undergoing a relatively fast secular precession. We considered two possible scenarios—a fast, 4-h orbit with high perigee height of 1047 km and a slow, 21-h path with a low perigee height of 642 km . HERO may detect, for the first time, the post-Newtonian orbital effects induced by the mass quadrupole moment J 2 of the Earth which, among other things, affects the semimajor axis a via a secular trend of ≃4–12 cm yr − 1 , depending on the orbital configuration. Recently, the secular decay of the semimajor axis of the passive satellite LARES was measured with an error as little as 0 . 7 cm yr − 1 . Also the post-Newtonian spin dipole (Lense-Thirring) and mass monopole (Schwarzschild) effects could be tested to a high accuracy depending on the level of compensation of the non-gravitational perturbations, not treated here. Moreover, the large eccentricity of the orbit would allow one to constrain several long-range modified models of gravity and accurately measure the gravitational red-shift as well. Each of the six Keplerian orbital elements could be individually monitored to extract the G J 2 / c 2 signature, or they could be suitably combined in order to disentangle the post-Newtonian effect(s) of interest from the competing mismodeled Newtonian secular precessions induced by the zonal harmonic multipoles J ℓ of the geopotential. In the latter case, the systematic uncertainty due to the current formal errors σ J ℓ of a recent global Earth’s gravity field model are better than 1 % for all the post-Newtonian effects considered, with a peak of ≃ 10 − 7 for the Schwarzschild-like shifts. Instead, the gravitomagnetic spin octupole precessions are too small to be detectable.

The status of DECIGO

DECIGO (DECi-hertz Interferometer Gravitational wave Observatory) is the planned Japanese space gravitational wave antenna, aiming to detect gravitational waves from astrophysically and cosmologically significant sources mainly between 0.1 Hz and 10 Hz and thus to open a new window for gravitational wave astronomy and for the universe. DECIGO will consists of three drag-free spacecraft arranged in an equilateral triangle with 1000 km arm lengths whose relative displacements are measured by a differential Fabry-Perot interferometer, and four units of triangular Fabry-Perot interferometers are arranged on heliocentric orbit around the sun. DECIGO is vary ambitious mission, we plan to launch DECIGO in era of 2030s after precursor satellite mission, B-DECIGO. B-DECIGO is essentially smaller version of DECIGO: B-DECIGO consists of three spacecraft arranged in an triangle with 100 km arm lengths orbiting 2000 km above the surface of the earth. It is hoped that the launch date will be late 2020s for the present..

TianQin: a space-borne gravitational wave detector

TianQin is a proposal for a space-borne detector of gravitational waves in the millihertz frequencies. The experiment relies on a constellation of three drag-free spacecraft orbiting the Earth. Inter-spacecraft laser interferometry is used to monitor the distances between the test masses. The experiment is designed to be capable of detecting a signal with high confidence from a single source of gravitational waves within a few months of observing time. We describe the preliminary mission concept for TianQin, including the candidate source and experimental designs. We present estimates for the major constituents of the experiment’s error budget and discuss the project’s overall feasibility. Given the current level of technological readiness, we expect TianQin to be flown in the second half of the next decade.

Three-Axis Drag-Free Control and Drag Force Recovery of a Single-Thruster Small Satellite

A drag-free spacecraft uses a gravitational reference sensor to shield an internal free-floating test mass from all external disturbances and disturbances caused by the spacecraft itself. Since the test mass is completely freed from nongravitational disturbances, it and its “tender” spacecraft follow a pure geodesic. The next generation of drag-free space systems will provide autonomous precision orbit determination, more accurately map the static and time-varying components of the Earth’s mass distribution, aid in the understanding of the fundamental force of gravity, and ultimately open up a new window to the universe through the detection and observation of gravitational waves. In this paper, a simple and cost-effective design for a drag-free nanosatellite for autonomous Earth observation and in situ atmospheric studies is explored. The nanosatellite is composed of a single thruster to compensate for drag and an attitude control system to orient the satellite in the direction of the external disturbance. The stability of the spacecraft and its ability to recover the external disturbance force vector are demonstrated on a flight-ready nanosatellite processor interfaced with a personal computer, modeling the spacecraft dynamics.

Construction and testing of the optical bench for LISA Pathfinder

eLISA is a space mission designed to measure gravitational radiation over a frequency range of 0.1–100 mHz (European Space Agency LISA Assessment Study Report 2011). It uses laser interferometry to measure changes of order in the separation of inertial test masses housed in spacecraft separated by 1 million km. LISA Pathfinder (LPF) is a technology demonstrator mission that will test the key eLISA technologies of inertial test masses monitored by laser interferometry in a drag-free spacecraft. The optical bench that provides the interferometry for LPF must meet a number of stringent requirements: the optical path must be stable at the few level; it must direct the optical beams onto the inertial masses with an accuracy of better than ±25 μm, and it must be robust enough not only to survive launch vibrations but to achieve full performance after launch. In this paper we describe the construction and testing of the flight optical bench for LISA Pathfinder that meets all the design requirements.

Astrodynamical Space Test of Relativity using Optical Devices I (ASTROD I)—a class-M fundamental physics mission proposal for cosmic vision 2015–2025: 2010 Update

ASTROD I is a planned interplanetary space mission with multiple goals. The primary aims are: to test General Relativity with an improvement in sensitivity of over 3 orders of magnitude, improving our understanding of gravity and aiding the development of a new quantum gravity theory; to measure key solar system parameters with increased accuracy, advancing solar physics and our knowledge of the solar system; and to measure the time rate of change of the gravitational constant with an order of magnitude improvement and the anomalous Pioneer acceleration, thereby probing dark matter and dark energy gravitationally. It is envisaged as the first in a series of ASTROD missions. ASTROD I will consist of one spacecraft carrying a telescope, four lasers, two event timers and a clock. Two-way, two-wavelength laser pulse ranging will be used between the spacecraft in a solar orbit and deep space laser stations on Earth, to achieve the ASTROD I goals.For this mission, accurate pulse timing with an ultra-stable clock, and a drag-free spacecraft with reliable inertial sensor are required. T2L2 has demonstrated the required accurate pulse timing; rubidium clock on board Galileo has mostly demonstrated the required clock stability; the accelerometer on board GOCE has paved the way for achieving the reliable inertial sensor; the demonstration of LISA Pathfinder will provide an excellent platform for the implementation of the ASTROD I drag-free spacecraft. These European activities comprise the pillars for building up the mission and make the technologies needed ready. A second mission, ASTROD or ASTROD-GW (depending on the results of ASTROD I), is envisaged as a three-spacecraft mission which, in the case of ASTROD, would test General Relativity to one part per billion, enable detection of solar g-modes, measure the solar Lense-Thirring effect to 10 parts per million, and probe gravitational waves at frequencies below the LISA bandwidth, or in the case of ASTROD-GW, would be dedicated to probe gravitational waves at frequencies below the LISA bandwidth to 100 nHz and to detect solar g-mode oscillations. In the third phase (Super-ASTROD), larger orbits could be implemented to map the outer solar system and to probe primordial gravitational-waves at frequencies below the ASTROD bandwidth. This paper on ASTROD I is based on our 2010 proposal submitted for the ESA call for class-M mission proposals, and is a sequel and an update to our previous paper (Appouchaux et al., Exp Astron 23:491–527, 2009; designated as Paper I) which was based on our last proposal submitted for the 2007 ESA call. In this paper, we present our orbit selection with one Venus swing-by together with orbit simulation. In Paper I, our orbit choice is with two Venus swing-bys. The present choice takes shorter time (about 250 days) to reach the opposite side of the Sun. We also present a preliminary design of the optical bench, and elaborate on the solar physics goals with the radiation monitor payload. We discuss telescope size, trade-offs of drag-free sensitivities, thermal issues and present an outlook.